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+Peer Review File
+
+Detangling electrolyte chemical dynamics in lithium sulfur batteries by operando monitoring with optical resonance combs
+
+Open Access This file is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. In the cases where the authors are anonymous, such as is the case for the reports of anonymous peer reviewers, author attribution should be to 'Anonymous Referee' followed by a clear attribution to the source work. The images or other third party material in this file are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.
+REVIEWER COMMENTS
+
+Reviewer #1 (Remarks to the Author):
+
+In this work, TFBGs were employed to operando track the chemical dynamics/states of the Li-S battery via electrolyte sulfur concentration, revealing the correlated relationship between the capacity fading and dynamic of dissolution/precipitation of polysulfides over cycling and at different cycling rates. Overall, I think is an interesting work, since the authors proposed a new application of optical fiber sensor for battery monitoring. Consequently, I will recommend its publication after a minor revision.
+
+（1） In Fig1c, why did the author choose the “*” region as the sensing mode? Can other modes also be used as sensing modes, and if so, what are the differences in sensing performance?
+
+（2） As we all know, the S cathodes exhibit around 80% volume changes during cycling. Therefore, in this manuscript, please explain whether the wavelength shift caused by the volume changes of the S cathode will affect the results.
+
+（3） In manuscript, the author filled 500 μL of electrolyte into the cell, which is different from the common application scenario of optical fiber (the fiber is placed in a huge amount of liquid). Therefore, the author should consider whether the electrolyte was sufficient to completely infiltrate the fiber and can evenly wrap the optical fiber, which will affect the result.
+
+（4） Ultimately, optical fiber is a linear sensor with a limited detection range. In manuscript, the author also mentioned that the “delay” due to position of the sensor in the cell. So can the author show the evolution of sulfur concentration in other locations, such as near the electrode or at the same level as the current fiber?
+
+（5） In Fig. 4b, I observed a slight dissonance in 12th cycle where the drop in temperature caused the wavelength to decrease. However, the double effect of temperature dropping and Li2S nucleation will result in smaller wavelength. Why is the valley of sulfur concentration in 12th cycle greater than that in other cycles?
+
+（6） In Fig. 4b, an increase of the background of sulfur concentration was attributed to the strong shuttle effect with less sulfur utilization caused by the high E/S ratio. However, other components in the electrolyte also undergo irreversible chemical reactions during cycling (> 400 h). So how can you confirm that the increase of the background of sulfur concentration is solely due to the strong shuttle effect with less sulfur utilization?
+
+（7） KB was better than SP as physical nonpolar sulfur confinement host. Therefore, the sulfur concentration in KB/S should be smaller than SP/S. In manuscript, the sulfur concentration in KB/S was ~700 mM and the sulfur concentration in SP/S was ~500 mM. Please explain it.
+
+（8） Typos or hard to understand. The authors need to rephrase the following parts.
+-In abstract, “...the nucleation pathway and crystallization of Li2S and sulfur governs the cycling performance...” should be “...the nucleation pathway and crystallization of Li2S and sulfur govern the cycling performance...”
+
+-On page 1, “…and shuttle effect caused by soluble polysulfide in electrolyte…” should be “…and the shuttle effect caused by soluble polysulfide in electrolyte…”
+
+-On page 11, “…On the upper voltage plateau the solid sulfur dissolution or recrystallization…” should be “…On the upper voltage plateau, the solid sulfur dissolution or recrystallization…”
+
+-On page 15, “…changing from progressive to an instantaneous pathway …” should be “…changing from a progressive to an instantaneous pathway …”
+
+Reviewer #2 (Remarks to the Author):
+
+The paper entitled “Detangling electrolyte chemical dynamics and evolution in Li-S batteries by operando monitoring with optical resonance combs” reports about TFBG technique for studying electrolyte chemical dynamics and evolution in Li-S batteries by tracking sulfur concentration and demonstrate that the nucleation pathway and crystallization of Li2S and sulfur governs the cycling performance. Although the similar technique has already been used in their previous work to track electrolyte concentration through refractive index (DOI: 10.1039/d1ee02186a), this work brings a new insight on understanding the mechanism and electrolyte chemical dynamics of LSB. Thus, this paper could be considered for publication after a minor revision, detailed in the following comments:
+
+1.Why the operando XRD in fig 2a doesn’t show the recrystallization process of sulfur at the end of charging?
+
+2.There is a sudden drop of sulfur concentration from A to B in the beginning of discharge in fig 3c, which also happens at the beginning of next discharge period. What leds to this? The sulfur concentration from A to B in fig 3c reacts different from in fig 3a and b. It dosen’t seem to be attributed to “delay”.
+
+3.The soluble sulfur transport flux calculation should be based on equilibrium state, as the result is used for representing the whole process. So I think it is more reasonable to exclude region from A to B and C to D during transport flux calculation. Then the net transport flux should be VBC/(S × t).
+
+4.The explanation of green triangle in fig 3e is “Transport flux of soluble sulfur based on current pulse (kinetics process) ”. Actually, the transport flux of soluble sulfur based on current pulse is (VBC-VDE) / (S × t), because the electrochemical process is accompanied by disproportionation process. Or the green triangle should be described as the net transport flux of soluble sulfur.
+5. Adding a fig comparing cycling performance under three cycle mode in fig 4e would clearly show how the five stage affect battery performance and enhance persuasion of this part.
+
+6. Please explain how you control internal temperature as well as strain stable during charging and discharging processes to eliminate their influence on the wavelength shift.
+
+7. Could you please specify the definition of the ratio which indicates the consumption rate of sulfur under the galvanostatic condition on Page 7? Furthermore, the sulfur concentration variation rate corresponding to each plateau would better be given in Fig.S4a.
+
+8. In “TFBG fabrication and sensing system”, please add the specific structure of the TFBG sensor employed in the measurements should be introduced, including the core/cladding diameter, the coating material, the period of grating and so on.
+
+9. In supplementary video, the amplitude and the wavelength have same trends. What is the difference between them? Can we draw the same conclusion from amplitude instead of wavelength?
+
+10. How to achieve optical fiber inserted into the battery without leaking electrolyte and how to make sure there is no side effect or carryover effect due to inserted fibre?
+
+11. How reproducible is the experiment?
+Reviewer #1:
+
+In this work, TFBGs were employed to operando track the chemical dynamics/states of the Li-S battery via electrolyte sulfur concentration, revealing the correlated relationship between the capacity fading and dynamic of dissolution/precipitation of polysulfides over cycling and at different cycling rates. Overall, I think is an interesting work, since the authors proposed a new application of optical fiber sensor for battery monitoring. Consequently, I will recommend its publication after a minor revision.
+
+Author response: We highly appreciate the positive comments from the reviewer, and they are all considered in corrected manuscript.
+
+Question 1: In Fig1c, why did the author choose the “*” region as the sensing mode? Can other modes also be used as sensing modes, and if so, what are the differences in sensing performance?
+
+Author response: The optical fiber sensor resonance marked by “*” was chosen as the preferred sensing mode due to the response sensitivity and particular optical polarization property.
+
+Regarding the sensing sensitivity, the primary advantage of the chosen resonance is that, for the accessible spectrum, it shows largest refractive index sensitivity (and hence response to sulfur concentration) compared to other guided modes at longer wavelengths that could also be considered [R1]. It is also referred to as the “cut-off” mode, where the surrounding refractive index (i.e. concentration of polysulfide dissolved in electrolyte) becomes equal to its mode effective index, and thereby it is observed that the mode resonance shifts more rapidly as its evanescent field penetrates more into the outer medium (electrolyte). With the goal of collecting valuable details regarding polysulfide chemical dynamics and evolution in electrolyte, the cut-off mode marked by “*” should be the best choice.
+
+Turning to the optical polarization of the relevant guided mode, it is well known that there are two group resonances in transmission spectra: P-polarization (blue line in Fig. 1(a)) corresponding to guide mode electric field azimuthally polarized; S-polarization (red line in Fig. 1(a)) corresponding to guided mode electric field radially polarized [R2]. Given the fact that the cutoff mode (marked by “*”) will be polarization insensitive (See Fig 1b, 1c insets) and there is no wavelength shift except some amplitude variation, it inspires confidence that it is possible to decouple the sulfur concentration in electrolyte by tracking the wavelength shift of cutoff mode with un-polarized input light and without a polarizer. By doing so, it allows for a simplified sensing system which still ensures that detection is both stable and repeatable.
+Fig. 1 | Optical polarization property of TFBG: (a) Experimental polarized transmission spectra in electrolyte (red, S-pol input, and blue, P-pol input); (b) Radial (P-pol) and (c) azimuthal (S-pol) dependence of simulated E-field intensity of cut-off guided mode (the arrows show the E-field vector orientations in both cases).
+
+[R1] Chan, C.-F., Chen, C., Jafari, A., Laronche, A., Thomson, D. J. & Albert, J. Optical fiber refractometer using narrowband cladding-mode resonance shifts. Appl. Opt. 46, 1142-1149 (2007).
+[R2] Alam, M.-Z., Albert, J. Selective excitation of radially and azimuthally polarized optical fiber cladding modes. J. Lightw. Technol. 31, 3167-3175 (2013).
+
+Question 2: As we all know, the S cathodes exhibit around 80% volume changes during cycling. Therefore, in this manuscript, please explain whether the wavelength shift caused by the volume changes of the S cathode will affect the results.
+
+Author response: The reviewer has rightfully noted a particular challenge with the Li-S system, but this is something where our sensor design has a particular advantage. The volume changes of sulfur during cycling (both expansive and contractive) don’t affect the wavelength shift of our sensor due to the specific cell design, mentioned in Fig. S3 in supplementary information. Basically, we are first placing a 2 mm thick, 12.8 mm diameter polyether ether ketone (PEEK) spacer ring into the swagelok assembly. This ring is pierced in the middle such that we can inject the fiber (which has a 1 cm long TFBG sensor inscribed segment) into the cross-sectional center of the cell. Within the Swagelok, the PEEK ring separates the cathode (sulfur and Super P carbon composite (60/40 wt.%)) and lithium anode so that fiber sensor is perfectly immersed inside the electrolyte but not touching, nor at risk of touching, either electrode regardless of the respective volume change.
+
+During our experiments, we ensure temperature and strain remain effectively constant because 1) the slow cycling rate gives minimal heat generation from overpotential and did not result in any temperature fluctuation of the sensor; additionally noted is that the cells are placed in a well-regulated thermostatic oven and 2) with the TFBG being effectively isolated and solely in the liquid electrolyte, it should not be sensitive to strain related to the electrodes. This is the particular case here, as we are using a high sulfur ratio (E/S ratio, ~ 100 μL/mg).
+Question 3: In manuscript, the author filled 500 \( \mu \)L of electrolyte into the cell, which is different from the common application scenario of optical fiber (the fiber is placed in a huge amount of liquid). Therefore, the author should consider whether the electrolyte was sufficient to completely infiltrate the fiber and can evenly wrap the optical fiber, which will affect the result.
+
+Author response: We fully agree with the reviewer's consideration that the fiber must be fully immersed in the electrolyte, which is the key point for ensuring that the sensor works properly. As mentioned above, a PEEK ring is used in the Swagelok assembly stack, and it is through the middle of this ring where the TFBG sensor is inserted. The volume inside this PEEK ring serves as a container, which is filled electrolyte. As the ring thickness of 2 mm is much greater than the fiber diameter of 0.125 mm, the PEEK ring provides a nice pool of liquid to constantly immerse the fiber during cell operation. To help illustrate the geometric considerations, Fig. 2 is shared below.
+
+![PEEK ring and TFBG sensor setup](page_374_682_495_246.png)
+
+Fig. 2 | The PEEK container.
+
+Question 4: Ultimately, optical fiber is a linear sensor with a limited detection range. In manuscript, the author also mentioned that the “delay” due to position of the sensor in the cell. So can the author show the evolution of sulfur concentration in other locations, such as near the electrode or at the same level as the current fiber?
+
+Author response: The question regarding the position of sensors is well spotted. This is an important aspect that we have also explored because any significant ion transport latency would have important implications for understanding dynamic reactions, as is the case here.
+
+Regarding our terminology, “delay” is used to refer to the time needed by the new polysulfide species generated at the positive electrode to lead an equilibrium state within the electrolyte. To quantify the extent of “delay”, a further experiment was carried out by placing two TFBGs sensors at different positions within the volume of electrolyte. This allows us to see the sulfur concentration dynamics close to Li metal and sulfur electrode surfaces, respectively. As shown in Fig. 3, the sulfur concentration detected by TFBG1, closer to the surface of Li (red line), typically “falls behind” that of the concentration detected by TFBG2, near to the surface of sulfur (blue line). A second and notable change is the lower amplitude of the S concentration near the surface of Li, as compared to the blue curve associated with the polysulfide of the positive electrode. While certainly the reviewer is aware of the value hidden within the details of the two sensor signals, given their positions, further assessment is beyond the scope of the work reported herein. Nevertheless, the position dependent differences observed here are small and do not impact our overall conclusions nor understanding of mechanisms.
+Fig. 3 | Decoding sulfur concentration gradient of LSB by two sensors close to electrode.
+
+Question 5: In Fig. 4b, I observed a slight dissonance in 12th cycle where the drop in temperature caused the wavelength to decrease. However, the double effect of temperature dropping and Li2S nucleation will result in smaller wavelength. Why is the valley of sulfur concentration in 12th cycle greater than that in other cycles?
+
+Author response: We thank the reviewer for this keen observation and would firstly like to apologize for the confusion stemming from this anomaly. The “valley” mentioned by the referee is not a “real” wavelength shift induced by a temperature change or generated polysulfides. It is the result of an error in plotting the data which we should have spotted ourselves. This anomaly comes from a recording failure of the integrator software that lasted for about 10 hours due to Windows update of computer system, and during this time period there was no data recorded. We have replotted Fig. 4b in the main text with “dot” instead of “line”, which we hope makes sense in terms of the wavelength shift.
+
+Regarding the second remark by the referee about the double effect of temperature, thermal effects can be totally removed by a thorough thermal calibration process that enlists several steps as follows:
+
+Step 1: By testing the temperature response of the fiber sensor in air (Fig. 4a,b), the thermal sensitivity of the core mode is determined to be 10.2 pm/°C and the target cladding mode sensitivity (cutoff mode in electrolyte) is 9.7 pm/°C (the cladding mode thermal sensitivity is always smaller than that of core mode) [R3].
+
+Step 2: By testing temperature response of the fiber sensor immersed in electrolyte (Fig. 4c,d), the total wavelength shift of the cutoff mode comprises two parts: temperature (9.7 pm/°C obtained from step 1) and the temperature-modulated refractive index of the electrolyte (-9.5 pm/°C in Fig. 4d).
+
+When the cell is cycled with the fiber sensor, the observed wavelength shift will be composed of temperature, temperature-induced refractive index, and polysulfide-induced refractive index of electrolyte. By manually compensating for the thermal effects on the basis of steps 1 and 2, the wavelength shift will be linked solely to the polysulfide generated.
+
+For the consideration of the reviewer and future readers, the above discussions have been added in the revised supplementary information as Fig. 4S.
+Fig. 4 | Thermal calibration of electrolyte: (a) The thermal response in air and (b) The corresponding thermal sensitivity of core mode and target cladding mode (cutoff mode in electrolyte); (c) The thermal response in electrolyte and (d) sensitivity.
+
+[R3] Imas, J. J., Bai, X., Zamarreño, C. R., Matias, I. R. & Albert, J. Accurate compensation and prediction of the temperature cross-sensitivity of tilted FBG cladding mode resonance. Appl. Opt. 62, E8-E15 (2023).
+
+Question 6: In Fig. 4b, an increase of the background of sulfur concentration was attributed to the strong shuttle effect with less sulfur utilization caused by the high E/S ratio. However, other components in the electrolyte also undergo irreversible chemical reactions during cycling (> 400 h). So how can you confirm that the increase of the background of sulfur concentration is solely due to the strong shuttle effect with less sulfur utilization?
+
+Author response: The reviewer has made another interesting suggestion concerning the increase in background noise, in addition to the lower sulfur usage caused by the high E/S ratio. It is certainly true that other irreversible reactions processes such as the formation of a solid electrolyte interphase (SEI) by the consumption of the additive LiNO₃, and the decomposition of the solvents DOL and DME [R4] could affect the sensing results by altering the interlinking refractive index of the electrolyte. However, this is exactly the reason why we have pursued a high E/S ratio so that the electrolyte consumption due to SEI formation is quite limited by using small amount of active material comparing to electrolyte (5-6 mg sulfur and 500 μL electrolyte). To us, this is well-confirmed by the experiment (Fig. 5d in the main text) involving the cathode composite based on Ketjen black carbon (KB) or MOF-801(Zr), which shows that the sulfur concentration background is fairly stable during cycling due to the higher efficiency of the nucleation pathway and crystallization of Li₂S.
+[R4] Xiong, S., Xie, K., Diao, Y & Hong, X. Characterization of solid electrolyte interphase on lithium anode for preventing the shuttle mechanism in lithium-sulfur batteries. J. Power Sources 246, 840-845 (2014).
+
+Question 7: KB was better than SP as physical nonpolar sulfur confinement host. Therefore, the sulfur concentration in KB/S should be smaller than SP/S. In manuscript, the sulfur concentration in KB/S was ~700 mM and the sulfur concentration in SP/S was ~500 mM. Please explain it.
+
+Author response: We totally agree with the reviewer's argument that theoretically higher surface area carbon (KB) should lead to trapping more sulfur. There could be several explanations for these discrepancies:
+
+To start with, both carbons are non-polar and the adsorption ability is very small compared to, for example, oxygenated porous architectures [R5]. Inspired by the reviewer's comment, we tested the adsorption ability of SP and KB carbons by mimicking the similar sulfur/carbon ratio we have used in our cells. Both carbons showed almost no adsorption ability, which was visually detected after resting for 22 hours (Fig. 5).
+
+![Two vials labeled SP and KB at beginning and 22 hours later](page_393_682_668_246.png)
+
+(a) Beginning        (b) 22 hours later
+
+10 mg SP or 10 mg KB in 100 mM Li2S6 (1 mL)
+
+Fig 5. The adsorption test of polysulfide by SP or KB carbon.
+
+In addition to that, as was pointed in Fig. S10 in supplementary information with the XRD patterns before and after heat treatment, sulfur only partially penetrated into the nanostructure of KB, contrary to our own expectation, as well as literature reports. Moreover, physical nonpolar sulfur confinement by Ketjen black (KB) is very limited in our experiment, supported by Fig. S11 in supplementary information there is no sulfur left tested by energy-dispersive X-ray spectroscopy (EDX) inside the KB after the first plateau of discharge. We must therefore infer that all sulfur is converted to polysulfide and dissolved in electrolyte where it is detected by the fiber sensor.
+
+Another reason may rise from our experimental condition in which we deliberately used a much higher E/S ratio (~100) than usual (< 8) so that the solubility of polysulfides would be feasible even for the highly porous hosts. To help with detection, a relatively small current density (C/20) gives time for dissolved polysulfide to equilibrate in the electrolyte, regardless of how much sulfur is trapped into the pores.
+
+Finally, the slightly higher sulfur concentration of KB/S than SP/S could be due to the fact that the weight of the active material is slightly larger than that of the Super P/S composite disk, which
+can be attributed to the manual process of mixing the electrode composite with PTFE, forming it into a film and punching it into disks. As a result, there will be some deviation in the weight of the active material, but this is generally within a controllable range, and doesn’t materially impact any of the results presented.
+
+[R5]. Demir-Cakan, R., Morcrette, M., Nouar, F., Davoisne, C., Devic, T., Gonbeau, D., Dominko, R., Serre, C., Ferey, G & Tarascon, J.-M. Cathode composites for Li-S batteries via the use of oxygenated porous architectures. J. Am. Chem. Soc. 133, 40, 16154–16160 (2011).
+
+Question 8: Typos or hard to understand. The authors need to rephrase the following parts.
+-In abstract, “…the nucleation pathway and crystallization of Li2S and sulfur governs the cycling performance…” should be “…the nucleation pathway and crystallization of Li2S and sulfur govern the cycling performance…”
+-On page 1, “…and shuttle effect caused by soluble polysulfide in electrolyte…” should be “…and the shuttle effect caused by soluble polysulfide in electrolyte…”
+-On page 11, “…On the upper voltage plateau the solid sulfur dissolution or recrystallization…” should be “…On the upper voltage plateau, the solid sulfur dissolution or recrystallization…”
+-On page 15, “…changing from progressive to an instantaneous pathway …” should be “…changing from a progressive to an instantaneous pathway …”
+
+Author response: We really appreciate the time spent by the referee in identifying and editing inconsistencies found in our submitted manuscript. We have accepted all suggestions and reworded the passages in the text accordingly.
+Reviewer #2:
+
+The paper entitled “Detangling electrolyte chemical dynamics and evolution in Li-S batteries by operando monitoring with optical resonance combs” reports about TFBG technique for studying electrolyte chemical dynamics and evolution in Li-S batteries by tracking sulfur concentration and demonstrate that the nucleation pathway and crystallization of Li2S and sulfur governs the cycling performance. Although the similar technique has already been used in their previous work to track electrolyte concentration through refractive index (DOI: 10.1039/d1ee02186a), this work brings a new insight on understanding the mechanism and electrolyte chemical dynamics of LSB. Thus, this paper could be considered for publication after a minor revision, detailed in the following comments:
+
+Author response: We highly appreciate the positive comments from the reviewer, and they are all considered in corrected manuscript.
+
+Question 1: Why the operando XRD in fig 2a doesn’t show the recrystallization process of sulfur at the end of charging?
+
+Author response: The reviewer has indeed made a careful observation. We believe it is a question of quantity and state of sulfur (amorphous vs crystallize). From our TFBG decoupling experiment we can deduce that only ~10% solid sulfur will be reformed without providing clues on its state (crystallize or amorphous). Ten percent of crystallized sulfur should be easily detected by XRDs. To check this point that the re-formed sulfur is amorphous, a fully charged sulfur-loaded carbon electrode was recovered by washing and drying to remove any soluble polysulfide as well as remaining electrolyte salts and investigated by SEM. Fig. 1 compares two SEM taken shots of the pristine and fully charge samples suggesting the presence of amorphous sulfur, hence confirming the XRDs. We may also note that sulfur is readily amorphized in the presence of organic compounds under mild conditions, which has been well-established in various sulfur industries going back 70 years, at least [R1]
+
+[R1] Bartlett, P.-D., Meguerian, G. Reactions of elemental sulfur. I. The uncatalyzed reaction of sulfur with triarylphosphines. J. Am. Chem. Soc. 78, 15, 3710-3715 (1956).
+
+![SEM images comparing cathode morphology at beginning and end of charging](page_420_1042_601_246.png)
+
+Fig. 1 | The morphology (SEM) of cathode (S: Super P=6: 4 wt%) at the beginning of discharging and end of charging
+Question 2: There is a sudden drop of sulfur concentration from A to B in the beginning of discharge in fig 3c, which also happens at the beginning of next discharge period. What leds to this? The sulfur concentration from A to B in fig 3c reacts different from in fig 3a and b. It dosen’t seem to be attributed to “delay”.
+
+Author response: Regarding the reason leading to the “tiny” sudden drop of sulfur concentration from A to B in Fig.3c during charging (transition from rest mode to cycle mode), this can be attributed to the instantaneous response of electrolyte to a current pulse, arising from the redistribution of polysulfide (concentration gradient) because of sudden electric field. In this way, it is not exactly a “delay”, as noted by the referee. While it is quite different for the case in Fig. 3a and b that concentration variation from A to B is opposite to that in Fig. 3c, this should be attributed to the change of the concentration gradient direction during discharge. We also note that the amplitude of concentration variation from A to B is smaller than that in Fig. 3c, resulting from the fact that the fiber sensor is physically/geometrically closer to cathode during assembly process, and therefore it leads to an asymmetric concentration variation.
+
+Question 3: The soluble sulfur transport flux calculation should be based on equilibrium state, as the result is used for representing the whole process. So I think it is more reasonable to exclude region from A to B and C to D during transport flux calculation. Then the net transport flux should be VBC/(S × t).
+
+Author response: We sincerely appreciate that the referee makes the definition of net transport flux clearer (\( V_{BC}/(S \times t) \)) and we fully agree with the change. It has been corrected in main text of Fig. 3.
+
+Question 4: The explanation of green triangle in fig 3e is “Transport flux of soluble sulfur based on current pulse (kinetics process)”. Actually, the transport flux of soluble sulfur based on current pulse is (VBC- VDE)/(S × t), because the electrochemical process is accompanied by disproportionation process. Or the green triangle should be described as the net transport flux of soluble sulfur.
+
+Author response: The referee is perfectly right to assert that the net transport flux of soluble sulfur is based on electrochemical process accompanied by disproportionation process in Fig. 3e. It has been corrected in main text.
+
+Question 5: Adding a fig comparing cycling performance under three cycle mode in fig 4e would clearly show how the five stages affect battery performance and enhance persuasion of this part.
+
+Author response: The referee’s suggestion is a very good one and accordingly a figure has been prepared regarding cycling performance. It can now be found added to Fig. 4 in main text.
+
+Question 6: Please explain how you control internal temperature as well as strain stable during charging and discharging processes to eliminate their influence on the wavelength shift.
+
+Author response: Interestingly, the same question was asked by referee 1 (questions 3 and 5) and we have provided effectively the same answers. To eliminate any deformation induced by the large volume changes (around 80%) of the active material, the cell is specifically designed as mentioned in Fig. S3 in supplementary information, as well as Fig 2 shared again below. Basically, we are first placing a 2 mm thick, 12.8 mm diameter polyether ether ketone (PEEK)
+spacer ring into the swagelok assembly. This ring is pierced in the middle such that we can inject the fiber (which has a 1 cm long TFBG sensor inscribed segment) into the cross-sectional center of the cell. Within the Swagelok, the PEEK ring separates the cathode (sulfur and Super P carbon composite (60/40 wt.%)) and lithium anode so that fiber sensor is perfectly immersed inside the electrolyte but not touching, nor at risk of touching, either electrode regardless of the respective volume change.
+
+![PEEK container diagram showing fiber, TFBG sensor, and electrolyte](page_328_579_1012_246.png)
+
+Fig. 2 | The PEEK container.
+
+During our experiments, we ensure temperature and strain remain effectively constant because 1) the slow cycling rate gives minimal heat generation from overpotential and did not result in any temperature fluctuation of the sensor; additionally noted is that the cells are place in a well-regulated thermostatic oven and 2) with the TFBG being effectively isolated and solely in the liquid electrolyte, it should not be sensitive to strain related to the electrodes. This is the particular case here, as we are using a high sulfur ratio (E/S ratio, ~ 100 \( \mu \)L/mg).
+
+Any thermal effect during cycling can be totally removed by a thorough thermal calibration process that enlists several steps as follows:
+
+Step 1: By testing the temperature response of the fiber sensor in air (Fig. 3a,b), the thermal sensitivity of the core mode is determined to be 10.2 pm/\( ^\circ \)C and the target cladding mode sensitivity (cutoff mode in electrolyte) is 9.7 pm/\( ^\circ \)C (the cladding mode thermal sensitivity is always smaller than that of core mode) [R2].
+
+Step 2: By testing temperature response of the fiber sensor immersed in electrolyte (Fig. 3c,d), the total wavelength shift of the cutoff mode comprises two parts: temperature (9.7 pm/\( ^\circ \)C obtained from step 1) and the temperature-modulated refractive index of the electrolyte (-9.5 pm/\( ^\circ \)C in Fig. 3d).
+
+When the cell is cycled with the fiber sensor, the observed wavelength shift will be composed of temperature, temperature-induced refractive index, and polysulfide-induced refractive index of electrolyte. By manually compensating for the thermal effects on the basis of steps 1 and 2, the wavelength shift will be linked solely to the polysulfide generated.
+
+For the consideration of the reviewer and future readers, the above discussions have been added in the revised supplementary information as Fig. 4S.
+Fig. 3 | Thermal calibration of electrolyte: (a) The thermal response in air and (b) the corresponding thermal sensitivity of core mode and target cladding mode (cutoff mode in electrolyte); (c) The thermal response in electrolyte and (d) sensitivity.
+
+[R2] Imas, J. J., Bai, X., Zamarreño, C. R., Matias, I. R. & Albert, J. Accurate compensation and prediction of the temperature cross-sensitivity of tilted FBG cladding mode resonance. Appl. Opt. 62, E8-E15 (2023).
+
+Question 7: Could you please specify the definition of the ratio, which indicates the consumption rate of sulfur under the galvanostatic condition on Page 7? Furthermore, the sulfur concentration variation rate corresponding to each plateau would better be given in Fig.S4a.
+
+Author response: We thank the referee for noting that this was not clear in our initial submission. The ratio indicating the consumption rate of sulfur under the galvanostatic condition is defined by: \( Ratio = \left| \frac{\text{first plateau concentration slope}}{\text{second plateau concentration slope}} \right| \). Therefore, the \( Ratio_{discharge} = \left| \frac{S_1}{S_2} \right| = 3.88,\ Ratio_{charge} = \left| \frac{S_4}{S_3} \right| = 0.84 \). A figure regarding to sulfur concentration variation rate has been added to Fig.S5 in the supplementary information, which should help visually clarify the origin of these ratios.
+Fig. 4 | The definition of consumption rate of sulfur under the galvanostatic condition.
+
+Question 8: In “TFBG fabrication and sensing system”, please add the specific structure of the TFBG sensor employed in the measurements should be introduced, including the core/cladding diameter, the coating material, the period of grating and so on.
+
+Author response: We have added more details about the specific structure of TFBG to “TFBG fabrication and sensing system” in main text in accordance with the referee’s request.
+
+Question 9: In supplementary video, the amplitude and the wavelength have same trends. What is the difference between them? Can we draw the same conclusion from amplitude instead of wavelength?
+
+Author response: Indeed, the amplitude and wavelength of TFBG cutoff resonance are strongly correlated by refractive index (sulfur concentration) variation. The cutoff resonance decreases sharply in amplitude together with the wavelength shift (Fig. 5), indicating loss of total internal reflection at the point where the cladding mode effective index becomes equal to the surrounding refractive index of polysulfide solution. Amplitude and wavelength will follow the same trend when the surrounding solution is a “pure” liquid, except in the special case of high turbidity, which leads to the irreversible disappearance of all cladding mode resonances [R3]. Thus, the observation of similar amplitude and wavelength trends in our video means that the effects of turbidity in our system, if any, are negligible.
+
+Fig. 5 | The TFBG response to 100 mM Li2S2, Li2S5 and Li2S8 in electrolyte of 1 M LiTFSI, 0.5 M LiNO3 in DOL/DME (1:1, v/v)
+[R3] Huang, J., Han, X., Liu, F., Gervillie, C., Blanquer, L. A., Guo, T. & Tarascon, J.-M. Monitoring battery electrolyte chemistry via in-operando tilted fiber Bragg grating sensors. Energy Environ. Sci. 14, 6464-6475 (2021).
+
+Question 10: How to achieve optical fiber inserted into the battery without leaking electrolyte and how to make sure there is no side effect or carryover effect due to inserted fibre?
+
+Author response: As shown in Fig. 2 we have used a Swagelok cell design for our experiments, which is nearly a worldwide standard in battery research labs because of its relative ease of assembly and air/moisture tightness. Swagelok ferrules typically rely on plastic deformation to ensure excellent sealing properties. The cell is then diametrically drilled through the PEEK spacer to accommodate the fiber that supports the TFBG and is hermetically sealed with epoxy at the fiber entry and exit positions in the Swagelok assembly. With this method we have never experienced electrolyte leakage.
+
+As far as secondary or carry-over effects due to the inserted fiber are concerned, they are minimal here because the fiber is immersed in an electrolyte bath (PEEK ring) and is largely separated from the positive and negative electrode. Of course, the story would have been very different if we had placed the fiber in the sulfur electrode, due to the limitations of ion transport and induced current inhomogeneity!
+
+Question 11: How reproducible is the experiment?
+
+Author response: These experiments enlist several key steps out of which three, namely i) the preparation of consistent C-S electrodes ii) the proper positioning of the fiber and iii) the feasibility of having similar TFBG sensors, were found to be the most critical for overall reproducibility. Nevertheless, we could well-master the first two steps in-house and the third one by working with our TFBG’s producer, such that highly reproducible and dependable data could be obtained. Overall, both sensors and cells needed to be developed to a point that we can ensure our data is repeatable and reproducible (with respect to sulfur concentration evolution during cell operation). As per the question of the referee we should have addressed this point by adding the sentence “all the data has been at least be duplicated 2 or 3 times prior to being reported”, which has now been included in the main text.
+REVIEWERS' COMMENTS
+
+Reviewer #1 (Remarks to the Author):
+
+The authors have well addressed the previous concerns. I think this paper can be accepted.
+
+Reviewer #2 (Remarks to the Author):
+
+The manuscript can be accepted.

0179e628a853118df9da75d50a227d9cf3c9b00dfa8825f8efe5e29d0d1c5f4c/preprint/preprint.md

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+Detangling electrolyte chemical dynamics and evolution in Li-S batteries by operando monitoring with optical resonance combs
+
+Jean-Marie Tarascon (jean-marie.tarascon@college-de-france.fr)
+UMR 8260 « Chimie du Solide et de l'Energie », https://orcid.org/0000-0002-7059-6845
+
+Fu Liu
+Collège de France
+
+Wenqing Lu
+École supérieure de physique et de chimie industrielles de la Ville de Paris
+
+Jiaqiang Huang
+the Hong Kong University of Science and Technology (Guangzhou) https://orcid.org/0000-0001-8250-228X
+
+Vanessa Pimenta
+École supérieure de physique et de chimie industrielles de la Ville de Paris
+
+Steven Boles
+NTNU - Norwegian University of Science and Technology https://orcid.org/0000-0003-1422-5529
+
+Rezan Demir-Çakan
+Gebze Technical University
+
+Article
+
+Keywords:
+
+Posted Date: August 4th, 2023
+
+DOI: https://doi.org/10.21203/rs.3.rs-3192096/v1
+
+License: This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License
+
+Additional Declarations: There is NO Competing Interest.
+
+Version of Record: A version of this preprint was published at Nature Communications on November 14th, 2023. See the published version at https://doi.org/10.1038/s41467-023-43110-8.
+Detangling electrolyte chemical dynamics and evolution in Li-S batteries by operando monitoring with optical resonance combs
+
+Fu Liu1,2, Wenqing Lu3, Jiaqiang Huang4, Vanessa Pimenta3, Steven Boles5, Rezan Demir-Cakan6,7* & Jean-Marie Tarascon1,2,8*
+
+1Collège de France, Chimie du Solide et de l’Energie—UMR 8260 CNRS, Paris, France.
+2Réseau sur le Stockage Electrochimique de l’Energie (RS2E)—FR, CNRS 3459, Amiens, France.
+3Institut des Matériaux Poreux de Paris (IMAP), ESPCI Paris, Ecole Normale Supérieure, CNRS, PSL University, Paris, France
+4The Hong Kong University of Science and Technology (Guangzhou), Sustainable Energy and Environment Thrust, Nansha, Guangzhou, Guangdong 511400, P. R. China
+5Department of Energy and Process Engineering, Faculty of Engineering, Norwegian University of Science and Technology (NTNU), Trondheim, Norway
+6Gebze Technical University, Institute of Nanotechnology, Gebze, Kocaeli, 41400, Turkey
+7Gebze Technical University, Department of Chemical Engineering, Kocaeli, 41400, Turkey
+8Sorbonne Université–Université Pierre-et-Marie-Curie Paris (UPMC), Paris, France
+
+Challenges in enabling next-generation rechargeable batteries with lower cost, higher energy density, and longer cycling life stem not only from combining appropriate materials, but from optimally using cell components given their respective evolutions. One-size-fits-all approaches to operational cycling and monitoring are limited in improving sustainability if they cannot utilize and capture essential chemical dynamics and states of electrodes and electrolytes. Herein we describe and show how the use of tilted fiber Bragg grating (TFBG) sensors to track, via the monitoring of both temperature and refractive index metrics, electrolyte-electrode coupled changes that fundamentally control lithium sulfur batteries. Through quantitative sensing of the sulfur concentration in the electrolyte, we demonstrate that the nucleation pathway and crystallization of Li2S and sulfur governs the cycling performance. With this technique, a critical milestone is achieved, not only towards developing chemistry-wise cells (in terms of smart battery sensing leading to improved safety and health diagnostics), but further towards demonstrating that the coupling of sensing and cycling can revitalize known cell chemistries and break open new directions for their development.
+
+Introduction
+
+Widescale utilization of renewable energy sources is essential to supplementing and perhaps replacing the carbon-based energy supply responsible for climate change. The recent success of electric vehicles made possible by lithium-ion battery technology, attributed to both improved reliability and cost reductions, demonstrates that new breakthrough chemistries may not be necessary for a ‘green transition’ if known electrochemical cell pairings can be mastered. Included among these chemistries are resurgent lithium sulfur batteries (LSB), which, in spite of their appeal in terms of theoretical specific energy (~2600 Wh/kg), are still not commercialized. This can be attributed to a number of unresolved challenges, including the insulating nature of sulfur and lithium sulfides, large volume expansion (80%) of the solid sulfur cathode during the formation of Li2S, and shuttle effect caused by soluble polysulfide in electrolyte1,2.
+Numerous characterization techniques have been deployed to clarify the underlying science of LSBs during operation, which have contributed significantly to a better understanding of the kinetics and thermodynamics of the dissolution/precipitation of polysulfides, whose critical role in LSBs has been known for nearly 50 years\textsuperscript{3}. Since then, methods such as X-ray diffraction (XRD)\textsuperscript{4,5}, electrochemical tests\textsuperscript{6-8}, and spectroscopic techniques\textsuperscript{9-16} have been used to provide valuable information regarding identification of polysulfide species and reaction kinetics. However, it is experimentally challenging to isolate the individual polysulfides due to the propensity of disproportionation, and these analytical techniques rely on special equipment and cell designs that cannot be directly deployed for long cycling periods. Recently, optical fiber sensors have attracted attention in battery sensing due to their low cost, compactness, remote sensing capabilities, and simple integration into batteries without interfering with their internal chemistry\textsuperscript{17}. Among the fiber sensor family, the most commercialized Fiber Bragg grating (FBG) sensors have been well integrated inside Na (Li)-ion batteries for monitoring heat and pressure\textsuperscript{18} or inside the solid-state batteries for tracking the stress dynamics\textsuperscript{19}. Indeed, recently Ziyun et al. demonstrated that the cathode stress evolution of LSB can be \emph{in-situ} monitored by FBG sensors for understanding the chemo-mechanics\textsuperscript{20}. Nevertheless, testing polysulfides with FBGs is still limited, owing to the fact that the sensing signals are totally confined inside the fiber core and cannot sense the electrolyte surrounding the fiber surface.
+
+In order to investigate the external medium of fiber, TFBGs (same structure as FBG without physical structure modification\textsuperscript{21}, but rotating the grating plane to a specific angle) have been proposed to excite hundreds of discrete cladding mode resonances that are sensitive to the external medium refractive index perturbation via evanescent fields\textsuperscript{22}, hence serving as an optical 'comb'. This has led to the development of high-performance sensors used in various areas, including biomedicine\textsuperscript{23}, magnetic detection\textsuperscript{24}, and gas monitoring\textsuperscript{25}. Recently, TFBGs have been integrated into commercial batteries to detect chemical dynamics/state of electrolytes related to chemical evolution\textsuperscript{26}. Interestingly, some TFBG-assisted surface plasmon resonance (TFBG-SPR) sensors with higher sensing sensitivity have also been developed for Zn-ion batteries to offer an alternative way of probing ion transport kinetics\textsuperscript{27}. Overall, TFBG sensors provide new opportunities to deal with the challenge of battery sensing as they combine direct optical sensing of the environment, as well as physio-mechanical sensing of the environment via the confined optical modes.
+
+Herein, TFBG sensors, enabling measurements with a wide array of parameters including refractive index, temperature, and strain, are proposed to operando track the chemical dynamics/states of the LSB via electrolyte sulfur concentration. We demonstrate that the capacity fading is strongly correlated with the dissolution/precipitation of polysulfides throughout the cycling and hence, with respect to cycling rates. By exploiting the kinetic and thermodynamic response of soluble sulfur in the electrolyte, the nonlinear transport flux clarifies the "invisible" disproportionation process together with their dynamic evolution. With this understanding, we show that altering the nucleation pathway of the crystalline Li\(_2\)S and sulfur can be attributed to real improvements in cell cycling performance. Subsequently, it is noted that TFBGs have the ability to obtain key chemical-physical-thermal metrics \emph{in operando} with notable time and spatial resolution that may extend beyond LSBs.
+Results
+
+Characteristics of TFBG sensing
+
+Prior to in operando battery inspection, it is appropriate to first briefly visit the suitability of TFBG sensing for such chemistries, as related to fundamental principles of their operation. TFBGs, immersed in an electrolyte (Fig. 1a), were made in the core of the commercial single-mode fiber by ultraviolet pulse laser to induce periodically permanent refractive modulation. They obey a phase matching condition by enhancing the coupling between fundamental core mode and backward-propagation cladding modes\(^{22}\) (Fig. 1b):
+
+\[
+\lambda = (n_{11}(\lambda) + n_{lm}(\lambda)) \Lambda / \cos \theta
+\]
+
+where \( \lambda \) is the cladding mode resonance wavelength, \( n_{11}(\lambda) \) is the effective index of core mode, and \( n_{lm}(\lambda) \) is the effective index of cladding mode with azimuthal order \( l \) and radial order \( m \). \( \Lambda \) is the period of grating along the fiber axis, and \( \theta \) is the grating tilt angle. The experimental spectra are presented in Fig. 1c, where the core mode resonance (\( i.e. \), Bragg resonance) is located at the longest wavelength around 1590 nm (sensitive to temperature and strain (\( T, \varepsilon \)))\(^{22}\). The cladding mode resonances guided by the fiber cladding (beside \( T, \varepsilon \), also sensitive to refractive index (\( Rl \)) of the surrounding media) are shown on the left of Bragg resonances. The leaky modes are located at the region where there is a discontinuity in the cladding mode envelope and their amplitude, indicating the loss of total internal reflection at the point where the cladding mode effective index becomes equal to or smaller than the surrounding \( Rl \). Therefore, with respect to soluble polysulfides which perturb electrolyte density, and hence the refractive-index, we focus on the high order guided cladding modes near the leaky mode region.
+Fig. 1 | Concept of optical fiber sensing for LSB. (a) Schematic of a fiber optic sensor immersed in electrolyte for in-situ detection of sulfur concentration originating from the generated dissolved polysulfide and their transport activities (i.e., shuttle effect). (b) Backward-propagation guided modes inside fiber for sensing (Supplementary information Fig. S1). (c) Experimental spectra response to polysulfide. (d) The wavelength shifts of cladding mode resonance at ~1560 nm to 100 mM polysulfide Li2Sx (x=1, 2, 3, ..., 8), shaded in green; (e) to concentration variation of Li2S4 and Li2S8 from 0 mM to 100 mM; (f) to same sulfur concentration of polysulfide Li2Sx (x=4, 5, 6, 7, 8).
+
+To investigate the response of our TFBG to polysulfides, depicted in Fig. 1c, the TFBG was thoroughly immersed in a series of 100 mM polysulfide containing electrolytes in a modified Swagelok cell. Bearing this in mind, the Bragg resonance remains stable because any strain and temperature variation were eliminated during the measurements, indicating that the cladding mode wavelength shift is only related to refractive index variation. When the chain length of polysulfides is increased while keeping the polysulfide concentration the same, the guided modes on the left side of cladding mode at 1560 nm becomes leaky due to the increased refractive index. This is a result of the number sulfur atoms in solution becoming larger and perturbing the corresponding mode effective refractive index, while guided modes on its right side are linearly shifted to longer wavelength (Fig. 1d,e and Supplementary Fig. S2a,b). Noteworthy is the fact that the refractive index tested by TFBG sensor is an “average effect” of all the pertinent refractive indices of lithium polysulfide solutions. Following this,
+dilution of the 100 mM polysulfide Li2Sx (x=4, 5, 6, 7, 8) to an equivalent concentration of sulfur (Supplementary Fig. S2c) yields an equivalent optical effect, stemming from the refractive index of polysulfide solutions converging to the same density, (Fig. 1f and Supplementary Fig. S2d,e). Therefore, rather than recognizing the specific species inside the electrolyte, the TFBG sensor will distinctly reveal the electrolyte sulfur concentration evolution of LSB cell (so long as temperature is kept constant).
+
+Operando measurement of chemical dynamic state of LSB
+
+Given the promising proof-of-concept of sulfur concentration measurement in electrolyte, we explored the capability of operando chemical dynamics/states testing of LSB cell by putting a 2 mm thick, 12.8 mm diameter polyether ether ketone (PEEK) ring (1 cm long TFBG can go through) in the middle of the Swagelok to separate the cathode (sulfur and Super P carbon composite (60/40 wt.%)) and lithium anode so that fiber sensor would not touch any of them (Supplementary Fig. S3). Filling the PEEK ring with electrolyte (500 μL, 1 M LiTFSI, 0.5 M LiNO3 in DOL/DME (1:1, v/v)) where the sensor is immersed, the effect of ion concertation gradient of electrolyte including Li+, TFSI- and NO3- in DOL and DME can be safely neglected. It should be noted that prior to LSB investigations, a control experiment was executed with lithium iron phosphate (LFP) as the cathode. Here it was found that the corresponding R/I of electrolyte variation is 20 times smaller than that in LSB in which dissolved polysulfide is formed (Supplementary Fig. S4). Therefore, the use of a TFBG can provide for the possibility of measuring sulfur concentration in the electrolyte during cell operation, and to a large extent, the measurement will be irrespective of the cell’s state of charge or state of health.
+Fig. 2 | Decoding electrolyte sulfur concentration dynamic of LSB. (a) Operando measurement of LSB by TFBG and XRD at C/20 (left panel: polysulfide dissolution allowed (electrolyte of 1 M LiTFSI, 0.5 M LiNO3 in DOL/DME (1:1, v/v)); right panel: polysulfide dissolution prohibited (electrolyte of LP30: 1 M LiPF6 in EC/DMC) of sulfur and Super P carbon composite (60/40 wt.%) cathode. (b) Morphology (SEM) and content of elemental sulfur and Super P carbon (energy-dispersive X-ray spectroscopy, EDX) of the cathode at the end of charging. (c) The quantitative analysis of sulfur before cycling, end of first plateau of discharge and end of charge. (d) The recrystallized sulfur governed by comproportionation reactions and potential voltage. The shaded region in blue stands for 15 hours of rest (OCV mode) starting at the end of charging demonstrating that the re-crystallized sulfur (marked by green asterisk "*") dissolves into the electrolyte in the form of soluble polysulfide through comproportionation reactions.
+Based on the aforementioned concept, we measured the electrolyte sulfur concentration variation with a TFBG sensor while simultaneously deploying *in operando* XRD during C/20 cycling to track phase transitions of the composite electrode (Fig. 2a,c). At the upper voltage plateau around 2.4 V, the highest sulfur concentration in the electrolyte was monitored (left panel of Fig. 2a) and found to be accompanied by a decrease in the sulfur peak intensity (XRD pattern) resulting from a series of phase transformations, *i.e.*, from solid sulfur to soluble intermediate polysulfides. On the other hand, when the carbonate–based electrolyte was used as a reference (*i.e.*, LP30, right panel of Fig. 2a), no concentration gradient was observed in the electrolyte and remained nearly stable due to the fact that no soluble polysulfide intermediates were formed. Instead this resulted in the formation of insoluble and undetected products, since it is known that there is a nucleophilic reaction between sulfur radical and ethylene carbonate of LP30 to form thiocarbonate–like solid electrolyte interphase\(^{29,29}\) (Supplementary Fig. S5). Turning to the lower voltage plateau around 2.1 V (Fig. 2a), the concentration of dissolved sulfur decreases as a result of the reduction of long-chain polysulfide into shorter chains, leading to insoluble Li\(_2\)S compound in the cathode (Supplementary Fig. S6a) confirmed by XRD\(^{30,31}\). Upon charging, the sulfur concentration indicates reversible recovery consistent with the decay of Li\(_2\)S peaks until complete disappearance at the voltage ~2.4 V, where crystallization of sulfur starts and thus sulfur concentration in electrolyte drops again, even though the deposited solid sulfur in the cathode is featureless by XRD\(^{31}\). To confirm the sulfur at the end of charge, the cathode powder was recovered in the glovebox by washing and drying to remove any soluble polysulfide as well as remaining electrolyte salts (Fig.2b,c), confirming that 1.4 % sulfur was detected and its surface topography was unchanged (*i.e.*, no formation of big crystalline particles)\(^{31}\). Furthermore, when setting the 15-hour open circuit voltage (OCV) after charging, the sulfur concentration increases and reaches a plateau within 9 hours (Fig.2c), whereas, on the other hand, no sulfur concentration changes were observed during rest periods applied at the end of discharge (Supplementary Fig. S6b). It is most likely explained by comproportionation reactions during the rest period when the recrystallized sulfur from the end of charging is transformed to soluble lower-order polysulfide via reacting with high-order polysulfide\(^{32}\). This is also supported by the beginning of 2 hours rest (first cycle before discharging) demonstrating relatively little variation of electrolyte since fresh electrolyte contains a minimum amount of high order polysulfide and the comproportionation reactions are thus not possible (Supplementary Fig. S6c). The crystalline sulfur at the end of charge is related to the cut-off potential that the sulfur recrystallization process disappears\(^{4}\) (disappearance of sulfur concentration valley at the end of charge in Fig.2d) if setting the potential below 2.4 V (indicated that less sulfur suppresses the related comproportionation reactions, also detailed in Supplementary Fig. S6c). Altogether, the dynamic of sulfur concentration of electrolyte decoded by TFBG sensor supports the simplified chemical reaction process: during discharging the sulfur receives electrons and transfers them first to soluble Li\(_2\)S\(_x\) at the high voltage plateau. This is followed by formation of insoluble Li\(_2\)S at the low voltage plateau and vice versa for the charging process, indicating that the consumption rate of sulfur under the galvanostatic condition can be expressed as a ratio. According to the “linear” sulfur concentration variation rate by monitoring the slope (mM/h) on each plateau tested by sensor during the discharge and charging steps (Supplementary Fig. S4a) it was
+observed that the ratio on the upper and lower plateaus at the discharge step is 3.9. This is similar to the value obtained during charging (0.9), suggesting that the rate of sulfur transformation to/from soluble polysulfide is ~4.3 times faster than that to/from insoluble Li2S and the respective polysulfides.
+
+![Decoding the disproportionation process and evolution.](page_186_370_1077_670.png)
+
+Fig. 3 | Decoding the disproportionation process and evolution. (a, b, c and d) The temporal voltage (black curve) and decoded electrolyte sulfur concentration (red curve) by GITT test (the capacity and optical spectra are given in supplementary Fig. S7). (a, b and c) Detailed view of electrolyte response to current pulse (kinetic process) and rest (thermodynamic process). (e) Transport flux of soluble sulfur based on current pulse (kinetics process, green triangle, \( D_t = V_{oc}/(S \times t) \)) and rest (thermodynamic process, blue square, \( D_t = V_{oc}/(S \times t) \)), where \( S \) is across section area of electrolyte that sensor is immersed in, \( t \) is corresponding time. It indicates the slope of soluble sulfur consumption (negative) or formation (positive) in electrolyte, which is also plotted by arrows in bottom (arrow up: sulfur increasing, arrow down: sulfur decreasing). The normalized ratio (red sphere) represents the sulfur consumption of rest (thermodynamic process) by \( Ratio = |D_t|/(|D_t| + |D_k|) \).
+The disproportionation and association reactions of likely intermediates are mesmerizing, but despite an awareness of their existence, their mysterious dynamics make LSBs seemingly incomprehensible. Nevertheless, the real-time quantification of soluble sulfur afforded by TFBGs provides a convincing way to straighten their story when combined with GITT (Fig. 3). As depicted in Fig. 3d, the overall profile of sulfur concentration variation matches well with dissolution/precipitation of polysulfides and sulfur already confirmed in Fig.2, and we focus on the temporal response of electrolyte to the current pulse and respective rest period. According to Fig. 3a,b,c the “tiny” variation of sulfur concentration from A to B (moving from the rest to cycling mode) is the electrolyte instantaneous response to the leading edge of current pulse with strong electrical field gradient, originating from polysulfide redistribution driven by the sudden electrical field33. This effect trends in the opposite direction as polysulfide diffusion in the region from B to C, which relates to the current pulse (referred to herein as the kinetic process). The reader may note a discrepancy between voltage and concentration from C to D during rest, which is attributed to the “delay” between the electrochemical reaction at the electrode surface and the position of the sensor in the cell. Hence a small lag exists even if removing the current pulse. Regarding the OCV relaxation (3 hours rest period) and movement towards equilibrium (herein coined as the thermodynamic process) in the region from C to E, the sulfur concentration fluctuation is most likely explained by polysulfide disproportionation process (i.e. \( Li_2S_6 \leftrightarrow Li_2S_4 + 1/4S_8 \))9 since the two best-remaining hypotheses, dissociation (i.e. \( Li_2S_6 \leftrightarrow Li^+ + LiS_6^- \) or \( Li_2S_6 \leftrightarrow 2LiS_3^-\))34 and non-uniform polysulfide distribution can be excluded: the dissociation of polysulfide including anions and radicals are rare while the neutral lithium polysulfide is dominant in electrolyte34; the polysulfide distribution reaches equilibrium within 1 min (time interval of spectra recording) that is nearly synchronous to electrochemistry (Fig. 2a), not matching the rest period situation with 3 hours of continuous soluble sulfur consumption or generation. After careful deliberation, we move forward with the idea that electrochemical and disproportionation processes can be extracted respectively by temporal response of electrolyte based on sulfur concentration decoded by TFBG sensor.
+
+Encouraged by the results mentioned above, we have next attempted to build a quantitative relation between kinetic and thermodynamic processes through a primitive estimation of transport flux of sulfur in the electrolyte (Fig. 3e). In STAGE I, on the higher voltage plateau, solid sulfur was continuously consumed upon discharge to form long chain polysulfide, Li2S8 (green triangle), together with the rapid disproportionation process \( Li_2S_8 \leftrightarrow Li_2S_6 + 1/4S_8 \)9,35–37 leading to soluble sulfur consumption during relaxation (blue square). At the same time the normalized ratio (red sphere) between the rest and current pulse process nearly remains the same and fixed at 0.1 (shaded in light green color), meaning that there is a competition reaction between the soluble long chain polysulfide species formation and the S8 reprecipitation in the beginning of the discharge step. In STAGE II, regarding the first-to-second plateau transition whereby a voltage slope forms between 2.3 and 2.1 V, the shorter chain polysulfide Li2S4 is expected to be generated38,39. This is accompanied by a reduction in the rate of formation of soluble sulfur in the electrolyte and hence, the sulfur concentration during resting keeps increasing while the generation of fresh long chain polysulfides winds down and the kinetic/thermodynamic ratio can reach 0.89. This indicates that polysulfide species formation via disproportionation is dominant due to fact that dissolved sulfur
+continues to react with polysulfide present in the electrolyte during rest\(^{38,41}\). Undoubtedly an enriched concentration of sulfur in the electrolyte contributes significantly towards driving the formation of more polysulfides. In STAGE III where the lower voltage plateau marks the conversion between Li\(_2\)S\(_4\) to shorter chain Li\(_2\)S\(_2\) and Li\(_2\)S forms, the potential disproportionation process \(Li_2S_2 \leftrightarrow 1/3Li_2S_4 + 2/3Li_2S^{0.41}\) is highlighted from the middle of the second plateau, and raises the sulfur concentration to about a normalized ratio of 0.2 which follows until the end of the half-cycle. Upon charging (STAGE IV and STAGE V), it is evident that the process is not a fully reversible one, as seen with STAGE IV where Li\(_2\)S\(_4\) and Li\(_2\)S\(_3\) reappear and the push towards thermodynamic equilibrium necessitates disproportionation processes leading to consumption of sulfur during rest periods, but an overall concentration increase. In STAGE V, the sulfur concentration in electrolyte drops very sharply, caused by the recrystallization of sulfur during current pulsing, even though that is not visible in the operando XRD studies shown in Fig. 2a. Interestingly, the rise of soluble sulfur during these late-stage rest periods suggests nucleation and/or growth limitations of the recrystallized sulfur, which will be addressed here later. Altogether, the quantitative disproportionation process decoupled by the fiber sensor based on GITT provides meaningful details to understand micro-mechanisms of complicated kinetics processes.
+
+![Operando monitoring over cycling and cycling rate. (a) Spectra contour of TFBG cladding mode resonances response (details are given in supplementary video). (b) Temporal voltage (grey line), decoded sulfur concentration (red line), and temperature of electrolyte (blue line) over the cycling. (c) Capacity variation of (b) upon time. (d) Soluble sulfur](page_355_670_1042_627.png)
+
+Fig. 4 | Operando monitoring over cycling and cycling rate. (a) Spectra contour of TFBG cladding mode resonances response (details are given in supplementary video). (b) Temporal voltage (grey line), decoded sulfur concentration (red line), and temperature of electrolyte (blue line) over the cycling. (c) Capacity variation of (b) upon time. (d) Soluble sulfur
+concentration dynamic related to cycling rate. (e) Soluble sulfur concentration dynamic related to cycling rate of first/second plateau. The concentration drop through the recrystallization of sulfur at the end of charge is marked by green asterisk "*". With Mode I, the cycling rate was set by upper plateau (C/20) and lower plateau (C/5); Mode II by upper plateau (C/5) and lower plateau (C/20) and Mode III by upper plateau (C/10) and lower plateau (C/10).
+
+Inspired by aforementioned exploration of internal mechanisms of LSBs, we decide to further investigate the operando monitoring over cycling and cycling rates (Fig. 4a,b). Bearing in mind that the temperature (blue curve in Fig. 4b), decoded by Bragg resonance located at 1589 nm\(^{26}\), initially rises to 25 C° and keeps a constant afterward due to the shipping from glovebox to oven to reach thermal equilibrium. The periodic sulfur concentration evolution (red curve in Fig. 4b), decoded by the wavelength shift of cladding mode located at ~1559.5 nm in Fig. 4a, indicates the reversible dissolution/precipitation of polysulfides and sulfur. Noteworthy here is the feasibility of observing the amplitude of soluble sulfur variation (supplementary Fig. S8) that matches the cycling behavior associated with capacity fading owning to less and less Li\(_2\)S and solid sulfur crystallization over cycles (Fig.4c), which could be reasonably attributed to the high electrolyte to sulfur ratio (E/S ratio, > 100 \( \mu \)L/mg), thereby inducing stronger polysulfide shuttle effect with less sulfur utilization. Regarding a sulfur concentration response to the cycling rate depicted in Fig. 4d, a lower cycling rate (C/15) leads to the largest sulfur concentration change, strongly supporting the idea that the most soluble sulfur in electrolyte is transformed to solid species (Li\(_2\)S) when given adequate time for completion of the redox process. Accelerating the cycling to C/10, C/5 and C/3, partially soluble sulfur transformation is seen (\emph{i.e.}, background of sulfur concentration rises) together with less sulfur crystallization (\emph{i.e.}, the “dip” of soluble concentration at the end of charge).
+
+Following the evidence thus far, it is then reasonable to conclude that regular galvanostatic operating conditions might not be perfect for LSBs, considering the various competing mechanisms explored above which are evident at different stages of charge and discharge. With this in mind, different modes of cycling protocols were also pursued to be able to tune the cycling performance. For instance, when setting a relatively low (high) cycling rate for the upper (lower) plateau depicted in Fig. 4e (Mode I), only half of the soluble sulfur inside electrolyte was transformed to Li\(_2\)S due to high cycling rate of lower plateau. On the upper voltage plateau the solid sulfur dissolution or recrystallization was 100% successful and which can be readily attributed to the low cycling rate in this voltage range. Further confirmation of the delicate cycling nature of LSBs was seen in Mode II as 80% of the soluble sulfur inside electrolyte was transformed to Li\(_2\)S due to long cycling in the lower plateau (C/20) but with less solid sulfur recrystallization at the end of charge (C/5). Overall, the quantitative relation of soluble sulfur evolution and cycling/cycling rate implies that the efficiency of solid sulfur and Li\(_2\)S formation governs the cycling performance and significant new progress might be made through cycling condition optimization alone.
+
+**High performance based on novel functional cathode**
+
+Extensive work has been conducted over the years to improve the LSB performance through variety of means: the use of high-conductivity cathodes, strong polysulfide binding to
+suppress the shuttling phenomenon, surface chemistry to control Li2S nucleation or dissolution, design of cathode architectures that are elastic to withstand volume expansion, and optimized electrolytes enabling high sulfur utilization42. Considering the strategy of trapping lithium polysulfides, it includes physical (spatial) entrapment by confining polysulfide in the pores of non-polar carbon materials43 or designing a sulfur host material that exhibits stronger chemical interaction such as dipolar configurations based on polar surfaces44, metal-sulfur bonding45 and surface chemistry for polysulfide grafting and catenation46, leading to long cycling without strong capacity fading. Nevertheless, the fundamental problem regardless of approach is all related to the polysulfides dissolving inside the electrolyte, thus a smart sensor that can reliably track the soluble sulfur in real time should be of particular value.
+
+In this respect, in addition to the less porous Super P carbon discussed above, the Ketjen black (KB) carbon whose BET surface area > 1200 m^2/g is utilized as physical nonpolar sulfur confinement host (KB/S, 40/60 wt.%), and the electrolyte was simultaneously monitored by a TFBG senor together with XRD to characterize the composite cathode phase transitions (left panel of Fig. 5a). After the melt-diffusion treatment process, part of sulfur penetrates into the nanostructure of KB (Supplementary Fig. S9); however, during cycling the nonpolar physical adsorption or confinement of polysulfide is very limited and massive soluble polysulfide is dissolved and detected. Surprisingly, the capability of Li2S crystallization is enhanced since more than 91 % soluble sulfur disappears and converts to solid short chain polysulfide at second plateau as indicated by the fiber sensor. Meanwhile, unlike linearly sulfur concentration change with super P carbon (BET surface area: 62 m^2/g) substrate cell in Fig. 2a, KB containing cell becomes “nonlinear” with a higher rate, indicating that the nucleation rate of Li2S is increasing. It could be reasonably assigned by instantaneous nucleation that depletion of the nucleation site of KB occurs at a very early stage, following the nonlinear kinetics of the nucleation pathway: \( N = N_0[1-\exp(-At)] \) where \( N \) is the density of nuclei, \( N_0 \) is the density of available nucleation site, and \( A \) is the nucleation rate47. In contrast, considering less porous Super P carbon containing cell in Fig.2a with a lower nucleation rate, the initial density of nuclei increases linearly with time: \( N = N_0 At \) (i.e. progressive nucleation)48,49. Moreover, the porous structure of KB also accelerates the dissolution and re-crystallization of sulfur, which results in a strong sulfur concentration saturation at the transient stage relating to semisolid Li2S4 generation (keeping a balance between electrochemical and disproportionation process) and enhanced soluble sulfur reduction to solid sulfur at the end of charging (Supplementary Fig. S10). The sulfur concentration dynamic responding to potential and cycling rate is consistent with the Super P substrate, detailed in Supplementary Fig. S11.
+Fig. 5 | Chemistry of LSB with outstanding polysulfide-trapping capability cathodes. (a) Operando measurement of LSB by TFBG and XRD at C/20 (left panel: nonpolar physical adsorption of polysulfide by KB carbon; right panel: polar adsorption of polysulfide by MOF-801(Zr)). (b) In-situ detection of polysulfide adsorption by MOF-801(Zr). (c) XRD spectra for MOF-801(Zr) before and after adsorption of Li2S6. (d) The temporal voltage (grey line), decoded sulfur concentration (red line) of cathode composite based on MOF-801(Zr), and decoded sulfur concentration (blue line) considering the cathode with KB substrate (same amount of active material) is used as a reference without showing the temporal voltage.
+
+To further extend the use of porous materials as host matrix for sulfur confinement, Metal-Organic Frameworks (MOFs) can be considered as efficient candidates for the selective adsorption of polysulfide species45,50. We have considered MOF-801(Zr), a microporous zirconium fumarate with pores of about 5–12 Å and a high specific surface area (1020 ±20) m²/g, to be considered as an efficient candidate for the adsorption of polysulfide species. Its 3D cubic structure is built-up from Zr6O4(OH)4 oxo-clusters linked to fumarate ligands and exhibits abundant missing linkers defect sites and reactive terminal –OH groups. Due to the
+Lewis acidic character of the Zr nodes and the reactivity of these terminal groups, the polysulfide species (soft Lewis bases) are expected to interact strongly with the framework\(^{51,52}\). Depicted in Fig. 5c, the 0.5 mL 100 mM polysulfide Li\(_2\)S\(_x\) (x=4, 6, 8) was monitored in real time by fiber sensor during adsorption, which is evidently finished within 1 hour ensuring efficient adsorption inside the cell. After fully adsorbing 100 mM Li\(_2\)S\(_x\) (Fig. 5d), the XRD pattern shows the appearance of new peaks in addition to the ones of MOF-801(Zr), matching with the peaks of pure solid sulfur (Supplementary Fig. S12) consistent with the “yellow” color of the powder. This explains why the operando test starts with the peaks of sulfur (XRD pattern on the right panel of Fig. 5a). The subsequent electrochemical reaction is the same as the cathode substrate with KB including concentration saturation in the transition region between the first and the second plateau, nonlinear sulfur consumption rate with instantaneous nucleation pathway and enhanced sulfur crystallization at the end of charge. However, a key point and difference is that the sulfur concentration inside the electrolyte dramatically decreases by 80.8 % with the same amount of active material due to the enhanced adsorption and localization of polysulfides through Lewis acid-base chemical interaction by MOF-801(Zr) (Fig.5d and Support information, Fig. S13).
+
+![Operando test showing voltage vs. time, sulfur concentration, and cycling performance plots](page_370_670_1097_495.png)
+
+Fig. 6 | The correlation between electrochemical performance and Li\(_2\)S nucleation, sulfur crystallization. (a) Content of Li\(_2\)S nucleation (h1) and solid sulfur crystallization (h2). (b) Cycling performance of cathode composite at C/15 over 30 cycles. (c and d) The corresponding ratio of Li\(_2\)S nucleation (c) and solid sulfur crystallization (d). (e) Cycling rate performance of cathode composite. (f and g) The corresponding ratio of Li\(_2\)S nucleation (f) and solid sulfur crystallization (g). Note that all the cycling cell pursed in the presence of TFBG fiber and the Li\(_2\)S (h1) and solid sulfur (h2) is normalized by comparing the consumption sulfur in current cycle to that of sulfur fully dissolved in first cycle.
+To evaluate the performance of cathode considering the three S cathode composites (with Super P, KB, MOF-801(Zr)), we decided to compare their long cycling performance together with capabilities of Li2S nucleation (h1) and sulfur crystallization (h2) (Fig. 6a). Depicted in Fig. 6b, the KB and MOF-801(Zr) cell both experienced better capacity retention over 30 cycles at C/15 with a fade rate as 0.99 %, 0.88% per cycles, respectively, while the super P cell is fading with 4.7% per cycles, which is consistent with the capability of crystallization of Li2S and sulfur shown in Fig. 6c,d. Surprisingly, the KB and MOF-801(Zr) cells have the similar efficiency of solid species crystallization (also supported by Fig. 6f) by taking the merit of high surface area, whereas the MOF-801(Zr) exhibits the best capacity retention due to its strong chemical interaction for polysulfide which also well explains the capability to trap and recrystallize sulfur(Fig. 6g). Meanwhile, less sulfur utilization will be induced as well by intrinsic adsorption together with its low conductivity nature, leading to the lower capacity of MOF-801(Zr) than that of KB cell over cycling. On the other hand, the Super P cell is fading fast because of high electrolyte volume with the E/S ratio over 100 μL/mg, presumably due to shuttle phenomenon enhancement. However, this problem does not affect the performance of KB and MOF-801(Zr) cells, revealing that perhaps the most important parameter for cycling performance is related to the capability of crystallization of Li2S and sulfur, which relies on a comprehensive balance with all involved factors such as high surface area, sulfur anion bonding and conductivity, in addition to cycling conditions.
+
+Discussions and conclusions
+
+Herein, TFBG sensors with low cost, easy integration into batteries, and long cycling capabilities during cell operation were demonstrated for operando testing of electrolyte sulfur concentration evolution of the LSB, which reveals the correlated relationship between the capacity fading and dynamic of dissolution/precipitation of polysulfides over cycling and at different cycling rates. Meanwhile, the chemical kinetics and thermodynamic response of soluble polysulfide in electrolyte were decoded with GITT experiments, with the disproportionation dynamic process linked to the transport flux of soluble species. Moreover, the cycling performance is well improved by designing the composite cathodes via porous carbon as nonpolar physical sulfur confinement and MOF-801(Zr) as polar adsorption of polysulfide, through a host-guest chemical interaction. These substrates indicate that the nucleation kinetics and growth of Li2S are changing from progressive to an instantaneous pathway due to enhanced soluble sulfur consumption rate, ultimately leading to the improvement of crystallization capability of Li2S and sulfur.
+
+Despite the encouraging insights supported by TFBG technology, a limitation of our operando testing stems from the refractive index link, which as mentioned, is an “average” effect of all species inside electrolyte. Thus, somewhat complicated data inference is required with critical external inputs, as comparing to direct evidence and measurement of species by infrared fiber operando measurement53 and Raman spectroscopy based on hollow-core optical fiber54. This could might be solved in future by machine learning algorithms to simplify analysis and hence lead to more efficient ‘combing’ of data. Second, the optical interrogator used here is both expensive and bulky (volume), so future efforts may warrant an optimized integrator system capable of capturing a sensing signal by energy (amplitude) instead of wavelength55, but intensity-based measurements may present other technical challenges.
+Finally, the cycling based on Swagelok is achieved with high E/S ratio which enhances the shuttle effect of polysulfide, leading to acceleration of capacity fading. Therefore, long-term cycling configurations such as coin or 18650 cells integrated with fiber sensors might reveal other prominent performance-governing mechanisms. Nevertheless, TFBG sensors still provide fruitful details of the chemical dynamics of polysulfide as a diagnostic technique to monitor the state of health of cells in real-time.
+
+Considering the specific properties of TFBG, including multi-resonance-peaks, high refractive index sensitivity, and ultrafast response, new opportunities of battery sensing can be envisioned, such that more than two gratings can be integrated inside the cell to map the sulfur gradient with more precision and accuracy, ultrathin solid electrolyte interphase (SEI) films could be characterized by sensitivity enhanced surface plasmon resonance based TFBG via surface and bulk refractive index discrimination\(^{56}\), the dynamic of electrons and phonon coupling inside cathode could be probed by ultrafast measurement through the pump-probe configuration of TFBG\(^{77}\). Overall, the non-disruptive diagnostic techniques based on the TFBG sensor allow us to monitor chemical-physical-thermal metrics *in operando* with notable time and spatial resolution. Therefore, with the use of these combs it becomes possible to detangle hidden high-value information such as states of charge, health estimations, and operational guidance along with non-electrochemical early-failure indicators, leading to increased straighter pathways to improving battery reliability, service life, and safety.
+
+Methods
+
+Materials and electrode preparation
+
+Synthesis of MOF-801(Zr)
+
+10.86 mmol of ZrOCl\(_2\)•8H\(_2\)O, 7.624 mmol of fumaric acid, 9 mL of formic acid and 40 mL of deionized water were mixed in the reactor\(^{58}\), following 5 h stirring when the solution becomes cloudy. The ultimate product was collected by centrifugation, abundantly washed with water and ethanol, and dried under vacuum.
+
+Preparation of polysulfides solutions: the 100 mM lithium polysulfides solution Li\(_2\)S\(_x\) (\(x=2,\ 3,\ \cdots,\ 8\)) were prepared by mixing lithium sulfide (99.9 % Li\(_2\)S, Sigma Aldrich) and sulfur (S, Sigma Aldrich) in stoichiometric ratio to organic electrolyte (1 M LiTFSI, 0.5 M LiNO\(_3\) in DOL/DME (1:1, v/v)), and the solution was continuously stirred with additional heating process at 55 C° for 4 days in argon filled glovebox.
+
+Preparation of sulfur composite electrodes: sulfur and Super P conductive carbon (Ketjen-black carbon) with a ratio 60/40 wt% were mixed by hand-grinding, followed by a heat-treatment (160 C° during 8 hours under air). The 5 % wt Poly(tetrafluoroethylene) dispersion (PTFE, Alfa Aesar) is mixed with the cathode composite, rolled to a film and punched into disks with sulfur loading around 5.3 mg/cm\(^2\), and dried under vacuum at 80 C° overnight. To make the cathode composite with MOF-801(Zr), the thoroughly adsorption of 100 mM Li\(_2\)S\(_x\) in DOL/DME (1:1, v/v) was achieved by MOF-801(Zr) with a stoichiometric ratio of 1 mL/40 mg, followed by washing the powder twice by DOL and tried in vacuum overnight. The sulfur contained MOF-801(Zr) (40% sulfur) was mixed with Super P conductive carbon with 50/50 wt% by hand-grinding without heat-treatment.
+TFBG fabrication and sensing system.
+
+Each 10 mm-long TFBG with 7° internal tilt angle was inscribed in hydrogen-loaded CORNING SMF-28 fiber by laser irradiation based on phase-mask method\(^{22}\). Hydrogen loading of the fibers, enhancing their photosensitivity to ultraviolet light, was performed at room temperature and a pressure of 15.2 MPa for 14 days. The input light from KrF pulsed excimer laser (model PM-848 from Light Machinery, Inc., emitting at 248 nm and 100 pulse/second) was cylindrically focused along the fiber axis with energy of ~40 mJ over the grating region and also having passed through a 1078.4 nm period phase mask to produce a permanent periodic refractive index modulation in the core of the fiber. Rotating the fiber and phase mask, the tilt of grating fringes was obtained at an angle in the core as 7°.
+
+Computational details
+
+The transmission spectra simulations were carried out based on three-layer cylindrical waveguide using analytical method\(^{37}\). First, the simulated spectra is calibrated by the experimental spectra in air; Second, the refractive index of electrolyte were obtained by increasing the simulation surrounding RI (third layer) manually to match the experimental spectra, which is 1.3858 at 1559 nm wavelength considering the dispersion (supplementary Fig. S2d,e). Finally, mode intensity profiles were simulated by a complex finite-difference vectoral simulation tool (FIMMWAVE, by Photon Design), consisting of a three-layer waveguide: 8.2 μm core diameter with refractive index 1.449311, 125 μm cladding diameter with refractive index 1.444078, 80 μm diameter medium of electrolyte (refractive index=1.3858).
+
+Integration of TFBG sensors into modified Swagelok
+
+A ring made of PEEK (12.8 mm diameter, 2mm thick to fit 10 mm length fiber sensor) is fixed in the middle of 19 mm diameter Swagelok cell where fiber sensor can go through by drilling two holes. The Li metal foil (0.38 mm thickness, 14 mm diameter) is attached to one side of PEEK ring as anode, and on the other side of ring there is a steel grid to hold one Whatman separator beneath sulfur composite cathode. The cells were assembled in an argon-filled glovebox.
+
+Electrochemical measurements
+
+The electrochemical performances of Swagelok cell were evaluated by BCS-810 or MPG2 potentiostat (Biologic, France) at 25 °C degree inside temperature-controlled oven (Memmert, ±0.1 °C). The galvanostatic discharge–charge cycling was carried out with the voltage range of 1.7 V–2.8 V.
+
+Operando measurement by TFBG sensors and XRD
+
+To achieve TFBG sensor operando measurement, the optical transmission spectra were recorded (1 min/spectra) by an optical integrator (CTP10, EXFO SOLUTIONS) with a resolution of 1 pm for wavelength ranging from 1500 nm to 1600 nm. Considering XRD operando measurement, it was performed on a D8 Advance diffractometer (Bruker) using a Cu Kα X-ray source (\( \lambda_{K\alpha1}=1.54056~\text{\AA}, \lambda_{K\alpha2}=1.54439~\text{\AA} \)) and a LynxEye XE detector. The XRD pattern and electrochemical data are simultaneously recorded by a custom designed airtight cell with a beryllium window producing a full pattern every 20 min.
+Preparation of cycled electrode samples for SEM and EDX imaging
+
+The samples, at the end of charging, were prepared by washing the cathode powder twice by DOL to remove any dissolved lithium polysulfide species and lithium salt, and dried in vacuum chamber overnight. Then the powder was coated with gold (plasma sputtering coater (GSL-1100X-SPC-12, MTI)) for SEM (FEI Magellan) equipped with an energy-dispersive X-ray spectroscopy detector (Oxford Instruments) performed under an acceleration voltage of 20 kV.
+
+Data availability
+
+All relevant data are included in the paper and Supplementary Information. Extra data are available on reasonable request from the corresponding author.
+
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+Acknowledgements
+
+J.-M. Tarascon acknowledges the International Balzan Prize Foundation and the LABEX STOREXII for funding. F. Liu and J.-M. Tarascon acknowledge the European Project "Innovative physical/virtual sensor platform for battery cell" (INSTABAT) (European Union’s Horizon 2020 research and innovation program under grant agreement No 955930). W. Lu acknowledges the support of the CSC scholarship (201906880002). R. Demir-Cakan is thankful to the French Embassy for the Visiting Researcher Fellowship (135694V). We thank Dr. J. Forero-Saboya for his assistance of scanning electron microscopy images. We thank Prof. J. Albert from Carleton University (Ottawa, Canada) for the fabrication of fiber sensors and assistance of simulation software. Finally, we gladly thank Dr. W. He, Dr. Y. Wang, Dr. X. Gao, Dr. B. Li, Dr. C. Gervillie-Mouravieff and Mr. C. Leau for extensive and valuable discussion and comments.
+
+Author Contributions
+
+F. Liu, J. Huang, R. Demir-Cakan and J.-M. Tarascon conceived the idea and designed the experiments. F. Liu performed the experiments. F. Liu, J. Huang, R. Demir-Cakan and J.-M. Tarascon performed the data analysis. W. Lu and V. Pimenta provided the MOF-801(Zr). Finally, F. Liu, S. Boles, R. Demir-Cakan and J.-M. Tarascon wrote the paper with contributions from all authors.
+
+Conflicts of interest
+
+The authors declare no competing financial interests
+
+Additional information
+
+Supplementary information: the online version contains supplementary material available at
+
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+Multiple valence bands convergence and strong phonon scattering lead to high thermoelectric performance in p-type PbSe
+
+Yingcai Zhu
+Beihang University
+Dongyang Wang
+Beihang University
+Tao Hong
+Beihang University
+Lei Hu
+Tokyo Institute of Technology   https://orcid.org/0000-0002-4647-1604
+Toshiaki Ina
+Japan Synchrotron Radiation Research Institute
+Shaoping Zhan
+Beihang University
+Bingchao Qin
+Beihang University
+Haonan Shi
+Beihang University
+Lizhong Su
+Beihang University
+Xiang Gao
+Center for High Pressure Science and Technology Advanced Research
+Li-Dong Zhao (zhaolidong@buaa.edu.cn)
+Beihang University   https://orcid.org/0000-0003-1247-4345
+
+Article
+
+Keywords:
+
+Posted Date: April 26th, 2022
+
+DOI: https://doi.org/10.21203/rs.3.rs-1575296/v1
+License: This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License
+
+Version of Record: A version of this preprint was published at Nature Communications on July 19th, 2022. See the published version at https://doi.org/10.1038/s41467-022-31939-4.
+Multiple valence bands convergence and strong phonon scattering lead to high thermoelectric performance in p-type PbSe
+
+Yingcai Zhu,1 Dongyang Wang,1 Tao Hong,1 Lei Hu,2 Toshiaki Ina,3 Shaoping, Zhan,1 Bingchao Qin,1 Haonan Shi,1 Lizhong Su,1 Xiang Gao,4 Li-Dong Zhao1*
+
+1School of Materials Science and Engineering, Beihang University, Beijing 100191, China
+2State Key Laboratory for Mechanical Behavior of Materials, Xi’an Jiaotong University, Xi’an 710049, China
+3Research and Utilization Division, Japan Synchrotron Radiation Research Institute (JASRI/SPRING-8), Sayo, Hyogo, Japan
+4Center for High Pressure Science and Technology Advanced Research (HPSTAR), Beijing, 100094, China
+
+Thermoelectric generators enable the conversion of waste heat to electricity, which is an effective way to alleviate the global energy crisis. However, the inefficiency of thermoelectric materials is the main obstacle for realizing their widespread applications and thus developing materials with high thermoelectric performance is urgent. Here we show that multiple valence bands and strong phonon scattering can be realized simultaneously in p-type PbSe through the incorporation of AgInSe₂. The multiple valleys enable large weighted mobility, indicating enhanced electrical properties. Local structure and microstructure analysis reveal that about 80 percent of Ag and In atoms form AgInSe₂ as nano-scale precipitates, which result in strong phonon scattering and thus ultralow lattice thermal conductivity. Consequently, we achieve an exceptional \( ZT \) of ~ 2.1 at 873 K in p-type PbSe. Our results demonstrate that a combination of band manipulation and microstructure engineering can be realized by tuning the composition. We expect our findings to be a general strategy for achieving high thermoelectric performance in bulk material, pushing the thermoelectric materials for realistic applications.
+The depletion of fossil fuels and the deteriorating environment motivate the human beings to find sustainable and clean energy solutions. Thermoelectric devices can be used in energy harvesting from waste heat or be utilized in refrigeration, which is favorable for raising energy efficiency, attracting widespread attention from around the world. The efficiency of thermoelectric devices is largely determined by the figure of merit \( ZT \) of their constituent thermoelectric materials, \( ZT = \frac{S^2 \sigma T}{\kappa_e + \kappa_L} \), where \( S \) represents the Seebeck coefficient, \( \sigma \) is the electrical conductivity, \( \kappa_e \) is the electrical contribution to the thermal conductivity, \( \kappa_L \) is the lattice thermal conductivity, and \( T \) is the absolute temperature, respectively. However, decoupling the interdependence between electrical and thermal transport properties is a crucial but challenging issue for improving the thermoelectric performance of materials. To achieve good electrical properties, various strategies such as band convergence\( ^{1-4} \), band sharpening\( ^5 \), band alignment\( ^6 \), carrier mobility optimization\( ^7 \) and resonant states introduction\( ^8 \) were adopted. On the other hand, materials with disordered or complex crystal structure\( ^9,^{10} \), giant anharmonicity\( ^{11,12} \), and lone pair electrons\( ^{13} \) often exhibit intrinsic low lattice thermal conductivity, which are promising candidates for thermoelectric applications. Moreover, the lattice thermal conductivity can be largely suppressed by microstructural engineering, including nano-scale precipitates\( ^{14,15} \), dislocations\( ^{16,17} \), grain boundaries\( ^{18} \), and all-scale hierarchical architectures\( ^{19-21} \). Therefore, a synergistic combination of electronic band modulation and microstructural engineering is expected to achieve advanced thermoelectric materials.
+
+PbTe has long been used for mid-temperature power generation, whereas the scarcity of element Te make it expensive for wide applications. PbSe is a perfect substitute for expensive PbTe due to the earth-abundant element Se. Hitherto, only limited studies show that the \( ZT \) of PbSe could reach 1.7\( ^{22-24} \), motivating us to search strategies to improve the thermoelectric properties of PbSe. The weighted mobility (\( \mu_w = \mu (m^*/m_0)^{3/2} \)) is a good descriptor for the inherent electrical performance of materials\( ^{25} \). Multiple degenerate electronic bands enable large density-of-states effective mass \( m^* \)
+without obvious effect on the carrier mobility (\( \mu \))\(^1\), facilitating the improvement of \( \mu_w \). Indeed, the interplay of multiple bands enable large power factor or \( \mu_w \) and thus ultrahigh \( ZT^{26,27} \). However, the two-band convergence is much difficult to realize due to the large energy offset between the valence band maximum (L) and the secondary valence band maximum (\( \Sigma \)) in PbSe and to date only limited works can promote band convergence in it\(^{23,28,29}\). It is more challenging to achieve multiple bands convergence in PbSe.
+
+The lattice thermal conductivity is another important parameter for the thermoelectric performance indicated by the quality factor \( B \) (\( B \propto \mu_w / \kappa_L \)). The introduction of materials with low lattice thermal conductivity in MTe (M = Pb, Ge) matrixes was proved to be an effective method to manipulate their thermal transport properties\(^{30,31}\). For example, the appearance of nanodots in AgPb\(_m\)SbTe\(_{2+m}\) (LAST) system is considered as the origin of their low lattice thermal conductivity and thus the enhanced thermoelectric performance\(^{30}\). Interestingly, the electrical properties of materials can also be optimized in similar way, such as in PbTe-AgInTe\(_2\) (LIST)\(^{32}\) and SnTe-AgInTe\(_2\)^{33}. These enhanced performances motivate us to search strategies for optimizing the \( \mu_w \) and \( \kappa_L \) simultaneously.
+
+Beyond the two-band convergence between the L and \( \Sigma \) bands, we found that a third valence band \( \Lambda \) with a degeneracy \( N_v = 8 \) could be activated (Figure 1a) through the incorporation of AgInSe\(_2\) in the PbSe matrix doped with 2% Na (LISS). These three-band convergence tendency enables large weighted mobility. Additionally, local structure analysis by the x-ray absorption fine structure (XAFS) spectra indicates that more than 80% of Ag and In atoms form AgInSe\(_2\) in the system. Interestingly, AgInSe\(_2\) is also a good thermoelectric material with intrinsic ultralow lattice thermal conductivity\(^{34-36}\). The tetragonal AgInSe\(_2\) is perfect inserted in the PbSe matrix as nano-scale precipitates revealed by the transmission electron microscopy (TEM), causing strong phonon scattering and hence resulting in ultralow lattice thermal conductivity. Therefore, a synergistic optimization of \( \mu_w \) and \( \kappa_L \) is realized. As a consequence, an
+exceptional high \( ZT \sim 2.1 \) is achieved at 873 K, which is much better than the single-band and two-band activated p-type PbSe-based materials\(^{28,29}\) (Figure 1b).
+
+Results
+
+Crystal structure. The LISS compounds crystallize in cubic structure (Space group, *Fm-3m*), which is reflected by the x-ray diffraction (XRD) measurements that the XRD patterns can be indexed on the basis of cubic PbSe and no secondary phase is observed within the instrumental detection limit (Figure 2a, 2b). The diffraction peaks tend to shift to higher angles with increment of AgInSe\(_2\). Therefore, the lattice parameter (\(a\)) slightly decreases with increasing AgInSe\(_2\) content (Figure 2c), which may be attributed to the smaller atomic radius of Ag, and In compared with that of Pb. This phenomenon also demonstrates that the AgInSe\(_2\) is incorporated in the Pb\(_{0.98}\)Na\(_{0.02}\)Se matrix.
+
+Electronic transport properties. The continuous decrease of the electrical conductivity with increasing temperature indicates a degenerate semiconducting property for LISS samples (Figure 3a). Additionally, the electrical conductivity is suppressed significantly after the introduction of AgInSe\(_2\). The electrical conductivity of Pb\(_{0.98}\)Na\(_{0.02}\)Se is as large as 3848 S/cm at room temperature, which decline to 774 S/cm for Pb\(_{0.98}\)Na\(_{0.02}\)Se-2.15% AgInSe\(_2\) sample. To uncover this behavior, room temperature Hall measurements were performed. Obviously, the carrier concentration is reduced largely with increasing AgInSe\(_2\) (Figure S1), explaining the depressed electrical conductivity. The reduction of carrier concentration may be due to the formation of In\(_{Pb}\) defects. These In\(_{Pb}\) defects are shallow donors in PbSe\(^{37}\), which will counteract with holes.
+
+The Seebeck coefficient increases with elevated temperature for all samples and no saturate peak appears (Figure 2b), demonstrating that no obvious bipolar effect occur at high temperatures. The Seebeck coefficient is largely enhanced over the whole temperature range with the increment of AgInSe\(_2\). Typically, the Seebeck coefficient of Pb\(_{0.98}\)Na\(_{0.02}\)Se is only 19.2 \( \mu \)V/K at room temperature, whereas a much larger Seebeck
+coefficient value of 116 \( \mu \)V/K is achieved for Pb_{0.98}Na_{0.02}Se-2.15% AgInSe_2 sample. This dramatically promoted Seebeck coefficients will facilitate the enhancement of power factor. Indeed, the *PF* have an apparent improvement especially at the 300 - 600 K temperature range for all doped samples (Figure 3c). The room temperature *PF* value of Pb_{0.98}Na_{0.02}Se is only ~ 1.4 \( \mu \)W cm^{-1} K^{-2}. In sharp contrast, the room temperature *PF* increases to ~ 11.1 \( \mu \)W cm^{-1} K^{-2} when x = 2.1 and this value is continuously improved to ~ 15.6 \( \mu \)W cm^{-1} K^{-2} at 423 K (Figure 3c).
+
+To understand the nature of the improvement of Seebeck coefficient, the relationship of Seebeck coefficient as a function of carrier concentration (Pisarenko curve) was compared at room temperature (Figure 4a). Generally, the Seebeck coefficient increases with decreasing carrier concentration. However, the Seebeck coefficient is largely departure from the theoretical values estimated by the single parabolic band (SPB) model, which indicate that a complex electronic band should be involved in the electrical transport properties. Accordingly, the effective mass (\( m^* \)) of LISS is largely increased from 0.44 \( m_e \) to 0.81 \( m_e \) with the introduction of AgInSe_2 (Figure 4a). In contrast, the effective mass of Na-doped PbSe is only ~ 0.28 \( m_e \) (Figure 4a). The Hall carrier mobility increases with doping and a maximum value of ~125 cm^2 V^{-1} s^{-1} is obtained when x=2 (Figure 4b), which is largely due to the depressed carrier concentration. Consequently, the weighted mobility (\( \mu_w \)) of LISS compounds is largely enhanced especially at the 300-600K temperature range, which is higher than that of single-band and two-band PbSe-based materials (Figure 3d).
+
+DFT calculations were also conducted to understand the origin of the enhanced Seebeck coefficients. We observed significant change of the electronic band structure with the incorporation of AgInSe_2 in PbSe matrix (Figure 5a). The bandgap is enlarged upon doping, which will depress the bipolar effect and facilitate the enhancement of Seebeck coefficient. These calculations are well in accordance with our experimental results. The experimental bandgap is ~ 0.24 eV for the pristine PbSe, while the bandgap increases obviously with the incorporation of AgInSe_2 and a large bandgap ~ 0.33 eV
+is achieved for the PbSe - 2% AgInSe₂ sample (Figure 2d). Interestingly, the bandgap is further enlarged to ~ 0.38 eV with Na doping (Figure 2d). In addition, the L band is flattened. The sharp peaks reflected in the density of states (DOS) for valence band also reveal the band flattening character (Figure 5b). Simultaneously, the Σ band is elevated and hence the energy offset (\( \Delta E_{1-2} \)) between L and Σ band is shortened. Surprisingly, a third valence band at the Λ point is activated and it remains at the same energy level compared with the Σ band (Figure 5a). These multiple valence bands enable large effective mass without significant affect the carrier mobility, which is the origin of enhanced Seebeck coefficient and the weighted mobility (\( \mu w \)). The electronic band structures of Ag and In doped PbSe were also calculated (Figure S2a, S2b). The Ag-doping and In-doping reflect p-type and n-type doping effect, respectively, which are consistent with previous experimental results\(^{38,39}\). Additionally, In-doping has a more important effect on decreasing energy offset (\( \Delta E_{1-2} \)) compared with the Ag-doping (Figure S2c), while Ag-doping plays a major role in enlarging the bandgap (Figure S2d). Both Ag and In atoms play an important role in band manipulation.
+
+Using the lattice parameters extracted from the temperature-dependent synchrotron radiation x-ray diffraction (SR-XRD) patterns (Figure S3), we calculated the band structures as a function of temperature (Figure 5c, Figure S4). Clearly, the bandgap increases with rising temperature, which is also verified experimentally (Figure 5d). However, the theoretical bandgap is smaller than the experimental result (Figure 5e), which may be attribute to the neglect of the effect of thermal disorder on the bandgap in our calculations. Moreover, the energy offset (\( \Delta E_{1-2} \)) between L and Σ bands decreases with increasing temperature (Figure 5e). Interestingly, the energy offset (\( \Delta E_{1-3} \)) between L and Λ also shows a decline tendency with rising temperature and its value is even smaller than \( \Delta E_{1-2} \) in the whole temperature range (Figure 5e). The convergence tendency and the involvement of the third valence band is also reflected in the DOS corresponding to the valence band increases with increasing temperature (Figure 5f). This convergence behavior is experimentally verified via Hall measurements, in which a maximum Hall coefficient (\( R_H \)) is observed (Figure S5a) and it is a sign of band
+convergence of the multi-valence bands\(^{20,23}\). Consequently, the effective mass (\(m^*\)) of Pb\(_{0.98}\)Na\(_{0.02}\)Se-2.05%AgInSe\(_2\) increases from \(0.73m_e\) to \(2.16m_e\) with rising temperature, which is much higher than the \(m^*\) of single Na-doped PbSe\(^{40}\) (Figure S5b).
+
+**Thermal transport properties and the figure-of-merit \(ZT\).** Thermal conductivity is another important property for thermoelectric performance. The total thermal conductivity (\(\kappa_{tot}\)) decreases significantly with increasing AgInSe\(_2\) (Figure 6a). The \(\kappa_{tot}\) is a compose of lattice thermal conductivity (\(\kappa_L\)) and electronic contributions to the thermal conductivity (\(\kappa_e\)). The \(\kappa_e\) was calculated by the Wiedemann-Franz relation, \(\kappa_e = L e T\), where \(L\) is estimated by SPB model (Figure S6a). The \(\kappa_e\) decreases remarkably with doping due to largely depressed electrical conductivity (Figure S6b). Furthermore, the \(\kappa_L\) is obtained by subtracting the electronic contribution from the total thermal conductivity (Figure 6b). Similarly, the \(\kappa_L\) is largely suppressed with doping and the room-temperature \(\kappa_L\) values are much lower than the theoretical estimation by the Callaway model (Figure 6b, inset). In addition, the \(\kappa_L\) decreases with rising temperature and a clear departure from \(T^{-1}\) relation is observed, demonstrating that the strong phonon scattering occurs. To further uncover the mechanism of the reduction of \(\kappa_L\), sound velocities were measured for all the samples at room temperature (Table S1). Interestingly, the average sound velocity (\(v_{avg}\)) slightly increases after doping (Figure 6c). The deduced Grüneisen parameters of LISS are almost unchanged. The lattice thermal conductivity can be expressed as \(\kappa_L = \frac{1}{3} C v_{avg}^2 \tau\) based on the simple kinetic theory\(^{41}\), where \(C\) is the specific heat, \(\tau\) is the phonon lifetime. Here, the \(v_{avg}\) increases upon doping and thus the reduction of lattice thermal conductivity should be derived from the decrease of phonon lifetime. In another word, enhanced phonon scattering is the main origin of the largely suppressed lattice thermal conductivity.
+
+Thanks to the complex band structure behavior and strong phonon scattering with the introduction of AgInSe\(_2\), the figure-of-merit \(ZT\) is largely enhanced in the whole temperature range and a maximum \(ZT\) value of ~ 2.1 is achieved at 873K for
+Pb_{0.98}Na_{0.02}Se-2.05\%~AgInSe_2 sample (Figure 6d). Considering the correction of heat capacity, we can also obtain a large \( ZT \) of \( \sim 1.9 \) at 873K (Figure 6d, Figure S7). The high thermoelectric properties of LISS samples are reproducible (Figure S8).
+
+**Microstructure and local structure analysis.** The TEM images of LISS sample display that abundant nanosized precipitates are embedded in PbSe matrix (Figure 7a, 7b). In addition, strip-like dislocations are also observed (circled regions in Figure 7a). Both nanoscale precipitates and multi-scale dislocations are effective phonon scattering centers. The annular dark-field (ADF) STEM image and the EDS elemental mappings exhibit obvious Ag-rich and In-rich patterns for the precipitates (Figure S9). Accordingly, the elemental distributions of Se and Na are relatively homogeneous in the entire area, whereas Pb-poor regions are observed within the precipitates (Figure S9). A more clearer microstructural features of the precipitate is revealed by performing HRTEM (Figure 7c). The corresponding SAED pattern indicate a main cubic structure along [111], whereas the precipitates shows a different crystal structure from the PbSe matrix as another series of diffraction spots are exhibited which can be indexed to AgInSe_2 (Figure 7d). The HAADF patterns show that the tetragonal AgInSe_2 is perfectly inserted in the cubic PbSe matrix as a nine-atom grid (Figure 7e). We can also observe lattice dislocation in the HAADF (Figure 7f). The lattice mismatch induced by precipitates and dislocations will introduce large strain fluctuations and thus enhance the phonon scattering^{42}. Therefore, the lattice thermal conductivity of LISS was largely reduced to its amorphous limit of 0.31 Wm^{-1}K^{-1} at 873 K arising from the strong phonon scattering.
+
+Understanding the atomic occupation of doping elements in the lattice allow us elucidate their role on manipulating the thermal or electrical transport properties. The x-ray absorption fine structure (XAFS) spectroscopy is a powerful tool to investigate the local structure in materials^{43-48}. Here, we performed XAFS measurements for PbSe, AgInSe_2 and LISS, respectively. The x-ray absorption near-edge structure (XANES) of Se K-edge and Pb \( L_3 \)-edge did not show any change after the introduction of AgInSe_2
+in PbSe (Figure S10), demonstrating a steady PbSe cubic matrix, which is well consistent with the XRD patterns. There are four main features in the XANES of In \( K \)-edge of LISS (Figure 7g), in which 1, 3, 4 features can well reflected in the In \( K \)-edge of AgInSe\(_2\), indicating that most of In atoms may form AgInSe\(_2\) in the system. Furthermore, we calculated the XANES spectra of In \( K \)-edge for the In-doped PbSe assuming that In occupy the Pb site, in which the peak B is well corresponding with the feature 2 of In \( K \)-edge of LISS. Moreover, after adding the second shell (twelve Pb atoms) as shown by the 19-atoms cluster calculation (Figure 7h), the feature B is well reflected and the calculation is almost convergent. Therefore, the origin of feature 2 is mainly arising from the multiple scattering of the photoelectrons by the second shell of Pb atoms in the PbSe matrix. The linear combination fitting (LCF) was used to evaluate the atomic occupied ratio of In atoms in each standards (Figure 7g). Similar analysis was performed for the XANES of Ag \( K \)-edge (Figure S11). The LCF fitting results indicate that more that 80% of Ag and In atoms form AgInSe\(_2\) in the system (Table S2), causing strong phonon scattering.
+
+Discussion
+
+In summary, a combined effect of three activated valence bands and strong phonon scattering is realized via introducing AgInSe\(_2\) in Pb\(_{0.98}\)Na\(_{0.02}\)Se matrix. These multiple valence bands convergence enable the enhancement of thermoelectric power factor at low temperature region and maintain at a high level at elevated temperature. Interestingly, local structure studies by XANES reveal that most of Ag or In atoms form AgInSe\(_2\) secondary phase. The numerous nanoscale AgInSe\(_2\) precipitates and multi-scale dislocations observed in the TEM will cause strong phonon scattering. Therefore, the lattice thermal conductivity is largely depressed. As a consequence, a distinguished figure-of-merit \( ZT \) of ~2.1 is achieved at 873K, which is among the best bulk thermoelectric materials. This work proves that multiple valence bands could be activated in p-type PbSe and highlights the strong phonon scattering effect through the introduction of secondary phase with ultralow thermal conductivity, which guide a new route to achieve excellent thermoelectric performance in bulk materials. The
+quantitative atomic occupation of doping elements provides a new perspective to understand their role on manipulating transport properties. We expect more advanced thermoelectric materials can be achieved by employing this strategy.
+
+Methods
+
+Synthesis. High-purity starting materials, Pb (99.999%), Se (99.999%), Na (99.9%), Ag (99.99%), In (99.99 %) were weighted in stoichiometric ratio (Pb_{0.98}Na_{0.02}Se - x% AgInSe_2) and loaded in carbon coating silica tubes under an N_2-filled glove box. The silica tubes were sealed under vacuum and then slowly heated to 1423 K in 24 h, soaked at this temperature for 10 h and followed by furnace cooling down to room temperature. The obtained ingots were grounded into powders and then densified at 873 K for 6 minutes with a pressure of 50 MPa using spark plasma sintering (SPS-211Lx). Finally, highly dense bulk samples (> 97% of theoretical density) were obtained.
+
+Thermoelectric property measurements. The bulk samples were cut into rectangular solids (3×3×10 \( mm^3 \)) and square pieces (10×10×1 \( mm^3 \)) for electrical and thermal transport properties measurements, respectively. The Seebeck coefficients and electrical conductivities were measured using the Ulvac Riko ZEM-3 instrument. We calculated the thermal conductivity using the equation of \( \kappa_{tot} = D \cdot C_p \cdot \rho \), where the thermal diffusivity (\( D \)) was determined using a laser flash method by the Netzsch LFA-457 facility, the heat capacity (\( C_p \)) was estimated using both the Dulong-Petit law and an empirical equation (\( C_p/k_B\ atom^{-1} = 3.07 + 4.7 \times 10^{-4}\ (T/K-300) \))^{29}, and the density is calculated by the dimensions and mass of the samples. The combined uncertainty of all measurements for determining the \( ZT \) is less than 20%.
+
+Characterizations. Room-temperature powder x-ray diffraction measurements were conducted using a D/MAX 2500 PC system with Cu K_\alpha radiation. High-temperature synchrotron radiation x-ray diffraction (SR-XRD) patterns were performed for Pb_{0.98}Na_{0.02}Se - 2% AgInSe_2 at the BL14B1 beamline of Shanghai synchrotron radiation facility (SSRF). The wavelength of the x-ray is 0.6887 Å. The sample was heated from 300 K to 875 K at a rate of 1.5 K min^{-1}. The bandgap was measured using the Shimadezu
+Model UV-3600 Plus instrument and was estimated by the Kubelka-Munk equation. The Hall coefficient (\( R_H \)) was conducted by the Van der Pauw method using the Lake Shore 8400 Series. Scanning transmission electron microscopy (STEM) and transmission electron microscopy (TEM) were performed using a JEOL ARM200F equipped with cold field emission gun and ASCOR probe corrector. More details can be found in the Supporting Information.
+
+First-principles calculations. Density functional theory (DFT) calculations were performed using the projector-augmented wave (PAW) method\(^{49}\), as implemented in the Vienna Ab initio Simulation Package (VASP)\(^{50,51}\). We utilized the revised Perdew-Burke-Ernzerhof (PBE)\(^{52}\) generalized gradient approximation (GGA) to estimate the exchange-correlation interactions. A cutoff energy was set to 450 eV for the plane-wave expansion of the electron density and the Monkhorst-Pack \( k \)-point sampling 0.1 Å\(^{-1} \) was used within all the calculations. The atomic positions were fully relaxed when the maximum residual ionic force and total energy difference are converged within 0.01 eV Å\(^{-1} \) and 10\(^{-7} \) eV, respectively. Several 3×3×3 supercells were constructed (Pb\(_{27}\)Se\(_{27}\), Pb\(_{26}\)AgSe\(_{27}\), Pb\(_{26}\)InSe\(_{27}\), Pb\(_{25}\)AgInSe\(_{27}\)), avoiding the defect-defect interaction. The occupations of Ag or/and In atoms in the supercells were relaxed in our calculations. The temperature-dependent electronic band structures were performed using the experimental lattice parameters at elevated temperatures deriving from the SR-XRD data.
+
+X-ray absorption fine structure (XAFS) spectroscopy measurements. The XAFS experiments were performed at BL01B1 beamline of Spring-8 in Japan. The electron energy of the storage ring is 8.0 GeV with a top-up filling of 99.5 mA accumulated current during the experiment. The Si (311) double-crystal monochromator was used for tuning the monochromatic beam. We measured the XAFS of Ag \( K \)-edge and In \( K \)-edge for AgInSe\(_2\) in transmission mode. The XAFS measurements of Se \( K \)-edge, and Pb \( L_3 \)-edge for PbSe and Pb\(_{0.98}\)Na\(_{0.02}\)Se - 2% AgInSe\(_2\) were conducted in transmission mode, while the measurements of Ag \( K \)-edge and In \( K \)-edge for Pb\(_{0.98}\)Na\(_{0.02}\)Se - 2% AgInSe\(_2\) were performed in fluorescence mode using 19-element Ge solid-state detector (SSD). All experimental XAFS spectra were preprocessed using the IFFEFIT package\(^{53}\).
+XAFS calculation and analysis . The x-ray absorption near edge structure (XANES) calculations of Ag \( K \)-edge for Ag-doped PbSe and In \( K \)-edge for In-doped PbSe were performed based on the full multiple scattering (FMS) theory using FEFF9 program\(^{54,55}\). We use self-consistent field (SCF) method to estimate the atomic scattering potential. To investigate the doping site of Ag or In in PbSe, we simply replace the central Pb absorber with Ag or In atom while maintaining the coordinates. To achieve good convergence, the cluster radius for SCF and FMS was fixed as 8 and 10 Angstrom, respectively. Linear combination fittings (LCF) of In \( K \)-edge for Pb\(_{0.98}\)Na\(_{0.02}\)Se - 2% AgInSe\(_2\) was performed using the Athena software assuming that the XANES of In \( K \)-edge of AgInSe\(_2\) and In-doped PbSe as the standards. A similar LCF analysis was applied for the XANES of Ag \( K \)-edge of Pb\(_{0.98}\)Na\(_{0.02}\)Se - 2% AgInSe\(_2\). Since we cannot ensure that the Ag or In atoms totally occupy the Pb site in PbSe matrix without formation of impurity phases, we thus used the calculated XANES as one of standards in the LCF analysis.
+
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+Acknowledgements
+The authors thank BL14B1 at Shanghai synchrotron radiation facility (SSRF) for the SR-XRD measurements. We thank BL01B1 at Spring-8 for the XAFS experiments (Proposal Number: 2021B1109). This work was supported by National Natural Science Foundation of China (51772012, 52002042 and 52002011), National Key Research and Development Program of China (2018YFA0702100 and 2018YFB0703600), National Postdoctoral Program for Innovative Talents (BX20200028), the Beijing Natural Science Foundation (JQ18004), and 111 Project (B17002). L.-D.Z. appreciates the support of the high performance computing (HPC) resources at Beihang University, the National Science Fund for Distinguished Young Scholars (51925101), and center for High Pressure Science and Technology Advanced Research (HPSTAR) for SEM and TEM measurements.
+
+Authors contributions
+Y.Z. and L.-D.Z. prepared the samples, carried out the experiments, analyzed the results and wrote the paper. T.H. and X.G. performed the microscopy experiments. D.Y.W. carried out the DFT calculations. Y.Z., L.H. and T.I. conducted the XAFS measurements and analyzed the data. S.Z., B.Q., H.S. and L.S. performed the SR-XRD experiments. All authors coedited the manuscript.
+
+Competing interests
+The authors declare no competing interests.
+
+Additional information
+Correspondence and requests for materials should be addressed to L.-D. Zhao.
+Fig. 1 Multiple valence bands enable high \( ZT \) values in p-type PbSe. **a** Schmatic diagram of multi-bands (L, \( \Sigma \), \( \Lambda \)) involvement in transport. The Brillouin zone shows that the degeneracies at the L, \( \Sigma \), and \( \Lambda \) points are 4, 12, and 8, respectively. **b** The activated third band \( \Lambda \) enables higher \( ZT \) values compared with the single-band and two-band PbSe-based materials.
+
+![Schmatic diagram of multi-bands involvement in transport and ZT vs T graph for PbSe-based materials](page_153_186_1147_496.png)
+Fig. 2 Crystal structure and band gap. a Schematic crystal structure of Pb_{0.98}Na_{0.02}Se - x% AgInSe_2 (LISS). b Powder XRD patterns of LISS. c Refined lattice constants of LISS. d Room-temperature infrared spectra for PbSe - x% AgInSe_2 and Pb_{0.98}Na_{0.02}Se - x% AgInSe_2.
+Fig. 3 Electrical properties as a function of temperature for Pb_{0.98}Na_{0.02}Se - x% AgInSe_2 (LISS) compounds. a Electrical conductivity. b Seebeck coefficient. c Power factor. d Weighted mobility. The hollow circles in d represent the weighted mobility of single-band and two-band PbSe-based materials.
+Fig. 4 Pisarenko plot and Hall carrier mobility. **a** Pisarenko plot of Seebeck coefficients as a function of Hall carrier concentration (\( n_H \)) for Pb_{0.98}Na_{0.02}Se - x% AgInSe_2 (LISS). The solid black line is calculated assuming \( m^* = 0.44m_e \) and the purple line represents the result assuming \( m^* = 0.81m_e \) within the SPB model. The gray circles show the Pisarenko plot for Na-doped PbSe reported by Wang et al.\(^{38}\) **b** Hall carrier mobility (\( \mu_H \)) versus Hall carrier concentration (\( n_H \)) at 303K.
+
+![Pisarenko plot and Hall carrier mobility graphs](page_153_120_1142_670.png)
+Fig. 5 Electronic band structure. a Electronic band structure of Pb27Se27 (blue) and Pb25AgInSe27 (red). b Electronic density of states (DOS) near the Fermi level for Pb27Se27 (black), Pb26AgSe27 (green), Pb26InSe27 (blue) and Pb25AgInSe27 (red), respectively. c Electronic band structure of Pb25AgInSe27 at 300K and 873K, respectively. d Temperature-dependent infrared spectra of PbSe-2%AgInSe2. e The experimental (red) and theoretical (blue) bandgap (\( E_g \)) and the theoretical energy offset between VBM1 and VBM2 (\( \Delta E_{1,2} \)) and between VBM1 and VBM3 (\( \Delta E_{1,3} \)) as a function of temperature. f Temperature-dependent electronic DOS of Pb25AgInSe27 near the VBM.
+Fig. 6 Thermal transport properties and figure-of-merit \( ZT \) as a function of temperature for \( \mathrm{Pb}_{0.98}\mathrm{Na}_{0.02}\mathrm{Se} - x\% \mathrm{AgInSe}_2 \) (LISS) compounds. **a** Total thermal conductivity. **b** Lattice thermal conductivity. Inset shows the room-temperature lattice thermal conductivities departure from the theoretical line calculated by the Callaway model. **c** The average sound velocity (\( v_{avg} \)) versus lattice thermal conductivity (\( \kappa_L \)) for LISS compounds at room temperature. **d** Temperature-dependent \( ZT \) for LISS samples.
+Fig. 7 Microstructures and local structure analysis for high-performance LISS sample. a Low magnification of bright-field TEM image for Pb0.98Na0.02Se - 2.05 % AgInSe2 sample. b The enlarged TEM pattern presents the nanoscale precipitates remarked by the arrows. c High resolution TEM (HRTEM) picture of a selected nanoprecipitate. d The corresponding selected area electron diffraction (SAED) pattern with cubic structure along [111]. e, f High angle annular dark field (HAADF) patterns for Pb0.98Na0.02Se - 2.05 % AgInSe2. g Experimental XANES spectra of In K-edge for Pb0.98Na0.02Se - 2 % AgInSe2 (red dots), and AgInSe2 (orange line), respectively. The blue line shows the theoretical XANES spectrum of In K-edge for In-doped PbSe assuming that In occupy the Pb site. The black line represents a linear combination fitting (LCF) result of In K-edge of Pb0.98Na0.02Se-2 % AgInSe2 considering that the In K-edge of AgInSe2 and In-doped PbSe serves as standards. h Multiple scattering calculations of In K-edge XANES for In-doped PbSe with different atomic clusters. The inset shows the nearest-two shell of In atom when it occupies the Pb site in PbSe matrix. The \( E_0 \) is the absorption edge energy of In K-edge of In foil.
+Supplementary Files
+
+This is a list of supplementary files associated with this preprint. Click to download.
+
+• SupplementaryInformation.docx

01cfd239b63d0b5b3bd8fba2f46c4523116e4ea7471e771fa2f189c14b26428e/preprint/preprint.md

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+Scalable production of ultrafine polyaniline fibres for tactile organic electrochemical transistors
+
+Bo Fang
+Hong Kong Polytechnic University
+Jianmin Yan
+Hong Kong Polytechnic University
+Dan Chang
+Zhejiang University
+Jinli Piao
+Hong Kong Polytechnic University
+Kit Ming Ma
+Hong Kong Polytechnic University
+Qiao Du
+Hong Kong University of Science and Technology
+Ping Gao
+Hong Kong University of Science and Technology
+Yang Chai
+Hong Kong Polytechnic University   https://orcid.org/0000-0002-8943-0861
+Xiaoming Tao ( xiao-ming.tao@polyu.edu.hk )
+Hong Kong Polytechnic University   https://orcid.org/0000-0002-2406-0695
+
+Article
+
+Keywords:
+
+Posted Date: December 8th, 2021
+
+DOI: https://doi.org/10.21203/rs.3.rs-1126903/v1
+
+License: This work is licensed under a Creative Commons Attribution 4.0 International License.
+Read Full License
+
+Version of Record: A version of this preprint was published at Nature Communications on April 19th, 2022. See the published version at https://doi.org/10.1038/s41467-022-29773-9.
+Scalable production of ultrafine polyaniline fibres for tactile organic electrochemical transistors
+
+Bo Fang1,2, Jianmin Yan1,3, Dan Chang4, Jinli Piao1,2, Kit Ming Ma1,2, Qiao Gu5, Ping Gao5, Yang Chai1,3*, Xiaoming Tao1,2*
+
+1Research Institute for Intelligent Wearable Systems, Hong Kong Polytechnic University, Hong Kong, 999077 China
+2Institute of Textiles and Clothing, Hong Kong Polytechnic University, Hong Kong, 999077 China
+3Department of Applied Physics, Hong Kong Polytechnic University, Hong Kong, 999077 China
+4Department of Polymer Science and Engineering, Zhejiang University, Hangzhou, 310027 China
+5Department of Chemical and Biological Engineering, The Hong Kong University of Science and Technology, Hong Kong, 999077 China
+
+Email: ychai@polyu.edu.hk; xiao-ming.tao@polyu.edu.hk
+
+The development of continuous conducting polymer fibres is essential for applications ranging from advanced fibrous devices to frontier fabric electronics. The use of continuous conducting polymer fibres requires a small diameter to maximize their electroactive surfaces, microstructural orientations, and mechanical strengths. However, regularly used wet spinning techniques have rarely achieved this goal due primarily to the insufficient slenderization of rapidly solidified conducting polymer molecules in poor solvents. Here we report a good solvent exchange strategy to wet spin the ultrafine polyaniline fibres at the large scale. The slow diffusion between good solvents distinctly decreases the viscosity of gel protofibers, which undergo an impressive drawing ratio. The continuously collected polyaniline fibres have a previously unattained diameter below 5 \( \mu \)m, high energy and charge storage capacities, and favorable mechanical performance. We demonstrated an ultrathin all-solid organic electrochemical transistor based
+on ultrafine polyaniline fibres, which substantially amplified microampere drain-source electrical signals with less one volt driving voltage and effectively operated as a tactile sensor detecting pressure and friction forces at different levels. The aggressive electronical and electrochemical merits of ultrafine polyaniline fibres and their great potentials to prepare on industrial scale offer new opportunities for high-performance soft electronics and large-area electronic textiles.
+
+The extended conjugated and easily doped \( \pi \)-system along the backbone enables conducting polymers to possess intriguing transport, optical, and electrochemical properties, which have rarely been found in conventional polymers and metal conductors\( ^{1-3} \). Processing conducting polymers into macroscopically fibrous materials makes it possible to translate their nano-object features to human-friendly products in a continuous manner. The combined merits, including but not limited to mechanical flexibility, intrinsic conductivity, and electrochemical activity, of conducting polymer fibres (CPFs) have introduced a new era of “electronic textiles”\( ^{4} \). For instance, highly conductive and electrochemically active poly(3-methylthiophene) fibres have been achieved by in situ electrochemical oxidation of monomers\( ^{5} \). Fast ion transport between CPFs and ionic liquids has given birth to long-term operation actuators, electrochromic windows, and numeric displays\( ^{6} \). In recent studies, the wet-spun poly (3,4-ethylene dioxythiophene) (PEDOT) fibres have been widely used in various frontier fields, such as flexible energy storage electrodes, implantable bioelectronics, and organic transistors\( ^{7,8} \).
+Unfortunately, due primarily to the large diameters, the performance and expectations of most achieved continuous CPFs have been limited by their insufficient electroactive surfaces and weak breaking strengths. Electrospinning and wet spinning are two mainstream strategies to produce continuous CPFs. In the case of electrospinning, the fairly rigid backbone due to the high aromaticity results into an insufficient elasticity of conducting polymer solutions, which fails to be solely electrospun into fine fibres\( ^{9} \). Although a two-fluid electrospinning technique has been proposed by coating a soluble and electrospinnable fluid on the conducting polymer cores, the complex procedures
+involving the addition and removal of second components defy the mass production of electrospun CPFs\(^{10,11}\). In the case of conventional wet spinning, conducting polymer dopes tend to occur a transient solidification in poor solvents, induced by the strong interactions of conducting polymer chains. The rapidly hardened gels suppress the post-stretching and slenderizing procedures, and cause the wet-spun CPFs to show a large diameter, generally beyond 10 \( \mu \)m\(^{12-14}\). The large diameters largely discount the mechanical properties and electrochemical activities of CPFs\(^{4,15}\). Thus, there is an urgent need to realize the mass production of ultrafine CPFs, which remains challenging. In this work, we report a good solvent exchange strategy in a modified wet spinning technique to prepare the ultrafine polyaniline (PAni) fibres (UFPFs) at the large scale. Beyond conventional wet spinning protocol, we replaced poor solvents by good solvents as the coagulation bath to decrease the viscosity of gel protofibres, which were subject to an ultrahigh drawing ratio and reduced to an ultrafine morphology. The obtained UFPGs own a small diameter below 5 \( \mu \)m, an unprecedented mechanical strength of 1080 \( \pm \) 71 MPa, a high area capacitance beyond 1008 mF cm\(^{-2}\), and an enormous charge storage capacity of 5.25\( \times \)10\(^4\) mC cm\(^{-2}\). Based on the structural and electrochemical merits of UFPGs, we demonstrated an ultrathin all-solid organic electrochemical transistor (OECT) with less one volt driving voltage, which substantially amplified drain-source electrical signals with a low power-consumption and responded to vertical pressure and horizontal friction forces at different levels. Our work opens an avenue to prepare continuous ultrafine CPFs and high-performance soft electronics.
+Fig. 1: Scalable production of UFPFs. a Schematic of the good solvent exchange strategy to prepare UFPFs in a modified wet spinning protocol. In the case of poor solvent exchange (light orange region, upper panel), PAni molecules are rapidly solidified into thick gels and protofibres with rough crystallized particles. In the case of good solvent exchange (light blue region, lower panel), the formed gels with low viscosity occur an impressive gel extension and are slenderized into ultrafine fibres. b Schematic of the modified wet spinning process. c Scanning electron microscope (SEM) image of the marked region in b, showing the sharp necking behavior of gel PAni fibres. The close observation to region 1 (d), region 2 (e), and region 3 (f) in the marked zone of c, illustrating the sharply necking process of PAni gels. g Photograph of a 5.4-kilometres-long UFPF collected in two hours. Scale bars: c 20 μm, d 2 μm, e 10 μm, g 150 mm.
+Results
+
+Preparation and characterization of UFPFs. In the modified one-step wet spinning process, we used good solvents as the coagulation bath to realize the mass production of UFPFs (Fig. 1a-b and Supplementary Fig. 1). After doping PAni power (emeraldine base) with camphor sulfonic acid (CSA) at a molar ratio of 2:1, we dispersed fully doped PAni into m-cresol as the raw spinning dopes (see the Methods section)\(^{16}\). Significantly, the direct use of doped PAni solutions as the dopes saves the trouble of conventional post-doping procedures, and further permits the uniform charge distribution throughout the fibre length\(^{17}\). A good solvent, dimethyl formamide (DMF), of PAni operated as the coagulation bath. A slow solvent exchange between m-cresol and DMF facilitated the formation of PAni gel protofibres with a quite low viscosity below 3000 cP. Subsequently, we observed a sharp decrease of diameter from ~0.1 mm to ~4.7 \( \mu \)m when stretching the gel fibres in bath (Fig. 1c-f), which, to our knowledge, is a record small value in the achieved wet-spun CPFs\(^{4}\). The ultrafine fibre shows a smooth surface (Fig. 1f and Supplementary Fig. 2) and highly crystallized microstructures (Supplementary Fig.3). Moreover, such an impressive drawing ratio enables a very high production efficiency of UFPFs beyond 40 meters per minute. For example, we prepared a 5.4-kilometres-long UFPF in two hours (Fig. 1e).
+Fig. 2: Mechanism and mechanical properties of UFPPFs. a SEM images of the PAni fibres produced in different solvating species. Specifically, the upper four panels showing the fibres prepared from poor solvents, and the lower two panels showing the fibres fabricated from good solvents. b Raman spectra of PAni fibres after placing in air for four weeks. c The diffusivity from PAni dispersions (in m-cresol) to various solvating species. d The viscosity of PAni gels formed in various solvating species. e Mechanics simulation results of extension behaviors of PAni gel fibres at different interfacial pressure. f Typical tensile stress-strain curves of UFPPFs. g Ashby plot comparing the mechanical strength of UFPPFs to previously reported CPFs. Scale bars in a: Water, Ethanol, EA, Acetone 20 μm (left) 10 μm (right); NMP 20 μm (left) 5 μm (right), DMF 20 μm (left) 2 μm (right).
+
+The sharp necking behaviors of gel protofibres are highly related to the use of good solvents as the coagulation bath. We recorded the evolution of surface morphologies of PAni fibres collected from different solvating species. As shown in Fig. 2a, the obtained fibres in poor solvating species, i.e., water, ethanol, ethyl acetate (EA), and acetone, generally present coarse surfaces and large diameters around 20 μm. By comparison,
+we clearly observed a necking phenomenon in both cases of good solvents, i.e., N-methyl-2-pyrrolidone (NMP) and DMF. Such necking effects promoted the finally produced fibres to behave ultrafine morphologies, which assists PAni fibres to behave better structure and performance stabilities due to the higher degree of orientation and crystallization (see the X-ray diffraction analysis in Supplementary Fig. 3). We used Raman spectra to evaluate their structural evolution after placing fibres in air for four weeks. As shown in Fig. 2b, we did not find obvious de-doping signals in Raman spectra of the PAni fibres from good solvents, whereas various de-doping peaks (1223 cm\(^{-1}\) and 1462 cm\(^{-1}\)) appeared in the cases of poor solvents.
+
+We speculate that this sharp necking phenomenon may be caused by two factors: diffusion difference and interfacial pressure. In the conventional wet spinning protocol, the diffusion from good solvents to poor solvents occurs quickly to solidify dope fluids into gel fibres\(^{18,19}\). The rapid diffusion could be aggravated in the system of conducting polymers due to the strong interactions of rigid chains. Thus, PAni molecules tend to bond into irregularly crystallized particles prior to undergoing extensive drawing, as present in the upper panels of Fig. 1a. In previous reports using poor solvents as coagulation bath, although CPFs with a smooth surface could be collected by enhanced shear flow and strong stretching\(^{12,14}\), diameters are unable to be decreased to the ideal level due to the insufficient stretching slenderization of solidified gels. In contrast, the diffusion from dope fluids to good solvents is quite slow. Such slow diffusion allows the formation of fibrous gels with a low viscosity and the following high drawing ratios. Note that most conventional polymers are incapable of gelling in good solvents due to the poor chain interactions\(^{20,21}\).
+
+We calculated the diffusivities between various solvents and measured the viscosity of corresponding formed gels to support our explanations. The diffusivity from A molecules to B molecules, \( D_{AB}^0 \), is determined by the equation
+
+\[
+\frac{D_{AB}^0 \mu_B}{T} = 8.52 \times 10^{-8} V_{pB}^{-1/3} \left[ 1.40 \left( \frac{V_{BB}}{V_{bA}} \right)^{1/3} + \frac{V_{BB}}{V_{bA}} \right]
+\]
+, where \( \mu_B \) is the solvent viscosity, T is the temperature, and \( V_b \) is the molar volume of solvent at its normal boiling temperature\(^{22}\). As displayed in Fig. 2c, the diffusivities from m-cresol to DMF (\(7.5\times10^{-6}~cm^2s^{-1}\)) and NMP (\(7.71\times10^{-6}~cm^2s^{-1}\)) are generally lower than that of poor solvents. Diffusion in bath further dominates the viscosity of protofibres. To monitor the viscosity of gel fibres in practical conditions, we conducted the viscometer tests at a low revolution (e.g., 10 Rev.). As summarized in Fig. 2d, the formed PAni gels in good solvents show a viscosity below 3000 cP, much lower than that of poor solvents (>4000 cP). The established solvating specie-diffusivity-viscosity formula accords well with our proposed explanations.
+
+Interfacial pressure during solvent exchange is another major factor relating to the necking behavior of PAni protofibres. In a two fluid system, the interfacial pressure between two kind of solvents is inclined to decrease with the improved solvent diffusion\(^{23}\). Based on the slow diffusion from m-cresol to good solvents (Fig. 2c), the interfacial pressure between gel fibres and coagulation bath is considerable, which further induces the necking of protofibres. To understand this, we conducted a mechanic simulation to the stretching behavior of gel fibres at different interfacial pressure (see the progressive results in Supplementary Fig.4 and Method section). According to the simulation results in Fig. 2e, the higher interfacial pressure drives gel fibres to occur the sharper necking and thinning effects at a given tensile stress. This probably explains the formation of UFPPFs in DMF bath.
+
+UFPPFs show impressive mechanical performance. Different from that of conventional polymer fibres, the typical linear strain-stress curves of UFPPFs demonstrate a brittle fracture behavior with a small tensile strain of 3.67±0.64% (Fig. 2f). It is reasonable if considering the rigid backbone of PAni chains, which likely gather and condense into fragile fibrous assemblies after undergoing strong shear flow in spinning microtubes. According to classical Griffith theory on brittle fracture, fibres’ strength generally improves with the decrease of diameter due to the depressed structural defects\(^{24}\). We compared the mechanical performance of UFPPFs with previously reported CPFs.
+Fig. 3: Energy and charge storage capacities of UFPFs. a Schematic of a micro capacitor constructed using two UFPF electrodes on a substrate. b Cyclic voltammetry curves with the increasing scan rates from 10 to 20, 50, 80 and 100 mV s^{-1}. c Galvanostatic charge/discharge curves at various current densities increasing from 0.32 to 0.63, 1.59 and 3.18 mA cm^{-2}. d The area capacitance of UFPFs comparing to previous reported electrodes. e Cycle galvanostatic charge/discharge curves during 120 cycles between 0 and 0.6 V at 1.59 mA cm^{-2}. f. The relationship between current and voltage at a slow rate of 10 mV s^{-1}. g The charge storage capacity of UFPFs comparing to other charge storage materials.
+
+Derived from the strain-stress curves, we concluded that UFPFs have a modulus of 29.89±5.6% GPa, and a strength of 1080±71 MPa, at least one order of magnitude higher than that of CPFs with larger diameters (Fig. 2g), mainly including PEDOT fibres (<450 MPa)^{7,25-29} and PAni fibres (<400 MPa)^{30-33}.
+
+Energy and charge storage capacities. Ultrafine morphology optimizes the
+electroactive surfaces, which enables UFPFs to exhibit superb energy and charge storage capacities. To evaluate the electrochemical activity of UFPFs, we constructed a micro capacitor using polyvinyl alcohol (PVA)-H3PO4 gel electrolyte and two UFPF electrodes (Fig. 3a). The electrochemical properties were checked by cyclic voltammetry (CV) and galvanostatic charge-discharge (GCD) measurements. At different scan rates, the nearly rectangular shape of CV curves and instantaneous current response to voltage reversal at each end potential suggest the good electrochemical activity of UFPFs34 (Fig. 3b). The nearly triangular shape of GCD curves at different current densities illustrates the formation of efficient electric double layers and charge propagation across the UFPF electrodes35 (Fig. 3c). According to the GCD results, we determined the electrochemical properties of UFPFs. Among of them, the area capacitance, \( C_A \), is between 1008 and 1666 mF cm\(^{-2}\) at the current densities between 0.32 and 3.18 mA cm\(^{-2}\), outperforming previously reported thick CPFs29 and other electrodes, such as carbon nanomaterials3434,36, metal oxides37 and conducting polymers38-41, and approaching to that of PAni nanowires42 (Fig. 3d). The volumetric capacitance, power density and energy density reach 83.8 F cm\(^{-3}\), 0.96 W cm\(^{-3}\) and 4.19 mWh cm\(^{-3}\), respectively (Supplementary Fig. 5). In lifetime tests of UFPF-based capacitor, both the potential and capacitance continued without significant decrease for 120 charge/discharge cycles at a low current density of 1.59 mA cm\(^{-2}\), indicating the reliable electrochemical performance stability of UFPFs (Fig. 3e).
+
+We were able to confirm the amount of transported charge per unit area to UFPF during the charge/discharge cycle. The charge during a triangular wave potential between -0.9 V and 1.0 V (water window, see the Supplementary Fig. 6) was calculated by integrating the measured current with respect to the time of period at a low scan rate of 10 mV s\(^{-1}\) (Fig. 3f)6. We determined that the charge storage capacity of UFPF was 5.25×10\(^{4}\) mC cm\(^{-2}\), a value at least two orders of magnitude higher than that of noble metals43, carbon bulk44 - 46 and previously reported conducting polymers47 (Fig. 3g). This value decreases slightly to 2.015×10\(^{4}\) mC cm\(^{-2}\) at a tenfold scan rate of 100 mV s\(^{-1}\) (Supplementary Fig. 7).
+Fig. 4: Demonstration and characterization of all-solid organic electrochemical transistor based on UFPFs. a Schematic of the all-solid OECT composed of three polymer layers, one silver wire as the gate electrode, and one UFPF as the drain-source channel. b Cross-section SEM image and schematic of OECT. The yellow break lines direct the charge flow along the fibre chains (green solid lines). c Transmittance of the OECT in the region of visible light. A typical output curve (d), transfer curve (e), and power consumption in operation (f) of OECT. Scale bars: b 20 μm.
+
+Structure and performance of all-solid OECT. Benefitting from the favorable energy and charge storage performance of UFPFs, we demonstrated a high-performance all-solid OECT. OECT amplifies drain-source current intensities at low operating voltages by ion penetration into the organic mixed ionic-electronic conductors, i.e., conducting
+polymers^{48,49}. This process is controlled by the gate bias, and, to date, has generally conducted in aqueous electrolytes. To preclude the interference of external environment, we promoted the working conditions of OECT from aqueous environments to all-solid state by using gel electrolytes as the ion matrix. As shown in Fig. 4a-b, our OECT is mainly constructed by three polymer layers. The upper layer is the cured polyurethane (PU) working as the dielectric coating and also protecting the device from the invasion of external action^{50}. A fibrous silver gate electrode with a diameter of 7 \( \mu \)m is fixed in PU. Since UFPFs have demonstrated reliable electrochemical activities in PVA-H$_3$PO$_4$ gel, we used PVA-H$_3$PO$_4$ gel as the middle layer to inject ions to or uptake ions from the drain-source channel materials. A UFPF right below the silver gate is fused in the ion gel, and operates as the channel material. The bottom layer is also pure PU acting as the supporter of the whole device. Due to the remarkable flexibility and transparency of PVA and PU, the all-solid OECT is very soft, and shows a transmittance beyond 80 % in the region of visible light (Fig. 4c), and a small thickness below 300 \( \mu \)m.
+
+Despite the long channel length (~0.48 cm), much larger than of conventional micrometer-scale device, the all-solid OECT showed favorable amplification performance with a high on-off current ratio (>10$^3$, Fig. 4e) at low voltages (<1 V, Fig. 4d). The relatively fair transconductance (g$_{m}$, < 60 \( \mu \)S) is probably ascribed to the small cross-sectional area, which dramatically magnifies the resistance of fibrillar channel. Note that the all-solid OECT is an energy saving device with extremely low power consumptions. For example, at a given drain-source voltage of 0.6 V, the consumed power is below 18 \( \mu \)W (Fig. 4f).
+Fig. 5: Electrical response of the all-solid OECT to mechanical deformations. a Schematic of the mechanism explaining the response to the action of external pressure. b Relative drain-source change (\( \Delta I_{DS}/I_{DS0} \)) and sensitivity as a function of pressure. c Response time of the all-solid OECT when pressing (rising edge) and releasing (falling part) under the instantaneous pressure of 17.8 KPa. d Cyclic response at three different pressure levels (0.92, 6.8, and 22.2 KPa). e, Schematic of the working principle of the response to friction. f Cyclic response at three different frictions (1.84, 4.69, and 5.55 KPa). g An enlarged curve of the marked part in (f). h Cyclic response at different friction speeds from 4, 6, 8, 10, 15, to 20 mm s\(^{-1}\).
+
+We proved that the all-solid OECT functioned to amplify small electrical signals in gel environments and respond to mechanical deformation as a tactile sensor. As illustrated in Fig. 5a, the applied vertical pressure on the surface of the all-solid OECT adjusted the ion penetration due to the improved gate-source electric field and the redistribution of intrinsic capacitance\(^{51}\). At a \( V_G \) of -0.1 V and a \( V_D \) of 0.35 V, we observed a stable increase of drain-source current, \( I_{DS} \), with the increasing pressure, up to a 92% amplification from 0 to 40 KPa (Fig. 5b). The sensitivity is at the level of 0.01-0.1 KPa\(^{-1}\) in this process (dark cyan dots in Fig. 5b). As shown in Fig. 5c, the average rising time and falling time under instantaneous pressure of 17.8 KPa is ~536 ms and ~698 ms,
+respectively. Such integrated parameters facilitated the all-solid OECT to respond to different pressure levels from 0.92 to 22.2 KPa (Fig. 5d). In addition to the response to pressure at the vertical direction, the all-solid OECT also reacted to friction at the horizontal direction (Fig. 5e and Supplementary Fig. 8). The forward and backward friction of a load on the surface changed the real-time distance between silver gate and UFPF channel repeatedly, thus producing a bimodal response curve (Fig. 5g). Note that, to enable the enlargement of \( I_{DS} \) with the increasing gate-channel distance under the repeated friction, we applied a positive \( V_G \) of 0.1 V at a \( V_D \) of 0.55 V. The all-solid OECT responded stably to friction at different magnitudes (Fig. 5f, from 1.84 to 5.55 KPa) and different speeds (Fig. 5h, from 4 to 20 mm s\(^{-1}\)) during our cyclic tests. For example, \( I_{DS} \) increased ~86% at 5.55 KPa.
+
+Discussion
+The past decades have witnessed great achievements in preparing high-performance CPFs, which made a vast difference to the rapid development of advanced electronics. However, due to the limitations of both technology and strategy, it is still difficult to produce ultrafine CPFs at the large scale. We proposed a good solvents strategy in a modified wet spinning technology. With a principle of diffusion-controlled slow gelation of protofibres, the new system successfully downsized the diameter of PAni fibres to below 5 \( \mu \)m, a value smaller than that of most previous work. Furthermore, the ultrafine morphology with highly improved electroactive surfaces promotes UFPFs to behave superb electrochemical activities and mechanical performance. It is of great importance to realize the mass production of ultrafine CPFs. We constructed an all-solid OECT to employ the impressive energy and charge storage capacities of UFPFs. A handful of fibres are robust enough to satisfy the operation as the tactile sensor. In view of the ability to produce on the industrial scale, UFPFs are promised to be extended to large-area electronics, such as textile-scale numeric displays, soft electrochromic windows, and wearable energy harvesting systems.
+Methods
+
+Characterizations. All the SEM images were collected on a tungsten thermionic emission SEM system (the Tescan VEGA3). XRD spectra were obtained from XRD system (Rigaku SmartLab) equipped with 9 kW rotating anode X-ray source (\( \lambda \sim 1.54\text{\AA} \)) coupling with high-quality semiconductor detector that supports 0D, 1D or 2D x-ray diffraction measurement. Raman spectra were recorded from Renishaw Micro-Raman Spectroscopy system fully integrated with confocal microscope spectrometer and a 785 nm laser source. Mechanical tests were conducted on an advanced rheometric expansion system at the Hong Kong University of Science and Technology. All the electrochemical tests were processed on an electrochemical workstation (VersaSTAT3). The measurements of OECT were conducted on probe station (Micromanipulator) with Keithley 4200A-SCS parameter analyzer.
+
+The fabrication of UFPFs. PAni power (emeraldine base, purchased from Sigma-Aldrich) was mixed with CSA at a molar ratio of 2:1. After being milled for 15 minutes, the uniform doped PAni was dispersed in m-cresol (after degassing) at a concentration of 0.05 g mL\(^{-1}\). The dispersions were used as spinning dopes after blending in air for 8 hours, and extruded through a PEEK microtube with an inner diameter of 100 \( \mu \)m at a rate of 1mL min\(^{-1}\). Coagulation bath was chosen according to the experimental requirements. PAni fibres were directly drawn out from bath and collected on a graphite roller continuously.
+
+Numerical method. The experimental result is verified by numerical method using commercial software ANSYS. The simulation is performed using workbench 18.0. In the simplified computational model, a geometric model of gel tube is developed, in which the ratio of diameter to length is chosen as 1:18, and the mechanical properties, density, Young’s modulus and Poisson’s ratio are selected as 300kg/m3, 1000Pa and 0.01, respectively. For the boundary conditions, one end of the gel model set as fixed support, and another end applies extend displacement to mimic the stretching effect in the actual situation. Meanwhile, the corresponding pressure is applied on the outer surface of the gel model to account for the function of the impressive interfacial pressure on the surface of gel fibres. To ensure the convergence of the result, a grid independence test is conducted by refining mesh size sequentially, and the finite element mesh with 162641 nodes and 37128 hexahedral elements are adopted finally.
+
+The fabrication of micro capacitor. Micro capacitor composed of two UFPF electrodes and the
+gel electrolyte was constructed on a glass substrate. To prepare the gel electrolyte, PVA power was dispersed into deionized water at a mass ratio of 9:1. PVA was dissolved after being heated for 5 hours at 85 °C. Then phosphoric acid was added at a mass ratio of 1:10 with deionized water. The mixture cooled at room temperature and were ready for use. Two UFPPFs were placed in parallel on the glass slide. The transparent PVA-H3PO4 gel was dropped between UFPPFs. Two cooper wires connected to the UPPFs with silver paste worked as the conductor lines. After condensing for 10 minutes at 40 °C, the whole device was subject to electrochemical tests.
+
+The fabrication of all-solid OECT. The OECT was built from three layers: two PU layers and one ion gel layer. PU dispersion in DMF was casted on a PVDF substrate. After being treated in oven at 60 °C, a thin and transparent layer of pure PU was obtained. One drop of PVA-H3PO4 gel electrolyte was added on the surface of solidified PU. An UFPPF was immersed into gel. After been dried at 45 °C for 15 minutes, a UFPPF channel locked in PVA-H3PO4 gel was obtained. Afterwards, another drop of PU was added and a silver wire operation as the gate electrode was putted in PU at the liquid state. After being dried at 60 °C, an all-solid OECT was prepared. Note that all the three electrodes were connected to cooper electrodes for following measurements.
+
+Data availability
+
+The data that support the findings of this study are available from the corresponding author upon reasonable request. Correspondence and requests for materials should be addressed to Y.C. and X.T.
+
+Acknowledgements
+
+This work is supported by the Research Grants Council of Hong Kong (No. 15201419 ), Hong Kong Polytechnic University Postdoctoral Fellowship and Endowed Professorship Fund (No. 847A).
+
+Author contributions
+
+X. T. supervised this study. B. F. designed and conducted the main experiments. J. Y., Y. C. and B. F. constructed and characterized the transistor. D. C. helped to build the wet spinning equipment and discussed the results. J. P. did the mechanic simulations. K. M. M. helped to draw a part of schematics. Q. G. and P. G. helped to conduct the mechanical tests. B.F., X. T. and Y. C. wrote the manuscript.
+
+Competing interests
+
+The authors declare no competing interests.
+
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+Supplementary Files
+
+This is a list of supplementary files associated with this preprint. Click to download.
+
+• Supplementaryinformation1130.pdf

0226534d35058c645a89e4e44377c8b2e4f25f5dddefbf9c78c868b60659db7b/preprint/preprint.md

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+Changes in limiting factors for forager population dynamics in Europe across the Last Glacial-Interglacial Transition
+
+Alejandro Ordonez ( alejandro.ordonez@bio.au.dk )
+Aarhus University
+Felix Riede
+Aarhus University
+
+Article
+
+Keywords:
+
+Posted Date: December 22nd, 2021
+
+DOI: https://doi.org/10.21203/rs.3.rs-1173690/v1
+
+License: This work is licensed under a Creative Commons Attribution 4.0 International License.
+Read Full License
+
+Version of Record: A version of this preprint was published at Nature Communications on September 6th, 2022. See the published version at https://doi.org/10.1038/s41467-022-32750-x.
+Changes in limiting factors for forager population dynamics in Europe across the Last Glacial-Interglacial Transition
+
+Alejandro Ordonez1,2,4 & Felix Riede1,3
+
+1, Center for Biodiversity Dynamics in a Changing World, Aarhus University
+2, Department of Biology, Aarhus University
+3, Department of Archaeology and Heritage Studies, Aarhus University
+4, Center for Sustainable Landscapes under Global Change, Aarhus University
+
+Abstract
+
+Population dynamics set the framework for human genetic and cultural evolution. For foragers, demographic and environmental changes correlate strongly, although the causal relations between different environmental variables and human responses through time and space likely varied. Building on the notion of limiting factors, namely that the scarcest resource regulates population size, we present a statistical approach to identify the dominant climatic constraints for hunter-gatherer population densities and then hindcast their changing dynamics in Europe for the period between 20kyBP to 8kyBP. Limiting factors shifted from temperature-related variables during the Pleistocene to a regional mosaic of limiting factors in the Holocene. This spatiotemporal variation suggests that hunter-gatherers needed to overcome very different adaptive challenges in different parts of Europe, and that these challenges vary over time. The signatures of these changing adaptations may be visible archaeologically. In addition, the spatial disaggregation of limiting factors from the Pleistocene to the Holocene coincides with and may partly explain the diversification of the cultural geography at this time.
+
+Introduction
+
+As the link between exogenous environmental factors and organismal physiology, demography is vital for understanding evolution, including cultural evolution ¹. The relevance of past demography for understanding culture change in prehistory specifically has long been recognised ²,³. Demographic conditions impinge on cultural transmission ⁴⁻⁶ but are also clearly implicated in the boom-and-bust patterns of population fluctuations – including periodic
+extirpations – suggested to have characterised the demographic histories of prehistoric foragers and incipient farmers in many regions 7–10. Numerous recent studies have focused on the drivers of population expansion to explain the pattern and timing of human colonisation using a variety of ecological comparative approaches 11,12 (but see ref. 13 for a discussion of points of concern of such approaches ). Yet, as foragers have a high intrinsic growth rate, population increase is, in the absence of cultural or environmental constraints, the default demographic trajectory. Evidently, however, past populations did not grow substantially, making it particularly germane to understand the factors that curtailed population growth 14,15. The approach adopted here builds on the central theorem that population sizes would always be regulated by the scarcest resource: the limiting factor 16.
+
+Foragers of the recent past persisted in a wide variety of environments, from the frigid Arctic to tropical rainforests. Each environment offered particular opportunities but also posed particular challenges. While several earlier studies have pointed at temperature or seasonality as key drivers of forager demography at global or continental scales 17,18, the specific factors that would have capped or even depressed population size are likely to have varied in both space and time. Only in understanding these limiting factors can we begin to conduct targeted investigations of how specific forager populations may have overcome them via either population-specific genetic adaptations or the sort of ‘extra-somatic adaptions’19 that are so characteristic of human culture.
+
+In this study, we focus specifically on forager palaeodemography in Europe from the Last Glacial Maximum (Greenland Stadial 2, GS2) to 8000 years before present (BP), a climatically volatile period also known as the Last Glacial-Interglacial Transition 20. Previous studies have identified broad patterns of population growth and expansion using different methods commonly used in ecological analyses 12,21–23. Correlations between temperature and overall population density have been identified, suggesting overall increases in energy availability as the key driver of the increase in human population size following the end of GS2 17. However, regional population collapses have been suggested to have occurred asynchronously and in different places 9,24. This raises the question of which specific limiting factors acted on forager populations and how these limiting factors varied over space and time.
+
+Like many related studies, we begin with the global ethnographic hunter-gatherer dataset originally assembled by Binford and now digitally available 25,26. We couple this to a suite of quantile Generalised Additive Models (qGAMs) to describe changes in maximum (90-
+percentile) population density as a univariate function of environmental variables related to the effect of temperature and precipitation on available energy, annual variability, and productivity. We then use the downscaled centennial average-conditions of each predictor derived from a transient climatic simulation (CCSM3 SynTrace-21 \(^{27}\)) and the best performing univariate qGAM models to hindcast hunter-gatherer population densities between 20ky to 8kyBP. We define the limiting environmental factor as the variable predicting the lowest population density at a given place and time. This approach allows us to query the spatial dynamics of forager limiting factors across the Last Glacial-Interglacial Transition and derive specific hypotheses as to which selection pressures acted most strongly on different forager communities in Late Pleistocene and Early Holocene Europe.
+
+Our analysis demonstrates that the dynamics on limiting factors for forager population densities showed marked differences in space and time. Temperature-related variables were the main limiting factors during the Pleistocene, whereas the Early Holocene was characterised by a regional mosaic of limiting factors. Furthermore, our model reveals geographic differences in the limiting factors between Fennoscandia, Southern, Central, and Eastern Europe. The spatiotemporal variation in limiting factors suggests that hunter-gatherers needed to overcome very different adaptive challenges in different parts of Europe across this period of climatic and environmental change.
+
+Results and discussion
+
+The relation between the environmental factors explored here and population density assessed using qGAMs (Fig. 1) was negative for temperature seasonality, positive for effective temperature, winter/fall temperature, and unimodal for the warmest temperature. Seasonal, monthly, and extreme precipitation, and topographic heterogeneity showed an overall flat trend (supplementary figure S1), yet these also differed from a mean model as determined by the high deviance explained (Table 1).
+
+No single environmental variable explained more than 81% of the population density variation among ethnographic foraging societies (Table 1). However, the performance of more complex multivariate models using machine learning approaches \(^{12}\) or Structural Equation Models \(^{11}\) that combine three or more variables perform only marginally better. The five environmental variables with the highest predictive accuracies (based on the deviance explained; Table 1) were Temperature of the Coldest Month; Temperature Seasonality; Winter Mean Temperature;
+Effective Temperature and Mean Annual Temperature. These variables display high collinearity (Pearson correlations range between 0.83 and 0.96), suggesting that temperature overall best captures the effect of temperature minima and energy availability in relation to forager demography. Two of the variables (Temperature of the Coldest Month and Winter Mean Temperature) represent the effect of extreme cold conditions (= winter mortality) on demographic trends and/or ecological performance \(^{28,29}\). The other two (Mean Annual Temperature, Effective Temperature, Temperature Seasonality) relate to overall energy availability \(^{28}\). These factors are linked to higher environmental productivity and are expected to increase available resources, leading to higher population densities, as already suggested by a plethora of earlier studies \(^{30-32}\). Other variables related to environmental productivity have lower predictive accuracy (explained deviances < 0.79, see Table 1) and lower collinearity with other variables related to energy availability.
+
+Most seasonal temperature and precipitation variables showed some of the lowest explained deviances (Table 1), indicating that seasonal climatology most likely did not impose a direct limit on past forager populations densities in Late Pleistocene/Early Holocene Europe (contra \(^{18}\)). Topographic complexity, a variable shown to influence population density in other studies \(^{11}\), showed only above-average predictive accuracy (Table 1). Like seasonal temperature and precipitation, the topographic complexity effect on population density may be indirect and mediated by variables describing available resources or climate extremes.
+
+Besides the well-known limitations of using foragers of the recent past for reconstructing prehistoric social and demographic conditions \(^{13}\), the issue of model truncation and non-analogy of climatic conditions present themselves as major potential caveats. Climatic non-analogy here refers to the problem of projecting models beyond the domain for which they have been calibrated \(^{33-35}\). Model truncation refers to the incomplete characterisation of hunter-gatherer populations' total climate space \(^{36-38}\) and has been a long noted limitation of ethnographic analogies for prehistoric foragers \(^{39}\). However, it has also been shown that the dataset assembled by Binford is not critically biased in terms of forager niche space \(^{25}\). Likewise, we do not see either truncation or severe non-analogy in a temporal context, as the climate space observed at different moments during the 21-to-8kyBP period show broad overlaps with the climate space used to develop our qGAMs (Fig. 2; supplementary figure S2). This means that our models are not unduly extrapolating into environmental regions where there is no clear indication of how population density changes as a function of evaluated
+climatic variables. By the same token, it is necessary to highlight that the distributions of some paleoclimatic conditions – including all those with the highest predictive values in our models – are skewed towards the lower end of contemporary values. This is especially pronounced for the Pleistocene and variables such as maximum temperatures (Fig. 2), affecting our inference power on changes in population densities at these extremes.
+
+Our models indicate that the estimated human population size in Europe was the lowest at 22kyBP (~294,000 individuals) and largest at 8kyBP (~706,000 individuals). Also, based on our model, we show that at the warmest point of the Greenland Interstadial 1 (~14.7kyBP; GI1), Europe’s human population size estimated by our model was ~617,000 individuals; a number that decreased to ~607,000 individuals at the coldest point of the Greenland Stadial 1 (~11.7kyBP; GS1). Overall occupied area (number of inhabited cells) was 62.4% of the region at the end of the GS2 (~22kyBP). This number increased to ~98.8% during GI 1, decreased to ~97.7% during the GS 1, and reached the highest point (~99.8%) by the mid-Holocene (~8kyBP). Taken at face value, these values are gross overestimation of actual sustained forager land-use at this time. Forager land-use was evidently extensive, including largely empty spaces \(^{40}\). By the same token, these numbers are in line with archaeologically derived trends of overall population growth and expansion during this time (red lines; Fig. 3A).
+
+During the evaluated period, the mean population density in the inhabited area varied between 2.6 and 6.2 persons per 100 km\(^2\) (GS2 = 2.7 p/100 km\(^2\); GI1 = 5.25 p/100 km\(^2\); GS1 = 5.17p/100 km\(^2\); mHol = 6p/100 km\(^2\); Fig. 3A). Although the temporal patterns in average population density derived from our limiting-factor analysis are similar to those of core area estimates by Bocquet-Appel, et al. \(^{21}\) (blue areas, Fig. 3A), these do not match numerically due to our focus on maximum population densities. Moreover, our population density estimates are consistent with those suggested by Tallavaara, et al. \(^{12}\), and more recently Kavanagh, et al. \(^{11}\).
+
+The estimated pattern of human population density (Fig. 3) indicates a population expansion starting almost 3ky after the ice sheet began to recede from its maximum extent 22kaBP. Evaluating the spatially explicit predictions of our model, we find that at the end of the GS2, hunter-gatherer societies in Europe extended as far north as central France, southern Germany and southern parts of modern-day Ukraine (Fig. 4A), a pattern that is consistent with archaeological evidence for the recolonisation of Europe \(^{41-44}\). Our models also suggest that by the end of the GS2, a relatively large proportion of the European continent may have been at least sporadically inhabited (~62%; Fig. 4A-B), with the Mediterranean region up to the north
+of the Alps showing population densities up to 12 individuals/100 km². This restricted occurrence pattern is supported by the archaeological record \(^{40}\). Furthermore, our model indicates a persistent southwest-northeast gradient of decreasing population densities in this southern region, with the most populated areas occurring in the Iberian Peninsula and the Mediterranean region (**Fig. 4A-B**). From this point, the recolonisation of the continent began at ~17kyBP (**Fig. 3**), reaching almost all the way to Scandinavia by the start of GI1 (~14.7kyBP, **Fig. 4c**). Earlier archaeological \(^{45,46}\) and modelling studies \(^{22}\) have already suggested that this colonisation was rapid but also that it proceeded in several steps where both climate and landforms served as barriers to expansion\(^{47}\). Our results expand on this discussion by highlighting that different climate variables limited human dispersal for a given location and that these limits changed over time.
+
+Using our limiting-factor approach, we improve our understanding of demographic mechanisms in Late Pleistocene and Early Holocene European hunter-gatherer societies by highlighting the spatiotemporal changes in the main factor restricting population density (**Fig. 4F-T; and Fig. 5**). Our modelled population density estimates can be linked to regional or local narratives or empirical tests of changes in occurrences and population sizes (e.g., refs. \(^{25,48}\)). The changes in limiting factors suggested in our models can be divided into three periods. The first period spans from the termination of GS2 to the onset of interstadial warming at around 15kyBP. During this period, energy availability measured as effective temperature (ET) was the main factor limiting population density across most of the continent (~50% of cells; **Fig. 5A**). Mean temperature of the warmest month (MWM) was also a strong limiting factor (~30% of cells; **Fig. 5**). However, limitations imposed by winter temperatures, could be also considered as likely limiting factors based on estimates of average conditions at a continental scale (**Fig. 5B**). The range of experienced temperature conditions, represented by ET, can thus be seen as the major limiting factor shaping human population density in Europe between GS2 and the initiation of warming associated with GI1 (**Fig. 5A**). With temperature related variables as the overwhelming limiting factor during this period (**Fig. 5B**), it is likely that the emergence of sophisticated sewing techniques and pyrotechnology \(^{49}\) facilitated the persistence and even moderate expansion of populations at this time.
+
+The second period covers the rapid warming (GI1) as well as cooling (GS1) events between 14.7kyBP to 11.7kyBP. During this period, the importance of ET steadily decreased, and mean temperature of the warmest month (~27% of cells) and temperature seasonality (~23% of cells)
+became the main factors limiting population density (Fig. 5A). The decrease of ET as a limiting factor indicates that during this period of rapid change, it was not temperature but energy availability (due to the link between MWM and productivity) what determined human population density in Europe (Fig. 5B). Our models suggest that overall population densities increased (Fig. 3), although a temporary reduction associated with GS1 cooling is also clear.
+
+The last period encompasses the Early Holocene from its onset at 11.7ky to 8kyBP. Here, temperature of the warmest month increased in importance as the main limiting factor (~50% of cells; Fig. 5A), while the effect of ET became marginal (Fig. 5B). Also, temperature seasonality became a critical limiting factor in many regions (Fig. 4I, J). These patterns indicate a complete shift from experienced temperature conditions to available resources as the main limiting factor of European forager population densities during the Holocene. Such a shift is interesting as the Early Holocene also witnessed a significant reorganisation of forager socio-ecological systems towards more varied use of resources and more pronounced territoriality focused on spatial circumscribed and regionally available resources, and a widespread shift from immediate-return to delayed-return economies. This also aligns with the idea that decreasing territory sizes and more marked boundary formation directly relate to the spatiotemporal dynamics of resource availability \(^{50}\).
+
+The regional disaggregation of patterns in limiting factors shows strong differences between Fennoscandia, Southern, Central, and Eastern Europe (Fig. 4F-J). These patterns are persistent over time, with regional shifts linked to the main feature of temperature change. In Fennoscandia and the British Isles, effective temperature was the main limiting factor for most of the Late Pleistocene. This changed after the onset of the Holocene when seasonal temperatures and precipitation became the dominant limiting factor. In Eastern and Western Europe, effective temperature was the main limiting factor at the end of the GS2 but were replaced by Winter temperature and MWM at the onset of the GI1. During the GS1 and the early Holocene, the main limiting factors where MWM and TS. In southern Europe and especially in the Mediterranean, MWM was the main limiting factor throughout most of the GS2, after which precipitation became the dominant limiting factor.
+
+Our analyses show that the main limiting factors that limited forager population densities across the Last Glacial-Interglacial Transition in Europe changed markedly over time (Fig. 5) and space (Fig. 4F-J). We can now return to the archaeological record with these insights, searching for material culture proxies that may have allowed these past communities to
+overcome these particular limiting factors \(^{51-53}\). While these may have related to water availability (= containers) in the Mediterranean, they are predicted to relate to temperature (= clothing or pyrotechnology) in higher latitudes. Where such technologies are absent in the archaeological record, we can also begin to think about population vulnerability to climatic factors at regional levels. Especially in higher latitudes, population fluctuations may have been pronounced at the sub-centennial scale, to the point of local population extirpations \(^{9,54}\).
+
+Finally, the marked shift in limiting factors at the onset of the Holocene may be indicative of a greater focus on resource access at a regional scale. The spatiotemporal dynamics of resource availability have a direct impact on land-use, mobility, territoriality, and the formation of information networks in foragers \(^{50,55}\). In the Holocene, regional cultural signatures became more pronounced and borders between different cultural zones more strongly articulated. This itself may be seen as a response to the fundamental shift in limiting factors we have identified in our models.
+
+Seeking correlations between environmental variables and past human population densities is not a new endeavour. Following recent calls for more theoretically-informed rather than mere statistical explorations of this relationship \(^{13}\), we highlight that while the environment can be said to strongly constrain forager lifeways, precisely which aspects of the environment do so at any one place and time vary. Our approach offers a robust way to infer the hierarchy of limiting factors and hence provide a spatiotemporal hypothesis for major selection pressures acting on forager populations in the past.
+
+Independent palaeodemographic estimates broadly support our models, but many questions remain. Climate models, for instance, only indirectly capture the interaction of human population dynamics with changes in biodiversity and ecosystem compositions. In addition, the match between modelled population densities and the field-validated presence of Late Pleistocene/Early Holocene populations is not equally robust everywhere. These deviations may stimulate targeted field-testing with the aim of assessing whether and why population densities periodically fell short of or exceeded modelled values. In conjunction with legacy data derived from archives and the literature, such fieldwork can also shed light on the specific strategies these past foragers employed to mitigate the risks posed by specific limiting factors.
+
+Small-scale societies have a variety of adaptive options at their disposal (see ref.\(^{56}\)), most of which can be captured through archaeological proxies \(^{57-59}\). Our limiting factor model here
+serves as an explicit spatiotemporal hypothesis of which risk mitigation measures should be in use at which time and place. The successful identification of these would throw significant new light on the resilience and adaptation – or lack of it – during this climatically and environmentally tumultuous time. Finally, the marked shifts in dominant limiting factors identified in our models map into the results of Late Pleistocene/Early Holocene Earth System tipping points recently discussed by ref. 60. It is likely that, just like analogues anthropogenic warming in the present, these periods of rapid and substantive climatic change would have created challenges for contemporaneous forager populations. In an effort to align archaeological perspectives on climate change with the quandaries of our time (cf. 61 ), future research would be well-advised to focus on such periods of major systemic transitions.
+
+Methods
+
+Models of hunter-gatherers’ population density
+
+We use ethnographic data on terrestrially adapted mobile hunter-gatherers and their climatic space 25 to construct a series of statistical models that predict hunter-gatherer population density based on one of 16 climatic predictors (see Table 1 for rezoning and source). While there are important caveats 13, this approach builds on multiple ethnographic studies showing a link between climate on the one hand and hunter-gatherer diet, mobility, and demography on the other 55,62-66. This statistical connection is the basis of recent studies focused on building complex multivariate models of population dynamics 11,12,67. A benefit of our statistical approach is that it overcomes some significant limitations, such as lack of quantitative population size data based on the archaeological record itself or genetic data, each associated with their own limitations (as reviewed in refs. 2,12).
+
+We omitted four observation classes in the original ethnographic dataset in defining the association between hunter-gatherer population density and climatic predictors. First, we removed observations associated with food producers. Second, sedentary populations or those that reside at a single location for >1 year. Third, populations using aquatic resources (>30% of their dietary protein comes from aquatic environments, as defined in 68,69). Forth, we excluded all observations related to horse-riding populations. The filters employed here correspond to those used by Tallavaara, et al. 12 to maximise the match between ethnographic data and the current knowledge of the highly mobile and overwhelmingly terrestrially oriented lifestyles of Late Pleistocene/early Holocene hunter-gatherers in Europe. The implemented
+filters are less restrictive than those used by other studies that have sought to reconstruct forager population dynamics during this time \(^{70}\) and thus allow for a relatively large degree of behavioural variation. This is important given that increasing evidence of marine and lacustrine resource use is emerging for at least certain times and regions in Late Pleistocene Europe \(^{71-73}\), and that a marked diversification characterises the resource base of early Holocene foragers. Finally, these filters remove any population using external supplements to their hunter-gatherer lifestyle, resulting in a database including information on 127 populations.
+
+We used climate data on historical averages (1970-2000) for 19-climate variables (Table 1) to build our ethnography-based population density models. These were obtained from the Worldclim version 2.1 \(^{74}\) at a 10-ArcMin resolution. Importantly, we used Worldclim data instead of climatic variables directly available from the ethnographic dataset to ensure comparability between climatic variables not in the database (i.e., seasonal means). Equally importantly, this approach prevents any estimation biases due to differences between the data used to define climate-density relations and paleoclimatic surfaces (*see the section estimating human populations density across the Pleistocene-Holocene transition below*) used to estimate population density changes and limiting factors over time.
+
+Initially, we model how population densities of hunter-gatherer communities change along current environmental gradients using Quantile Generalised Additive Models (qGAMS). Modelling such dynamics using qGAMs offers a transparent way to determine the non-linear changes in different percentiles of a response variable (= population densities) to one or multiple environmental variables. This approach is commonly used in the ecological literature to determine the likelihood of occurrence or abundance of a given species under a particular environmental regime \(^{75-79}\) but has never before been applied to human palaeodemography. In contrast to previous studies evaluating past human population density changes, we do not consider the synergies between multiple climatic variables when describing the relation between population densities and climate. Instead, we focus on the individual effects of evaluated variables on the top 90-percentile of population densities to identify the most pronounced limiting factor that acted on palaeodemographic growth. The tendencies in population densities as a function of environmental variables were consistent for different percentiles (see supplementary figures S1).
+
+The population density derived from the ethnographic data followed a log-normal distribution, so these were log-transformed for subsequent analyses, and a gaussian response distribution
+was used in our qGAMs models. Annual, monthly, and seasonal precipitation variables were similarly transformed. The ability of each of the evaluated variables to predict hunter-gatherer population densities was determined using the mean deviance explained (1 - (Residual Deviance/Null Deviance)). These were calculated both for the whole dataset, and using a 1000-fold cross-validation approach (70% random sample for calibration and 30% for validation). All models and prediction accuracy estimates were implemented in R (version 3.6; \(^{80}\)) using the mgcv (version 1.8.24; \(^{81}\)) and qgam (version 1.3.2; \(^{82}\)) packages.
+
+Estimating human populations density across the Pleistocene-Holocene transition
+
+The monthly average temperature and annual precipitation values for Europe for the 21ky to 8kyBP period come from the CCSM3 SynTrace paleoclimate simulations \(^{83}\). These were bias-corrected and downscaled to 0.5° × 0.5° following the methods described by Lorenz, et al. \(^{84}\). The paleoclimatic simulation data used here was originally generated to evaluate changes in European and North American fossil pollen data and vegetation novelty since the Last Glacial Maximum \(^{27}\). Source climate surfaces were aggregated to centennial means from the original decadal averages of monthly values.
+
+Past hunter-gatherer population densities were then predicted for every 30ArcMin cell above sea level. For visualization we also show the areas covered by glaciers using the glacier extent shapefiles derived by PaleoMIST \(^{85}\). To generate 90% percentile population density estimates for each variable/century combination, only those qGAM models parametrised using the ethnographic data and current climatic conditions with cross-validated deviances above 70% were projected into past climatic conditions. As our objective was to establish the climatic variable that imposed the strongest constraints on hunter-gatherer population density at any one time, we determined the variable estimating the lowest 90%-percentile population density for a given cell at each evaluated time-period to be the limiting factor (the scarcest resource that would then limit population size cf. \(^{16}\)). For each evaluated time-period, we summarised the proportion of the available land area (i.e., land area not covered by ice) where each of the assessed variables was determined to be the limiting factor.
+
+We calculated the changes in the percentage of inhabited land area in Europe during the evaluated period by estimating the proportion of the inhabited area, here defined as the region where population densities were above 1 individual per 100km\(^2\). To calculate human-population size in Europe during every century, we multiplied the predicted population density
+in each cell by the land area of the corresponding cell to arrive at per cell population size. We then and summed these values to arrive at the total population size for each century.
+
+Uncertainties in population density, size, occupied area, and limiting factor estimates were determined using a cross-validation approach, where model fitting was iterated 1000 times using a random sample (70%) of the ethnographic and climate data at each time step. Each model was used to hindcast populations densities, estimate the percentage of inhabited land area and human population size, and define the relevant limiting factor. Uncertainty in continental-scale estimates of population densities, occupied area and population size was determined using 95% confidence intervals. The variable selected as the limiting factor in most cross-validation folds was selected as the limiting factor.
+
+Validation of population density estimates
+
+To assess the validity of our population density estimations, we use the International Union for Quaternary Science (INQUA) Radiocarbon Palaeolithic Europe Database v28 86. Changes in the density of records are a useful continental-scale proxy-measurement of prehistoric population size changes and are increasingly used to describe prehistoric human population dynamics trends 87-92. We extracted proxy dates (based on \(^{14}\mathrm{C}\) dates) from the INQUA Radiocarbon Palaeolithic Europe Database, aggregating these to the closest 1000 years. Our goal is to determine the match between our qGAM derived populations densities and prehistoric population occupation derived from the frequencies of radiocarbon dates between 20kaBP and 10kaBP as done by Tallavaara, et al. 12. This approach allowed validating our hindcasted estimates of absolute prehistoric population density since our model is not archaeologically informed, avoiding any possible circularity between model development and validation.
+
+We also used site-based estimates of population density as derived using the Cologne Protocol by Schmidt, et al. 23. We focus on estimates of extended interconnected socio-economic areas (Core Areas) for five unequal time bands between 25kaBP and 11.7KaBP. Although ultimately also based on Binford 25, these estimates present independently derived spatially implicit estimates of population density for the Late Palaeolithic in Europe.
+
+Data availability
+The ‘Binford’ ethnographic database \( ^{25} \) is available from the Database of Places, Language, Culture, and Environment (D-PLACE; https://d-place.org/about). Current and Late Quaternary environmental datasets are publicly available from the associated references. International Union for Quaternary Science (INQUA) Radiocarbon Palaeolithic Europe Database v28 is available from https://pandoradata.earth/am/dataset/radiocarbon-palaeolithic-europe-database-v28. Contemporary climate databases are available form the WorldClim project (https://www.worldclim.org), and late-Pleistocene climate sources are available at https://doi.org/10.6084/m9.figshare.c.4673120.v2.
+
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+Acknowledgements
+
+AO was supported by the AUFF Starting Grant (AUFF-F-2018-7-8). FR’s contribution is part of CLIOARCH, an ERC Consolidator Grant project that has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 817564).
+Author contributions
+
+AO: Conceptualization; Methodology; Formal analysis; Resources; writing – original draft, writing – review & editing; Visualization.
+
+FR: Conceptualization; Methodology; writing – original draft, writing – review & editing.
+Table 1. Variables used to generate ethnographic based models of the effect of climate on hunter-gatherer population density and summary of cross-validated deviance explained for the evaluated variables. Estimates correspond to those of a 1000-fold cross-validation approach (1000 samples of 70% training and 30% testing observations) or the full dataset
+
+<table>
+  <tr>
+    <th>Variable name</th>
+    <th>Acronym</th>
+    <th>Units</th>
+    <th>How does the variable determine population density?</th>
+    <th>Cross-validated Deviance explained. Mean [95% CI]</th>
+    <th>Full-dataset Deviance explained</th>
+  </tr>
+  <tr>
+    <td>Effective Temperature *</td>
+    <td>ET</td>
+    <td>C</td>
+    <td>Energy availability</td>
+    <td>0.774<br>[0.8 - 0.826]</td>
+    <td>0.792</td>
+  </tr>
+  <tr>
+    <td>Potential Evapotranspiration**</td>
+    <td>PET</td>
+    <td>mm/yr</td>
+    <td>Energy availability</td>
+    <td>0.751<br>[0.8 - 0.81]</td>
+    <td>0.774</td>
+  </tr>
+  <tr>
+    <td>Mean Annual Temperature</td>
+    <td>MAT</td>
+    <td>C</td>
+    <td>Energy availability</td>
+    <td>0.733<br>[0.7 - 0.777]</td>
+    <td>0.757</td>
+  </tr>
+  <tr>
+    <td>Mean temperature of the Coldest Month</td>
+    <td>MCM</td>
+    <td>C</td>
+    <td>Extreme Events</td>
+    <td>0.798<br>[0.8 - 0.839]</td>
+    <td>0.812</td>
+  </tr>
+  <tr>
+    <td>Mean temperature of the Warmest Month</td>
+    <td>MWM</td>
+    <td>C</td>
+    <td>Extreme Events</td>
+    <td>0.705<br>[0.7 - 0.762]</td>
+    <td>0.737</td>
+  </tr>
+  <tr>
+    <td>Temperature Seasonality</td>
+    <td>TSeason</td>
+    <td>C</td>
+    <td>Annual Variability</td>
+    <td>0.777<br>[0.8 - 0.839]</td>
+    <td>0.811</td>
+  </tr>
+  <tr>
+    <td>Spring Mean Temperature</td>
+    <td>SpMT</td>
+    <td>C</td>
+    <td>Seasonal trends</td>
+    <td>0.789<br>[0.8 - 0.828]</td>
+    <td>0.804</td>
+  </tr>
+  <tr>
+    <td>Summer Mean Temperature</td>
+    <td>SmMT</td>
+    <td>C</td>
+    <td>Seasonal trends</td>
+    <td>0.773<br>[0.8 - 0.817]</td>
+    <td>0.786</td>
+  </tr>
+  <tr>
+    <td>Fall Mean Temperature</td>
+    <td>FMT</td>
+    <td>C</td>
+    <td>Seasonal trends</td>
+    <td>0.725<br>[0.7 - 0.786]</td>
+    <td>0.750</td>
+  </tr>
+  <tr>
+    <td>Winter Mean Temperature</td>
+    <td>WMT</td>
+    <td>C</td>
+    <td>Seasonal trends</td>
+    <td>0.765<br>[0.8 - 0.808]</td>
+    <td>0.782</td>
+  </tr>
+  <tr>
+    <td>Annual precipitation</td>
+    <td>PREC</td>
+    <td>mm/yr</td>
+    <td>Energy availability</td>
+    <td>0.701<br>[0.7 - 0.757]</td>
+    <td>0.712</td>
+  </tr>
+  <tr>
+    <td>Precipitation of the Driest Month</td>
+    <td>PDM</td>
+    <td>mm/month</td>
+    <td>Extreme Events</td>
+    <td>0.746<br>[0.7 - 0.793]</td>
+    <td>0.760</td>
+  </tr>
+  <tr>
+    <td>Precipitation of the Wettest Month</td>
+    <td>PDM</td>
+    <td>mm/month</td>
+    <td>Extreme Events</td>
+    <td>0.77<br>[0.8 - 0.804]</td>
+    <td>0.784</td>
+  </tr>
+  <tr>
+    <td>Precipitation Seasonality</td>
+    <td>PSeson</td>
+    <td>mm/month</td>
+    <td>Annual Variability</td>
+    <td>0.737<br>[0.7 - 0.772]</td>
+    <td>0.748</td>
+  </tr>
+  <tr>
+    <td>Spring Precipitation</td>
+    <td>SpPREC</td>
+    <td>mm/month</td>
+    <td>Seasonal trends</td>
+    <td>0.773<br>[0.8 - 0.814]</td>
+    <td>0.788</td>
+  </tr>
+  <tr>
+    <td>Summer Precipitation</td>
+    <td>SmPREC</td>
+    <td>mm/month</td>
+    <td>Seasonal trends</td>
+    <td>0.753<br>[0.8 - 0.8]</td>
+    <td>0.779</td>
+  </tr>
+  <tr>
+    <td>Fall Precipitation</td>
+    <td>FPREC</td>
+    <td>mm/month</td>
+    <td>Seasonal trends</td>
+    <td>0.7<br>[0.7 - 0.772]</td>
+    <td>0.711</td>
+  </tr>
+  <tr>
+    <td>Winter Precipitation</td>
+    <td>TPREC</td>
+    <td>mm/month</td>
+    <td>Seasonal trends</td>
+    <td>0.774<br>[0.8 - 0.826]</td>
+    <td>0.792</td>
+  </tr>
+  <tr>
+    <td>Topographic Ruggedness Index ***</td>
+    <td></td>
+    <td>m</td>
+    <td>Habitat Heterogeneity</td>
+    <td>0.751<br>[0.8 - 0.81]</td>
+    <td>0.774</td>
+  </tr>
+</table>
+
+* Calculated following \(^{25}\)
+** Calculated following on \(^{93}\).
+*** Calculated following \(^{94}\).
+Figure 1. Quantile Generalised Additive Models (qGAM) describing the relation between environmental factors and population density for 10-percentiles (dashed lines), 50-percentiles (solid lines), and 90-percentiles (doted lines). Here, only the six most limiting factors during the 22kaBP to 8kaBP are presented. Full explorations of evaluated variables presented in Supplementary material S1.
+Figure 2. Convergence between current climatic conditions (hashed density plots) and paleoclimatic conditions at four different periods (coloured density plots). Paleoclimatic periods are Greenland Stadial 2, Greenland Interstadial 1, Greenland Stadial 1, and Holocene. As in Figure 1, only the six most limiting factors during the 22kaBP to 8kaBP are presented. Full explorations of evaluated variables presented in Supplementary material S2.
+Figure 3. Contrast between Europe wide mean population density (top panel), and trends in key environmental variables (bottom). Estimated average population density for all Europe based on a randomization approach (top panel) are compared to archaeological population proxy based on number of calibrated radiocarbon dates for Europe between 21 and 11kyBP based on \(^{12}\) summaries of the Radiocarbon Palaeolithic Europe Database v28 \(^{86}\) (red), and core area (cf. \(^{23}\) population density mean and upper/lower estimates based on the Cologne Protocol (blue). On the bottom panel, plotted variables are: Effective temperature, Minimum temperature of the Coldest Month, and Maximum temperature of the Warmest Month.
+Figure 4. Estimated human population density and range (areas where population density > 1 individual per 100km^2) (A-E) and factors limiting population density (F-J) across Europe for selected times during the 22ky to 8kyBP period. (A, F) Greenland Stadial 2; (B, G) Greenland Interstadial 1; (C, H) Greenland Stadial 1 warming terminations (D, I) Holocene initiation; (E, J) Mid-Holocene. Areas in grey scale represent the glacier extent as derived by PaleoMIST 85.
+Figure 5. Proportion of the ice-free area of Europe where each variable was estimated to be the factor limiting population density (A); and estimated population size based on the mean environmental conditions for each century (B). In both panels, only the six variables with the highest percentages of cells where the variable is the limiting factor are presented.
+Supplementary material S1 Quantile Generalised Additive Models (qGAM) describing the relation between the six most important environmental factors explored and population density for 10-percentiles (dashed lines), 50-percentiles (solid lines), and 90-percentiles (doted lines). Title acronyms as in Table 1.
+Supplementary material S2. Overlap between current climatic conditions (hashed density plots) used for model building and paleoclimatic databases (coloured density plots) used to hindcast human population density for all 19-climatic variables used. Title acronyms as in Table 1.

02381398ad3c168dad4fb3121959ba38b9f694fc8f5d7aeae79ef0842f4b081a/preprint/preprint.md

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+Reference-free and cost-effective automated cell type annotation with GPT-4 in single-cell RNA-seq analysis
+
+Zhicheng Ji
+zhicheng.ji@duke.edu
+
+Duke University   https://orcid.org/0000-0002-9457-4704
+Wenpin Hou
+Columbia University   https://orcid.org/0000-0003-0972-2192
+
+Brief Communication
+
+Keywords:
+
+Posted Date: May 2nd, 2023
+
+DOI: https://doi.org/10.21203/rs.3.rs-2824971/v1
+
+License: This work is licensed under a Creative Commons Attribution 4.0 International License.
+Read Full License
+
+Additional Declarations: There is NO Competing Interest.
+
+Version of Record: A version of this preprint was published at Nature Methods on March 25th, 2024. See the published version at https://doi.org/10.1038/s41592-024-02235-4.
+Reference-free and cost-effective automated cell type annotation with GPT-4 in single-cell RNA-seq analysis
+
+Wenpin Hou1,† and Zhicheng Ji2,†
+
+1Department of Biostatistics, The Mailman School of Public Health, Columbia University, New York City, NY, USA
+2Department of Biostatistics and Bioinformatics, Duke University School of Medicine, Durham, NC, USA.
+†Corresponding author. E-mail: wh2526@cumc.columbia.edu; zhicheng.ji@duke.edu
+
+ABSTRACT
+
+Cell type annotation is an essential step in single-cell RNA-seq analysis. However, it is a time-consuming process that often requires expertise in collecting canonical marker genes and manually annotating cell types. Automated cell type annotation methods typically require the acquisition of high-quality reference datasets and the development of additional pipelines. We demonstrate that GPT-4, a highly potent large language model, can automatically and accurately annotate cell types by utilizing marker gene information generated from standard single-cell RNA-seq analysis pipelines. Evaluated across hundreds of tissue types and cell types, GPT-4 generates cell type annotations exhibiting strong concordance with manual annotations, and has the potential to considerably reduce the effort and expertise needed in cell type annotation.
+
+Main
+
+In single-cell RNA-sequencing (scRNA-seq) analysis1–2, cell type annotation is a fundamental step to elucidate cell population heterogeneity and understand the diverse functions of different cell populations within complex tissues. Standard single-cell analysis software, such as Seurat3 and Scanpy4, routinely employ manual cell type annotation. These software tools assign single cells into clusters by cell clustering and conduct differential analysis to identify differentially expressed genes across cell clusters. Subsequently, a human expert compares canonical cell type markers with differential gene information to assign a cell type annotation to each cell cluster. This manual annotation approach requires prior knowledge of canonical cell type markers in the given tissues and is often laborious and time-consuming. Although several automated cell type annotation methods have been developed5–13, manual cell type annotation using marker gene information remains widely used in scRNA-seq analysis14–28.
+
+Generative Pre-trained Transformers (GPT), including GPT-3, ChatGPT, and GPT-4, are large language models trained on massive amounts of data and capable of generating human-like text based on user-provided contexts. Recent studies have demonstrated the competitive performance of GPT models in answering biomedical questions29–32. Thus, we hypothesize that GPT-4, one of the most advanced GPT models, has the ability to accurately identify cell types using marker gene information. GPT-4 will potentially transform the manual cell type annotation process into a semi-automated procedure, with optional help from human experts to fine-tune GPT-4-generated annotations (Figure 1a). Compared to other automated cell type annotation methods that require building additional pipelines and collecting high-quality reference datasets, GPT-4 offers cost-efficiency and seamless integration into existing single-cell analysis pipelines, such as Seurat3 and Scanpy4. The vast amount of training data enables GPT-4 to be applied across a wide variety of tissues and cell types, overcoming the limitations of other automated cell type annotation methods restricted to specific reference datasets. Additionally, the chatbot-like nature of GPT-4 allows users to easily adjust annotation granularity and provide feedback for iterative answer improvement (Figure 1a-b)31.
+
+To validate the hypothesis, we systematically assessed GPT-4’s cell type annotation performance across five datasets, hundreds of tissue types and cell types, and in both human and mouse (Figure 2a). Computationally identified differential genes in four scRNA-seq datasets (Azimuth by HuBMAP22, Human Cell Atlas (HCA)17, Human Cell Landscape (HCL)19, and Mouse Cell Atlas (MCA)18), and canonical marker genes identified through literature search in one dataset (literature)17, were used as inputs to GPT-4. Cell type annotation for HCL and MCA was performed and evaluated once by aggregating all tissues, similar to the original studies. In other studies, cell type annotation was performed and evaluated within each tissue. GPT-4 was queried using prompts similar to Figure 1b, and its cell type annotations were compared to those provided by the original studies. The comparison results were classified as “fully match” if GPT-4 and manual annotations refer to the same cell type, “partially match” if the two annotations refer to similar but distinct cell types (e.g., monocyte and macrophage), and “mismatch” if the two annotations refer to different cell types (e.g., T cell and macrophage). If the granularity of the manual annotation
+exceeded GPT-4 annotation, GPT-4 was asked to give more specific annotations (Figure 1b). Figure 2b shows an example of evaluating GPT-4 cell type annotations in a human prostate tissue literature search dataset. Supplementary Table 1 contains all cell type annotations generated manually or by GPT-4 across different tissue types and datasets, as well as agreement between manual and GPT-4 annotations.
+
+The performance of cell type annotation can be affected by the number of top differential genes used as reference. So we first assessed whether the number of top differential genes would affect the performance of GPT-4 cell type annotation. To facilitate comparison, we assigned agreement scores of 1, 0.5, and 0 to cases of “fully match”, “partially match”, and “mismatch” respectively, and calculated the average scores across cell types within a tissue or dataset. The comparison was only performed in HCA, HCL, and MCA datasets, as full lists of differential genes were available. Figure 2c shows that GPT-4 has the best agreement with human annotation when using the top 10 differential genes, and using more differential genes may reduce agreement. A plausible explanation is that human experts may only rely on a small number of top differential genes if they already provide a clear cell type annotation. In subsequent analyses, we used GPT-4 cell type annotation with the top 10 differential genes for HCA, HCL, and MCA datasets.
+
+In almost all studies and tissues, GPT-4 annotations fully or partially match manual annotations for at least 75% of cell types (Figure 2d), demonstrating GPT-4’s ability to generate cell type annotations comparable to those of human experts. The agreement is highest for marker genes identified through literature search, with GPT-4 annotations fully matching manual annotations for approximately 75% of cell types. The agreement decreases in marker genes identified by differential analysis, which may be attributable to a lower proportion of canonical marker genes being identified as top differential genes. We then grouped cell types into major cell categories according to the manual cell type annotations (Figure 2e, Supplementary Table 1). The agreement between GPT-4 and manual annotations is highest among cell categories that are more homogeneous (e.g., erythroid cells and adipocytes), and lowest among cell categories that are more heterogeneous (e.g., stromal cells).
+
+The low agreement between GPT-4 and manual annotations in some cell types does not necessarily imply that GPT-4 annotation is incorrect. For instance, cell types classified as stromal cells include fibroblasts and osteoblasts, which express type I collagen genes, as well as chondrocytes, which express type II collagen genes. For cells manually annotated as stromal cells, GPT-4 assigns cell type annotations with higher granularity (e.g., fibroblasts, osteoblasts, and chondrocytes), resulting in partial matches and a lower agreement. For cell types manually annotated as stromal cells, the type I collagen genes appear in the differential gene lists in 80% of cases annotated as fibroblast or osteoblast by GPT-4 and in 0% of cases annotated as chondrocyte by GPT-4 (Figure 2f). This agrees with prior knowledge and the pattern observed in cell types manually annotated as chondrocyte, fibroblast, and osteoblast (Figure 2f), suggesting that GPT-4 provides more accurate cell type annotations than manual annotations for stromal cells.
+
+We further tested the performance of GPT-4 when dealing with more complicated situations in real data analysis (Figure 1c). We first tested GPT-4’s ability to identify a cell cluster representing a mixture of cell types, which may occur when a cluster contains a large number of doublets or has low-resolution cell clustering. We generated simulated datasets by combining canonical markers from two distinct cell types in half of the instances and using canonical markers from a single cell type in the other half (Methods). GPT-4 discriminated between single and mixed cell types with an average accuracy of 94% (Figure 2g). We then tested GPT-4’s ability to identify new cell types with marker genes not documented by existing literature. We created simulation datasets using randomly selected genes as cell type markers in half of the cases and canonical markers from a single cell type in the other half (Methods). GPT-4 is able to differentiate known and unknown cell types with an average accuracy of 100% (Figure 2h). We also tested the reproducibility of GPT-4 annotations leveraging results in previous simulation studies (Methods). On average, GPT-4 generated identical annotations for the same cell type markers in 91.2% of cases (Figure 2i), showing a high level of reproducibility. In conclusion, GPT-4 exhibits robust performance across various scenarios encountered in real data analysis.
+
+In conclusion, our findings demonstrate a high level of agreement between cell type annotations generated by GPT-4 and by human experts. Remarkably, GPT-4 exhibits higher accuracy in annotating specific cell types. GPT-4 can be employed as a dependable tool for automated cell type annotation of single-cell RNA-seq data, substantially reducing the time and effort required for manual annotation.
+
+Methods
+
+Dataset collection
+For the HuBMAP Azimuth project, manually annotated cell types and their marker genes were downloaded from the Azimuth website (https://azimuth.hubmapconsortium.org/). Azimuth provides cell type annotations for each tissue at different granularity levels. We selected the level of granularity with the fewest number of cell types, provided that there were more than 10 cell types within that level.
+
+For HCA17, HCL19, and MCA18, manually annotated cell types and corresponding differential gene lists were downloaded directly from the original studies. Lists of marker genes through literature search and the corresponding cell types were
+downloaded from the HCA study\(^{17}\), and only cell types with at least 5 marker genes were used.
+
+Gene set preparation and GPT-4 prompts
+Before using GPT-4 to identify cell types, one needs to first prepare a list of top differential genes for each cell cluster. For example, one can use the following R code to extract gene lists of top 10 differential genes obtained from the standard Seurat pipeline. In the extracted results, each row is a list of differential genes for one cell cluster, separated by ','.
+
+# d is the differential gene table generated by Seurat ordered by p-values
+cat(tapply(d$gene,list(d$cluster),function(i) paste0(i[1:10],collapse=',')),sep='\n')
+
+The gene lists used in this study were prepared using customized code.
+
+GPT-4 was accessed by visiting the ChatGPT website (https://chat.openai.com/). The “Mar 23” version of GPT-4 was used for this study. The following words were pasted on top of the differential gene lists and used as the initial prompt for GPT-4. The word “prostate” in the following prompt was replaced with the appropriate tissue names when annotating cell types for each tissue.
+
+Identify cell types of human prostate cells using the following markers.
+Identify one cell type for each row. Only provide the cell type name.
+
+GPT-4 returned a list of cell type names for each query. The following prompt was used to increase the granularity of cell type annotations when needed.
+
+Be more specific
+
+To annotate cell clusters that could be a mixture of multiple cell types, the following words are added to the prompt.
+
+Some could be a mixture of multiple cell types.
+
+To annotate cell clusters that cannot be characterized by known cell type markers and are potentially new cell types, the following words are added to the prompt
+
+Some could be unknown cell types.
+
+Finally, the following prompt can be used to convert the list of cell type annotations generated by GPT-4 into R code that directly creates a vector of cell type names in R.
+
+Use "'','" to concatenate all results into a single sentence.
+Put "c('\" in front of the sentence and "\')" after the sentence
+
+Simulation studies and reproducibility
+To generate simulation datasets of mixed cell types, we used the canonical cell type markers through literature search of human breast cells. In each simulation iteration, ten mixed cell types were generated. The marker genes for each mixed cell type were created by combining the marker gene lists of two randomly selected cell types. Additionally, we incorporated the original cell type markers of ten randomly chosen cell types as negative controls of single cell types. This entire simulation process was repeated five times. Subsequently, GPT-4 was queried using these simulated marker gene lists, and its performance in differentiating between mixed and single cell types was assessed.
+
+To generate simulation datasets of unknown cell types, we compiled a list of all human genes using the Bioconductor org.Hs.eg.db package\(^{33}\). In each simulation iteration, ten simulated unknown cell types were generated. The marker genes for each unknown cell type were produced by combining ten randomly selected human genes. Additionally, we included the literature-based cell type markers of ten randomly chosen human breast cell types as negative controls of known cell types, similar to the previous simulation study. This entire simulation process was repeated five times. Subsequently, GPT-4 was queried using these simulated marker gene lists, and its performance in distinguishing between known and unknown cell types was assessed.
+
+We assessed the reproducibility of GPT-4 responses by leveraging the repeated querying of GPT-4 with identical marker gene lists of the same negative control cell types in both simulation studies. For each cell type, reproducibility is defined as the proportion of instances in which GPT-4 generates the most prevalent cell type annotation. For instance, in the case of vascular endothelial cells, GPT-4 produces "endothelial cells" 8 times and "blood vascular endothelial cells" once. Consequently, the most prevalent cell type annotation is "endothelial cells," and the reproducibility is calculated as \( \frac{8}{9} = 0.89 \).
+Acknowledgments
+Z.J. was supported by the National Institutes of Health under Award Number 1U54AG075936-01. The manuscript was polished by GPT-4.
+
+Author contributions
+All authors conceived the study, conducted the analysis, and wrote the manuscript.
+
+Competing interests
+All authors declare no competing interests.
+a
+
+single-cell RNA-seq (scRNA-seq) datasets
+standard processing pipeline (e.g., Seurat or Scanpy)
+cell clusters and differential genes
+human expert manual annotation
+canonical marker collection
+manual annotation
+GPT-4 automated annotation
+GPT-4 automated annotation
+Optional:
+fine tuning by human expert
+other automated cell type annotation software
+reference data collection
+building and running pipelines
+
+<table>
+  <tr>
+    <th>requires strong biology expertise</th>
+    <th>no biology expertise required</th>
+    <th>no biology expertise required</th>
+  </tr>
+  <tr>
+    <td>no coding expertise required</td>
+    <td>no coding expertise required</td>
+    <td>requires medium coding expertise</td>
+  </tr>
+  <tr>
+    <td>reference scRNA-seq not needed</td>
+    <td>reference scRNA-seq not needed</td>
+    <td>may need to collect reference scRNA-seq</td>
+  </tr>
+  <tr>
+    <td>significant effort required</td>
+    <td>minimum effort required</td>
+    <td>moderate effort required</td>
+  </tr>
+  <tr>
+    <td>fits into existing pipeline</td>
+    <td>fits into existing pipeline</td>
+    <td>standalone pipeline</td>
+  </tr>
+  <tr>
+    <td>tissue type not restricted</td>
+    <td>tissue type not restricted</td>
+    <td>tissue types restricted to reference data</td>
+  </tr>
+  <tr>
+    <td>allows adjusting granularity</td>
+    <td>allows adjusting granularity</td>
+    <td>single granularity level</td>
+  </tr>
+</table>
+
+b
+Identify cell types of human prostate cells using the following markers. Identify one cell type for each row. Only provide the cell type name.
+
+CR2, CD24, FAS, CXCR3, CD1c
+KLK3, KRT8, KLK2, MSMB, ACPP, KLK1, KLK4
+MMRN1, FLT4, RELN, CCL21, PROX1, LYVE1
+TPSAB1, FCER1A, TPSB2, KIT, CD69, HDC
+ACTA2, MYO1B, ACTA2, ANPEP, DES, MCAM, PDGFBR, CSPG4
+
+1. Dendritic cells
+2. Luminal epithelial cells
+3. Lymphatic endothelial cells
+4. Mast cells
+5. Pericytes
+
+Be more specific
+
+1. Myeloid Dendritic cells (mDCs)
+2. Prostate Secretory Luminal Epithelial cells
+3. Prostate Lymphatic Endothelial cells
+4. Prostate Tissue-resident Mast cells
+5. Prostate Vascular Pericytes
+
+c
+Identify cell types of human prostate cells using the following markers. Identify one cell type for each row. Only provide the cell type name. Some could be a mixture of multiple cell types. Some could be unknown cell types.
+
+KLK3, KRT8, KLK2, MSMB, ACPP, KLK1, KLK4
+MMRN1, FLT4, RELN, CCL21, PROX1, LYVE1
+CD88, IL7RC, CD3D, CD3E, COSL, ACTA2, MYO1B, ACTA2, ANPEP, PDGFBR, CSPG4
+DIX4A3BLOC05B5T19REMTND1P30LLOC160579682,YAGLN2ZNF698,ZNP677COILP1
+
+1. Prostate epithelial cells
+2. Lymphatic endothelial cells
+3. T-cell and smooth muscle cell mixture
+4. Unknown cell type
+
+Figure 1. a, Diagram comparing cell type annotations by human experts, GPT-4, and other automated methods. b, An example showing GPT-4 prompts and answers for annotating human prostate cells with increasing granularity. c, An example showing GPT-4 prompts and answers for annotating single cell types (first two cell types), mixed cell types (third cell type), and new cell types (fourth cell type).
+<table>
+  <tr>
+    <th>Dataset</th>
+    <th>Species</th>
+    <th>Number of tissues</th>
+    <th>Number of cell types</th>
+    <th>Gene list source</th>
+  </tr>
+  <tr>
+    <td>Azimuth</td>
+    <td>Human</td>
+    <td>11</td>
+    <td>276</td>
+    <td>Differential analysis</td>
+  </tr>
+  <tr>
+    <td>Human Cell Atlas (HCA)</td>
+    <td>Human</td>
+    <td>7</td>
+    <td>72</td>
+    <td>Differential analysis</td>
+  </tr>
+  <tr>
+    <td>Human Cell Landscape (HCL)</td>
+    <td>Human</td>
+    <td>60*</td>
+    <td>101</td>
+    <td>Differential analysis</td>
+  </tr>
+  <tr>
+    <td>literature (from HCA)</td>
+    <td>Human</td>
+    <td>7</td>
+    <td>30</td>
+    <td>Literature search</td>
+  </tr>
+  <tr>
+    <td>Mouse Cell Atlas (MCA)</td>
+    <td>Mouse</td>
+    <td>51*</td>
+    <td>65</td>
+    <td>Differential analysis</td>
+  </tr>
+</table>
+
+* Cell type annotations were done by aggregating across tissues in the original studies
+
+<table>
+  <tr>
+    <th>Manual annotation</th>
+    <th>GPT-4 answer</th>
+    <th>Agreement</th>
+  </tr>
+  <tr>
+    <td>Adipocyte</td>
+    <td>Adipocytes</td>
+    <td>Full</td>
+  </tr>
+  <tr>
+    <td>B cell_memory</td>
+    <td>B cells</td>
+    <td>Partial</td>
+  </tr>
+  <tr>
+    <td>Fibroblast</td>
+    <td>Fibroblasts</td>
+    <td>Full</td>
+  </tr>
+  <tr>
+    <td>Luminal Epithelial</td>
+    <td>Luminal epithelial cells</td>
+    <td>Full</td>
+  </tr>
+  <tr>
+    <td>Lymphatic Endothelial</td>
+    <td>Lymphatic endothelial</td>
+    <td>Full</td>
+  </tr>
+  <tr>
+    <td>Macrophage</td>
+    <td>Macrophages</td>
+    <td>Full</td>
+  </tr>
+  <tr>
+    <td>Mast Cell</td>
+    <td>Mast cells</td>
+    <td>Full</td>
+  </tr>
+  <tr>
+    <td>Pericyte</td>
+    <td>Pericytes</td>
+    <td>Full</td>
+  </tr>
+  <tr>
+    <td>Smooth Muscle</td>
+    <td>Smooth muscle cells</td>
+    <td>Full</td>
+  </tr>
+  <tr>
+    <td>T cell</td>
+    <td>T cells</td>
+    <td>Full</td>
+  </tr>
+  <tr>
+    <td>Vascular Endothelial</td>
+    <td>Endothelial cells</td>
+    <td>Partial</td>
+  </tr>
+</table>
+
+![A violin plot showing proportions of cell types across different datasets and tissues](page_184_613_495_312.png)
+
+![A bar chart showing agreement levels between manual and GPT-4 annotations](page_1012_613_495_312.png)
+
+Figure 2. Evaluation of cell type annotation by GPT-4. **a**, Datasets included in this study **b**, Agreement between original and GPT-4 annotations in identifying cell types of human prostate cells. **c**, Averaged agreement score (y-axis) and the number of top differential genes (x-axis) in HCA, HCL, and MCA datasets. **d**, Proportion of cell types with different levels of agreement in each study and tissue. Averaged agreement scores are shown as black dots. **e**, Proportion of cell types with different levels of agreement in each cell category. Averaged agreement scores are shown as black dots. **f**, Proportion of cell types that include type I collagen gene in the differential gene lists. The cell types are either classified as stromal cells by manual annotations and fibroblast, osteoblast, or chondrocyte by GPT-4 annotations, or classified as fibroblast, osteoblast, or chondrocyte by manual annotations. **g**, Proportion of cases where GPT-4 correctly identifies mixed and single cell types. Each dot represents one round of simulation. **h**, Proportion of cases where GPT-4 correctly identifies known and unknown cell types. Each dot represents one round of simulation. **i**, Reproducibility of GPT-4 annotations. Each dot represents one cell type.
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+Supplementary Files
+
+This is a list of supplementary files associated with this preprint. Click to download.
+
+• supptable1.csv

02624773f6e6ce56158b53f0fcddcdef4027c464f514126d8dae690687431871/preprint/preprint.md

@@ -0,0 +1,413 @@
+Sphingosine d18:1 Promotes Nonalcoholic Steatohepatitis by Inhibiting Macrophage HIF-2α
+
+Changtao Jiang
+jiangchangtao@bjmu.edu.cn
+
+Department of Physiology and Pathophysiology, School of Basic Medical Sciences, Center for Reproductive Medicine, Peking University   https://orcid.org/0000-0002-5206-2372
+
+Jialin Xia
+School of Basic Medical Sciences, Center for Reproductive Medicine, Peking University
+
+Hong Chen
+School of Basic Medical Sciences, Center for Reproductive Medicine, Peking University
+
+Xiaoxiao Wang
+Peking University People’s Hospital
+
+Weixuan Chen
+School of Basic Medical Sciences, Center for Reproductive Medicine, Peking University
+
+Jun Lin
+School of Basic Medical Sciences, Center for Reproductive Medicine, Peking University
+
+Feng Xu
+School of Basic Medical Sciences, Center for Reproductive Medicine, Peking University
+
+Qixing Nie
+School of Basic Medical Sciences, Center for Reproductive Medicine, Peking University
+
+Chuan Ye
+School of Basic Medical Sciences, Center for Reproductive Medicine, Peking University
+
+Bitao Zhong
+School of Basic Medical Sciences, Center for Reproductive Medicine, Peking University
+
+Min Zhao
+School of Basic Medical Sciences, Center for Reproductive Medicine, Peking University
+
+Chuyu Yun
+School of Basic Medical Sciences, Peking University
+
+Guangyi Zeng
+School of Basic Medical Sciences, Center for Reproductive Medicine, Peking University
+
+Sen Yan
+School of Basic Medical Sciences, Center for Reproductive Medicine, Peking University
+
+Xuemei Wang
+School of Basic Medical Sciences, Center for Reproductive Medicine, Peking University
+Lulu Sun
+School of Basic Medical Sciences, Center for Reproductive Medicine, Peking University
+Feng Liu
+Peking University People’s Hospital
+Huiying Rao
+Peking University People’s Hospital
+Yanli Pang
+Center for Reproductive Medicine, Department of Obstetrics and Gynecology, Peking University Third Hospital   https://orcid.org/0000-0003-1967-2416
+
+Article
+
+Keywords: NASH, macrophage, HIF-2α, sphingosine
+
+Posted Date: July 11th, 2023
+
+DOI: https://doi.org/10.21203/rs.3.rs-3092076/v1
+
+License: © This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License
+
+Additional Declarations: There is NO Competing Interest.
+
+Version of Record: A version of this preprint was published at Nature Communications on June 4th, 2024. See the published version at https://doi.org/10.1038/s41467-024-48954-2.
+Sphingosine d18:1 Promotes Nonalcoholic Steatohepatitis by Inhibiting Macrophage HIF-2α
+
+Jialin Xia1,2,3,7, Hong Chen1,4,7, Xiaoxiao Wang6,7, Weixuan Chen4, Jun Lin1,2,3, Feng Xu1,2,3, Qixing Nie1,2,3, Chuan Ye1,2,3, Bitao Zhong1, Min Zhao4, Chuyu Yun4, Guangyi Zeng1,2,3, Sen Yan4, Xuemei Wang1,2,3, Lulu Sun5, Feng Liu6, Huiying Rao6,*, Changtao Jiang1,2,3,* and Yanli Pang1,4,*
+
+1Department of Physiology and Pathophysiology, School of Basic Medical Sciences, Center for Reproductive Medicine, Third Hospital, Peking University, Beijing, China
+
+2Center of Basic Medical Research, Institute of Medical Innovation and Research, Peking University Third Hospital, Beijing, China.
+
+3Center for Obesity and Metabolic Disease Research, School of Basic Medical Sciences, Peking University, Beijing, China.
+
+4State Key Laboratory of Female Fertility Promote, Center for Reproductive Medicine, Department of Obstetrics and Gynecology, Peking University Third Hospital, Beijing, China.
+
+5Department of Endocrinology and Metabolism, Peking University Third Hospital, Beijing, China.
+
+6Peking University People’s Hospital, Peking University Hepatology Institute, Beijing Key Laboratory of Hepatitis C and Immunotherapy for Liver Diseases, Beijing International Cooperation Base for Science and Technology on NAFLD Diagnosis, Beijing, China.
+
+7These authors contribute equally.
+
+*Correspondence: yanlipang@bjmu.edu.cn (Yanli Pang), jiangchangtao@bjmu.edu.cn (Changtao Jiang), raohuiying@pkuph.edu.cn (Huiying Rao)
+Conflict of interest
+
+The authors declare no conflicts of interest that pertain to this work.
+
+Financial support
+
+This work was supported by the National Natural Science Foundation of China (No. 82130022, 31925021, 82022028, 82288102, 91857115, 81921001, and 92149306), and the National Key Research of Development Program of China (no. 2018YFA0800700 and 2022YFA0806400).
+
+Author contributions
+
+Y.P, C.J. and J.X. conceptualized and designed the study. J.X, H.C., X.W., F.X., Q.N., C.Y., B.Z., M.Z., CY.Y., G.Z., S.Y. and F.L. performed the experiments and analyzed the data. Y.P., C.J. and H.R supervised the study. J.X. and H.C. wrote the manuscript with input from all authors. J.L., XM.W. and L.S. revised the manuscript. J.X, H.C. and X.W. contributed equally to this work. All authors edited the manuscript and approved the final manuscript.
+Abstract
+
+Non-alcoholic steatohepatitis (NASH) is a severe type of the non-alcoholic fatty liver disease (NAFLD). NASH is a growing global health concern due to its increasing morbidity, lack of well-defined biomarkers and lack of clinically effective treatments. Using metabolomic analysis, the most significantly changed active lipid sphingosine d18:1 [So(d18:1)] was selected from NASH patients. So(d18:1) inhibits macrophage HIF-2α as a direct inhibitor and promotes the activation of NLRP3 inflammasome. Macrophage-specific HIF-2α knockout and overexpression mice verified the effect of HIF-2α on NASH progression. Importantly, the HIF-2α stabilizer FG-4592 alleviated liver inflammation and fibrosis in NASH, which indicated that macrophage HIF-2α was a potential drug target for NASH treatment. Overall, this study confirms that So(d18:1) promotes NASH and clarifies that So(d18:1) inhibits the transcriptional activity of HIF-2α in liver macrophages by suppressing the interaction of HIF-2α with ARNT, suggesting that macrophage HIF-2α may be a new target for the treatment of NASH.
+
+Key words
+
+NASH, macrophage, HIF-2α, sphingosine
+
+Introduction
+
+With lifestyle changes, nonalcoholic fatty liver disease (NAFLD) has become a major chronic disease in contemporary society[1]. NAFLD is a chronic metabolic disease characterized by excessive accumulation of fat in hepatocytes. NAFLD can be divided into simple fatty liver (NAFL) and nonalcoholic steatohepatitis (NASH)[2].
+Chronic liver injury in NASH significantly increases the risk of end-stage liver diseases (such as cirrhosis and liver cancer). However, there is no effective drug for NASH in clinical practice[3]. Therefore, clarifying the key molecular mechanism of the occurrence and development of NASH will help to develop new strategies for anti-NASH treatment.
+
+The classical theory of NASH pathogenesis is that NASH is caused by the excessive accumulation of lipids in hepatocytes. Then, extreme oxidative stress and inflammation further induce hepatocyte death and the development of inflammation and fibrosis[4]. Sphingolipids are lipids with high biological activity and are one of the main factors affecting the progression of NASH. Sphingolipids mainly include ceramide and sphingosine-1-phosphate (S1P), and sphingosine is an intermediate product between them[5]. Previous studies have found changes in ceramide and S1P levels in NASH patients[6]. However, they both failed to act as sensitive biomarkers to guide disease diagnosis in NASH because of their widespread variation in many other early-stage NAFLD patients. Sphingosine has not only been found to vary in NAFL[7, 8] but has even been found to be useful as a biomarker to predict cirrhosis[9].
+
+Here, we found that So(d18:1) increases significantly in patients with NASH by metabolomics profiling analysis. So(d18:1) promotes liver inflammation and fibrosis in the NASH model. RNA-seq data revealed that So(d18:1) inhibits HIF-2α expression. Macrophage-specific knockout or overexpression of HIF-2α has been used to clarify the role of macrophage HIF-2α in NASH development. Mechanistically, So(d18:1) inhibits macrophage HIF-2α by inhibiting its combination with ARNT and then
+promotes the excessive activation of the macrophage NLRP3 inflammasome, increasing the secretion of inflammatory factors. Notably, we found that the pharmacological activation of macrophage HIF-2\( \alpha \) by FG-4592, a HIF prolyl hydroxylase inhibitor that is approved for the treatment of anaemia in China, had preventive effects on NASH in mice. This work suggests that macrophage HIF-2\( \alpha \) is a novel target for the treatment of NASH.
+
+Results
+
+1. Disturbances in sphingolipid metabolism in NASH patients
+
+In the Chinese patient population, we employed a metabolomics screen of NASH patients and healthy volunteers (Table S1). The results showed that the changes in the sphingolipid pathway are the most concentrated, significant and dramatic compared to other lipids that are considered to change routinely (Figure 1A). After that we further examined the whole sphingolipidome using targeted metabolomics (Figure 1B). Principal component analysis (PCA) showed a clear separation between the healthy volunteers and NASH patients (Figure 1C). The VIP score indicated a significant increase in the levels of several sphingolipids, especially So(d18:1) (Figure 1D).
+
+We fed the mice with CDAA-HFD for 8 weeks to establish NASH mice model. Serum So(d18:1) concentrations was assayed in NASH model mice, and the trend of increasing serum So(d18:1) concentrations in mice was exactly the same as the trend of increasing ALT and AST levels (Figure S1H-J). In human cohort, So(d18:1) accumulated largely in serum of NASH patients (Figure S1D) and increased as the
+disease progresses (Figure S1E). Moreover, the concentration of So(d18:1) was positively correlated with serum ALT, AST levels and Fibrosacn index (Figure 1E-1G). These results suggested that So(d18:1) concentrations may be closely related to NASH progression. However, So(d18:1) relative concentration in whole liver tissue didn’t show any change between healthy and NASH mice (Figure S1K), that suggests the origin of So(d18:1) may not from hepatocytes.
+
+In our sphingolipidome results, the upstream and downstream metabolites of sphingosine, ceramide and S1P, were also altered in content. In our previous study, we had found that ceramide was enriched in NASH patients similarly[6]. But ceramides did not increase more with disease progression (Figure S1A). S1p and the other type of sphingosines also failed to show any growth trends during the progression of NASH (Figure S1B-C). These results further demonstrated the unique indicative role of So(d18:1) in the progression of NASH.
+
+Hepatic steatosis and lobular inflammation are two important features of the NASH. We analysed the relationship between So(d18:1) levels and these two aspects. There was no significant increase in the So(d18:1) level as hepatic steatosis progressed (Figure S1F). However, the So(d18:1) concentration gradually increased with the aggravation of lobular inflammation (Figure S1G), suggesting that the function of So(d18:1) may be related to lobular inflammation.
+
+2. So(d18:1) aggravates inflammation and fibrosis in NASH
+
+To test whether So(d18:1) is involved in the progression of NASH, CDAA-HFD-fed mice accepted a simultaneous intraperitoneal injection of So(d18:1). There was no
+significant difference in the liver weight or body weight between the two groups of mice (Figure 2A-B and S2A). The levels of ALT and AST in the serum of mice injected with So(d18:1) were significantly higher than those in control mice (Figure 2C-D), which suggests that So(d18:1) exacerbated liver damage in mice. While there were no differences in liver triglyceride (TG), serum TG and serum non-esterified fatty acid (NEFA) levels, there was also no difference in liver and serum cholesterol (CE) levels (Figure S2B-F). For a clearer image of the liver damage in mice, we made pathological sections and performed H&E staining and Sirius red staining. The pathological sections showed that So(d18:1) treatment increased the fibrosis, lobular inflammation and NASs but did not affect the histology score of hepatic steatosis (Figures 2E–2J). Consistently, the mRNA expression of inflammation genes and fibrosis genes was significantly upregulated in the liver of the So(d18:1) group compared with that of the vehicle group (Figure 2K-L), while the lipid metabolism genes were mostly not different between the two groups (Figure S2G). Collectively, these results suggest that So(d18:1) can exacerbate lobular inflammation and fibrosis in the livers of NASH mice.
+
+3. So(d18:1) inhibits HIF-2α transcription function in liver macrophages
+
+So(d18:1) can exacerbate lobular inflammation in the liver of NASH, suggesting that it alters the immune status of the liver, so we focused on immune cells for in-depth study. To confirm the changes of various immune cells during the development of NASH, a set of public single-cell RNA-sequencing data from the livers of NASH mice was located and analysed[10]. The results showed an increase of all kinds of immune cells in the livers of NASH mice. However, the largest proportion of these cells were
+macrophages and monocytes. Importantly, they were recruited to the livers much earlier than other immune cells (Figure S3A-B). We therefore wanted to see whether So(d18:1) would also cause changes in macrophage proportion. We administered So(d18:1) intraperitoneally to mice for 1 week, results showed that So(d18:1) increased the proportion of liver macrophages among all immune cells (Figure S3C, 3A-B).
+
+To search for the mechanisms by which So(d18:1) promotes macrophages activation, we treated mouse bone-marrow derived macrophages (BMDM) with So(d18:1) or control vehicle under inflammatory stimulation and performed RNA sequencing to explore the changed genes pathways. GO:BP pathway enrichment showed that hypoxia-related pathways were changed significantly between the control and So(d18:1) groups (Figure 3C). There are two transcription factors that play a major role in the hypoxia-related signalling pathway, HIF-1\( \alpha \) and HIF-2\( \alpha \). We further targeted the signalling pathways regulated by these two transcription factors for enrichment analysis. BP pathway enrichment revealed transcriptional changes in the HIF-2\( \alpha \)-regulated signalling pathway (Figure 3D), while HIF-1\( \alpha \) signalling pathway was not changed (Figure S3D).
+
+To validate the RNA-seq results, we treated mouse BMDMs with So(d18:1). The results showed that the transcription levels of the *Hif2a* gene were not changed, but its downstream genes *Arg1*, *Vegf*, *Spint*, *Depdc7* and *Il10* decreased after So(d18:1) treatment (Figure 3E). We also detected *Hif1a* and its downstream genes and their expression levels were unchanged (Figure S3E). As for the protein levels of HIF-2\( \alpha \), the results showed that So(d18:1) treatment could significantly inhibit the protein
+expression of HIF-2α (Figure 3F).
+
+Intrahepatic macrophages IL-1β and IL-18 secretion due to NLRP3 inflammasome activation is an important mechanism that promotes the progression of NASH[11]. Our previous study also found that macrophage HIF-2α could suppress NLRP3 inflammasome activation by inhibiting CPT1A[12]. Results showed that So(d18:1) administration could increase NLRP3 inflammasome assembly therefore increase Caspase-1 cleavage, while HIF-2α overexpression could quell the stimulation caused by So(d18:1) (Figure 3G). IL-1β and IL-18 secretion levels also confirmed that So(d18:1) promoted NLRP3 inflammasome activation, but not in HIF-2α overexpressing macrophages (Figure 3H-I).
+
+This may be the cellular mechanism by which So(d18:1) activates macrophages to promote hepatic inflammation in NASH. And the above mechanism was regulated by HIF-2α.
+
+4. Macrophage-specific HIF-2α deletion aggravates inflammation and fibrosis in NASH
+
+To investigate whether HIF-2α-mediated activation of the NLRP3 inflammasome can influence NASH disease progression, we fed Hif2afl/fl and Hif2aALysm mice a GAN diet for 24 weeks to compare the severity of inflammation and fibrosis in the liver. There was no significant difference in body weight between the two groups of mice (Figure S4A). Liver weight and the ratio of liver weight to body weight were significantly increased in Hif2aALysm mice compared with Hif2afl/fl mice (Figures 4A–B). Moreover, the levels of ALT and AST in the serum of Hif2aALysm mice were
+significantly higher than those in \( Hif2a^{fl/fl} \) mice, suggesting that knockdown of \( Hif2a \) exacerbates the disease symptoms of NASH (Figure 4C-D). Next, we examined the changes in lipids in the liver tissue and plasma of the two groups of mice. The results revealed that the concentrations of serum TG, CE, and NEFAs and hepatic TG and CE were not significantly different between \( Hif2a^{fl/fl} \) mice and \( Hif2a^{\Delta Lysm} \) mice (Figure S4C-F). This result suggests that knockdown of macrophage \( Hif2a \) does not affect total lipid metabolism or consequently exacerbate lipid accumulation in the liver.
+
+To further determine the changes in the levels of inflammation and fibrosis within the mouse liver to determine the progression of NASH, pathological sections were made from the livers of the two groups of mice to observe the extent of liver injury in the mice (Figure 4E). The degree of hepatic steatosis was consistent between the two groups of mice (Figure 4G), and there was no significant difference in the ballooning score (Figure 4I). However, mice in the \( Hif2a^{\Delta Lysm} \) group had more foci of inflammation in the liver, with a large number of mononuclear macrophages diffusely distributed and a significantly higher inflammation score in the liver lobules than in the \( Hif2a^{fl/fl} \) group (Figure 4H). The sections were also stained with Sirius red (Figure 4E), and the fibrosis area was quantified to show that the \( Hif2a^{\Delta Lysm} \) group had a significantly greater fibrosis area than that of the \( Hif2a^{fl/fl} \) group (Figure 4F). These results demonstrate that macrophage \( Hif2a \) knockdown can indeed significantly exacerbate NASH symptoms and promote inflammatory activation and fibrosis formation.
+
+Consistently, the mRNA expression of inflammation genes and fibrosis genes was significantly upregulated in the livers of \( Hif2a^{\Delta Lysm} \) mice compared with that of \( Hif2a^{fl/fl} \)
+mice (Figure 4K-L), while the lipid metabolism genes were not different between the two groups (Figure S4G). Collectively, these data showed that genetic disruption of macrophage-specific HIF-2α accelerated hepatic inflammation and fibrosis but did not affect hepatic steatosis.
+
+5. Macrophage-specific HIF-2α overexpression alleviated inflammation and fibrosis in NASH
+
+To further verify the role of macrophage HIF-2α overexpression in NASH, Hif2a+/+ and LysMHif2aLSL/LSL mice were fed a GAN diet for 24 weeks. There was no significant difference in body weight between the two groups of mice (Figure S5A). The liver weight and the ratio of liver weight to body weight tended to decrease in LysMHif2aLSL/LSL mice compared with Hif2a+/+ mice (Figures 5A–B). The levels of ALT and AST in the serum were significantly lower in LysMHif2aLSL/LSL mice than in Hif2a+/+ mice (Figures 5C–5D), suggesting that Hif2a overexpression can protect the liver and reduce liver injury. We also measured TG, total CE and NEFA levels in the liver and plasma to investigate whether macrophage-specific Hif2a overexpression could reduce fat accumulation in the liver, but there were no differences between the two groups in any of these parameters (Figure S5B-F).
+
+The liver tissues of Hif2a+/+ and LysMHif2aLSL/LSL mice were also paraffin sectioned and stained with H&E and Sirius red. The H&E staining results showed that there was no significant difference in the steatosis scores between the two groups (Figure 5G). However, the LysMHif2aLSL/LSL group mice had fewer inflammatory foci in the liver, so their hepatic lobular inflammation scores were significantly lower than those of the
+Hif2α+/+ group mice (Figure 5H), their hepatocyte ballooning scores were also significantly lower (Figure 5I), and the final calculated NAS of the LysMHi2αLSL/LSL group mice was significantly lower than that of the Hif2α+/+ group mice (Figure 5J). We next examined Sirius red-stained sections, and it was evident that intrahepatic fibrosis production was reduced in the LysMHi2αLSL/LSL group of mice (Figure 5E-F). The above results suggest that macrophage Hif2α overexpression may inhibit macrophage activation and thus stellate cell activation, reducing fibrogenesis and protecting the liver from damage during NASH.
+
+Consistently, the mRNA expression of inflammation-related genes and fibrosis-related genes was significantly downregulated in the livers of LysMHi2αLSL/LSL mice compared with Hif2α+/+ mice (Figure 5K-L), while the lipid metabolism-related genes were not different between the two groups (Figure S5G). Collectively, these data showed that macrophage-specific HIF-2α overexpression ameliorated hepatic inflammation and fibrosis but did not affect hepatic steatosis.
+
+6. So(d18:1) reduces the transcriptional activity of HIF-2α
+
+In previous results, we have verified that So(d18:1) could promote NLRP3 inflammasome activation in macrophages and identified HIF-2α as a key transcription factor by which So(d18:1) alters the inflammatory state of macrophages. Therefore, how does the increased So(d18:1) in NASH patients affect HIF-2α protein function in macrophages? We conducted a more in-depth mechanistic study to address this question. First, to determine whether So(d18:1) could inhibit HIF-2α transcriptional activity, we constructed a HIF response element (HRE)-based luciferase reporter assay and treated
+the cells with control solvent, So(d18:1) and HIF-2α-specific inhibitor PT2385 as positive control. Fluorescein detection showed that So(d18:1) could significantly inhibit the transcriptional activity of HIF-2α (Figure 6A). The transcriptional action of HIF-2α requires binding to the ARNT subunit. Thus, we utilized a mammalian two-hybrid system that could further verified that So(d18:1) repressed the transcriptional function of HIF-2α by inhibiting the binding of ARNT (Figure 6B). In addition, coimmunoprecipitation was performed to determine that So(d18:1) directly disrupted the direct binding of HIF-2α to ARNT (Figure 6C).
+
+HIF-2α has a hydrophobic pocket PAS-B domain to bind with ARNT[13]. Structural prediction by docking revealed some potential for So(d18:1) to fill into this hydrophobic pocket (Figure 6D). So, we constructed a HIF-2α plasmid with two proven missense mutations in the pocket which disabled other molecules to bind with HIF-2α. Luciferase reporter system was performed, and the results showed that So(d18:1) could normally inhibit the binding of wild-type HIF-2α to ARNT but not that of mutant HIF-2α to ARNT (Figure 6E). From these results, we learned that So(d18:1) may fill into the hydrophobic pocket of HIF-2α and thereby inhibit the binding of HIF-2α to ARNT, which impedes HIF-2α entry into the nucleus for transcriptional regulation. HIF-2α that remains in the cytoplasm is very easily hydrolysed and therefore protein levels are reduced. This finding also explained why So(d18:1) can only change the protein expression level of HIF-2α but not the mRNA expression level.
+
+HIF-2α regulates metabolism reprogramming by binding to the rHRE region on the Cpt1a promoter[12]. We therefore transfected a luciferase reporter gene plasmid
+containing a Cpt1a rHRE region with a HIF-2α plasmid or empty plasmid into cells, treated with control solvent or So(d18:1) and observed the fluorescence activity ratio. The results showed that in the vehicle group, the fluorescence values of HIF-2α™-transfected cells were lower than those with empty plasmid, indicating that overexpression of HIF-2α inhibited the transcription of Cpt1a rHRE-linked luciferase. In contrast, the overexpression of HIF-2α in the So(d18:1) group did not affect the transcription of Cpt1a rHRE-linked luciferase, as it was unable to bind to ARNT and localize to the rHRE region in the nucleus, so the fluorescence values of HIF-2α™ plasmid-transfected cells were similar to the fluorescence values of the empty plasmid group (Figure 6F).
+
+The above results suggest that So(d18:1) could inhibits the binding of HIF-2α to ARNT, thus promoting NLRP3 inflammasome activation and promotes NASH disease progression. These results also suggest to us the possibility that lipids bind directly to transcription factors and regulate their functions, showing us new mechanisms by which lipids influence cellular metabolism.
+
+7. Stabilization of HIF-2α expression in macrophages significantly alleviated inflammation and fibrosis in NASH
+
+We further investigated the therapeutic effect of the specific HIF-2α agonist FG-4592 in treating NASH. SPF mice were given a CDAA-HFD diet for 8 weeks and were administered vehicle or FG-4592 (25 mg/kg) by intraperitoneal injection. At the end of the treatment, there was no significant difference in body weight between the two groups of mice (Figure S6A), but there was a significant reduction in liver weight
+(Figure 7A), as well as a significant reduction in the calculated liver weight/body weight ratio (Figure 7B). Measurement of the blood levels of ALT and AST showed significant decreases in both transaminase levels suggestive of liver injury (Figure 7C-D). To assess whether FG-4592 could improve intrahepatic fat accumulation, we also measured intrahepatic TG (Figure S6B) and blood TG levels (Figure S6C), neither of which showed a significant change. Total intrahepatic CE (Figure S6D) and total plasma CE levels (Figure S6E) were also tested, and there was no significant improvement in either of these results. With respect to NEFAs in the blood, there was also no improvement after FG-4592 injection (Figure S6F). The above results suggest that although FG-4592 may improve liver injury, it does not improve lipid accumulation in the liver.
+
+To further observe liver injury in mice, we made paraffin sections of liver tissue from both groups and stained them with H&E and Sirius red. In the H&E-stained sections, we observed that the degree of steatosis in the livers of the two groups of mice was the same, and therefore, there was no difference in the steatosis score (Figure 7G). However, there were significantly fewer foci of inflammation than in the vehicle group, and therefore, the score of the lobular inflammation was lower than that of the vehicle group (Figure 7H). The final calculation of the NASs also showed that FG-4592 injection reduced the symptoms of NASH in mice (Figure 7J). In Sirius red-stained sections, fibrosis was significantly reduced in the FG-4592-injected group, and this result could be better visualized by counting the fibrosis area proportion (Figure 7E-F).
+
+After FG-4592 injection, inflammation-related genes were significantly
+downregulated in the mouse liver (Figure 7K). Additionally, genes related to fibrosis were significantly reduced (Figure 7L). However, genes related to fatty acid uptake and de novo synthesis were slightly changed, with only the expression level of Fasn being reduced (Figure S6G).
+
+In conclusion, FG-4592 injection can reduce liver fibrosis and improve NASH symptoms by reducing intrahepatic inflammation.
+
+Discussion
+
+Chronic liver injury caused by NASH can significantly increase the risk of end-stage liver diseases. However, there is currently no effective drug to treat NASH in the clinic. Here, we found that the abundance of So(d18:1) in patients with NASH was significantly increased through metabolomics analysis. So(d18:1) significantly aggravated hepatic lobular inflammation and fibrosis in the livers of NASH model mice. Mechanistically, So(d18:1) inhibits macrophage HIF-2α binding with ARNT, thus promoting overactivation of the macrophage NLRP3 inflammasome and increasing the secretion of inflammatory factors. This mechanism reveals that macrophage HIF-2α may be a new target for the treatment of NASH. Based on this finding, we tried to use the HIF-2α stabilizer FG-4592 to improve NASH, and the results showed that FG-4592 alleviated inflammation and fibrosis in NASH.
+
+Liver steatosis is an early event of NASH. A large amount of lipid accumulation in hepatocytes leads to excessive oxidative stress in hepatocytes, which further induces hepatocyte death, thereby activating inflammation and fibrosis in hepatic lobules[4]. In NASH patients, we have seen several significant changes in sphingolipids, such as Cer
+(d18:1/16:0), Cer (d18:1/14:0), Cer (d18:1/20:0), Cer (d18:1/22:0), Cer (d18:1/18:0) and Cer (d18:1/18:0). Their abundances significantly increased in the serum of NASH patients. Our previous work found that the excessive accumulation of nicotine in the intestine can promote the secretion of intestinal ceramide by upregulating the phosphorylation level of SMPD3, thus promoting the progression of NAFLD to NASH[6]. In addition, knocking out alkaline ceramidase 3 (Acer3), which is upregulated in NASH, increases liver Cer (d18:1/18:0) in mice fed a Western diet, reduces oxidative stress and reduces the severity of NASH[14]. S1P released from apoptotic hepatocytes damaged by lipids induces the expression of Trem2 in liver macrophages through S1PR, thereby limiting the occurrence and development of chronic inflammation in NAFLD[15]. These studies suggest that sphingolipid metabolism may play an important role in the pathogenesis of NAFLD. However, none of changes in these sphingolipids perfectly fit the trend of NASH disease exacerbation and indicate the severity of NASH. But So(d18:1) closely related to the disease progression of NASH and was completely consistent with the trends of the changes in the ALT and AST levels representing liver injury. Thus, So(d18:1) is a better indicator of the progression of NASH.
+
+In addition, although sphingosine has not been deeply discussed in previous studies, some studies have found sphingosine in metabolomics[7, 8], and they have even found that So(d18:1) in stool can be used as a biomarker to predict cirrhosis[9]. However, So(d18:1) is usually regarded just as an intermediate product of metabolism between ceramide and S1P, and in-depth mechanistic and functional research is lacking. In this study, we found that So(d18:1) can exist stably in cells at a certain concentration and
+will not be rapidly converted into ceramide or S1P. Our results showed that So(d18:1) can not only promote overactivation of the NLRP3 inflammasome in BMDMs but can also aggravate liver inflammation and fibrosis and promote the progression of NASH in animals.
+
+Regarding the origin of the increased circulating So(d18:1) in NASH patients, we examined the amount of So(d18:1) in the whole liver tissue of NASH-modelled mice and found that the rise in total So(d18:1) in liver tissue was not significant, so we inferred that the increased circulating So(d18:1) was not produced by the liver. The metabolism of ceramide is also known to occur in the gut and adipose tissue, so we will subsequently examine the levels of So(d18:1) in the gut and adipose tissue of NASH-modelled mice at different time points to further investigate the source of the increased circulating So(d18:1). There are also results showed that increased levels of So(d18:1) in the faeces of NASH-cirrhotic patients, which may serve as one of the biomarkers for predicting NASH-cirrhosis[16]. This also suggests that the role of microbiota in sphingolipid metabolism should not be underestimated.
+
+HIF is a heterodimer made up of an oxygen-sensitive \( \alpha \) subunit and a constitutively expressed \( \beta \) subunit (ARNT). Under normoxic conditions, HIF-\( \alpha \) is rapidly hydroxylated and degraded by prolyl hydroxylase (PHD). In contrast, under hypoxia, the activity of prolyl hydroxylase was inhibited, and the HIF protein was stable. HIF-2\( \alpha \) accumulates and translocates to the nucleus and combines with ARNT to form an active transcription factor complex[17]. In NASH, HIF-1\( \alpha \) in macrophages induced by palmitic acid damages autophagic flux and increases IL-1\( \beta \) production, aggravating
+liver injury induced by an MCD diet[18]. Digoxin inhibits the transcription of the HIF-1a pathway by directly binding to pyruvate kinase M2, thus changing the chromatin structure and reducing NASH[19]. However, the role of HIF-2α in macrophages in the progression of NASH is still unclear. In this article we have validated the role of HIF-2α in NASH progression using mice with macrophage-specific knockdown or overexpression of HIF-2α. Identified that HIF-2α as a potential target for intervention in NASH.
+
+Rosalistat (FG-4592) is a mature small-molecule drug that is mainly used to treat chronic kidney disease and anaemia, but its role in metabolic diseases has not yet entered clinical trials. In our previous studies, FG-4592 injection was used to improve insulin resistance[20]. In this study, FG-4592 injection significantly reduced the levels of ALT and AST in the livers of mice, suggesting that the degree of liver injury was reduced. In addition, the expression of genes related to inflammation and fibrosis also decreased. The above results showed that FG-4592 injection can reduce the incidence of NASH. However, many articles have also clarified that the overexpression of HIF-2α in liver cells plays a worsening role in insulin resistance and fatty liver[21, 22]. Continuous activation of hepatocyte HIF-2α can damage the transcription of fatty acid β-oxidation-related genes, leading to fat accumulation in the liver[22, 23]. Hepatocyte HIF-2α stimulated the production of histidine-rich glycoprotein (HRGP) to activate macrophages to polarize to the M1 type, thus causing liver damage. In our study, the administration of FG-4592 can block the response ability of proinflammatory macrophages, thus playing a protective role. After FG-4592 reaches the liver, it may
+indeed lead to the accumulation of lipids in the liver, but it also ensures that hepatocytes damaged by lipotoxicity will not cause further macrophage inflammation. Therefore, from the overall animal experimental data, the administration of FG-4592 still protects the liver from damage in NASH disease. In addition, FG-4592 can also act on other targets, such as adipose tissue HIF-2\( \alpha \), and promote the production of erythropoietin\(^{[24, 25]}\), which will delay or even improve the disease in many chronic metabolic diseases. Of course, we are also actively seeking ways to improve FG-4592 drug delivery methods, such as using liposome encapsulation to minimize the side effects induced by FG-4592 activation of hepatocyte HIF-2\( \alpha \).
+
+In summary, our study found that the active sphingolipid So(d18:1) has good indicating ability in patients with NASH and that it can bind to HIF-2\( \alpha \) to promote the activation of the NLRP3 inflammasome in macrophages and aggravate liver inflammation and fibrosis in NASH model mice. Macrophage-specific knockout or overexpression of HIF-2\( \alpha \) showed that macrophage HIF-2\( \alpha \) can reduce liver injury and can reduce intrahepatic inflammation and fibrosis. These results not only provide us with a possibility that So(d18:1), a long-chain lipid, binding transcription factor to regulate cellular immune metabolism, but also suggest that the proinflammatory function of So(d18:1) in NASH cannot be ignored. Finally, we used FG-4592 to improve inflammation and fibrosis in NASH. This study provides new targets and potential therapeutic strategies for NASH.
+
+**Conclusions**
+
+Starting from the metabolomics of NASH patients, this study identified So(d18:1),
+which could activate the liver macrophage inflammasome, and found that it could inhibit the binding of the transcription factor HIF-2α with ARNT. We clarified the role of HIF-2α in the development of NASH and explored the role of FG-4592, a stabilizer of HIF-2α, in combating NASH disease progression. The results suggest that HIF-2α is a possible new therapeutic target for the treatment of NASH.
+
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+Figure
+
+![Clustering heatmap of metabolic pathway (A), targeted metabonomic detection of sphingolipids (B), PLS-DA analysis of sphingolipids in serum of patients (C), VIP scores plot (D), scatter plots showing correlations between So(d18:1) concentration and ALT (E), AST (F), Fibroscan (G)](page_124_153_1207_1642.png)
+
+Figure 1 Metabolomic analysis revealed changes of sphingosine in NASH patients
+
+Metabolic analysis of serum samples collected from NASH patients (n=20) and healthy control (n=20). A, clustering heatmap of metabolic pathway. B, targeted metabonomic detection of sphingolipids. C, PLS-DA analysis of sphingolipids in serum of patients.
+D, VIP score plot of the difference sphingolipids between the two groups. E-G, correlative analysis of So(d18:1) concentration in serum with ALT (E), AST (F) and Fibroscan index (G). Correlations between variables were assessed by linear regression analysis. Linear correction index R square and P values were calculated. Data are the means ± s.e.m. One-way ANOVA with Tukey’s post hoc test.
+Figure 2 Sphingosine 18:1 aggravates NASH.
+
+CDAA-HFD-fed mice were treated with vehicle or sphingosine 18:1 for 8 weeks (n=6 mice/group). A, liver weights. B, ratios of liver mass to body mass. C, serum ALT. D, serum AST. E, representative H&E (up), and Sirius Red (down) staining of liver sections. The circles marked the inflammation foci. n=3 mice per group, 3 images per
+mouse. Scale bar is 100 μm. F, the percentage of fibrosis area. G-J, Histology scores of hepatic steatosis (G), lobular inflammation (H), ballooning (I), and NAFLD activity (J). K-L, relative mRNA levels of genes related to hepatic inflammation (K) and fibrosis (L).
+
+Data are the means ± s.e.m. A-D, F, J-L, statistical analysis was performed using two-tailed Student’s t-tests; G-I, *Il1b* in J, statistical analysis was performed using two-tailed Mann-Whitney U-tests.
+Figure 3 So(d18:1) inhibits HIF-2α transcription function in liver macrophages.
+
+A and B, flow cytometry representative chart representative showing that macrophages increased after So(d18:1) treatment. (n=3). C, GO:BP pathway enrichment showing the transcriptional level changes of some immune-related pathways. (n=4). D, Epas1 targets enrichment. E, relative mRNA levels of Hif2a and its downstream target genes in macrophages treated with vehicle or different concentration of So(d18:1). (n=6). F, assessment of HIF-2α protein level of BMDMs stimulated with vehicle and So(d18:1). (n=3). G, representative immunoblot analysis of pro-caspase-1 and caspase-1 from
+Hif2α+/+ and LysMHif2αLSL/LSL BMDMs that were treated with So(d18:1) or not under NLRP3 inflammasome stimulation. (n=3). H and I, protein level of IL-1β (H), IL-18 (I) from Hif2α+/+ and LysMHif2αLSL/LS BMDMs treated with So(d18:1) or not under NLRP3 inflammasome stimulation. (n=6).
+
+Data are the means ± s.e.m. B, H, I, statistical analysis was performed using two-tailed Student’s t-tests; E, statistical analysis was performed using Kruskal-Wallis test with Dunn’s test.
+Figure 4 HIF-2α KO in macrophages accelerated inflammation and fibrosis in NASH mice.
+
+Eight-week-old male Hif2afl/fl and Hif2αLysm mice were administered a GAN diet for 24 weeks (SPF, n=6 mice/group). A, liver weights. B, ratios of liver mass to body mass. C, serum ALT. D, serum AST. E, representative H&E (up), and Sirius Red (down) staining of liver sections. The circles marked the inflammation foci. n=3 mice
+per group, 3 images per mouse. Scale bar is 100 μm. F, the percentage of fibrosis area.
+
+G-J, Histology scores of hepatic steatosis (G), lobular inflammation (H), ballooning (I), and NAFLD activity (J). K-L, relative mRNA levels of genes related to hepatic inflammation (K) and fibrosis (L).
+
+Data are the means ± s.e.m. A-D, F, K-L, statistical analysis was performed using two-tailed Student’s t-tests; G-J, *Col2a1* in L, statistical analysis was performed using two-tailed Mann-Whitney U-tests.
+Figure 5 HIF-2α overexpression in macrophages ameliorated inflammation and fibrosis in NASH mice
+Eight-week-old male Hif2α+/+ and LysMHif2αLSL/LSL mice were administered a GAN diet for 24 weeks (SPF, n=6 mice/group). A, liver weights. B, ratios of liver mass to body mass. C, serum ALT. D, serum AST. E, representative H&E (up), and Sirius Red (down) staining of liver sections. The circles marked the inflammation foci. n=3 mice per group, 3 images per mouse. Scale bar is 100 μm. F, the percentage of fibrosis area. G-J, Histology scores of hepatic steatosis (G), lobular inflammation (H), ballooning (I), and NAFLD activity (J). K-L, relative mRNA levels of genes related to hepatic inflammation (K) and fibrosis (L).
+
+Data are the means ± s.e.m. A-D, F, J-L, statistical analysis was performed using two-tailed Student’s t-tests; G-I, Ccl2 in K, statistical analysis was performed using two-tailed Mann-Whitney U-tests.
+Figure 6 So(d18:1) suppress the binding of HIF-2α and ARNT
+A, PT2385 and So(d18:1) could inhibit HIF-2α transcription ability. (n=6). B, schematic diagram of mammalian two-hybrid system. PT2385 and So(d18:1) could inhibit HIF-2α to bind to ARNT. (n=6). C, Co-immunoprecipitation for ARNT and HIF-2α in HEK293T cells treated with control solvent, So(d18:1) or PT2385, PT2385 and So(d18:1) could inhibit HIF-2α to bind to ARNT. D, molecule docking prediction of So(d18:1) binding sites in HIF-2α PAS-B domain. E, schematic diagram of site missense mutation experiment. PT2385 and So(d18:1) could inhibit normal HIF-2α transcription ability but not HIF-2α with missense mutations. (n=6). F, Cpt1a promoter rHRE constructs plasmid were co-transfected with HIF-2αTM followed by control
+solvent or So(d18:1) treatment. So(d18:1) could inhibit HIF-2α binding ability to rHRE. (n=3).
+
+Data are the means ± s.e.m. A, statistical analysis was performed using One-way ANOVA with Tukey’s post hoc test. B, E, statistical analysis was performed using Kruskal-Wallis test with Dunn’s test. F, statistical analysis was performed using Mann-Whitney U test.
+Figure 7 FG-4592 significantly mitigates CDAA-HFD diet induced NASH
+
+CDAA-HFD-fed mice were treated with vehicle or FG-4592 for 8 weeks (n=6 mice/group). A, liver weights. B, ratios of liver mass to body mass. C, serum ALT. D, serum AST. E, representative H&E (up), and Sirius Red (down) staining of liver
+sections. The circles marked the inflammation foci. n=3 mice per group, 3 images per mouse. Scale bar is 100 \( \mu \)m. F, the percentage of fibrosis area. G-J, Histology scores of hepatic steatosis (G), lobular inflammation (H), ballooning (I), and NAFLD activity (J). K-L, relative mRNA levels of genes related to hepatic inflammation (K) and fibrosis (L).
+
+Data are the means \( \pm \) s.e.m. A-D, F, K-L, statistical analysis was performed using two-tailed Student’s t-tests; G-J, *Il1b* in K, *Timp1* and *Col5a2* in L, statistical analysis was performed using two-tailed Mann-Whitney U-tests.
+Materials and Methods
+
+Human participants
+
+The clinical patient cohorts of this study were collected from Peking University People’s Hospital. With the approval of the Ethics Committee of Peking University People’s Hospital (Ethics Review Approval No.: 2021PHB124-001), all volunteers who participated in the study signed a written informed consent form.
+
+The inclusion criteria were as follows: NASH disease diagnosis was in accordance with the Guidelines of Prevention and Treatment of Non-Alcoholic Fatty Liver Disease: a 2018 Update prepared by the National Workshop on Fatty Liver and Alcoholic Liver Disease, Chinese Society of Hepatology, Chinese Medical Association; Fatty Liver Experts Committee, Chinese Medical Doctor Association. The diagnosis requires the patient to have histological evidence of diffuse hepatocyte steatosis, intrahepatic inflammation and fibrosis, and persistent serum ALT and GGT increases. Patients with alcoholic liver disease, type 3 hepatitis C virus infection, autoimmune hepatitis, hepatolenticular degeneration and drug-induced liver disease were excluded. A FibroScan liver elasticity test was performed to support the diagnosis. All patients were newly diagnosed with NASH and did not receive relevant treatment. Healthy volunteers were also recruited from Peking University People’s Hospital. They were required to have normal serum ALT and GGT levels. FibroScan indicated that their liver elasticity was normal. Their age, sex and BMI were matched to those of NASH patients.
+
+Animals
+
+C57BL/6J wild-type mice were purchased from the Department of Laboratory
+Animal Science, Peking University Health Science Center. *Hif2α*^fl/fl*, *Hif2α*^ΔLysm*, *Hif2α*^+/+* and LysMHif2α^LSL/LSL* mice were purchased from Jackson Lab.
+
+Mice were randomly divided into different groups and raised in cages under standard SPF laboratory conditions with free access to water and feed. The temperature was maintained at 21-24 °C, and the humidity was maintained at 40-70%. The light was on from 08:00 to 20:00. The animal use licence number was SYXK (Beijing) 2011-0039. All animal experiments complied with the rules for the use of experimental animals, treatment and euthanasia approved by Peking University Health Science Center (permit: LA2020481).
+
+A normal chow diet (NCD) was purchased from Beijing Keaoxieli Feed Co., Ltd., in which fat supplies 20% of calories for energy. The GAN diet (D09100310) was purchased from Research Diets, USA, in which fat provides 40% of calories for energy (including palm oil), fructose provides 20% of calories for energy, and 2% cholesterol is added. Mice were fed the GAN diet for 24 weeks to create the NASH model. The CDAA-HFD (A06071302) was purchased from Research Diets, USA, in which fat supplies 60% of calories for energy, and the diet contains 0.1% methionine and does not contain any added choline. Mice were fed the CDAA-HFD for 8 weeks to create the NASH model.
+
+For the So(d18:1) intraperitoneal injection experiment, 6-week-old male mice were randomly fed the CDAA-HFD for 8 weeks with So(d18:1) (10 mg/kg body weight) injected intraperitoneally every day. For the FG-4592 intraperitoneal injection experiment, 6-week-old male mice were randomly fed the CDAA-HFD for 8 weeks
+with FG-4592 (25 mg/kg body weight) injected intraperitoneally every day.
+
+Cell lines
+
+The HEK293T cell line used in this study was purchased from the National Collection of Authenticated Cell Cultures.
+
+Primary mouse bone marrow-derived macrophage culture
+
+Bone marrow-derived macrophages were isolated from the bone marrow of C57BL/6J wild-type mice, macrophage-specific knockout HIF-2α mice (\(Hif2a^{\Delta Lysm}\)) and macrophage-specific overexpressing HIF-2α mice (LysMHif2a^{LSL/LSL}).
+
+BMDMs were prepared as previously described[26]. The bone marrow collected from the femur and tibia of mice was inoculated on sterile petri dishes and cultured in RPMI 1640 containing 10% FBS, 100 units/ml penicillin, 100 mg/ml streptomycin and 10 ng/ml macrophage colony stimulating factor (M-CSF) for 5-6 days. When activating the NLRP3 inflammasome, BMDMs were incubated with LPS (500 ng/ml, 4 hours) and then were treated with nigericin (6.7 μM, 1 hour).
+
+Separation of liver nonparenchymal cells
+
+As mentioned earlier[27], primary hepatic macrophages were isolated from male mice by injecting type IV collagenase into the liver. Mice were anaesthetized with isoflurane and perfused through the portal vein. Krebs buffer was used to remove blood from the liver. Then, Krebs buffer supplemented with type IV collagenase was used for digestion. After digestion, the liver was collected and rinsed with RPMI 1640. The digested liver cell suspension was passed through a 70-μm cell filter (BD). The samples were centrifuged at \(50 \times g\) for 3 minutes, and the supernatant was retained. The cells
+were centrifuged at 1200 rpm for 10 minutes again to precipitate the nonparenchymal cells from the supernatant.
+
+Flow cytometry
+
+Isolated liver nonparenchymal cells were washed in PBS buffer containing 10% FBS, and red cells were removed. The cells were stained with specific antibodies (7AAD BD, APC/cy7 anti-CD45 BioLegend, PE anti-CD11b BioLegend, APC anti-F4/80 BioLegend) at 4 °C for 30 minutes protected from light, washed with cold PBS 3 times, and analysed by flow cytometry using FACS SORP flow cytometry (BD). The data were analysed using FlowJo software (TreeStar).
+
+Dual-luciferase reporter assay
+
+Cells were seeded into a 48-well plate at a density of \(2 \times 10^4\) per well. The luciferase constructs for the HIF response element (HRE) and the oxygen-stable HIF-2α triple mutant (HIF-2αTM) plasmid were previously described[20, 28]. To explore the effect of So(d18:1) on the transcriptional regulatory activity of HIF-2α, HIF-2αTM plasmid, p2.1 HRE-Luc plasmid and Renilla positive control plasmid mixed with Lipo8000 transfection reagent were added to each well cells.
+
+For the Mammalian Two-Hybrid System, pG5 luciferase vector was cotransfected with pBIND-HIF-2a and pACT-ARNT into cells using the protocol described in the CheckMate™ Mammalian Two-Hybrid System (Promega)[29].
+
+For the mutant assay, HIF-2αTM plasmid and mHIF-2a G324E+S305M plasmid were used. For the *Cpt1a* rHRE binding assay, the pGL3 basic vector (Promega) was cloned with the presumed rHRE1 region in the *Cpt1a* promoter upstream of the firefly
+luciferase gene as the reporter plasmid. The reporter plasmid, HIF-2α™ plasmid or corresponding control empty vector were transfected into HEK293T cells together. The luciferase assay was performed as previously described.
+
+The cells were treated with control vehicle, 2 μM HIF-2α-specific inhibitor PT2385 and 2 μM So(d18:1) for 24 h, the supernatant was discarded, and the samples were gently rinsed with PBS buffer. Next, 100 μL of PLB lysis solution was added to the cells, and they were incubated at room temperature for 10 minutes. Ten microlitres of the cell lysate was added to a white flat-bottomed 96-well plate, and the following procedure was used in the multifunction microplate reader (Tecan): 40 μL of luciferase substrate was added, the fluorescence value was detected, and 40 μL of stop liquid was added. Finally, the ratio of the two fluorescence values was calculated.
+
+Mass spectrometry
+
+Targeted lipidomics was performed according to a previous study with minor modifications[30]. Liver tissue (20 mg) was added to 80 μL of water and homogenized for 1 minute. Then, 400 μL of chloroform and methanol (v/v, 2:1) was added, and the samples were vortexed for 10 minutes and centrifuged at 4 °C and 12,000 rpm for 10 minutes. The lower layer was transferred into a new 1.5-ml tube and dried by a SpeedVac. Subsequently, 100 μL of cold methanol and isopropanol (v/v, 4:1) was added, and the tubes were vortexed for 10 minutes and centrifuged at 4 °C and 18,000 rpm for 10 minutes. The supernatant was transferred to a vial for MS detection. For plasma (100 μL), 400 μL of chloroform and methanol (v/v, 2:1) was added, and the remaining processes were the same as for liver tissue. A Waters UPLC BEH C18 column (2.1 mm
+(inner diameter) × 100 mm (length), 1.7 μm (particle dimension)) was used for separation. The mobile phase consisted of water (containing 5 mM ammonium acetate and 0.1% formic acid; phase A) and isopropanol:acetonitrile (1:1, v/v, containing 5 mM ammonium acetate and 0.1% formic acid; phase B) at a flow rate of 0.4 ml/min and a column temperature of 40 °C, with an injection volume of 2 μL. The UPLC and MS parameters used were chosen according to a previous study[30].
+
+For the quantification of ceramides, S1P and sphingosine, 25 μl of plasma or 20 mg of liver tissue was homogenized with 400 μl of chloroform and methanol (v/v, 2:1) containing 5 μM sphingosine-d7 d18:1 and 25 μM ceramide-d7 d18:1/15:0 (Avanti Polar Lipids) as the internal standards. The mixture was oscillated immediately and then centrifuged at 13,000 rpm for 20 min. The lower phase was dried using a SpeedVac. The sediment was dissolved in 100 μl of isopropanol and acetonitrile (v/v, 1:1) and analysed using the Waters Acquity UPLC coupled with the AB SCIEX QTRAP 5500 system using a Waters UPLC CSH C18 column (3.5 μm, 2.1 × 100 mm). The UPLC and MS parameters used were chosen according to a previous study[31]. The lipid metabolites were quantified using MultiQuant 2.1 (AB SCIEX).
+
+NAS scoring
+
+The NAS, also known as the NAFLD activity score (NAS), is calculated as the sum of three histological components, that is, steatosis (0-3), ballooning (0-2) and lobular inflammation (0-3). Patients with NAS \( \geq 5 \) were considered definite NASH, patients with scores of 3 or 4 were considered borderline NASH, and patients with scores of less than 3 were diagnosed as NAFL.
+Enzyme-linked immunosorbent assay (ELISA)
+
+The levels of IL-1β (Abclonal, RK00006) and IL-18 (Abclonal, RK00104) were measured by ELISA kits according to the manufacturer’s instructions. In short, the standard or sample was added to the antibody-coated plate and incubated at 37 °C for 120 minutes. Bio-coupled antibody solution, avidin HRP solution and TMB substrate solution were added to the microporous plate in turn. The absorbance at 450 nm was measured within 15 minutes after adding the termination solution.
+
+Western blot and immunoprecipitation
+
+Whole cell lysates were prepared with RIPA buffer. The cell homogenate was incubated on ice in RIPA buffer for 15-20 minutes and then centrifuged at 10,000 rpm at 4 °C for 10 minutes. The supernatant was transferred into a new tube and mixed with 5× loading buffer. The mixture was boiled for 10 minutes.
+
+For co-IP, Protein A/G PLUS agarose beads (Santa Cruz) were placed in the cell lysate supernatant. The samples were incubated upside down overnight at 4 °C. TBST buffer was used to wash 3 times. Then, 50 μl of 2× loading buffer was added to the beads and boiled for 10 minutes.
+
+Each well containing 50 μg of protein lysate was separated by SDS–PAGE, transferred to a nitrocellulose membrane, and immunoblotted at 4 °C overnight. The antibodies were anti-caspase-1 (AdipoGen, AG-20B-0042), anti-HIF-2α (Novus, NB100-132), anti-ARNT (Santa Cruz, sc-17811), anti-GAPDH (CST, #5174) and anti-β-Actin (Abclonal, AC038). All primary antibodies were used at a dilution of 1:2000. The HRP-coupled secondary antibodies used were anti-rabbit (Abclonal, AS014) and
+anti-mouse (Abclonal, AS003) secondary antibodies at a dilution of 1:2000, and immunoblotting was carried out using a chemical imaging system (ChemiDoc, Bio-Rad).
+
+RT-qPCR analysis
+
+Liver tissues were flash-frozen in liquid nitrogen and stored at -80 °C.
+
+Total RNA from frozen liver tissues was extracted using TRIzol reagent (Invitrogen). cDNA was synthesized from 2 µg of total RNA using 5× All-In-One RT MasterMix (Abm). A list of quantitative PCR (qPCR) primer sequences is provided in Supplementary Table 2. The relative amount of each mRNA was compared to the corresponding gene and normalized, and the results are expressed as fold changes relative to the control group.
+
+RNA sequencing and analysis
+
+Library preparation and transcriptome sequencing were conducted by GENEWIZ LLC. The Illumina HiSeq platform was used for sequencing. For the data analysis, we first evaluated the quality of the sequence data by fastqc v0.11.9, and the sequence quality was considered to be good for subsequent analysis. Trim-galore v0.6.7 was used for adapter trimming and low-quality reads. Clean read mapping was conducted by Hisat2 v2.2.1, and we used mm10 as the mouse reference genome. After that, gene expression was quantified by featureCounts v2.0.1. All downstream analyses were performed in R v4.2.1. We used the edgeR v3.38.4 R package for differential expression analysis. We set the cut-off of differentially expressed genes as follows: p value of 0.05 and absolute value of fold change of 1.5. Gene Ontology (GO) enrichment analysis and
+transcription factor enrichment analysis were conducted by the clusterProfiler v4.4.4 R package. We used the ARCHS4 transcription factor coexpression database from the Enrichr library as the database for transcription factor enrichment analysis. The record GSE228548 has been submitted to GEO database.
+
+Single-cell RNA sequencing analysis
+
+We downloaded the count matrix of the GSE166504 dataset from the GEO database and analysed it using R. This is a single-cell transcriptome dataset of livers where mice were fed a chow diet, a HFHFD diet for 15 weeks, and a HFHFD diet for 30 weeks. We clustered these cells by mRNA expression level using the Seurat package, and then we annotated these cell clusters using the SingleR package.
+
+Statistics analysis
+
+This study used GraphPad Prism software v.9.0. and SPSS software v.27.0 for analysis and statistics. The experimental results of this study are presented as the mean ± standard error of the mean (SEM). First, the Kolmogorov-Smirnov statistical method was used to detect the normality of all data. If the data conformed to a normal distribution, Student’s t test was used to compare two groups, one-way ANOVA was used for three or more groups, and Tukey’s post-test was used for statistical analysis. If the data did not conform to a normal distribution, a nonparametric test was used. Mann-Whitney’s statistical method was used for analysis between two groups, and the Kruskal-Wallis and Dunn’s time tests were used for statistical analysis of three or more groups.
+Supplementary Files
+
+This is a list of supplementary files associated with this preprint. Click to download.
+
+• Supplementary.pdf

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+Dose-Efficient Cryo-Electron Microscopy for Thick Samples using Tilt-Corrected Scanning Transmission Electron Microscopy, Demonstrated on Cells and Single Particles
+
+Yue Yu
+yue.yu@czii.org
+
+Chan Zuckerberg Institute for Advanced Biological Imaging   https://orcid.org/0000-0002-3248-9678
+Katherine Spoth
+Hauptman-Woodward Medical Research Institute   https://orcid.org/0000-0003-1168-5829
+Michael Colletta
+School of Applied and Engineering Physics, Cornell University
+Kayla Nguyen
+Department of Physics, University of Oregon
+Steven Zeltmann
+PARADIM, Materials Science & Engineering Department, Cornell University,
+Xiyue Zhang
+School of Applied and Engineering Physics, Cornell University
+Mohammadreza Paraan
+Chan Zuckerberg Institute for Advanced Biological Imaging
+Mykailo Kopylov
+The National Resource for Automated Molecular Microscopy, Simons Electron Microscopy Center, New York Structural Biology Center, New York, NY
+Charlie Dubbeldam
+New York Structural Biology Center
+Daniel Serwas
+Chan Zuckerberg Institute for Advanced Biological Imaging
+Hannah Siems
+Chan Zuckerberg Institute for Advanced Biological Imaging
+David Muller
+School of Applied and Engineering Physics, Cornell University   https://orcid.org/0000-0003-4129-0473
+Lena Kourkoutis
+School of Applied and Engineering Physics, Cornell University
+Article
+
+Keywords:
+
+Posted Date: August 29th, 2024
+
+DOI: https://doi.org/10.21203/rs.3.rs-4917330/v1
+
+License: This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License
+
+Additional Declarations: There is NO Competing Interest.
+
+Version of Record: A version of this preprint was published at Nature Methods on September 23rd, 2025. See the published version at https://doi.org/10.1038/s41592-025-02834-9.
+Dose-Efficient Cryo-Electron Microscopy for Thick Samples using Tilt-Corrected Scanning Transmission Electron Microscopy, Demonstrated on Cells and Single Particles
+
+Yue Yu1,2*, Katherine A. Spoth1,3*, Michael Colletta1, Kayla X. Nguyen1,4*, Steven E. Zeltmann1,5, Xiyue S. Zhang1, Mohammadreza Paraan2, Mykhailo Kopylov6, Charlie Dubbeldam6, Daniel Serwas2, Hannah Siems2, David A. Muller1,7†, Lena F. Kourkoutis1,7
+
+1 School of Applied and Engineering Physics, Cornell University, Ithaca, NY, 14853, USA
+2 Chan Zuckerberg Institute for Advanced Biological Imaging, Redwood City, CA, 94063, USA
+3 Hauptman-Woodward Medical Research Institute, 700 Ellicott Street, Buffalo, NY, 14203, USA
+4 Department of Physics, University of Oregon, Eugene, OR 97403, USA
+5 PARADIM, Materials Science & Engineering Department, Cornell University, Ithaca, NY, 14853, USA
+6 New York Structural Biology Center, New York, NY 10027, USA
+7 Kavli Institute at Cornell for Nanoscale Science, Cornell University, Ithaca, NY14853, USA
+† Corresponding authors: yue.yu@czii.org, david.a.muller@cornell.edu
+
+Abstract:
+Cryo-EM is a powerful tool in structural biology, providing insights through techniques like single-particle analysis (SPA) and cryogenic electron tomography (cryo-ET). In thick specimens, challenges arise as an exponentially larger fraction of the transmitted electrons lose energy from inelastic scattering and can no longer be properly focused as a result of chromatic aberrations in the post-specimen optics. Rather than filtering out the inelastic scattering at the price of reducing potential signal, as is done in energy-filtered transmission electron microscopy (EFTEM), we show how a dose-efficient and unfiltered image can be rapidly obtained using tilt-corrected bright-field scanning-TEM (tcBF-STEM) data collected on a pixelated detector. Enhanced
+contrast and a 3-5x improvement in collection efficiency are observed for 2D images of intact bacterial cells and large organelles using tcBF-STEM compared to EFTEM for thicknesses beyond 500 nm. As a proof of concept for the technique’s performance in structural determination, we present an SPA map at subnanometer resolution for a highly symmetric virus-like particle (VLP) with 789 particles. These findings suggest applications for tcBF-STEM in cryo-EM of thicker cellular volumes where current approaches struggle.
+
+Main:
+Cryogenic electron microscopy (cryo-EM) provides powerful insights into the study of biological systems by revealing molecular structures in their close-to-native environments\( ^{1-3} \). Single particle analysis (SPA) has enabled structural determination of purified macromolecular complexes up to atomic resolution\(^{4,5}\). Cryogenic electron tomography (cryo-ET) with subtomogram averaging (STA) has been developed to resolve macromolecular structures in biological contexts including within slices of whole cells\(^{6,7}\). Compared to SPA, fewer structures have been resolved at high resolution by cryo-ET with STA with one of the main limitations being the increased specimen thickness for cellular structures compared to the preparations for the purified molecules. This increased sample thickness leads to an exponential decrease in the elastically-scattered signal, especially at high sample tilts\(^{8}\) or lower beam voltages\(^{9}\). In the conventional transmission electron microscopy (TEM) geometry, the imaging optics are placed after the sample, and chromatic blur in the post-specimen optics leads to a strong defocusing of the inelastically scattered electrons. Energy-filtered TEM (EFTEM) removes this blur caused by inelastic scattering but in doing so reduces the collected signal and dose-efficiency compared to an ideal microscope\(^{10,11}\). Chromatic aberration correction could in principle correct some of this
+inelastic blur over a limited energy range and it is an ongoing topic of active research to improve the energy range, stability and resolution\(^{12,13}\).
+
+It has also long been recognized that in the scanning transmission electron microscopy (STEM) geometry, where the electron beam is focused to a small spot and then rastered across the specimen, that post-specimen chromatic aberrations should not compromise the probe size. This is because in STEM the probe-forming optics are placed before the sample, and before any inelastic scattering can occur, thus STEM imaging should be less susceptible to specimen-induced chromatic blurring (instead the chromatic blur in the post-specimen optics degrades the angular coherence of the diffraction pattern). Consequently, the possibility of studying \( \mu \)m-thick biological samples with STEM tomography has been explored both experimentally and theoretically, utilizing coherent, incoherent signals and a combination of both\(^{14-18}\).
+
+Recent advances in the design of STEM detectors\(^{19-22}\) have enabled rapid 4D-STEM data acquisition, where almost all of the scattered electrons are collected as 2D images of convergent beam electron diffraction (CBED) patterns, and recorded over a 2D grid of probe positions, as sketched in Fig.1a. 4D-STEM has simplified the implementation of other STEM phase imaging techniques such as (integrated) differential phase contrast (iDPC-)STEM\(^{23}\) and electron ptychography\(^{24-26}\). Efforts have been made to optimize these techniques for applications in structural biology studies. iDPC-STEM has generated the first SPA map of macromolecules embedded in vitrified ice by a STEM technique at near-atomic resolution\(^{23}\). Initial attempts at low-dose ptychography have been performed on purified virus-like-particles (VLPs) at nanometer resolution with a limited number of particles\(^{24,25}\). More recent demonstrations have shown that SPA of thin sections with ptychography can resolve protein structures at a sub-nanometer level\(^{26}\), including a 5.8Å SPA map of apoferritin reconstructed from ~11,000 particles.
+This performance is still worse than EFTEM and TEM when beam-induced motion is corrected, and suggests the resolution limit is not the instrument optics, but likely related to uncorrected sample motion under the beam. To date, both the iDPC and ptychography studies have focused on relatively thin samples that were optimized for SPA applications.
+
+Here we describe how, in STEM geometry, a new dose-efficient phase-contrast imaging technique—tilt-corrected bright-field (tcBF-) STEM—could prove useful for imaging thick samples, while still providing comparable spatial resolution for thin samples. With this technique, we were able to resolve features in thick samples (roughly 500-800 nm thick) that were not visually discernible with EFTEM under comparable conditions in intact bacterial cells and large organelles. Additionally, with single particle approach, we present a ~7 Å nominal resolution 3D map for a highly symmetric virus-like particle (VLP) from 789 particles as proof of feasibility for structural determination with tcBF-STEM. Our earlier work on tcBF can be found in a series of short conference abstracts\(^{27-31}\) but a detailed writeup of the method had been delayed by the illness and untimely passing of our colleague Lena Kourkoutis, and here we provide a more in-depth description. This technique is computationally much faster than iterative ptychography, so could be used for live monitoring while collecting 4D-STEM data. We note this technique is starting to find applications in the development of low-dose ptychography for cryo-EM applications and materials science studies\(^{26,32}\).
+
+The starting point for tcBF-STEM is the collection of a 4D-STEM data set (Fig.1a), similar to what might be recorded for an out-of-focus ptychographic reconstruction\(^{33}\). For tcBF-STEM, each pixel within the bright-field (BF) disk functions as a coherent BF detector subtending a sufficiently small collection angle. From the theorem of reciprocity\(^{34}\), the STEM image produced from the detector pixel on the optical axis is equivalent to a conventional BF
+TEM image, and those STEM images produced by off-axis detector pixels are equivalent to BF TEM images formed with tilted illumination (Fig. 1b). These equivalent beam tilts give rise to image shifts that depend on the aberration function\(^{35,36}\), and are particularly simple when the dominant aberration is defocus. (There are some important differences for inelastic scattering\(^{37}\) that we discuss below and more details are given in the online methods section, where we follow the image analysis framework laid out by Rose\(^{37}\).) Such an image shift is demonstrated with two images obtained with two off-axis detector pixels (Fig. 1c-d). The shifts are measured and corrected on a (detector) pixel-by-pixel basis. Fig. 1e and 1g illustrate the resolved shift map overlaid on the averaged CBED pattern. Each individual image, after shift correcting, is then combined to create the final tcBF-STEM image (Fig. 1h). Compared to the BF images formed by single detector pixel (Fig. 1d), the tcBF-STEM image has a significantly improved SNR because almost all the signal-relevant signals are utilized. Furthermore, compared to the image formed by directly integrating over the full BF disk (Fig. 1f), tcBF preserves phase contrast. When reconstructing a tcBF-STEM image, a simultaneous measurement of the probe aberration function can be obtained. In fact, one of the early applications of a shift analysis of 4D-STEM datasets was for aberration measurement\(^{38}\), by analogy with the TEM beam tilt methods\(^{35}\). In tcBF-STEM, like in conventional BF-TEM, defocus is deliberately introduced to enhance contrast. Consequently, in Fig.1 e and g, the magnitudes are linearly proportional to the defocus and the off-axis angles, and are oriented outwards. The linearity of the shift with angle also makes it possible to measure the depth of objects by the resulting parallax effect\(^{22}\).
+
+We are now also in a position to understand the challenges for dose-efficient STEM with a single-pixel detector, and why tcBF-STEM overcomes that. By reciprocity, the conventional TEM geometry would be reproduced in STEM with a single small-pixel detector on the optic
+axis. The smaller the angular range of the detector, the more coherent the signal – in TEM mode, this would be equivalent to the illumination angle. But in STEM mode, such a small detector collects only a tiny fraction of the incident beam – a 0.1 mrad wide collector, and a 10 mrad probe convergence angle would have a collection efficiency of 1 part in 10,000, whereas a TEM with a 0.1 mrad illumination convergence, and a 10 mrad post-specimen objective aperture would have almost perfect collection efficiency. To improve the collection efficiency in STEM, we could increase the collection angle of the detector but this will eliminate the phase contrast signal (a much weaker amplitude contrast in an incoherent image will still be present – e.g. chapter 3 of reference 39). This is because the phase-contrast signal is only measurable when there is a phase shift on the lens, but the phase shift from aberrations generates an image shift that is different for each angle. In other words, simply summing over a wide range of angles leads to a blurred image. If the dominant aberrations are defocus and coma, the images recorded on the off-axis detector pixels have similar contrast transfer functions to the on-axis pixel^{39} (except towards the edge of the aperture – full treatment in online methods), so the tilt-correct summation of tcBF corrects for these shifts, allowing a coherent image to be retained, and uses almost all of the incident beam -i.e. a similar dose efficiency to TEM. The presence of the aperture complicates the analysis compared to aperture-free TEM, but the end result for tcBF is a similar-looking contrast transfer function (CTF) that has an information limit at double the aperture size (see results and online methods). This is the same information limit cutoff for iDPC and bright-field ptychography, although the shapes of the CTF are very different. As we will discuss in the results section, iDPC is less efficient than tcBF at transferring low-frequency information, although it is simpler to interpret.
+Moreover, tcBF-STEM has an advantage over EFTEM for thick samples. The post-specimen lenses for EFTEM are the image formation lenses so chromatic aberrations in the post-specimen lenses degrade the image resolution. However, for tcBF-STEM, the post-specimen lenses simply transfer an image of the diffraction pattern so chromatic aberrations result in a small loss of angular resolution -i.e. a small increase in the effective detector pixel size and hence a reduction in coherence. In a thick sample, most electrons undergo both elastic and inelastic scattering, but the elastic contrast is preserved when scattered to the inelastic channels\(^{37,40}\). This is largely because the most-likely inelastic scattering events are very delocalized compared to the elastic scattering, leading to weak and low-frequency modulations of the real space signal, and only a small (~0.03-0.1 mrad) blurring of the angular distributions.
+
+For a qualitative comparison of EFTEM and tcBF-STEM in thick specimens, we imaged the same area in a mitochondrion in succession with the two techniques (Fig.1i-n) using the same incident dose of 14 e/\(\text{\AA}^2\), and the same acceleration voltage of 300 kV. In the thinnest part of the sample at the organelle’s edge, the membrane bilayers are similarly resolved with both methods. However, in thicker regions (Fig.1 j and m), tcBF-STEM clearly shows the bilayers (orange arrow) of the mitochondrial inner membranes whereas with EFTEM these features are less visible. In the thickest portion of the image, tcBF can still resolve some parts of the inner membranes (Fig.1 k) whereas in the EFTEM image (Fig.1 n) these features are hardly discernible. Using the unfiltered and 10-eV EFTEM images and the inelastic mean free path (MFP) for vitrified ice of ~310 nm\(^{41}\) at 300 kV, the sample’s thickness can be estimated (see online methods). At the mitochondrion’s edge, the sample thickness is approximately 500 to 520 nm thick, while the regions shown in Fig. 1j-m is about 570 to 600 nm, and Fig. 1k-n corresponds to around 600 to 620 nm (thickness map in Fig S1). In the thickest parts (k-n), the
+EFTEM signal has dropped to ~14% of the incident dose, but the tcBF still retains 50% of the incident dose, i.e. almost 3.6x more signal remaining for tcBF. Similar trends are also observed in multiple samples shown later in Fig.3, where the differences in collection efficiencies are compared quantitatively, with the relative efficiency of tcBF-STEM over EFTEM growing exponentially as the sample thickness increases.
+
+Results
+
+Fast Data Acquisition with tcBF-STEM Upsampling and the CTF of tcBF-STEM
+
+In tcBF-STEM the number of pixels in the reconstructed image can be made much larger than the number of diffraction patterns recorded, as at a finite defocus each diffraction pattern contains information about an extended region of the sample. This trade-off between real space and reciprocal space sampling helps speed up the data collection as the multi-pixel detectors used for tcBF tend to be slower to readout than single-pixel sensors. For instance, if each diffraction pattern records information about 8*8 subsampled regions, the data collection rate is sped up 64-fold, so a 10 kHz detector frame rate becomes a 640 kHz image-pixel rate. The recovery of information beyond the limits of the real-space probe sampling uses the information collected in the shadow images in the diffraction plane. The information retrieval is achieved by a real-space upsampling through sub-(scan)-pixel image shifting. To understand the implementation of this upsampling technique, we start with a demonstration on a standard gold-on-carbon sample. This same approach is then also applied in the data reconstruction workflow for all the examples shown in the paper.
+Figure 2 shows a tcBF-STEM dataset acquired with 256*256 scan positions, spaced 8Å apart. With the chosen defocus value and scan step size (see the online method section), we expect over 90% information overlap collected in the reciprocal space. This information surplus is used to upsample a tcBF image. Details on upsampling can be found in online methods and Fig.S2 to S4. Figure 2a and 2b demonstrate the process of upsampling with part of the detector pixels. Fig. 2d is the final upsampled result with sub-scan-pixel features resolved compared to the original image (c). In Fig. 2e, Thon rings and the 2.3-Å spacing of Au are recovered through upsampling. An FFT radial average profile (g) is shown to confirm that upsampling restores the information beyond the scan Nyquist frequency without altering the information within the frequency range. The upsampling procedure achieves information transfer up to 7 times the real-space Nyquist sampling limit, effectively speeding up data acquisition by a factor of 49.
+
+The number of pixels in the image is separate from the optical resolution limit. Notably, with the \( \alpha = 5.5\text{-mrad} \) convergence semi-angle, the information transfer limit at a cutoff of \( 1\alpha \) corresponds to 3.6 Å and 1.8 Å at \( 2\alpha \). The 2.3-Å spacing we observed exceeds the \( 1\alpha \) cutoff and but is just within the \( 2\alpha \) limit. As discussed in the previous section, tcBF has a similar-looking PCTF (Fig.2f) to BF TEM but with an information limit at double the aperture size. This is because the information limit is set by the highest spatial frequency that can be transferred, i.e. the maximum possible momentum transfer. For an axial detector, this would be from an incident wavevector on the radius of the probe-forming aperture to the axis. An off-axis detector that is displaced in the opposite direction to the incident wavevector allows for a maximum momentum transfer that spans the diameter of the aperture, doubling the information limit compared to the axial case.
+The calculated phase contrast transfer function (PCTF) shown in Fig. 2f shows the tcBF image has twice the information limit compared to the BF image formed using only the axial detector pixel, as a result of exploiting this off-axis information. Details can be found in the online method section and Fig. S5-S7, including a discussion of practical limits.
+
+Comparison of cryo-tcBF-STEM, conventional TEM, and EFTEM for imaging thick samples
+
+Indeed, we believe tcBF has an advantage for thick specimens. To compare the performance of tcBF-STEM with EFTEM, the most-widely-adopted imaging technique in cryo-EM, we performed successive imaging with the two techniques on various thick specimens, including intact bacterium cells and large cellular organelles. The incident dose is chosen to be the same for each comparison, slit width for EFTEM is 10 eV and the acceleration voltage is 300 kV. As the samples are much thicker than the depth of field, quantitative metrics on the full projection convey less information than they would for thin sections, or individual molecules at different depths (which can be determined by the parallax shift in tcBF). Instead we present comparative cases with different acquisition orders, and different defocus choices for the two techniques. Even though no high-resolution information is compared, the image acquired first still introduces radiation damage and conformation change prior to the second. Therefore, we present scenarios where EFTEM images were acquired first, as well as scenarios where tcBF-STEM images were acquired first. Additionally, CTF modulation can affect the qualitative comparison. However, achieving the exact same defocus for the two techniques can be challenging because the samples are thick (~ 550 nm to 700 nm, table) and not flat, and switching between TEM and STEM
+modes is a significant change in optical alignments. As a result, we present a series of cases where EFTEM images are measured to have defoci larger, equivalent to or smaller than those of tcBF, alongside a scenario where both techniques are targeted at the same nominal defocus.
+
+In Fig.1 (i-n), we showed a comparison on a mitochondrion where tcBF performs better at resolving inner membrane especially towards the thicker part of the organelle. This tcBF image was acquired first with less measured defocus (1.9\( \mu \)m, Fig.3 table I) than EFTEM (3.9\( \mu \)m). EFTEM defoci are measured with CTFFIND4\(^{42}\) and tcBF defoci are measured from the image shifts. In this case, membrane contrast in the images is compared across the two techniques but the orientation of the membrane relative to the beam can affect its contrast so differences might be a result of warping of the sample. Another possibility is that the inherent range of tilts in tcBF illumination (up to ~7 mrad) improves contrast for a larger range of membrane orientations. But in general, we observe improved contrast in thick specimen regions for tcBF where other features instead of membranes were compared. Fig.3a-b are EFTEM and tcBF images of an intact E.coli cell. With tcBF, features within the cell's interior (Fig.3d with arrows) are effectively resolved, while in EFTEM the same features (possibly condensates or surface contamination) are discernible but less prominent. For this comparison, EFTEM has a lesser value of measured defocus (3.7 \( \mu \)m) than STEM (4.2 \( \mu \)m). In (e) and (f), images with tcBF and EFTEM of a vesicle were acquired with very close defoci (2.8\( \mu \)m). Again, the features in the thick region are clearer compared to EFTEM. We attribute the improved contrast with tcBF to a more efficient use of electrons. In table (I) we compare the ratio of preserved electrons with the two methods. For the samples measured here, tcBF is observed to collect more than 3 times the number of electrons than EFTEM for the same incident dose. For another comparison on E. coli
+at a low dose of 0.5 e-/Ų (i-l), tcBF is capable of resolving features that are otherwise indiscernible with EFTEM. Table I provides a summary of information on specimen, acquisition orders, doses, pixel sizes, measured or nominal defocus, thickness estimate using the EFTEM image, and a comparison of dose efficiency.
+
+Overall, a common trend is that tcBF is more likely to retain higher SNR features in thick regions of samples compared to EFTEM. Figure 4a shows the measured fraction of electrons collected for tcBF and EFTEM, where tcBF collects a factor of 3-3.5x more signal, an advantage that grows with thickness. We expect both signals to decay exponentially with thickness (t), i.e. exp(-t/λ_{in}) for EFTEM and exp(-t/λ_{el}) for tcBF. Fitting to the tcBF data in table I, we find the elastic MFP is \( \lambda_{el} = 830 \pm 50 \) nm assuming an inelastic MFP \( \lambda_{in} \) of 310 nm, close to the expected \( \lambda_{el} = 774 \pm 45 \) nm of the online methods (Figure 4a). Some sense of the relative dose efficiency of the two approaches is given by the ratio of these two exponential decays, i.e. \( \exp(t/\lambda_{eff}) = \exp(-t/\lambda_{el}) / \exp(-t/\lambda_{in}) \) where \( -1/\lambda_{eff} = 1/\lambda_{el} - 1/\lambda_{in} \), so \( \lambda_{eff} \approx 500 \) nm. This gives the factor of 3 advantage for tcBF at 550 nm, and it grows to 5x at ~800 nm. Beyond a thickness of one elastic MFP, much of the phase contrast signal will be lost to multiple elastic scattering and leaving mostly amplitude contrast. This identifies an effective dose advantage window for tcBF over EFTEM for thicknesses beyond ~400 nm.
+
+For low spatial frequencies, the collection efficiencies for tcBF and EFTEM can be compared directly because of their similar contrast transfer functions (Figure 4b). STEM methods that also collect the entire bright field disk such as DPC and iDPC can also be compared after accounting for their differences in information transfer as a function of spatial frequency. This is captured by the detective quantum efficiency (DQE) of the imaging system (online methods equations A15-17). Figure 4c shows that tcBF is more efficient at low spatial
+frequencies. The iDPC CTF and DQE peak at zero defocus and degrade with increasing defocus\(^{43}\), unlike EFTEM and tcBF.
+
+To understand the sample damage as a function of dose, we consecutively acquire tcBF-STEM images with doses ranging from 1.5 e\(^{-}\)/Å\(^{2}\) to 210 e\(^{-}\)/Å\(^{2}\) (Fig.S8 a-d). After a cumulative exposure of 280 e\(^{-}\)/Å\(^{2}\), no obvious sign of bubbling is observed, consistent with previous STEM studies\(^{16}\), while visible bubbling effects start to form after a total exposure over 150 e\(^{-}\)/Å\(^{2}\) for conventional TEM\(^{16}\). This does not mean no damage has occurred, but rather damage products have not migrated over long length scales. This suggests that for cryo-ET, the STEM operation mode might offer a higher total dose tolerance, but it also depends on the desired resolution of information from a tomogram.
+
+**Single particle analysis 3D reconstruction with cryo-tcBF-STEM imaging**
+
+To quantitatively assess the current performance of tcBF-STEM for molecular structure analysis, we performed SPA of bacteriophage PP7 coat protein, achieving a nominal resolution of ~7 Å at 0.143 FSC cutoff using a generic cryoSPARC SPA workflow\(^{44}\). For this analysis 789 particles are extracted from 19 tcBF-STEM micrographs. Fig. 5a displays a cropped representative micrograph with 2D class average of the particles in the inset. Per-micrograph CTF estimation was performed by CTFFIND4\(^{42}\) without local refinement due to the limited number of particles. Approximately 200 particles were manually picked to generate the template for template picking, and 789 particles were selected. The selected classes were then used for ab initio model generation, as a starting model for the homogeneous refinement with icosahedral symmetry applied. Fig. 5b presents the cryo-EM density map sharpened with Guinier B factor of 351 Å\(^{2}\) based on the Guinier plot analysis of the 3D reconstruction. A zoom-in view of the EM density
+with X-ray crystal structure of the particle docked inside (Protein Data Bank code 1DWN^{45}) is shown in (c). Fourier shell correlation (FSC) indicates a nominal resolution of 7.03 Å with cryoSPARC dynamic mask and 9.6 Å with no mask.
+
+VLP PP7 possesses an icosahedral symmetry with triangulation number T=3, theoretical molecular weight of 2MDa, containing a high number of repeated units per particle which allows efficient structural averaging with a smaller number of particles. ~7-Å resolution demonstrates the feasibility of using tcBF-STEM for structural analysis at a resolution that can resolve some secondary structures such as alpha helices. We also have preliminary experimental results suggesting no resolution limit improvements with the current ptychography algorithms with a similar number of particles. On the other hand, state-of-art EFTEM imaging under similar doses and the same accelerating voltage can achieve 3.5 Å nominal resolution with 900 particles (Fig. S10). We also attempted iDPC on the same specimen with a 1000kHz segmented detector (Fig. S11) and observed lower-quality phase contrast. We suspect this was mainly due to a poor experimental focus determination as we found iDPC to be very sensitive to focus settings. The supporting Quantifoil material for this sample is gold and the thickness is 50 nm. Low-dose constraints restricted focusing to be only on the supporting foil instead of the sample and the 50-nm-thick supporting foil can introduce a focus offset.
+
+Discussion
+
+We demonstrate tcBF-STEM imaging on purified single particle VLPs and vitrified cellular specimens. A comparative analysis with EFTEM highlights the higher dose efficiency of tcBF-STEM, particularly for thick specimens. The performance of tcBF-STEM on thick specimens in two scenarios was further demonstrated, under low-dose imaging and under cumulative
+exposures, suggesting potential advantages of tcBF for cryo-ET applications. As a proof-of-concept for using this technique for structural determination, tcBF SPA with VLPs shows a ~7 Å nominal resolution 3D map using a generic processing workflow for conventional TEM with ~800 particles.
+
+A key advantage of tcBF is in imaging thick specimens, as it is relatively insensitive to specimen-introduced energy losses. tcBF-STEM stands out as a STEM technique due to its high-dose efficiency, as it takes advantage of nearly all the forward-scattering electrons, making it a potentially powerful imaging technique for studying thick, dose-sensitive specimens, showing a twofold dose advantage over EFTEM at 400 nm growing to fivefold at 800 nm.
+
+Figure 4b compares the CTF for tcBF and DPC, which are the recorded signals we need for estimating the signal/noise ratios for the two methods. The detective quantum efficiencies (DQE) for tcBF and iDPC are proportional to squares of the CTFs plotted in Figure 4b (see online methods equation A16 for it is the DPC CTF and not the iDPC CTF that determines the iDPC DQE). While both approaches have the same information limit, tcBF has a higher information transfer at low spatial frequencies where much of the relevant structural information in a thick sample is located. In the language of ptychography\(^{46}\), tcBF is able to access both the double and triple-overlap regions, while DPC and single-sideband ptychography access only the double overlap (see online methods). tcBF is also able to surpass the real-space scanning Nyquist limit, offering a possibility for rapid data acquisition by trading detector pixels for real-space positions, important for out-running environmental noise in cryogenic experiments. Compared to ptychography, we find tcBF will still produce a robust image under thickness and dose conditions where our current ptychographic forward models fail to converge, and indeed there is a benefit to starting the ptychographic reconstruction from the information provided by
+tcBF, especially the estimate of the probe shape. Furthermore, at low doses where the signal is dominated by the central disk, our analysis summarized in Figure 4b,c gives insight into where the signals accessible to ptychography are encoded. Close to in-focus conditions, only the anti-Friedel term of the PCTF used in DPC and SSB imaging is available. At large defocus, the Friedel term of the PCTF used in tcBF and provides phase contrast at low frequencies is also accessible. This suggests low-dose pychography should be performed at large defocii conditions similar to those used for tcBF.
+
+Overall, there are many lessons learned in the decades it took for EFTEM SPA to reach its present resolution that can also be applied to both the algorithm development and experimental design for tcBF and ptychography to boost their performances to comparable levels for thin specimens, and potentially well beyond for thick samples. One of the directions to improve is specimen motion correction. The movie mode and motion correction developed for conventional TEM operation mode effectively accounts for the thermal and mechanical drift and the beam-induced specimen motion\(^{47,48}\). In tcBF-STEM, upsampling effectively reduces the data acquisition time, thereby mitigating the impact of slow drift but beam-induced motion is not handled. Beam-induced motion, reflected by the large B factors in our tcBF reconstruction and other contemporary ptychography reconstructions, are probably the major factor limiting resolution. Current 4D-STEM pixel array detectors are still too slow to incorporate these corrections directly, but analogous correction modes should be possible. Both tcBF and ptychography already contain information in the overlapping probe positions that could be used to correct the beam-induced motion. At present this correction is limited by the dose/recorded diffraction pattern, but a fast detector design with a larger pixel count could address this by allowing for a larger illuminated area/pattern. In summaey, to fully exploit this information may
+require a new, faster generation of detectors and scan systems to meaningfully decipher the underlying specimen motion and time-ordered information. Future efforts aimed to enhance the performance of tcBF-STEM involve addressing beam-induced specimen motion and exploring the practical resolution limits of this technique. This includes using an increased probe convergence angle and higher-order probe aberrations, as well as exploiting the parallax effect to determine and correct the defocus for individual structures within thick sections.
+
+Online methods
+
+tcBF-STEM upsampling
+
+For the dataset shown in Fig.2, there are 256×256 scan positions with a 5.5 mrad convergence semi-angle probe-forming aperture (α). A scan step size of 8 Å is used, which sets a real-space Nyquist limit corresponding to 16 Å. With a defocus of 1.3 μm (nominal) is applied, the diameter of the illumination spot size on the sample plane is about 13 nm. With an 8-Å scan step size, the collected diffraction patterns contain a substantial amount of overlapping information. This surplus of information is utilized to achieve real-space upsampling through sub-(scan)-pixel image shifting. To implement upsampling, each image formed by a single detector pixel is padded before shift-correcting (Fig. S2), and then combined. The combined image is then weighted by the distribution of sub-pixel image shifts (Fig. S3). Different padding options are also compared and assessed in the supplemental information (Fig. S4). Zero-padding is observed to preserve information-transfer beyond the scan sampling. The PCTF simulation for tcBF and BF uses 5.5 mrad for convergence semi-angle and 700 nm defocus. Measuring image shifts in tcBF-STEM can also be regularized using the probe aberration function. All cryogenic tcBF
+images presented here benefit from this regularization, and a comparison with and without regularization is shown in (Fig. S9).
+
+The limits of upsampling practically depends on several factors in addition to the optical resolution limit. Reciprocal-space sampling, real-space probe overlapping, and real-space image shift accuracy are critical factors for information retrieval through upsampling. Reciprocal-space sampling is primarily determined by the camera length, which is chosen to optimize the collection angle and angular resolution for a given detector. The degree of upsampling we can achieve is also limited by the accuracy of the image shift determination. Insufficient SNR in cross correlation can hinder the accuracy of image shift determination, which usually happens when the image SNR is low. It is possible to improve the accuracy by leveraging knowledge of the expected probe aberration function. It is also important to note that there is a trade-off between fineness of the reciprocal-space sampling and the SNR in the images formed by individual pixels in real space. Additionally, variations in the CTFs from higher-order aberrations and the impact of the aperture edge at different angular positions in the diffraction space, can also lead to false shift determinations.
+
+The contrast transfer function for tilted-beam imaging
+
+In linear imaging theory the image contrast \( C(\omega) \) can be written as
+
+\[
+C(\omega) = PCTF(\omega) \frac{F_p(\omega)}{\lambda}
+\]
+
+where \( F_p \) is the elastic scattering amplitude of the projected object and \( \lambda \) is the electron wavelength\(^{48}\). In general, the phase contrast transfer function (PCTF) can be complex, with the real part corresponding to angularly symmetric (i.e. Friedel-like) scattering, and the imaginary part to antisymmetric scattering. (At the lowest order of approximation, these terms would
+correspond to weak phase and weak amplitude approximations). Rose considered the phase contrast for samples which have undergone both elastic and inelastic scattering, with the case for a tilted beam given by equation 26 of reference \(^{48}\). For weakly scattering objects, the quadratic and higher-order terms in his equation (26) can be neglected and a simpler, linear PCTF is given by Rose’s equation (33)
+
+\[
+PCTF(\omega) = \frac{i}{2\Omega_0} \int A(\Theta)D(\Theta)\{A(\omega - \Theta)e^{-i[\chi(\omega-\Theta)-\chi(\Theta)]} - A(\omega + \Theta)e^{+i[\chi(\omega+\Theta)-\chi(\Theta)]}\}d^2\Theta
+\]
+
+which we interpret here in terms of the STEM geometry where \( \omega, \Theta \) are momentum vectors projected onto the detector in the diffraction plane and normalized as scattering angles (which are a vector in this plane, hence the bold notation). We also introduce the factor of \(1/2\) to be consistent with the modern definition that the magnitude of the PCTF is \( \leq 1 \) (See reference 48, 2nd column, top of pg 259). \(A(\Theta)\) and \(D(\Theta)\) are the probe-forming and detector functions, which are 1 inside the apertures, and 0 outside. \( \chi(\omega) \) is the aberration function of the objective lens and \( \Omega_0 \approx \pi a^2 \) is the solid angle subtended by the objective aperture, which cuts off at angle \( \alpha \). For a pixelated detector with small pixels (i.e. the change in \( \chi \) across a single pixel is small), \( D(\Theta) \approx \delta(\Theta) \) and equation (A2) simplifies to
+
+\[
+PCTF(\omega, \Theta) = i/\Omega_0\ A(\Theta)\{A(\omega - \Theta)e^{-i[\chi(\omega-\Theta)-\chi(\Theta)]} - A(\omega + \Theta)e^{+i[\chi(\omega+\Theta)-\chi(\Theta)]}\}
+\]
+
+where \( \omega \) is the spatial frequency in the image, and \( \Theta \) is the collection angle (i.e. pixel) on the detector, so \( PCTF(\omega, \Theta) \) gives the PCTF for the image formed by scanning the probe in sample plane and collecting the signal at pixel \( \Theta \) on the detector. The \( PCTF(\omega, \Theta) \) without an aperture is shown in Fig. S5 for a range of different tilts \( \Theta \) and the corresponding \( PCTF(\omega, \Theta) \) for an aperture is shown in Fig. S6.
+For the special case of axial illumination (\( \Theta = 0 \)) the PCTF reduces to the bright field CTF of \( -\sin(\chi(\omega)) \). This would also have a cutoff at \( |\omega| = \alpha \). The tilted beam case has non-zero contributions outside the aperture, up to a cutoff of \( 2\alpha \) when \( |\Theta| = \alpha \) from the terms \( A(\Theta)A(\omega - \Theta), A(\Theta)A(\omega + \Theta) \). This is the same information limit as the ADF and iDPC imaging, and double that of the axial bright field signal. The power spectrum of the apertured PCTF (Fig. S7) shows the double-resolution limit.
+
+We can get a sense of how the aberrations lead to shifts in the image, by considering the special case where the dominant aberration is defocus so
+
+\[
+\chi(\Theta) = -\frac{1}{2}k_0 \Delta f |\Theta|^2
+\] --(A4)
+
+where \( k_0 = \frac{2\pi}{\lambda} \). The PCTF then further simplifies to
+
+\[
+PCTF(\omega, \Theta) = i/\Omega_0\; A(\Theta)\{A(\omega - \Theta)e^{+\frac{1}{2}ik_0 \Delta f \omega^2} - A(\omega + \Theta)e^{-\frac{1}{2}ik_0 \Delta f \omega^2}\}e^{-i(\Delta f \Theta)\cdot(k_0 \omega)}\] --(A5)
+
+From the Fourier shift theorem, when transforming from the diffraction plane \( k_0 \omega \) to the image plane \( x \), the \( e^{-i(\Delta f \Theta)\cdot(k_0 \omega)} \) term in (A5) gives a shift of the image in real space of \( \Delta f \Theta \), i.e. a shift proportional to the defocus and the angle from the axis on the detector. This is the tilt that is corrected by tcBF. The defocus aberration from the \( e^{\pm \frac{1}{2}ik_0 \Delta f \omega^2} \) terms are still present in the CTF and the tilt-corrected PCTF becomes
+
+\[
+PCTF(\omega, \Theta) = i/\Omega_0\; A(\Theta)\{A(\omega - \Theta)e^{+\frac{1}{2}ik_0 \Delta f \omega^2} - A(\omega + \Theta)e^{-\frac{1}{2}ik_0 \Delta f \omega^2}\}\] --(A6)
+
+The tcBF CTF is obtained by summing over all tilt angles \( \Theta \). This is most easily accomplished by first summing symmetrically over pairs of angles at \( \Theta \) and \( -\Theta \):
+
+\[
+PCTF(\omega, +\Theta) + PCTF(\omega, -\Theta)
+= (-2/\Omega_0\; A(\Theta)\{A(\omega - \Theta) + A(\omega + \Theta)\}\sin(\frac{1}{2}k_0 \Delta f \omega^2))\] --(A7)
+
+and then completing the sum over half of the central disk (say all \( \Theta_x > 0 \)). In polar coordinates \( \Theta = (\Theta,\ \phi) \) and for a disk of diameter \( \alpha \) we integrate over \( \Theta \) and \( \phi \)
+\[
+CTF_{tcBF}(\omega) = -(2/\pi \alpha^2) \left[ \int_0^\pi d\phi \int_0^\alpha \Theta d\Theta\ A(\Theta)\{A(\omega - \Theta) + A(\omega + \Theta)\} \right] \sin(\frac{1}{2}k_0 \Delta f \omega^2)
+\]
+\[(A8)\]
+
+The integral over \( \Theta \) gives the area of the overlap of disks of diameter \( \alpha \) that are \( \omega \) apart, and can be found in the appendix of reference 48 as
+
+\[
+\mathcal{L}(\omega) = \begin{cases}
+\frac{2}{\pi} \left[ \cos^{-1}\left( \frac{1}{2} \omega \right) - \frac{1}{2} \sqrt{1 - \frac{1}{4} \omega^2} \right], & 0 \leq \omega \leq 2 \\
+0, & \omega \geq 2
+\end{cases}
+\]
+
+\( \mathcal{L}(\omega) \) is the well-known envelope for a self-luminous object, such as for the annular dark field contrast transfer function. The tcBF CTF can then be written more compactly as
+
+\[
+CTF_{tcBF}(\omega) = -\mathcal{L}(\omega) \sin(\frac{1}{2}k_0 \Delta f \omega^2)
+\]
+\[(A9).\]
+
+**Comparison of the contrast transfer function for tcBF with DPC**
+
+The optimal CTF for DPC and iDPC is the in-focus condition with no aberrations inside the aperture. Then \( \chi(\Theta) = 0 \) and the general PCTF simplifies to
+
+\[
+PCTF(\omega) = (i/\Omega_0)\ A(\Theta)\{A(\omega - \Theta) - A(\omega + \Theta)\}
+\]
+\[(A10)\]
+
+i.e. \( \Re(PCTF) = 0 \) at zero defocus, and only the antisymmetric component remains (Fig S6c).
+
+The DPC_x signal is produced by subtracting all the left-tilted (\( \Theta_x < 0 \)) from the right-tilted (\( \Theta_x > 0 \)) detector signals and then summing to produce the DPC CTF of Figure 4b.
+
+At \( \Theta = 0 \) the \( PCTF(\omega) = 0 \), and the PCTF remains 0 so long as \( |\omega| < \alpha \), \( |\omega - \Theta| < \alpha \) and \( |\omega + \Theta| < \alpha \) giving the white regions in each frame of Fig. S6c. In ptychography, this is referred to as the triple overlap region^{46}, reflecting the simultaneous overlap of the \( +\omega \) and \( -\omega \) beams with the incident beam (in ptychography, this is usually displayed in detector plane \( \Theta \) for a range of selected \( \omega \) while we have displayed the \( \omega \) plane for a range of selected \( \Theta \)), and is zero
+for in-focus imaging. When a phase shift is deliberately introduced, this triple-overlap provides the phase contrast for BF imaging, but still remains zero for DPC and single-side band (SSB) ptychography (white regions of Fig S6b). DPC and SSB rely on the double-overlap region where \( |\omega| < \alpha \) and either \( |\omega - \Theta| < \alpha \) or \( |\omega + \Theta| < \alpha \), but not both. Again, the information limit is the largest value of \( \omega \) for which the PCTF is non-zero. This occurs at \( |\Theta| = \alpha \) and \( \omega = 2\Theta \), so the largest non-zero value of \( |\omega| \) is \( \omega = 2\alpha \), double the radius of the aperture.
+
+It is important to note that the CTF in the triple-overlap region has double the amplitude of that of the double-overlap region(Figure 3 of reference 46). This suggests that tcBF should have the potential to reach double the dose-efficiency of DPC at below spatial frequencies where \( |\omega| < \alpha \) and a \( \pi/2 \) phase shift can be introduced through the aberration function. This difference becomes very noticeable at low spatial frequencies where the double overlap terms tend to zero, and the triple overlap contrast can be boosted by increasing defocus.
+
+Comparison of the Detective Quantum Efficiency (DQE) for tcBF and iDPC
+
+The iDPC CTF is obtained from the DPC CTF by integration in real space, corresponding to a division by spatial frequency in Fourier space as
+
+\[
+PCTF_{iDPC}(\omega) = \frac{PCTF_{DPCx}(\omega) + i\ PCTF_{DPCy}(\omega)}{i(k_x + i k_y)}
+\] -(A11)
+
+The power spectrum of the recorded DPC image in the presence of a noise spectrum \( N(\omega) \) is
+
+\[
+P_{DPC}(\omega) = |PCTF_{DPCx}(\omega)|^2\ |F_p(\omega)|^2 / \lambda^2 + \alpha^2 |N(\omega)|^2
+\] -(A12)
+
+The power spectrum for iDPC based on the DPC measurement with noise is
+
+\[
+P_{iDPC}(\omega) = \frac{|PCTF_{DPCx}(\omega)|^2 + |PCTF_{DPCy}(\omega)|^2}{(k_x^2 + k_y^2)} |F_p(\omega)|^2 / \lambda^2 + \alpha^2 \frac{|N_x(\omega)|^2}{(k_x^2 + k_y^2)}
+\] - (A13)
+
+The DQE of the measurement with a noise power spectrum, \( NPS(\omega) \), is
+
+\[
+DQE(\omega) = DQE(0) \frac{|PCTF(\omega)|^2}{|NPS(\omega)|^2}
+\] –(A14)
+
+For an ideal detector pixel, \( DQE(0) = 1 \) and for DPC imaging the \( DQE(\omega) \) becomes
+\[
+DQE_{DPCx}(\omega) = \frac{|PCTF_{DPCx}(\omega)|^2}{\alpha^2|N(\omega)|^2}
+\] –(A15)
+
+and after integrating, the DQE for iDPC becomes
+
+\[
+DQE_{iDPC}(\omega) = \frac{|PCTF_{DPCx}(\omega)|^2 + |PCTF_{DPCy}(\omega)|^2}{2\alpha^2|N(\omega)|^2}
+\] –(A16)
+
+This has a very similar shape to the DPC DQE since the noise is amplified in the same way as the signal.
+
+Similarly, applying equation A10 for tcBF we find the tcBF DQE to be,
+
+\[
+DQE_{tcBF}(\omega) = \frac{|PCTF_{tcBF}(\omega)|^2}{\alpha^2|N(\omega)|^2}
+\] –(A17)
+
+For an ideal detector the noise spectrum is only from Poisson noise, which is flat, so the differences in DQE for tcBF and iDPC can understood by comparing the squares of the PCTFs for tcBF and DPC (not iDPC). These are shown in figure 4b. As a consequence, iDPC has a poor DQE at low spatial frequencies compared to tcBF.
+
+Mean Free Paths and Thickness Estimates
+
+Measurements of the inelastic MFP (scaled to 300 keV\(^{49}\)) range from 100 nm for amorphous carbon to 275 nm for proteins to 310 nm for vitreous ice\(^{50}\), scaling roughly with the degree of hydrogenation. For our thickness measurements we use the inelastic MFP of ice. The elastic MFP is more strongly dependent on the range of collection angles as the elastic scattering has a much wider angular distribution than inelastic scattering. Thus, what is often reported is n, the ratio of elastic to inelastic scattering for a given measurement geometry, and this is in the range 2-5, with 3 being a typical value for cryoEM of organic systems\(^{51}\), suggesting a typical elastic MFP is about 700-900 nm. We calculated the elastic MFP from a multislice simulation of amorphous ice, for a 50 and 200 nm thick supercell and a 5.5 mrad convergence and collection angle at 300 keV. Averaging over multiple configurations, we fit the decay of the central beam to find the elastic MFP, \( \lambda_{el} = 774 \pm 45 \) nm. The elastic MFP sets a thickness for which the dominant contrast mechanism crosses over from phase contrast to scattering absorption contrast.
+In relating the signal remaining in an energy filtered image, \( I_{EFTEM}(t) = I_{TEM} \exp(- t / \lambda_{in}) \) and \( I_{TEM} \) is the corresponding unfiltered image. Even when no objective aperture is used, there is still some high-angle elastic scattering (including backscattering) that does not reach the detector, so not all of the incident beam is collected and \( I_{TEM}(t) = I_0 \exp(- t / \lambda_{HA}) \). Combining these results, we get
+
+\[
+I_{EFTEM}(t) = I_0 \exp(- t / \lambda_{HA}) \exp(- t / \lambda_{in}) = I_0 \exp(- t / \lambda_{in'})
+\] -(A18)
+
+For our microscope, we measured \( \lambda_{HA} = (46 \pm 1) \, \lambda_{in} \), and it is convenient to keep the functional form \( \lambda_{HA} = \alpha \, \lambda_{in} \) From eqn (A14) we can calculate the high angle correction to the inelastic mean free path as
+
+\[
+\lambda_{in'} = \lambda_{in} \, \alpha / (\alpha + 1)
+\] (A19).
+
+so \( \lambda_{in'} = 0.979 \, \lambda_{in} = 303 \) nm for ice.
+
+Comparative analysis on thick samples
+
+The organelles shown in Fig. 1i-n and Fi. 3e-h were isolated and purified from the HEK293T cells. Cells were mechanically lysed by osmotic shock and needle shearing\(^{52}\). The STEM images were recorded using an EMPAD\(^{19}\) on a TFS Krios G4 with a 7 mrad semi-convergence angle and a 2.8nm scan step size. 256*256 scan positions were collected. The corresponding EFTEM images were recorded using a Falcon 4i detector and the Selectris X energy filter with a slit width of 10 eV on the same TFS Krios G4. Acceleration voltage was 300 kV and the spherical aberration of the objective lens was 2.7 mm. tcBF images are reconstructed with the iterative alignment provided in py4DSTEM\(^{32}\) and upsampling is implemented in an in-house Python package based on the method described in the upsampling section.
+The E. coli specimen shown in Fig. 3 were prepared from the GL002 strain and plunge frozen with 200-mesh Quantifoil 2/1 holey carbon copper TEM grids. For Fig. 3i-l, the images were recorded on a customized Thermo Scientific Titan Themis with Gatan 626 cryo-transfer holder at 300 kV. The STEM images were recorded using an EMPAD\(^{20}\) with 2 mrad convergence angle. tcBF images were reconstructed with in-house Python package where the alignment algorithm is based on rigid shift registration between every possible pair\(^{53}\) and upsampling algorithm as described in the section. The EFTEM images were acquired with a K2 Summit direct detector (Gatan) operating in linear mode. For all the EFTEM images, short exposures were collected in the movie mode and cross-correlated with the number of frames chosen to match the dose of the corresponding STEM image.
+
+Single particle analysis on VLPs
+
+The specimen is a coat protein of bacteriophage PP7 self-assembled during recombinant expression in E. coli. TEM grids used are R1.2/1.3 mesh 300 UltrAuFoil. STEM images were acquired on the customized Thermo Scientific Titan Themis with a Gatan 626 cryo-transfer holder. Images were recorded with 300 kV acceleration voltage on an EMPAD-G2 detector\(^{20}\), 8 mrad semi-convergence angle, 11 Å scan step size, 45 e/\(\text{\AA}^2\) total exposure dose and upsampled to an image pixel size of 2.77 Å. A typical scan size is 512*512 with 100 \(\mu\)s dwell time. tcBF images are reconstructed with the iterative alignment provided in py4DSTEM\(^{32}\) and upsampling is implemented in an in-house Python package based on the method described in the upsampling section. The SPA reconstruction is obtained with cryoSPARC\(^{44}\) where CTFFIND4\(^{42}\) is used to
+estimate global CTF. Particles are picked with a template generated by manually-picked particles. The final 3D reconstruction has icosahedral symmetry and a dynamic mask imposed. The comparative analysis of the VLPs with EFTEM is performed with a Cs-corrected TFS Krios, shown in Fig. S11. The EFTEM data were acquired at an accelerating voltage of 300 kV, a pixel size of 1.076 Å and a total dose is 52.18 e-/Ų. The defocus ranges from -1μm to -2μm. The final reconstruction is obtained with 900 particles and the analysis is also done with cryoSPARC⁴².
+
+Acknowledgements
+
+This work is supported by NSF (DMR-1654596, DMR-1429155, DMR-1719875, DMR-2039380), the Packard Foundation, and Chan Zuckerberg Institute for Advanced Biological Imaging. This work made use of the instruments at Chan Zuckerberg Institute for Advanced Biological Imaging, the Cornell Center for Materials Research (CCMR) Shared Facilities and PARADIM. CCMR facilities and X.S.Z. are supported through the NSF MRSEC program (DMR-1719875). PARADIM and S.E.Z. are supported by the NSF MIP program (DMR-2039380). We are grateful for all the time that Lena was able to share with us. May her memory be a blessing. The authors thank Dr. Tianhong for inspiring discussions on tcBF upsampling. The authors appreciate Dr. Yasu Xu for providing the E.coli specimens, and Dr. Manuel D. Leonetti’s group for providing the cell lines for the organelle specimens. In addition, the authors want to thank Dr. Earl J. Kirkland for helpful discussions on tilted BF CTFs and Paul Cueva (NSF PHY-1549132) for help with aberration and tilt measurements in 4D-STEM. The authors acknowledge Dr. Georgios Varnavides, Dr. Stephanie M. Ribet, and Dr. Colin Ophus for helpful discussions on improving algorithms for tcBF. The authors also thank Dr. Bridget Carragher, Dr. Clinton S.
+Potter, and Dr. David Agard for advice on experimental designs for comparing tcBF-STEM to EFTEM, as well as for insights on future steps to improve the technique.
+
+Author Contributions
+
+Y.Y., K.A.S., D.A.M., and L.F.K. designed the tcBF experiments. Y.Y, K.A.S., and K.X.N. performed the tcBF experiments. Y.Y., K.A.S., M.C., K.X.N, D.A.M. and L.F.K. developed tcBF algorithm and analyzed the tcBF data. S.E.Z. and D.A.M. calculated the tcBF CTFs. R.P. D.S. and H.S. prepared the purified cellular organelle samples. Y.Y., R.P., M. K. and C.D. analyzed the single particle data. X.Z. and Y.Y. performed iDPC experiments. X.Z. analyzed iDPC data. Y.Y., K.A.S., L.F.K., and D.A.M. wrote the manuscript with input from all authors.
+
+Data Availability
+
+The 4D-STEM data sets for Fig. 1l-n and Fig.2a-h are available on Zenodo (DOI: 10.5281/zenodo.10825339), along with the corresponding EFTEM images.
+
+Code Availability
+
+House built python packages for tcBF-STEM are available on Github at https://github.com/yyu2017/tcBFSTEM.
+a. 4D-STEM schematic
+
+Source
+Obj. Aperture
+Obj. Lens
+Specimen
+Pixelated Array STEM Detector
+
+b. Principle of Reciprocity
+
+BF-STEM ↔ BF-TEM
+
+Source
+Obj. Aperture
+Obj. Lens
+Specimen
+Δf Defocus
+Detector
+Obj. Aperture
+Obj. Lens
+Specimen
+Source
+Detector
+BF-STEM   BF-TEM
+Off-axis BF-STEM   Tilted-beam BF-TEM
+Figure 1. | Direct phase-contrast imaging with 4D STEM: tilt-corrected bright-field (tcBF) - STEM employs a pixelated STEM detector to collect the entire convergent beam electron diffraction (CBED) pattern (a). Each detector pixel within the bright-field (BF) disk is a coherent BF STEM detector though located off the optical axis. By reciprocity (b), off-axis BF-STEM (top down) is equivalent to tilted-illumination TEM (bottom up). Similar to BF TEM, defocus is applied to introduce phase contrast. For a standard gold-on-carbon sample and a defocused
+probe, integrating the signals collected by two off-axis detector pixels (red and green) in (c) produces two images with relative shifts between them (d). For every detector pixel, the image shifts determined through cross-correlation with the on-axis detector pixel are shown by the arrows overlaid on the averaged CBED pattern in (e) with a zoom-in and binned view in (g). The arrows are color-coded corresponding to the shift directions. Integrating the full forward-scattered bright-field (BF) signals without correcting for the angle-dependent shifts results in blurring (f) due to the defocus. A tcBF-STEM image (h) is generated by summing the images after shift correction. In a tcBF-STEM image, the signal-to-noise ratio (SNR) is increased compared to (d) and the blurring due to defocus (f) is corrected. To compare the performance of tcBF-STEM with energy-filtered TEM (EFTEM) on thick samples, (i) and (l) are the images acquired in the same area in a mitochondrion. The dose measured over vacuum is 14 e-/Ų, and the acceleration voltage is 300 kV for both acquisitions. More information can be found in table I. The membrane bilayer was similarly resolved in the thin part of the sample for both methods. However, in thicker regions (j) and (m), tcBF still shows the membrane bilayers clearly (indicated by the orange arrowheads), while this feature is less visible with EFTEM. In the even thicker region (k and n), tcBF can still resolve some parts of the inner membranes whereas with EFTEM these features are less discernible. A thickness estimate map, obtained from the fraction of electrons remaining in the energy-filtered image, is given in Fig. S1, with thicknesses ranging
+from 470 nm to 620 nm
+Masked detector regions overlaid with shift map and averaged CBED
+
+a.
+
+Selected detector pixels
+
+Sum of zero-padded and shift-corrected signals
+
+b.
+
+Real-space scan sampling
+
+c.
+
+2 nm
+
+Upsampled by 8×8
+
+d.
+
+2 nm
+
+FFT
+
+e.
+
+2.3 Å
+
+Simulated CTF
+
+f.
+
+tcBF   BF
+
+α   2α
+
+PCTF
+
+![Six panels showing masked detector regions, sum of signals, real-space scan sampling, upsampled image, FFT, and simulated CTF](page_154_120_1277_1627.png)
+Figure 2. | Up-sampling by 8 speeds up data acquisition by 64-fold. Up-sampling for tcBF-STEM of a gold-on-carbon combined test sample is accomplished by exploiting the image shifts from different detector pixels as a result of defocus (and higher order aberrations). (a) The colored arrows show the shift measured for the scanned images synthesized at each detector pixel inside the bright field disk. Scanned images formed by the two white pixels on the detector shown in (a) will be shifted from each other. Correcting for these shifts and accumulating signals collected from the selected detector regions fills in different regions of the scanned image (b) at a spacing finer than the recorded probe positions, demonstrating the first step of a complete up-sampling. A tcBF-STEM image (c) is collected with a defocused probe at an 8-Å scan step size. In the up-sampled tcBF-STEM image (d), additional sub-scan-pixel features are resolved compared to the original image (c). (e) Experimental power spectrum from the full image of the test sample showing Thon rings and the 2.3-Å ring of gold lattice spacing beyond the scan Nyquist frequency (1/16 Å^{-1}, black box) are recovered by up-sampling. An FFT radial average profile (g) shows that up-sampling recovers information beyond the scan Nyquist frequency without altering the signal within the electron-optical information limit. (f) The calculated phase contrast transfer function (PCTF) for a tcBF image after shift correction shows twice the information limit compared to the BF image formed using only the axial detector pixel, as a
+result of exploiting off-axis information. The simulation uses 5.5 mrad convergence semi-angle probe-forming aperture (\( \alpha \)), 300 kV acceleration voltage and 700 nm defocus.
+EFTEM        tcBF-STEM
+
+a.
+
+b.
+
+c.
+
+d.
+
+![Four micrographs labeled a, b, c, d showing EFTEM and tcBF-STEM images with square regions highlighted and arrows pointing to specific features.](page_184_120_1207_1207.png)
+e.
+
+f.
+
+g.
+
+h.
+
+![Four grayscale images labeled e, f, g, h, each showing regions of interest marked by squares or triangles, with scale bars indicating nanometer distances.](page_124_120_1347_1347.png)
+i.
+
+j.
+
+k.
+
+l.
+Figure 3. | Comparison of EFTEM and tcBF-STEM with different doses, defoci and acquisition orders. The same region of interest in various specimens was imaged successively in order to compare the techniques. For each comparison, the total dose measured over vacuum and the electron acceleration (300 kV) are the same, and the average thickness can be estimated with the EFTEM images using the ratio of I0/I and the inelastic MFP, similar to Fig. S1. The dose efficiency of the two techniques is compared by the ratio of remaining electrons in the images to the incident total electrons. Overall, for the samples demonstrated here, tcBF is observed 3-3.5x higher collection efficiency than EFTEM at a similar incident dose/unit area. For EFTEM images, slit widths are all 10 eV and defoci are measured with CTFFIND4\(^{42}\). For tcBF images, defoci are measured with the image shifts. (a) and (b) are EFTEM and tcBF images of an intact *E.coli* cell. With tcBF (d), features in the interior region of the cell are effectively resolved, whereas in EFTEM (c), although the same features are discernible, they are less visible. In (e) and (f), images with EFTEM and tcBF of a vesicle at similar measured defoci are shown. Again, in the thick region tcBF reveals clearer features compared to EFTEM. For another comparison on *E.coli* at a low dose of 0.5 e\(^{-}/\)Å\(^{2}\) (i-l), tcBF is able to resolve features that are otherwise indiscernible with EFTEM. Thickness and other experimental details in Table I.
+<table>
+  <tr>
+    <th rowspan="2">Specimen</th>
+    <th rowspan="2">Acquired first</th>
+    <th rowspan="2">Dose (e<sup>-</sup>/Å<sup>2</sup>)</th>
+    <th colspan="2">Pixel size (Å)</th>
+    <th colspan="2">Defocus (nm)</th>
+    <th rowspan="2">Average thickness estimate* (nm)</th>
+    <th colspan="2">Fraction of incident electrons in the image</th>
+  </tr>
+  <tr>
+    <th>EFTEM</th>
+    <th>tcBF</th>
+    <th>EFTEM</th>
+    <th>tcBF</th>
+    <th>EFTEM</th>
+    <th>tcBF</th>
+  </tr>
+  <tr>
+    <td>Fig.1i-n</td>
+    <td>mitochondrion</td>
+    <td>STEM</td>
+    <td>14</td>
+    <td>2.37</td>
+    <td>3.59<br>(up-sample 8)</td>
+    <td>3978.4</td>
+    <td>1943.6</td>
+    <td>547</td>
+    <td>0.171</td>
+    <td>0.533</td>
+  </tr>
+  <tr>
+    <td>Fig.3a-d</td>
+    <td>E.coli</td>
+    <td>EFTEM</td>
+    <td>14</td>
+    <td>2.37</td>
+    <td>3.59<br>(up-sample 8)</td>
+    <td>3743.8</td>
+    <td>4262.9</td>
+    <td>673</td>
+    <td>0.114</td>
+    <td>0.403</td>
+  </tr>
+  <tr>
+    <td>Fig.3e-h</td>
+    <td>vesicle</td>
+    <td>EFTEM</td>
+    <td>14</td>
+    <td>2.37</td>
+    <td>3.59<br>(up-sample 8)</td>
+    <td>2849.2</td>
+    <td>2825.0</td>
+    <td>586</td>
+    <td>0.151</td>
+    <td>0.522</td>
+  </tr>
+  <tr>
+    <td>Fig.3i-l</td>
+    <td>E.coli</td>
+    <td>STEM</td>
+    <td>0.5</td>
+    <td>12.96<br>(bin by 4)</td>
+    <td>10.8<br>(up-sample 4)</td>
+    <td>4000<br>(nominal**)</td>
+    <td>4000<br>(nominal)</td>
+    <td>--</td>
+    <td>--</td>
+    <td>--</td>
+  </tr>
+</table>
+
+All data were acquired with 300 kV acceleration voltage at cryogenic temperature
+* Average thickness is estimated with inelastic scattering MFP using the ratio of electrons in the 10-eV EFTEM image and the incident electrons over vacuum.
+** Nominal defocus is the calibrated instrument defocus after focusing using a nearby area
+
+Table I. Summary for the information on specimen, doses, pixel sizes, measured or nominal defocus, thickness estimate using the inelastic MFP, and a comparison of the dose efficiency of EFTEM and tcBF.
+a.
+
+Fraction of electrons remaining
+
+tcBF
+EFTEM
+
+Sample Thickness (nm)
+
+b.
+
+Axial BF
+tcBF
+tcBF Envelope
+DPC
+
+PCTF
+
+α    2α
+
+c.
+
+tcBF
+tcBF Envelope
+iDPC
+
+DQE
+
+q [Å^{-1}]
+Figure 4. (a) Collection efficiency of EFTEM (no objective aperture) and tcBF (7 mrad aperture), showing the measured fraction of electrons left in the image compared to the incident beam as a function of sample thickness from the data sets in table 1. tcBF is seen to retain over 3-4x more signal than EFTEM. The sample thickness is determined from the EFTEM fraction, assuming an inelastic MFP of 310 nm. From this, the decay of the unfiltered tcBF images gives an elastic MFP of 830±50 nm. (b) Comparison of the contrast transfer functions for tcBF, axial BF, and in-focus DPC for a 5.5 mrad probe-forming aperture, \( \alpha \). The axial BF CTF cuts off at \( \alpha \), while the DPC and tcBF information limits extend to \( 2\alpha \). The damping envelope for tcBF follows the classic double-overlap form expected from summing over the tilted CTF functions in supplementary figures S6 and S7. The DPC signal peaks close to \( \alpha \) and is suppressed at low frequencies compared to the defocus-optimized tcBF but is more efficient from \( \alpha \) to \( 2\alpha \). The iDPC CTF has the same shape as the damping envelope but does not reflect the true information transfer. The iDPC CTF is obtained by dividing the measured DPC signal by spatial frequency, which also amplifies noise by the same proportion, resulting in a vanishingly small signal/noise ratio at low spatial frequencies (see online methods for analytic derivations). (c) The result is the DQE for iDPC is the same as that for DPC and both have poor efficiency at transferring low frequencies. Defocused tcBF is very efficient at transferring low frequencies.
+Figure 5. | Single particle analysis 3D reconstruction from tcBF-STEM imaging of hydrated vitrified coat protein of bacteriophage PP7. A representative up-sampled tcBF- STEM image at 300 kV with 11 Šscan step size and a total dose of 45 e-/Ų is shown in (a) with a 2D class average in the inset. The 3D density map resolved from 789 particles is shown in (b) with a zoom-in view of the PDB 1DWN model fit inside the density map in (c). ~7 Šnominal resolution is reached based on the Fourier Shell Correlation (FSC) with 0.143 cutoff.
+Fig. S1| A contour plot of the thickness estimate for the sample shown in Fig.1i-n. The thickness is estimated with the inelastic MFP using Beer’s law. Using the EFTEM dataset, we obtain a ratio of I0/I, where I0 is the intensity recorded over vacuum, and I is the energy filtered intensity with a 10-eV slit recorded over the sample. The thickness is estimated ln(I0/I)*inelastic MFP. The inelastic MFP used here is 310 nm for vitrified ice at 300 kV41.
+
+![EFTEM image and thickness estimate with inelastic MFP contour plot](page_256_180_1024_480.png)
+Fig. S2| To facilitate sub-scan-pixel image shifting, each real-space image formed by a single detector pixel is first padded with zero-intensity pixels. In (a), there is a bright field image formed using a single detector pixel for a standard gold-on-carbon sample under the previously described imaging condition in Fig.2. Each pixel (b) in the image (a) becomes an 8x8 pixel block (c) after padding. The padding process only involves inserting zero values between the original pixels without altering their values.
+Fig. S3| Normalization of uneven distributions of sub-pixel shifts: the same up-sampled image shown in Fig. 2d with the periodic intensity variations amplified in the blue-boxed area (b) for better visibility. By tracking the sub-pixel shift distribution (d) and applying an intensity normalization based on this distribution, the periodic artifacts can be corrected (c).
+Fig. S4| Higher-order interpolation padding: line profiles (left) illustrate in 1D the results of padding with zero-intensity pixels and progressing to quintic interpolation values. The corresponding FFTs of the up-sampled images are shown on the right.
+Fig. S5| The aperture-free, complex PCTF for 300 kV electrons and 700 nm defocus in a Zemlin tilt-tableau out to 5.5 mrad of tilt. The x-y coordinates within each frame are spatial frequencies of the image, \( \boldsymbol{\omega} \), and the tilt offset of each frame is \( \boldsymbol{\theta} \). With no objective (condenser) aperture and no higher order aberrations, the power spectrum of each image under tilted illumination is identical.
+Fig. S6| The symmetric and antisymmetric components of the PCTF for 300 kV electrons with a 5.5 mrad objective (condenser for STEM) in a Zemlin tilt-tableau out to 5.5 mrad of tilt.
+
+(a) \( \Re(PCTF) \) at 700 nm defocus showing the symmetric, Friedel term, (b) \( \Im(PCTF) \) at 700 nm defocus showing the anti-symmetric, anti-Friedel term. The phase ramp across each individual PCTF reflects a shift in real space of the imaged object. Shifting the individual images corrects for the tilt-induced phase ramp, and subsequently summing the tilt-corrected images gives the PCTF shown in Figure 2f. (c) \( \Im(PCTF) \) at zero defocus, again showing its anti-symmetric nature. The DPC-x image is formed by subtracting the left tilts from the right.
+Fig. S7| The power spectrum for 300 kV electrons and 700 nm defocus with a 5.5 mrad objective (condenser) in a Zemlin tilt-tableau out to 5.5 mrad of tilt. This highlights the strong modulations in the overlap region, and the weaker transfer in the sidelobes, but with an information limit of twice the aperture radius.
+
+![The power spectrum for 300 kV electrons and 700 nm defocus with a 5.5 mrad objective (condenser) in a Zemlin tilt-tableau out to 5.5 mrad of tilt.](page_184_120_1207_670.png)
+Fig.S8| Dose Tolerance for tcBF-STEM images collected sequentially with increasing dose: (a) 1.3 e⁻/Ų, (b) 15.2 e⁻/Ų, (c) 57.6 e⁻/Ų, (d) 210.5 e⁻/Ų. Large-length-scale features in the specimen appear tolerant to a high cumulative dose, with no bubbling appearing even in the final exposure where the cumulative dose is 286 e⁻/Ų.
+
+![Dose tolerance STEM images showing sequential dose effects](page_184_180_1207_246.png)
+Fig. S9| To overcome the low-SNR challenge for imaging frozen-hydrated apoferritin, 4-by-4 detector pixels are combined for successful cross-correlation (a). Fitting the shifts to the aberration function and applying the results to the original detector pixels help restore the information from individual detector pixels and improve image shift accuracy (b). The maps in the insets (i) present the shifts of images formed by each detector pixel, with the intensities indicating the magnitudes and the colors corresponding to the directions. The Fourier Ring Correlating (FRC) in the inset (ii) confirms the resolution enhancement by leveraging aberration, improving the cut-off resolution from 38.5 Å to 6.9 Å. For the thicker E.coli sample, the tcBF image with image shifts resolved on binned detector pixels (c) reveals the bilayer cell membrane and details in the interior of the cell. Leveraging aberration fitting results (d) pushes the resolution from 28.1 Å to 11.6 Å (inset (ii)). The 1/7 correlation threshold and the Nyquist
+sampling limit are labelled in the FRC plot. The images in (a) to (d) are cropped to show and the FRCs are computed with the full field of view. To calculate the FRC for tcBF-STEM, we generate two tcBF-STEM images from a single dataset by choosing alternating pixels within the BF disks and then reconstructing each subset independently. The normalized cross-correlation coefficient between the two resulting images represents the FRC of the dataset.
+Fig S10| EFTEM of VLP PP7 SPA with 900 particles reaches a nominal resolution of 3.36Å. The EFTEM data is acquired on a Cs-corrected TFS Krios at an accelerating voltage of 300 kV. The image pixel size is 1.076 Å and the total dose is 52.18 e-/Ų. The defocus ranges from -1μm to -2μm. The final reconstruction is obtained with 900 particles and the analysis is done with cryoSPARC44.
+Fig S11| Cryo-iDPC on VLP PP7: the iDPC data was acquired using the TFS Panther detector on a TFS Spectra at 300 kV. Utilizing an in-house MATLAB code, iDPC images were generated (left), incorporating a high-pass filter (right) to eliminate low-frequency noise51.
+
+![Cryo-iDPC images before and after high-pass filtering](page_246_180_1092_420.png)
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03e6375d91ba2acc0d93fa9c97f15a5154400d7aed2f4249391cfd96e1971e8e/peer_review/peer_review.md

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+Peer Review File
+
+Ultra-rapid and highly efficient enrichment of organic pollutants via magnetic nanoparticles/mesoporous nanospunge for ultrasensitive nanosensors
+
+Open Access This file is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. In the cases where the authors are anonymous, such as is the case for the reports of anonymous peer reviewers, author attribution should be to 'Anonymous Referee' followed by a clear attribution to the source work. The images or other third party material in this file are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.
+Reviewers’ comments:
+
+Reviewer #1 (Remarks to the Author):
+
+The manuscript titled ‘Ultra-rapid and highly efficient enrichment of organic pollutants via magnetic nanoparticles/mesoporous nanospone compounds for ultrasensitive nanosensors’ written by Zhang et al presented a strategy for enrichment sensing of organic pollutants based on a powerful porous composite material, consisting of magnetic nanoparticles immobilized porous β-cyclodextrin polymers. The results showed that the ~90% removal efficiency can reach within ~1 min and the polymer adsorbent can be easily recycled from water and re-dispersed in ethanol so that the target molecules in the cavity of adsorbent is concentrated, with an enrichment factor up to ~103. The manuscript is carefully written and the logic is clear, so I think it belongs to Nature Communication with the following issues being addressed:
+1. In the introduction section, the author introduced the background of surface-enhanced Raman scattering (SERS) and its limitations in detecting organic pollutants. I think this work has mainly reported a sample preparation method and doesn’t face to resolve the scientific problems about SERS, so it is better to add some current sample preparation methods for organic pollutants detection based on magnetic nanoparticle and reduce some description about SERS limitations.
+2. In Figure 2d, the FT-IR spectrum of the MN-PCDP displayed a new peak at 1265 cm-1 in relation to the newly formed C-F group, it is better to draw the chemical structure of the formed C-F bond. And I wonder the reasons about the selection of cross-linking agent TFT, and does the author has another try to combine the cross-linking agent and the β-CD? Figure 2a also showed the TEM images of MN, PCDP, and MN-PCDP. The high surface area and permanent porosity of MN-PCDP mesoporous nanospone enable the rapid removals. It is better to show some screening experiments results in the supporting information to prove the optimal experimental condition.
+3. In Figure 3a, the time-dependent adsorptions of various organic micropollutants adsorbed by MN-PCDP usually contain aromatic model compounds, does the absorption for organic molecules which are rich in alkane chain also work? And can the author also explain the mechanism about the high removal efficiency?
+4. In Supplementary Figure 13, the fluorescence spectra of BPA before and after the enrichment of MN-PCDP adsorbent seems different and there are many spikes in Figure S13a and it is very smooth in Figure S13b, does it completely caused by the counts difference or exist other reasons? The author may unify it in both spectrums.
+5. The study of nanoparticles sensing has been reached to single-particle level, such as single-nanoparticle electrochemistry. Also, some other nano-techniques for example, nanopore sensing based on single-molecule detection at confined space has been developed to improve the limits of detection (LOD). I wonder could the authors give some perspective on measurements science at single nanoparticle level in the manuscript. Please see the examples, ACS Sens. 2019, 4, 1185-1189., Anal. Chem. 2020. 92, 8, 5621-5644., Small Methods 2018, 1700390., Angew. Chem. Int. Ed. 2013, 52, 6011 –6014., Electrochem. Comm. ,2011, 13, 335–337.
+
+Reviewer #2 (Remarks to the Author):
+
+The manuscript is about the fabrication of a polymer based on the combination of beta-CD and magnetic NPs with high performance for rapid and highly efficient enrichment of organic pollutants. I found in the literature that the similar porous materials also combining magnetic NPs and CD have been already used for extraction of different organic molecules. Therefore the novelty of the paper is compromised.
+Therefore the novelty is limited to the performance of the materials. Nevertheless, it is not demostrated the selectivity or the preformance in samples with mixture of pollutants. Therefore, this work is not suitable for Nat. Comm.
+
+On the other hand the work is well presented and the data analysis is correct.
+
+Reviewer #3 (Remarks to the Author):
+
+My major concern is this study’s novelty. Above of all, the concept of target enrichment is not novel, and magnetic nanoparticles functionalized with β-cyclodextrin have been extensively studied with widespread applications including organic pollutant sensing. In addition, the proposed method failed to offer a significantly improvement with respect to sensitivity and reproducibility compared to other related methods. Thus, it is not recommended for publication in Nature Communications.
+Response to Reviewers' comments:
+
+Reviewer #1 (Remarks to the Author):
+The manuscript titled ‘Ultra-rapid and highly efficient enrichment of organic pollutants via magnetic nanoparticles/mesoporous nanosponge compounds for ultrasensitive nanosensors’ written by Zhang et al presented a strategy for enrichment sensing of organic pollutants based on a powerful porous composite material, consisting of magnetic nanoparticles immobilized porous β-cyclodextrin polymers. The results showed that the ~90% removal efficiency can reach within ~1 min and the polymer adsorbent can be easily recycled from water and re-dispersed in ethanol so that the target molecules in the cavity of adsorbent is concentrated, with an enrichment factor up to ~103. The manuscript is carefully written and the logic is clear, so I think it belongs to Nature Communication with the following issues being addressed:
+
+1. In the introduction section, the author introduced the background of surface-enhanced Raman scattering (SERS) and its limitations in detecting organic pollutants. I think this work has mainly reported a sample preparation method and doesn’t face to resolve the scientific problems about SERS, so it is better to add some current sample preparation methods for organic pollutants detection based on magnetic nanoparticle and reduce some description about SERS limitations.
+
+Response: Thanks for the suggestion from the reviewer. With the enlightenment from such questions, we have rewrote the manuscript. In fact, it seems surprising that after fifty decades, SERS has not yet been widely used in practical applications. This is owing to the fact that, besides the stability of SERS substrates and reproducibility of spot-to-spot, SERS still faces two major bottlenecks in commercial market. The first is the low detection sensitivity to the molecules of intrinsic small cross-sections or weak affinity to metal surface. The second is the interference from the complex matrices in real-sample detection. With the revised version, we reconsidered the work and highlighted the capability of current detection strategy in selective adsorption to interested molecules, particularly from the complex matrix in the real-sample environment. This point is the key scientific problems about SERS. Certainly, the current enrichment strategy can be used in a wide detection protocols such as SERS, fluorescence, UV-vis, even Mass Spectrometry, Chromatography, and others.
+
+Thus, in the revised version, we added some experiments and discussions about the SERS detection in real-sample environments, inspired by the comments from reviewers. The correlated
+revised parts in the Introduction section 2 and 3 has been updated.
+
+2. In Figure 2d, the FT-IR spectrum of the MN-PCDP displayed a new peak at 1265 cm^{-1} in relation to the newly formed C-F group, it is better to draw the chemical structure of the formed C-F bond. And I wonder the reasons about the selection of cross-linking agent TFT, and does the author has another try to combine the cross-linking agent and the β-CD? Figure 2a also showed the TEM images of MN, PCDP, and MN-PCDP. The high surface area and permanent porosity of MN-PCDP mesoporous nanospounce enable the rapid removals. It is better to show some screening experiments results in the supporting information to prove the optimal experimental condition.
+
+Response: We appreciate the suggestion from the reviewer. First, we are regretful for a mistake about the description of FT-IR peak at 1265 cm^{-1}. This peak in relation to the C-F group was existing in TFT, but the signal intensity of this absorption peak at 1265 cm^{-1} is weaker than that in TFT owing to the partial replacement of F, implying that the β-CD has been crosslinked with TFT. Second, as a comparison, in the revised version, we chose anther cross-linking agent (epichlorohydrin, EPI), which is the most extensively studied β-CD polymer for water purification, to combine the β-CD. As shown in Supplementary Fig. 6, the removal efficiency of BPA by MNEPI-CDP was much lower than MNP-CDP. The correlated revised parts of the manuscript are shown as following:
+
+Page 5, Paragraph 1: The signal intensity of absorption peak at 1265 cm^{-1} in relation to C-F stretching vibration is weaker than that in TFT owing to the partial replacement of F,\(^{23,24}\) implying that the β-CD has been crosslinked with TFT (Supplementary Fig.2).
+
+Page 6, Paragraph 1: In this work, different cross-linking agent, e.g. epichlorohydrin (EPI) is compared (Supplementary Fig. 7). As shown in Supplementary Fig. 8, the removal efficiency of BPA by MNEPI-CDP in 1 min is 19.5%, which is much lower than MN-PCDP.
+
+![Schematic about the synthesis of β-CD polymer (PCDP)](page_101_1042_1242_222.png)
+
+Supplementary Figure 2 | schematic about the synthesis of β-CD polymer (PCDP).
+Supplementary Figure 7 | schematic about the synthesis of β-CD polymer crosslinked by EPI (EPI-CDP).
+
+Supplementary Figure 8 | Uptake of pollutant by MNEPI-CDP. UV–vis spectra and removal efficiency recorded at different contact times of bisphenol A solution (0.1 mM) by MNEPI-CDP (1 mg mL^{-1}).
+
+3. In Figure 3a, the time-dependent adsorptions of various organic micropollutants adsorbed by MN-PCDP usually contain aromatic model compounds, does the absorption for organic molecules which are rich in alkane chain also work? And can the author also explain the mechanism about the high removal efficiency?
+
+Response: Thanks for the advice from the reviewer. We added some absorption experiments of organic molecules with alkane chain to explain the mechanism about the high removal efficiency. The correlated revised parts of the manuscript are shown as following:
+Page 6, Paragraph 2: As is known, the hydroxyl groups of β-CD are located at the outer surface of the molecule, that is, primary hydroxyls at the narrow side and secondary hydroxyls at the wider side, which makes β-CD water-soluble but simultaneously generates an inner cavity that is relatively hydrophobic.\(^{27}\) Because of their hydrophobic interior cavity, β-CD can either partially or entirely accommodate suitably sized lipophilic low molecular weight molecules or even polymers.\(^{28}\) For example, MN-PCDP exhibits a remarkable adsorption capability and selectivity
+for most aromatics and some chain compounds, as shown in Fig. 2a and Supplementary Fig. 10-11. Furthermore, by means of particular treatments such as changing pH value of solution,\(^{29}\) the adsorption feature of molecules can be tuned. Thus, the MN-PCDP mesoporous nanospone will display a wide applicability and selectivity in a variety of molecules.
+
+![UV–vis spectra at different contact times of DMF (0.1 mM, a), PFOA (1 mM, b), CTAB (0.1 mM, c), CCC (1 mM, d), TMTD (0.1 mM, e) and HMTA (1 mM, f) with the adsorbent (1 mg mL\(^{-1}\)).](page_347_682_1057_627.png)
+
+Supplementary Figure 10 | Uptake of pollutant by MN-PCDP. UV–vis spectra at different contact times of DMF (0.1 mM, a), PFOA (1 mM, b), CTAB (0.1 mM, c), CCC (1 mM, d), TMTD (0.1 mM, e) and HMTA (1 mM, f) with the adsorbent (1 mg mL\(^{-1}\)).
+Supplementary Figure 11 | Uptake of pollutant by MNP-CDP. UV–vis spectra at different contact times of MG (0.01 mM, a) and SY (0.01 mM, b) with the adsorbent (1 mg mL^{-1}).
+
+4. In Supplementary Figure 13, the fluorescence spectra of BPA before and after the enrichment of MN-PCDP adsorbent seems different and there are many spikes in Figure S13a and it is very smooth in Figure S13b, does it completely caused by the counts difference or exist other reasons? The author may unify it in both spectrums.
+
+Response: Thanks for your reminder. In the Supplementary Figure 13, the concentration of BPA in the fluorescence spectra after the enrichment of MN-PCDP adsorbent was the original concentration of BPA. In this circumstance, after the enrichment of MN-PCDP adsorbent, the “concentration” of BPA was much high than the original. Thus, the Figure S13b seemed like more smooth. Here, in order to avoid this misunderstand, we used the lower concentration of BPA in Figure S13b and estimated the concentration after enrichment (according the enrichment factor ~500 fold). The correlated revised parts of the manuscript are shown as following:
+
+![Fluorescence spectra of BPA before and after enrichment](page_276_682_900_320.png)
+
+Supplementary Figure 18 | Fluorescence spectra of BPA a before and b after the enrichment of MN-PCDP adsorbent. The concentration in the parentheses was estimated the concentration after enrichment (enrichment ~500 fold).
+
+5. The study of nanoparticles sensing has been reached to single-particle level, such as single-nanoparticle electrochemistry. Also, some other nano-techniques for example, nanopore sensing based on single-molecule detection at confined space has been developed to improve the limits of detection (LOD). I wonder could the authors give some perspective on measurements science at single nanoparticle level in the manuscript. Please see the examples, ACS Sens. 2019, 4, 1185-
+Response: Thanks for your advice. Here, we give two kind of perspective about the single-molecule detection at confined space. The correlated revised parts of the manuscript are shown as following:
+Page 11, Paragraph 1: In the future, single particle-MN-PCDP combining with Au NPs (SERS substrate) could dramatically lower the detection limit and enables higher spatial and temporal resolution,\(^{35-39}\) thus build single NP sensor to improve detection sensitivity (Supplementary Fig. 24).
+
+![Schematic of measurements at single nanoparticle level. by MN-PCDP. a Single Fe3O4-Au core-shell structure nanoparticle with crosslinked porous β-CD polymer on the surface, detection solution with target molecular is concentrated from 50 μL to 3.4×10^{-8} μL (enrichment ~1.5×10^9 fold). b MN-PCDP with Au NPs on the surface, detection solution with target molecular is concentrated from 50 μL to 4.2×10^{-6} μL (enrichment ~1.2×10^7 fold).](page_320_670_1007_377.png)
+
+Supplementary Figure 24 | Schematic of measurements at single nanoparticle level. by MN-PCDP. **a** Single Fe\(_3\)O\(_4\)-Au core-shell structure nanoparticle with crosslinked porous β-CD polymer on the surface, detection solution with target molecular is concentrated from 50 μL to 3.4×10^{-8} μL (enrichment ~1.5×10^9 fold). **b** MN-PCDP with Au NPs on the surface, detection solution with target molecular is concentrated from 50 μL to 4.2×10^{-6} μL (enrichment ~1.2×10^7 fold).
+
+References
+35 Li, Q. et al. Detection of single proteins with a general nanopore sensor. *ACS Sens.* **4**, 1185–1189, doi: 10.1021/acssensors.9b00228 (2019).
+36 Lu, S. et al. Electrochemical sensing at a confined space. *Anal. Chem.* **92**, 5621–5644, doi: 10.1021/acs.analchem.0c00931 (2020).
+37 Ying, Y. et al. Electrochemical confinement effects for innovating new nanopore sensing mechanisms. Small Methods **2**, 1700390, doi: 10.1002/smtd.201700390 (2018).
+38 Shi, L. et al. Plasmon resonance scattering spectroscopy at the single nanoparticle level: real-time monitoring of a click reaction. Angew. Chem. Int. Ed. **52**, 6011 –6014, doi: 10.1002/ange.201301930 (2013).
+39 Gao, Q. et al. Highly sensitive impedimetric sensing of DNA hybridization based on the target DNA-induced displacement of gold nanoparticles attached to ssDNA probe. Electrochem. Commun. **13**, 335–337, doi: 10.1016/j.elecom.2011.01.018 (2013).
+
+Reviewer #2 (Remarks to the Author):
+The manuscript is about the fabrication of a polymer based on the combination of beta-CD and magnetic NPs with high performance for rapid and highly efficient enrichment of organic pollutants. I found in the literature that the similar porous materials also combining magnetic NPs and CD have been already used for extraction of different organic molecules. Therefore, the novelty of the paper is compromised. Journal of Chromatography A, 1503 (2017) 1–111; https://doi.org/10.1016/j.scitotenv.2020.138789. Therefore the novelty is limited to the performance of the materials. Nevertheless, it is not demostrated the selectivity or the preformance in samples with mixture of pollutants. Therefore, this work is not suitable for Nat. Comm.
+
+Response: Thanks for your comments. After receiving the comments from referees, we noticed that probably, referees provided such commens is because that we cannot demonstrate the novelty and significance of this work clearly in the introduction part. In fact, after carfully read the suggested two papers, i.e. *Science of the Total Environment* **728 (2020) 138789** and *Journal of Chromatography A*, **1503 (2017) 1–11**, we would like to highlight the concept of extraction in mentioned two papers and our “enrichment” in our manuscript. In addition, with the enlightenment from referees, we have noticed that the selectivity and the performance in detection of complex matrix in real-sample environment indeed are very important. Thus, in the revised version, we have updated these data, and rewrote the manuscript. In the following, we shall explain in details.
+
+1) Concerning the concept of extraction in mentioned two papers and our “enrichment” in our
+manuscript. I have read the extraction related references (including the suggested papers, Science of the Total Environment 728 (2020) 138789 and Journal of Chromatography A, 1503 (2017) 1–11). Yes, they indeed used the similar porous materials. However, reviewer is interesting of “the selectivity or the performance of the materials” since extraction is to select target molecule from complex system. E.g., extraction (adsorption) of organic molecules (microcystins or PAHs) from environmental water or soil sample in suggested two papers. Selectivity is the first importance in this kind of work, i.e. selective adsorption interested molecules from multiple-molecules system. They did not notice to improve the removal speed, and enrichment capability, thus you may see that in above two papers, one used nearly one hour to extract and 7 min to desorb and the other paper used high concentration adsorption materials and desorbed in a large volume of desorption solvent. The extraction process if operation into a traditional solid state extraction cartridges, the separating rate is relatively slow. Normally, the speed of extraction is 0.5-5 mL/min, which can not meet our current study motivation with very fast enrichment operation. Extraction seems to be more the work for environmental scientists, e.g. water or soil treatment.
+
+However, in our current work, we are aiming our work to develop a new detection strategy for trace pollutants, and we paid our attention to the enrichment capability and fast operation, (in the following, we shall list the novelty and advance of this work), which is very important for the practical application in protable, fast, on site detection. Thus, our enrichment strategy is different from classical extraction process.
+
+With the enlightenment of referees, we reconsidered and updated the significance and novelty of this work, and we want to emphasize here: we explored a very effective enrichment and detection strategy with remarkable performance including
+
+1) ultra-fast removal speed within ten second to ~1 min,
+2) high removal efficiency up to ~90%,
+3) ultra-fast desorption speed, within ten seconds to ~1 min,
+4) high desorption efficiency up to ~100%,
+
+5) selectivity to interested target molecules thus benefit to the detection of real-samples free from interference of impurities or fluorescence background (this point is new enlightened by referees),
+
+6) totally high enrichment factor thus high increased sensitivity up to 10(3) level within 2~3
+min operation period which is very critical for the practical application in portable, fast, on site detection.
+
+7) wide application potential for SERS, fluorescence, UV-vis and other sensing strategies.
+
+In addition, to improve our enrichment capability and fast operation, we referred a recent reported best processes to prepare the mesoporous -cyclodextrin polymer published in Nature, 2016, 529, 190, cited in our manuscript in ref 20 in the revised version. We added magnetic particles into this best mesoporous CD polymer. If you compare our results, you may found we demonstrated the best and carefully designed protocols so that we realized (repeated here again) above seven performance.
+
+In the revised version, with the enlightenment from referees, we have updated the data and added the new experiments on the selectivity and the performance in detection of complex matrix in real-sample environment, which are indeed very important.
+
+In our revised version of manuscript, we have added Figure 5, and related text description, and also some data in supporting information. These include,
+
+Fig. 5a shows that the adsorbent was easily collected on the wall of beaker with a magnet by our porous composite material from the complex matrix, such as mud and microorganism.
+
+Page 9, Paragraph 2: Based on the distinguishing and selective absorption capacity for different molecules (Fig. 2 and Supplementary Fig. 10-11),\(^{34}\) the mesoporous nanospone is expected to be used in the separation of interested molecules from the mixed systems. As shown in Fig. 5b and Supplementary Fig. 19a-c, the MG (malachite green) and sunset yellow (SY) molecules are firstly mixed together and became to be the mixture solution (MG+SY) (Fig. 5b-i-ii). Then, after adsorption and separation processes using MN-PCDP, clearly, there is only SY left in the mixture solution (Fig. 5b-iii). Similarly, with a desorption process, the MG molecule is also successfully separated (Fig. 5b-iv). Following, two different pesticide molecules, namely CCC and TMTD, are used to further evaluate the selective separation using SERS detection (Fig. 5c-i-iii). Obviously, once TMTD is captured and separated by MN-PCDP adsorbent, the SERS signals of CCC in the mixture solution significantly increases (Fig. 5c-iv), indicating that most TMTD molecules have been adsorbed. Moreover, only TMTD molecules from Raman (Fig. 5c-v) and UV-vis spectra (Supplementary Fig. 20) can be observed, illustrating only TMTD is effectively selected and separated by MN-PCDP.
+
+Page 9, Paragraph 3: Another advantage of the current enrichment protocol is that the
+interference of complex matrix can be effectively eliminated in the detection of real-sample system. After adsorption process, the MN-PCDP adsorbent can be easily separated by a magnet from a complicated environment containing, e.g. mud and microorganism (Fig. 5a). Fig. 5d and Supplementary Fig. 21 exhibit the UV-vis spectra of carbendazim at a concentration of 0.01 mM in the filtered soil solution. It can be observed that the characteristic absorption peaks of carbendazim are very weak even after filtration. However, using current selective separation and enrichment protocol, the absorption peaks intensity of carbendazim (Fig. 5d), BPA (Supplementary Fig. 21a) and MG (Supplementary Fig. 21b) are respectively increased 463, 550, and 516 times comparing with pure carbendazim solution. Similarly, as shown in Fig. 5e and Supplementary Fig. 22, when the concentration of detection molecules goes down to 0.1 \( \mu \)M, the SERS signals of carbendazim molecule in practical soil solution samples even after filtration are almost unobservable, whereas they can be easily detected after selective enrichment by MN-PCDP.
+
+Page 10, Paragraph 2: In addition, in the real environment, more than one molecule is always studied, thus it is very important to realize the simultaneous detection of multiple molecules, especially in the existence of matrix interference. Fig. 5f reveals that both the characteristic peaks of BPA (830 and 1179 cm\(^{-1}\)) and carbendazim (1008, 1244 and 1263 cm\(^{-1}\)) evidently appear in the Raman spectra of mixture solution, e.g. 1 \( \mu \)M BPA and 10 nM carbendazim, indicating the great absorption and detection capability for different molecules at the same time
+Fig. 5 Separation and selective enrichment in complex matrix used this strategy. a Optical photographs about the enrichment process of MN-PCDP in mud water. b UV–vis spectra of SY (i, 0.01 mM), MG (i, 0.01 mM) and SY/MG (ii, both with 0.01 mM) mixture solution before and after absorption, desorption. iii The filtration mixture solution after the absorption of MN-PCDP for MG. iv The desorption solution of captured molecules (MG) redispersed in ethanol from the cavity of MN-PCDP adsorbent. c Raman spectra of CCC (i, 0.1 mM), TMTD (ii, 1 μM) and iii CCC (0.1 mM) /TMTD (1 μM) mixture solution before and after iv absorption, v desorption. d UV-vis spectra about selective enrichment of organic pollutant molecules (carbendazim, 0.01 mM) from practical samples. e Raman spectra about selective enrichment of organic pollutant molecules (carbendazim, 0.1 μM) from practical samples. f Raman spectrum of mixture after the enrichment process of MN-PCDP in real samples.
+Supplementary Figure 19 | Separation of SY/MG mixture dyes: a photograph of SY (0.01 mM), MG (0.01 mM) and SY/MG (both with 0.01 mM) mixture solution, b photograph of SY/MG mixture solution after absorption by MN-PCDP, c photograph of SY/MG mixture solution after desorption by MN-PCDP.
+
+![Photographs and UV-vis spectra showing separation of SY/MG and CCC/TMTD mixture dyes](page_246_180_755_377.png)
+
+Supplementary Figure 20 | Separation of CCC/TMTD mixture pesticides: UV–vis spectra of CCC (1 mM), TMTD (0.1 mM) and CCC (1 mM)/TMTD (0.1 mM) mixture solution before and after absorption, desorption.
+Supplementary Figure 21 | UV–vis spectra about selective extraction and enrichment of organic pollutant molecules (0.01 mM) from practical samples: **a** BPA in industrial wastewater, **b** MG in pond water.
+
+Supplementary Figure 22 | Raman spectra about selective extraction and enrichment of organic pollutant molecules (0.01 mM) from practical samples: **a** BPA in industrial wastewater, **b** MG in pond water.
+
+Reviewer #3 (Remarks to the Author):
+*My major concern is this study’s novelty. Above of all, the concept of target enrichment is not novel, and magnetic nanoparticles functionalized with \( \beta \)-cyclodextrin have been extensively studied with widespread applications including organic pollutant sensing. In addition, the proposed method failed to offer a significantly improvement with respect to sensitivity and reproducibility compared to other related methods. Thus, it is not recommended for publication in Nature Communications.*
+Response: Thanks for your comments. After receiving the comments from referees, we noticed that probably, referees provided such comments because that we cannot demonstrate the novelty and significance of this work clearly in the introduction part. In fact, after carefully investigate the comments, two points are including, one is that referees said the similar materials have been reported, and the other is that this kind materials has been used for sensing.
+
+Concerning above two points, in the revised version, we have rewrote the introduction, and supplemented new experiments and added them.
+
+For the materials, we want to explain two concept of “extraction” in some publications and our “enrichment” in our manuscript. I have read many extraction related references. Yes, they indeed used the similar porous materials. However, these materials in these publications were mainly used for extraction, which is to select target molecule from complex system. E.g., extraction (adsorption) of organic molecules (microcystins or PAHs) from environmental water or soil sample in suggested two papers. Selectivity is the first importance in this kind of work, i.e. selective adsorption interested molecules from multiple-molecules system. They did not notice to improve the removal speed, and enrichment capability, thus you may see that in above two papers, one used nearly one hour to extract and 7 min to desorb and the other paper used high concentration adsorption materials and desorbed in a large volume of desorption solvent. The extraction process if operation into a traditional solid state extraction cartridges, the separating rate is relatively slow. Normally, the speed of extraction is 0.5-5 mL/min, which can not meet our current study motivation with very fast enrichment operation. Extraction seems to be more the work for environmental scientists, e.g. water or soil treatment.
+
+However, in our current work, we are aiming our work to develop a new detection strategy for trace pollutants, and we paid our attention to the enrichment capability and fast operation, (in the following, we shall list the novelty and advance of this work), which is very important for the practical application in protable, fast, on site detection. Thus, our enrichment strategy is different from classical extraction process.
+
+With the enlightenment of referees, we reconsidered and updated the significance and novelty of this work, and we want to emphasize here: we explored a very effective enrichment and detection strategy with remarkable performance including
+
+1) ultra-fast removal speed within ten second to ~1 min,
+2) high removal efficiency up to ~90%,
+3) ultra-fast desorption speed, within ten seconds to ~1 min,
+4) high desorption efficiency up to ~100%,
+5) selectivity to interested target molecules thus benefit to the detection of real-samples free from interference of impurities or fluorescence background (this point is new enlightened by referees),
+6) totally high enrichment factor thus a high increased sensitivity up to 10(3) level within 2~3 min operation period which is very critical for the practical application in portable, fast, on site detection.
+7) wide application potential for SERS, fluorescence, UV-vis and other sensing strategies.
+
+In addition, to improve our enrichment capability and fast operation, we referred a recent reported best processes to prepare the mesoporous -cyclodextrin polymer published in Nature, 2016, 529, 190, cited in our manuscript in ref 20 in the revised version. We added magnetic particles into this best mesoporous CD polymer. If you compare our results, you may found we demonstrated the best and carefully designed protocols so that we realized (repeated here again) above seven performance.
+
+Concerning the comments of referee “this kind materials has been used for sensing”, we have carefully studied the literatures and according to our knowledge, the organic pollutant sensing from literatures based on the magnetic nanoparticles functionalized with β-cyclodextrin, can be divided into two categories. One is that some magnetic materials decorated with β-cyclodextrin monomer to build up such as electrochemical sensing. In this case, they did not use crosslinked β-cyclodextrin polymers and the absorption capacity of β-cyclodextrin monomer was much less than the crosslinked β-cyclodextrin polymers. Moreover, they did not carry out enrichment related study. The other kind of sensing using this kind of materials is to use crosslinked β-cyclodextrin polymers, but they use for liquid chromatography (HPLC) or photoluminescence spectroscopy sensing, e.g. solid-phase extraction adsorbent. Again, they are studying the extraction and selectivity of target molecule from complex pollutants.
+
+Above two kinds of sensing are quite different as our enrichment and concentration-strategy for detection. More importantly, up to now, we have not found the reports of SERS or fluorescence related sensing based on the current reported highly effective enrichment strategy of magnetic
+nanoparticles immobilized with crosslinked porous β-CD polymer.
+
+Actually, like the nature paper we cited in Ref. 20 in the revised version, the crosslinked porous β-CD polymer have also reported before this work, but this work again reported an improved and excellent performance. Thus we think it is valuable to be published again in Nature. For our work, besides of above senven remarkable performance. We cited this excellent method in Nature, and we added new magnetic design and obtain excellent enrichment properties, and seslectivity capability to eliminate the interference of complex matrix in the real-sample detection environment.
+
+Therefore, the novelty and significance of our manuscript are still there and we are believing it is valuable to be considered for publish in Nature Communications.
+
+----------
+
+As for “the proposed method failed to offer a significantly improvement with respect to sensitivity and reproducibility compared to other related methods.” We listed seven remarkable performance of the current strategy. Actually, item-2), 4), and 6) are related to this questions. Using the current protocol, we realized high efficient adsorption up to ~90%, selective seperation by means of the effects of host-guest inclusion and magnet, desorption with necarly ~100% efficiency, thus the total enrichment capability up to ~1000 times, hence an improved and increased sensitivity up to 10(3) level can be obtained. Particularly, within 2~3 min operation period which is very critical for the practical application in portable, fast, on site detection. These data have been shown in Figure 4 and Figure 5 according to the detection method of SERS or fluorescence spectroscopies.
+
+As for the reproducibility, in the Fig. S22, we provided the adsorption efficiency of different experiment times and consecutive regeneration cycles, indicating the great reproducibility.
+
+In addition, with the enlightenment from referees, we have added many new data in the revised version and we rewrote the manuscript, we added the new results on the selectivity to interested target molecules, thus benefit to the detection of real-samples free from interference of impurities or fluorescence background (Presented in new Figure 5 and supporting information 19-22).
+
+Therefore, I sincerely hope this revised version with many supplemented data can be considered and accept for publication as soon as possible.
+REVIEWER COMMENTS
+
+Reviewer #1 (Remarks to the Author):
+
+The authors addresses my comments very well. I learned a lot from it. Thanks you, I recommend the publication in Nature Communications.
+
+Reviewer #2 (Remarks to the Author):
+
+I think that the authors have made a lot of effort in improving the manuscript, they have included further data regarding the selectivity and multiplexing capabilities of the sensing and extraction platform. But from my point of view, the work is not relevant enough to publish in this journal. I think that it is more suitable for a sister journal.
+
+Reviewer #3 (Remarks to the Author):
+
+By introducing magnetic nanoparticles to an established system (Nature, 2016, 529, 190–194), this study achieved ultra-rapid and highly efficient enrichment of organic pollutants. Magnetic SERS has been extensively studied and applied in organic pollutant sensing (Journal of Environmental Sciences, 2019, 80, 14-34). Compared with those related researches, the proposed study mainly focused on removal speed, and enrichment capability. However, sensitivity and spectral reproducibility are two crucial factors for SERS-based nanosensors, which are more important and should not be neglected. The enrichment ability of such materials makes sense for me, but as an ultrasensitive nanosensor, the following issues haven’t been addressed in the revised manuscript.
+1. No significant improvement in sensitivity has been achieved in this study, comparing with other magnetic SERS-based sensors for organic pollutants.
+2. The authors did nothing to improve the SERS spectral reproducibility, so the accuracy of the proposed method is not convincing.
+3. In my opinion, a SERS nanosensor that combines ultrahigh sensitivity (achieved by high enrichment ability and signal enhancement ability), high spectral reliability, and fast removal speed, is publishable in the high-level journal of Nature Communication.
+Response to Reviewer' comments
+
+Reviewer #1 (Remarks to the Author):
+The authors addresses my comments very well. I learned a lot from it. Thanks you, I recommend the publication in Nature Communications.
+
+Response: Thank you very much for the reviewer’s comments and suggestions.
+
+Reviewer #2 (Remarks to the Author):
+I think that the authors have made a lot of effort in improving the manuscript, they have included further data regarding the selectivity and multiplexing capabilities of the sensing and extraction platform. But from my point of view, the work is not relevant enough to publish in this journal. I think that it is more suitable for a sister journal.
+
+Response: Thank you very much for the reviewer’s comments, just as the recommendation from reviewer-1 and -3, we believe a highly efficient and ultrafast enrichment protocol and a high sensitivity, fast operation, and good repeatability of SERS detection is important to the field and valuable to be published in Nature Communications.
+
+Reviewer #3 (Remarks to the Author):
+By introducing magnetic nanoparticles to an established system (Nature, 2016, 529, 190–194), this study achieved ultra-rapid and highly efficient enrichment of organic pollutants. Magnetic SERS has been extensively studied and applied in organic pollutant sensing (Journal of Environmental Sciences, 2019, 80, 14-34). Compared with those related researches, the proposed study mainly focused on removal speed, and enrichment capability. However, sensitivity and spectral reproducibility are two crucial factors for SERS-based nanosensors, which are more important and should not be neglected.
+The enrichment ability of such materials makes sense for me, but as an ultrasensitive nanosensor, the following issues haven’t been addressed in the revised manuscript.
+
+1. No significant improvement in sensitivity has been achieved in this study, comparing with other magnetic SERS-based sensors for organic pollutants.
+
+Answer: Thanks for the advice from the reviewer. In this manuscript, we realize highly efficient
+enrichment capability up to ~1000 times and the LODs of fluorescence detections for enriched molecules were enhanced by 2~3 orders. Depending on the reviewer comment, in the revised manuscript, the SERS sensitivities of our enrichment method were measured and compared with other reports. As for the SERS sensitivity for the organic pollutants, we chose a more common molecular, TMTD (also called thiram), as the probe molecule to explain the superiorities of our protocol. As shown in Fig. 4a-b, the LOD of TMTD after the enrichment of MN-PCDP is up to 5 fM (Fig. 4c), that is superior to most of the magnetic SERS-based sensors (generally no better than \(10^{-12}\) M). Moreover, as for carbendazim and diquat, the detectabilities are obtained in 5 pM (Supplementary Fig. 18) and 1 pM (Supplementary Fig. 19), respectively, while the similar SERS sensor just achieve to ~nM level. Furthermore, the detectabilities of several analytes are summarized in Table 1, comparing with the similar magnetic SERS-based sensors, the LODs of TMTD, carbendazim, diquat, BPA and anthracene are reached in great sensitivity. The correlated revised revisions are shown as following:
+
+Page 8, Paragraph 2: As shown in Figure 4a-b, without the enrichment process, the LOD of SERS for TMTD is around 1 pM. However, after the enrichment using MN-PCDP adsorbent, this value reaches to ~5 fM, showing an increase of \(10^2\sim10^3\). Meanwhile, based on this enrichment protocol, the detachabilities of BPA, carbendazim, diquat anthracene are up to 0.1 nM, 5 pM, 1 pM, and 1 nM (Supplementary Fig. 17-20), which are much lower than most of the magnetic SERS-based sensors (Table 1).
+
+![Enhanced Raman spectra of TMTD before and after enrichment process of MN-PCDP.](page_682_1042_627_246.png)
+
+Fig. 4 Enhanced Raman spectra of TMTD **a** before and **b** after enrichment process of MN-PCDP.
+Supplementary Figure 19 | Enhanced Raman spectra of diquat **a** before and **b** after the enrichment of MN-PCDP adsorbent. The characteristic peaks of diquat were at 1061, 1170, 1376 and 1563 cm\(^{-1}\).
+
+Supplementary Figure 20 | Enhanced Raman spectra of anthracene **a** before and **b** after the enrichment of MN-PCDP adsorbent. The characteristic peaks of anthracene were at 748, 1160, 1389, and 1540 cm\(^{-1}\).
+
+Table 1 Detectability of the MNPs for organic pollutants reported in the literature
+
+<table>
+  <tr>
+    <th>Types of MNPs<sup>a</sup></th>
+    <th>Analyte</th>
+    <th>LOD</th>
+    <th>Ref.</th>
+  </tr>
+  <tr>
+    <td>MN-PCDP</td>
+    <td>TMTD</td>
+    <td>5×10\(^{-15}\) M</td>
+    <td>This work</td>
+  </tr>
+  <tr>
+    <td>Fe\(_3\)O\(_4\)@SiO\(_2\)@Ag nanospindles</td>
+    <td>TMTD</td>
+    <td>10\(^{-7}\) M</td>
+    <td>[31]</td>
+  </tr>
+  <tr>
+    <td>Fe\(_3\)O\(_4\)@Au NRs array</td>
+    <td>TMTD</td>
+    <td>10\(^{-9}\) M</td>
+    <td>[32]</td>
+  </tr>
+  <tr>
+    <td>Fe\(_3\)O\(_4\)@SiO\(_2\)@Ag core-shell MNPs</td>
+    <td>TMTD</td>
+    <td>10\(^{-9}\) M</td>
+    <td>[33]</td>
+  </tr>
+  <tr>
+    <td>Cube-like Fe\(_3\)O\(_4\)@SiO\(_2\)@Au@Ag</td>
+    <td>TMTD</td>
+    <td>5×10\(^{-11}\) M</td>
+    <td>[34]</td>
+  </tr>
+  <tr>
+    <td>Flower-like Fe\(_3\)O\(_4\)@SiO\(_2\)@Ag</td>
+    <td>TMTD</td>
+    <td>10\(^{-11}\) M</td>
+    <td>[35]</td>
+  </tr>
+  <tr>
+    <td>Fe\(_3\)O\(_4\)@Ag-PEI-Au@Ag</td>
+    <td>TMTD</td>
+    <td>5×10\(^{-12}\) M</td>
+    <td>[36]</td>
+  </tr>
+  <tr>
+    <td>Au@Fe\(_3\)O\(_4\) network</td>
+    <td>TMTD</td>
+    <td>5×10\(^{-14}\) M</td>
+    <td>[37]</td>
+  </tr>
+</table>
+<table>
+  <tr>
+    <th>MN-PCDP</th>
+    <th>Diquat</th>
+    <th>10^{-12} M</th>
+    <th>This work</th>
+  </tr>
+  <tr>
+    <td>Fe_{3}O_{4}@AuNRs assemblies</td>
+    <td>Diquat</td>
+    <td>10^{-9} M</td>
+    <td>[32]</td>
+  </tr>
+  <tr>
+    <td>Fe_{3}O_{4}@Ag-PEI-Au@Ag</td>
+    <td>Paraquat<sup>b</sup></td>
+    <td>10^{-10} M</td>
+    <td>[36]</td>
+  </tr>
+  <tr>
+    <th>MN-PCDP</th>
+    <th>Carbendazim</th>
+    <th>5\times10^{-12} M</th>
+    <th>This work</th>
+  </tr>
+  <tr>
+    <td>Au/Fe_{3}O_{4} nanocomposite</td>
+    <td>Carbendazim</td>
+    <td>2.3\times10^{-9} M</td>
+    <td>[38]</td>
+  </tr>
+  <tr>
+    <th>MN-PCDP</th>
+    <th>BPA</th>
+    <th>10^{-10} M</th>
+    <th>This work</th>
+  </tr>
+  <tr>
+    <td>Magnetic gold nanoclusters</td>
+    <td>BPA</td>
+    <td>10^{-9} M</td>
+    <td>[39]</td>
+  </tr>
+  <tr>
+    <td>Magnetic-bead biosensing platform</td>
+    <td>BPA</td>
+    <td>4.3\times10^{-10} M</td>
+    <td>[40]</td>
+  </tr>
+  <tr>
+    <th>MN-PCDP</th>
+    <th>Anthracene</th>
+    <th>10^{-9} M</th>
+    <th>This work</th>
+  </tr>
+  <tr>
+    <td>Fe_{3}O_{4}@Ag MNPs-thiol</td>
+    <td>Anthracene</td>
+    <td>10^{-9} M</td>
+    <td>[41]</td>
+  </tr>
+</table>
+
+aMNP: magnetic nanoparticles; diquat and paraquat have the similar structure.
+
+References
+
+31 He, Q. et al. Fabrication of Fe_{3}O_{4}@SiO_{2}@Ag magnetic-plasmonic nanospindles as highly efficient SERS active substrates for label-free detection of pesticides. New J. Chem. **41**, 1582-1590, doi: 10.1039/c6nj03335k (2017).
+
+32 Tang, S. et al. Efficient enrichment and self-assembly of hybrid nanoparticles into removable and magnetic SERS substrates for sensitive detection of environmental pollutants. ACS Appl. Mater. Interfaces **9**, 7472-7480, doi: 10.1021/acsami.6b16141 (2017).
+
+33 Wang, C. et al. Seed-mediated synthesis of high-performance silver-coated magnetic nanoparticles and their use as effective SERS substrates. Colloids and Surfaces A: Physicochem. Eng. Aspects **506**, 393-401, doi: 10.1016/j.colsurfa.2016.05.103 (2016).
+
+34 Sun, M. et al. Cube-like Fe_{3}O_{4}@SiO_{2}@Au@Ag magnetic nanoparticles: a highly efficient SERS substrate for pesticide detection. Nanotechnology **29**, 165302, doi: 10.1088/1361-6528/aaae42 (2018).
+
+35 Wang, C. et al. Sonochemical synthesis of highly branched flower-like Fe_{3}O_{4}@SiO_{2}@Ag microcomposites and their application as versatile SERS substrates. Nanoscale **8**, 19816-19828, doi: 10.1039/c6nr07295j (2016).
+36 Wang, C. et al. Polyethylenimine-interlayered core-shell-satellite 3D magnetic microspheres as versatile SERS substrates. Nanoscale **7**, 18694-18707, doi: 10.1039/c5nr04977f (2015).
+37 Yang, T. et al. Au dotted magnetic network nanostructure and its application for on-site monitoring femtomolar level pesticide. Small **10**, 1325-1331, doi: 10.1002/smll.201302604 (2014).
+38 Li, Q. et al. A gold/Fe$_3$O$_4$ nanocomposite for use in a surface plasmon resonance immunosensor for carbendazim. Microchimica Acta **186**, 313, doi: 10.1007/s00604-019-3402-0 (2019).
+39 Kadasala, N. R. & Wei, A. Trace detection of tetrabromobisphenol A by SERS with DMAP-modified magnetic gold nanoclusters. Nanoscale **7**, 10931-10935, doi: 10.1039/c4nr07658c (2015).
+40 Xiao, R., Wang, W. C., Zhu, A. N. & Long, F. Single functional magnetic-bead as universal biosensing platform for trace analyte detection using SERS-nanobioprobe. Biosens. Bioelectron. **79**, 661-668, doi: 10.1016/j.bios.2015.12.108 (2016).
+41 Du, J. J. & Jing, C. Y. Preparation of thiol modified Fe$_3$O$_4$@Ag magnetic SERS probe for PAHs detection and identification. J. Phys. Chem. C **115**, 17829-17835, doi: 10.1021/jp203181c (2011).
+46 Song, D. et al. A label-free SERRS-based nanosensor for ultrasensitive detection of mercury ions in drinking water and wastewater effluent. Anal. Methods **9**, 154–162, doi: 10.1039/c6ay02361d (2017).
+
+2. The authors did nothing to improve the SERS spectral reproducibility, so the accuracy of the proposed method is not convincing.
+
+Answer: Thanks for the suggestion from the reviewer. Following the suggestion, the reproducibility of the enrichment SERS detection was studied in the revised manuscript. In current protocol, the excellent SERS performance is achieved by the enrichment (adsorption and desorption) from the MN-PCDP adsorbent. For the SERS spectral reproducibility, **first of all**, we measured the removal efficiencies and enrichment efficiencies from different independent experiments. As shown in Supplementary Fig. 21-23 and Supplementary Table 5-6, the relative standard deviations (RSDs) of
+the removal efficiencies and enrichment efficiencies for target molecules (BPA, carbendazim, TMTD diquat and anthracene) are less than 1% and 5%, respectively, indicating that the enrichment performance of MN-PCDP adsorbent is stable and effective. **Second**, we optimized the detection method based on the hydrophobic slippery SERS platform to further improve the SERS reproducibility. As shown in Supplementary Fig. 24, initial droplets of 50 \( \mu \)L (contain Au NPs and analyte) are concentrated into smaller spots with diameter less than 0.25 mm. Meanwhile, the enhanced Raman spectra of TMTD in 1 pM, 0.5 pM, 0.1 pM, 50 fM, 10 fM and 5 fM are shown in Supplementary Fig. 25-30, indicating the good reproducibility of this magnetic SERS-based sensor. Another SERS substrate, the wet-chemical synthesized Au NPs with addition of inorganic salt, was adopted to explain the consistency of SERS signal, which was the simplest and effective way in commercial detection platforms at present. For the aggregating approach with Au colloid, the reproducibility was consistent in aggregation states from different batches. As shown in Fig 4d and Supplementary Fig. 31-32, the detection probability is up to 100%. **Third**, the SERS detection about analyte with lower concentration in real-sample system was also tested. In Fig. 5e, carbendazim molecule with 1 nM in soil solution is distinctly detected by the selective enrichment of MN-PCDP. The correlated revisions are shown as following:
+
+Page 9, Paragraph 1: Furthermore, multiple adsorption and desorption experiments by MN-PCDP for above five organic molecules are implemented to illustrate the reproducibility of this adsorbent. In Supplementary Fig. 21-23, Supplementary Table 5-6, the removal efficiencies and enrichment efficiencies of MN-PCDP adsorbent are excellent for target molecules with RSD less than 1% and 5%, respectively. The Raman detectable reproducibility of TMTD by hydrophobic slippery SERS platform is shown in Supplementary Fig. 24-30. In Fig. 4c, the Raman signals of TMTD characteristic peaks are acquired with 100% detection probability in 0.5 pM, ~65% in 50 fM and ~10% in 5 fM. In addition, the solution-based aggregation approach, a simplest and effective way in commercial detection platforms at present, is adopted to clarify the consistency of SERS signal. As shown in Fig 4d and Supplementary Fig. 31-32, the SERS signals display superior spectral reproducibility and uniformity with 100% detection probability and RSD value of ~5%, even at TMTD concentration of \( 10^{-12} \) M.
+Fig. 4 c Probability of SERS signals with different concentrations of TMTD after enrichment process of MN-PCDP by hydrophobic slippery SERS platform. The inserted schematic diagram shows hydrophobic slippery SERS platform. d Detection probability (red) and intensity of SERS signals (black) with different concentrations of TMTD after enrichment process of MN-PCDP by aggregating approach with Au colloid. The inserted schematic diagram shows aggregating approach with Au colloid.
+Supplementary Figure 21 | Adsorption reproducibility of MN-PCDP. UV–vis spectra recorded as a function of different absorption experiments by MN-PCDP for removal BPA (0.1 mM, **a**), carbendazim (0.1 mM, **b**), TMTD (0.1 mM, **c**), diquat (0.01 mM, **d**) and anthracene (0.01 mM, **e**) by MN-PCDP (1 mg mL\(^{-1}\)).
+Supplementary Table 5 | The enrichment efficiency of BPA, carbendazim, TMTD, diquat and anthracene by different absorption cycles in Figure S21
+
+<table>
+  <tr>
+    <th>Removal efficiency (%)</th>
+    <th>BPA</th>
+    <th>Carbendazim</th>
+    <th>TMTD</th>
+    <th>Diquat</th>
+    <th>Anthracene</th>
+  </tr>
+  <tr>
+    <td>1</td>
+    <td>89.17</td>
+    <td>91.37</td>
+    <td>69.20</td>
+    <td>96.17</td>
+    <td>93.24</td>
+  </tr>
+  <tr>
+    <td>2</td>
+    <td>90.01</td>
+    <td>92.67</td>
+    <td>68.98</td>
+    <td>96.05</td>
+    <td>94.59</td>
+  </tr>
+  <tr>
+    <td>3</td>
+    <td>89.59</td>
+    <td>91.62</td>
+    <td>69.29</td>
+    <td>96.03</td>
+    <td>94.59</td>
+  </tr>
+  <tr>
+    <td>4</td>
+    <td>88.63</td>
+    <td>90.94</td>
+    <td>69.17</td>
+    <td>96.42</td>
+    <td>93.24</td>
+  </tr>
+  <tr>
+    <td>5</td>
+    <td>89.01</td>
+    <td>90.94</td>
+    <td>69.15</td>
+    <td>96.37</td>
+    <td>93.24</td>
+  </tr>
+  <tr>
+    <td>6</td>
+    <td>87.51</td>
+    <td>92.31</td>
+    <td>68.42</td>
+    <td>94.92</td>
+    <td>93.24</td>
+  </tr>
+  <tr>
+    <td>7</td>
+    <td>89.71</td>
+    <td>91.20</td>
+    <td>70.15</td>
+    <td>94.70</td>
+    <td>94.59</td>
+  </tr>
+  <tr>
+    <td>8</td>
+    <td>90.51</td>
+    <td>91.21</td>
+    <td>69.74</td>
+    <td>95.06</td>
+    <td>93.24</td>
+  </tr>
+  <tr>
+    <td>9</td>
+    <td>88.26</td>
+    <td>90.78</td>
+    <td>69.41</td>
+    <td>96.08</td>
+    <td>93.24</td>
+  </tr>
+  <tr>
+    <td>10</td>
+    <td>88.93</td>
+    <td>91.92</td>
+    <td>69.92</td>
+    <td>95.89</td>
+    <td>94.59</td>
+  </tr>
+  <tr>
+    <td>Average</td>
+    <td>89.13</td>
+    <td>91.49</td>
+    <td>69.34</td>
+    <td>96.17</td>
+    <td>94.78</td>
+  </tr>
+  <tr>
+    <td>RSD</td>
+    <td>0.98%</td>
+    <td>0.69%</td>
+    <td>0.71%</td>
+    <td>0.66%</td>
+    <td>0.074%</td>
+  </tr>
+</table>
+Supplementary Figure 22 | Enrichment reproducibility of MN-PCDP. UV-vis spectra recorded as a function of triplicate desorption experiments by MN-PCDP for enrichment BPA (0.01 mM, a), carbendazim (0.01 mM, b), TMTD (0.01 mM, c), diquat (0.01 mM, d) and anthracene (0.01 mM, e) by MN-PCDP (100 mg in 250 mL×4 times absorption).
+Supplementary Table 6 | The enrichment efficiency of BPA, carbendazim, TMTD, diquat and anthracene by different enrichment cycles in Figure S22
+
+<table>
+  <tr>
+    <th>Enrichment efficiency (times)</th>
+    <th>BPA</th>
+    <th>Carbendazim</th>
+    <th>TMTD</th>
+    <th>Diquat</th>
+    <th>Anthracene</th>
+  </tr>
+  <tr>
+    <td>1</td>
+    <td>605.29</td>
+    <td>642.71</td>
+    <td>435.12</td>
+    <td>598.02</td>
+    <td>521.49</td>
+  </tr>
+  <tr>
+    <td>2</td>
+    <td>595.01</td>
+    <td>589.34</td>
+    <td>449.48</td>
+    <td>586.95</td>
+    <td>547.61</td>
+  </tr>
+  <tr>
+    <td>3</td>
+    <td>624.69</td>
+    <td>613.36</td>
+    <td>475.62</td>
+    <td>572.63</td>
+    <td>526.94</td>
+  </tr>
+  <tr>
+    <td>Average</td>
+    <td>608.33</td>
+    <td>615.14</td>
+    <td>453.41</td>
+    <td>585.87</td>
+    <td>532.01</td>
+  </tr>
+  <tr>
+    <td>RSD</td>
+    <td>2.48%</td>
+    <td>4.34%</td>
+    <td>4.53%</td>
+    <td>2.17%</td>
+    <td>2.59%</td>
+  </tr>
+</table>
+
+![Bar graph showing enrichment efficiencies of five organic pollutants after enrichment process of MN-PCDP.](page_420_624_627_312.png)
+
+Supplementary Figure 23 | Enrichment efficiencies of five organic pollutants after enrichment process of MN-PCDP.
+
+![Optical photograph and bright-field optical images of analyte and Au nanoparticles on the hydrophobic slippery SERS platform.](page_120_1042_1342_246.png)
+
+Supplementary Figure 24 | **a** Optical photograph and **b** bright-field optical images of analyte and Au nanoparticles on the hydrophobic slippery SERS platform.
+Supplementary Figure 25 | Enhanced Raman spectra of TMTD (1 pM) in five independent batches after the enrichment of MN-PCDP measured by hydrophobic slippery SERS platform.
+
+Supplementary Figure 26 | Enhanced Raman spectra of TMTD (0.5 pM) in five independent batches after the enrichment of MN-PCDP measured by hydrophobic slippery SERS platform.
+Supplementary Figure 27 | Enhanced Raman spectra of TMTD (0.1 pM) in five independent batches after the enrichment of MN-PCDP measured by hydrophobic slippery SERS platform.
+
+Supplementary Figure 28 | Enhanced Raman spectra of TMTD (50 fM) in five independent batches after the enrichment of MN-PCDP measured by hydrophobic slippery SERS platform.
+Supplementary Figure 29 | Enhanced Raman spectra of TMTD (10 fM) in five independent batches after the enrichment of MN-PCDP measured by hydrophobic slippery SERS platform.
+
+Supplementary Figure 30 | Enhanced Raman spectra of TMTD (5 fM) in five independent batches after the enrichment of MN-PCDP measured by hydrophobic slippery SERS platform.
+Supplementary Figure 31 | Enhanced Raman spectra of TMTD a before and b after the enrichment of MN-PCDP adsorbent measured by aggregating approach with Au colloid. The characteristic peaks of TMTD were at 558 and 1379 cm\(^{-1}\).
+
+Supplementary Figure 32 | Enhanced Raman spectra of TMTD with a 1 nM, b 0.1nM, c 10 pM and d 1pM in five independent batches after the enrichment of MN-PCDP adsorbent measured by aggregating approach with Au colloid.
+Fig. 5 e Raman spectra about selective enrichment of organic pollutant molecules (carbendazim, 1 nM) from practical samples.
+
+3. In my opinion, a SERS nanosensor that combines ultrahigh sensitivity (achieved by high enrichment ability and signal enhancement ability), high spectral reliability, and fast removal speed, is publishable in the high-level journal of Nature Communication.
+
+Answer: Thanks for the comment and very good suggestions from the reviewer. Following the suggestion, the revised manuscript has been obviously improved. After revision, we think the manuscript realize the review's criteria for publishing in the high-level journal. In this work, we show an enrichment-typed sensing strategy by using a powerful mesoporous nanospone. Based on the excellent capturing selectivity of and fast removal capability for organic micropollutants from β-cyclodextrin polymers as well as the magnetic nanoparticles, great enrichment and detection performance on analyte are achieved, e.g. ~90% removal efficiency (RSD<1%) within ~1 min, concentrated and enriched from complex matrix with an enrichment factor up to ~\(10^3\) (RSD<5%), ultrahigh detection sensitivity (0.5 pM with 100% detection possibility and 5 fM with ~10% detection possibility for TMTD molecule). By means of the current absorption strategy, the mesoporous nanospone is used to separate and selectively enrich (2~3 orders of magnitude) target molecules from the real-sample system. Importantly, the current enrichment strategy is proved to be helpful tool in a variety of fields for portable and fast detection, such as UV-vis, Raman and fluorescent. Therefore, we believe this revised version with many supplemented data can be considered and accepted for publication.

03e6375d91ba2acc0d93fa9c97f15a5154400d7aed2f4249391cfd96e1971e8e/preprint/preprint.md

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+Ultra-rapid and highly efficient enrichment of organic pollutants via magnetic nanoparticles/mesoporous nanosponge compounds for ultrasensitive nanosensors
+
+Lingling Zhang
+Xi'an Jiaotong University   https://orcid.org/0000-0002-6272-7171
+Rui Hao
+Xi'an Jiaotong University
+Hongjun You
+School of Science, Xi'an Jiaotong University   https://orcid.org/0000-0002-9389-3076
+Hu Nan
+Xi'an Jiaotong University
+Yanzhu Dai
+School of Science
+Jixiang Fang (jxfang@mail.xjtu.edu.cn)
+Xi'an Jiaotong University   https://orcid.org/0000-0003-3618-2144
+
+Article
+
+Keywords: nanosensors,SERS technique
+
+Posted Date: January 6th, 2021
+
+DOI: https://doi.org/10.21203/rs.3.rs-127668/v1
+
+License: This work is licensed under a Creative Commons Attribution 4.0 International License.
+Read Full License
+
+Version of Record: A version of this preprint was published at Nature Communications on November 25th, 2021. See the published version at https://doi.org/10.1038/s41467-021-27100-2.
+Abstract
+
+Developing advanced sensing and detection technologies to effectively monitor organic micropollutants in water is under urgent demand in both scientific and industrial communities. Currently, owing to the ultrahigh sensitivity on the single-molecule level with highly informative spectra characteristics, SERS technique is regarded as the most direct and effective detection technique. However, some weakly adsorbed molecules, such as most of persistent organic pollutants, cannot exhibit strong SERS signals, which is a long-standing key challenge that has not been solved. Here, we show an enrichment-typed sensing strategy based on a powerful porous composite material, call mesoporous nanosponge. The nanosponge consists of magnetic nanoparticles immobilized porous β-cyclodextrin polymers, demonstrating remarkable capability of effective and fast removal of organic micropollutants, e.g. ~90% removal efficiency within ~1 min. With the anchoring of magnetic nanoparticles, the current new polymer adsorbent can be easily recycled from water and re-dispersed in ethanol so that the target molecules in the cavity of adsorbent is concentrated, with an enrichment factor up to ~103. By means of the current enrichment strategy, the limit of detection (LOD) of the typical organic pollutants can be significantly improved, i.e. increasing 2~3 orders of magnitude, compared with the detection without molecule enrichment protocol. Consequently, the current enrichment strategy is proved to be applicable in a variety of fields for portable and fast detection, such as Raman and fluorescent.
+
+Introduction
+
+The Stockholm Convention on Persistent Organic Pollutants (POPs) was endorsed by 131 nations in 2004 to eliminate most persistent bioaccumulative and toxic substances in the world.\(^1\) Organic micropollutants of ground and surface water resources, such as pesticides and plastic components, have aroused great concerns about potential negative effects on aquatic ecosystems and human health.\(^2,\ ^3\) Therefore, parallel to the researches of adsorbent materials to remove organic pollutants from water, the ultrasensitive detection of organic pollutants is another crucial field, since the solubility of organic micropollutants in water is always at the trace level.\(^4\) Among diverse detection approaches, surface-enhanced Raman scattering (SERS), which achieved significant breakthroughs in 1997 and became the first vibrational spectroscopy technique that could provide delicate information on molecular fingerprints with potential single-molecule level of sensitivity,\(^5-8\) is regarded as the most simple, fast, flexible and portable detection technique.
+
+However, up to date, the superiority of single-molecule SERS in the detection of diverse molecules with intrinsic small cross-sections or low affinity for the plasmonic surface has not been into full play, particularly in real complex situation.\(^9\) As is well known, the SERS process involves complicated coupled three-body interactions among photons, molecules, and nanostructures.\(^{10,\ ^11}\) Besides the interaction between light and nanostructures, the investigation on the interaction between molecule and plasmonic surface is of importance.\(^{12}\) On the one hand, SERS is an optical near-field effect.\(^{12-14}\) A high activity can be obtained only when the target molecule is very close to the plasmonic surface. On the other hand,
+most organic pollutants in water can not be effectively adsorbed onto a metallic surface because of their low affinity toward the metal.\(^7\) Therefore, recently, some strategies, such as selective enrichment and spatial localization of target molecules,\(^{15-17}\) are suggested to solve this long-standing challenge.
+
+In this work, we propose a new sensing strategy based on the efficient enrichment and rapid separation of POPs by means of the magnetic nanoparticles immobilized porous β-CD polymer (MN-PCDP), called mesoporous nanosponge. The microporous β-cyclodextrin (β-CD) material, an inexpensive and renewable carbohydrate, which is featured by small pores and high surface areas,\(^{18,19}\) was used in this work as an excellent adsorbent. In fact, microporous β-CD material has been widely studied because of outstanding adsorption efficiency through forming host-guest inclusion with many hydrophobic organic pollutants.\(^{20,21}\) The magnetic nanoparticles are introduced into the MN-PCDP compounds to rapidly separate the adsorbent from water. The current strategy (the schematic description of the protocol is shown in Fig. 1) demonstrates several remarkable advantages. Firstly, as shown in Fig. 1a, when the MN-PCDP adsorbent (shown in Fig. 1b) is dispersed into water in the beaker, e.g. ~1000 ml, containing organic pollutants, ultra-rapid adsorption and magnetic separation can be accomplished, i.e., totally within ~ 1 min. Secondly, the adsorbed pollutant in MN-PCDP from water can be desorbed in ethanol with a volume of ~1 ml, for further analysis such as UV-vis, Raman and fluorescent spectroscopy. Thus, an ultra-high enrichment efficiency with an enrichment factor up to ~\(10^3\) times can be obtained (Fig. 1c). With current enrichment strategy, the limit of detection (LOD) in a variety of sensing applications, such as SERS and fluorescent, can be lowered by 2~3 orders of magnitude. Furthermore, through the magnetic separation, the MN-PCDP mesoporous nanosponge can selectively adsorb the target organic pollutants, avoiding the disturbance of complex matrix. The current sensing strategy can be believed to be applicable to a wider range of sensing areas for an economical, simple, fast, flexible, and portable detection.
+
+Results
+
+Synthesis and characterization. The MN-PCDP was prepared by cross-linking polymerization of β-CD and cross-linking agent (tetrafluoroterephthalonitrile (TFT)), with magnetic nanoparticles (Fe\(_3\)O\(_4\)) in one-step solvothermal reaction. Fig. 2a-c show the transmission electron microscope (TEM) images of magnetic nanoparticles (MN, Fe\(_3\)O\(_4\)), porous β-CD polymer (PCDP) and MN-PCDP, respectively. As shown in Fig. 2a, the synthesized MN exhibits regular spheres with good dispersibility and uniform size (average size ~200 nm). The Fourier transform-infrared spectroscopy (FT-IR) spectrum of MN is displayed in Fig. 2d. The absorption bands at 1652 cm\(^{-1}\) and 1396 cm\(^{-1}\) of the MN can be associated with carboxylate group\(^{22}\) and that also appear in the MN-PCDP. Fig. 2b and Supplementary Fig. 1 exhibit that the PCDP is porous network structure. After the immobilization of MN, as shown in Fig. 2c, the porous network structure of MN-PCDP is not disrupted. The FT-IR spectrum of the MN-PCDP not only obviously combines the characteristic peaks of the TFT and the β-CD but also displays a new peak at 1265 cm\(^{-1}\) in relation to the newly formed C-F group, implying that the β-CD has been crosslinked with TFT.\(^{23,24}\) Fig. 2e indicates that the Brunauer-Emmett-Teller surface areas (\(S_{BET}\)) of MN-PCDP is about 66 m\(^2\) g\(^{-1}\). The pores with diameter
+of 1.7-3.0 nm comprise the majority of the free volume of MN-PCDP and its average pore diameter is 2.12 nm.
+
+Adsorption of MN-PCDP nanosponges. The high surface area and permanent porosity of MN-PCDP mesoporous nanosponge enable the rapid removal of organic micropollutants from water.\(^{25}\) As shown in Supplementary Fig. 2, the PCDP and MN-PCDP displays the same properties in time-dependent adsorptions of bisphenol A (BPA), illustrating the immobilization of magnetic nanoparticles has no remarkable influence on the adsorption performance of PCDP. The time-dependent adsorptions of various organic micropollutants adsorbed by MN-PCDP, including plastic components, pesticide and aromatic model compounds (Fig. 3a), are shown in Fig. 3b, Supplementary Fig. 3 and Supplementary Table S1. The removal rate of the above organic micropollutants is very fast, which tends to be constant within 1 min. The removal efficiencies of BPA, parathion, carbendazim and 2-naphthol (2-NO) are more than 80% in 30 sec, which is much higher than the Norit ROW 0.8 supra extruded activated carbon (NAC) as presented in Fig. 3c, Supplementary Fig. 4-5 and Supplementary Table S2. We further probe the readily accessible binding sites of MN-PCDP by determining the flow-through uptake of different organic micropollutants. In these experiments, the adsorbent (~5 mg) was trapped as a thin layer on a 0.22 \( \mu \)m syringe filter, and aqueous organic pollutants (5 ml, 0.1 mM) passed rapidly through the filter at a flow rate of 10 ml min\(^{-1}\) (Supplementary Fig. 6). Under these conditions, for example, 76% of the BPA is removed from the solution, corresponding to more than 84% of its equilibrium adsorption, confirming that the host-guest interaction plays a major role in the filtration process by syringe.\(^{26}\) The superior performance of MN-PCDP can be further indicated that its \( \beta \)-CD moieties are easily accessed by most of organic micropollutants. Furthermore, these molecules are rapidly trapped. In addition, the influence of the concentrations of adsorbent on the BPA adsorption efficiency is studied as shown in Fig. 4b, Supplementary Fig. 7 and Supplementary Table S3. When the concentration of adsorbent increases from 0.1 mg L\(^{-1}\) to 1.0 mg L\(^{-1}\), the adsorption efficiency of BPA is enhanced from 25.12% to 87.09% within 1 min and from 35.07% to 89.82% within 10 min.
+
+Desorption and enrichment of MN-PCDP nanosponges. As we all know, organic micropollutants exhibit good solubility in organic solution, such as ethanol and methanol.\(^{18}\) Hence, after adsorption process, we utilized ethanol to desorb the organic micropollutants from MN-PCDP mesoporous nanosponges, and then obtained the enriched pollutant solution through magnetic nanoparticle separation. In order to obtain higher concentration of desorbed micropollutant solution, in this work, we chose 1 mL ethanol to desorb organic micropollutants adsorbed in 100 mg MN-PCDP adsorbent. As shown in Supplementary Fig. 8, using current enrichment processes, the concentration of BPA can be increased to 88.5 times of its initial concentration with a recipe of 100 mL organic pollutant (BPA) solution and 100 mg MN-PCDP adsorbent. This result reveals that more than 98% of the adsorbed organic micropollutants are desorbed into the ethanol solution. That is to say, for 100 mL organic pollutant solution, we realize \( \sim 10^2 \) times enrichment of target molecule. As the amount of adsorbent increases, the adsorption efficiency tends to reach equilibrium. Considering the cost increase of sample preparation and the operation in the
+desorption process (with 1 mL ethanol) resulting from the increase of adsorbent dosage, 100 mg of adsorbent is selected as the amount of material for subsequent experiments.
+
+In order to further improve the enrichment effect of 100 mg adsorbent in total 1000 mL organic micropollutants, herein, we attempted three methods, including 100 mL×10 times, 250 mL×4 times and 500 mL×2 times, to optimize the adsorption and desorption processes. Importantly, the adsorbent can be simply separated by magnet in every adsorption cycle, and desorbed in ethanol in the last adsorption cycle. As shown in Fig. 4c, Supplementary Fig. 9 and Supplementary Table S4, with adsorption times increasing, the removal efficiencies of these three methods gradually decrease. The removal efficiencies of these three methods (100 mL×10 times, 250 mL×4 times and 500 mL×2 times) are 50.78%, 62.58% and 41.22%, respectively. Meanwhile, the enrichment efficiencies of these three methods are 485, 605 and 396 times of the initial concentration (Fig. 4d), respectively. Therefore, we achieve over 600 times’ enrichment of organic pollutants (with 1000 mL of initial micropollutants) in the optimized adsorption and desorption processes. Here, the selected parameters (100 mg adsorbent in 250 mL organic solution for 4 cycle times) were used for the succedent experiments. Meanwhile, it is also worth pointing out that the separation process by magnet is very fast and facile, such as 90 sec for 250 mL solution (Fig. 4a and Supplementary Fig. 10b), 60 sec for 100 mL (Supplementary Fig. 10a), and 150 sec for in 500 mL (Supplementary Fig. 10c), fully meeting the requirement of immediate-pretreatment detection application.
+
+SERS and fluorescence measurement of pollutants based on the enrichment of MN-PCDP nanosponges.
+Many POPs are mutagenic, carcinogenic and not degradable by direct biological treatment, some of which damage nerve, endocrine systems of human body, and the ecological balance due to their toxicity in nature.\(^{27}\) Based on the above experimental researches, the MN-PCDP nanosponges were used to absorb organic micropollutants and then were collected from water (Fig. 5a), so as to realize the rapid removal and enrichment of POPs. Moreover, we evaluated fluorescence and enhanced Raman spectra of POPs (carbendazim and BPA) to demonstrate the enrichment effect of current enrichment strategy. The enhanced Raman spectra of carbendazim molecular with ~55 nm Au nanoparticles (Supplementary Fig. 11) were measured under 785 nm laser. As shown in Figure 5b-c, without the enrichment process, the LOD of SERS for carbendazim is 1 nM, but after the enrichment using MN-PCDP adsorbent, this value reaches to ~5 pM, which shows an increase of \(10^2\sim10^3\). In Supplementary Fig. 12, for BPA molecule, with the help of adsorbent, the LOD of fluorescence is also greatly improved. In Fig. 5d-e and Supplementary Fig. 13, based on the current enrichment sensing strategy, the LODs of fluorescence detections for the pure solution of carbendazim and BPA are lower by 2~3 orders of magnitude. In this study, the enrichment strategy based on the adsorption and desorption processes of MN-PCDP adsorbent may significantly increase the sensitivity of plasmonic sensors, compared with the LOD for similar molecules,\(^{28-30}\) illustrating its wide applicability.
+
+Owing to the excellent enrichment and easily-separated features, the current strategy was believed that the mesoporous nanosponges could be served as a preprocessing for direct, rapid and ultrasensitive detection of contaminants in complex situations. After adsorption process, the MN-PCDP adsorbent was easily collected on the wall of beaker (Fig. 5a) with a magnet, avoiding the interference of complex
+matrix, such as mud and microorganism. Fig. 5f reveals that both the characteristic peaks of BPA (830 and 1179 cm\(^{-1}\)) and carbendazim (1008, 1244 and 1263 cm\(^{-1}\)) evidently appear in the Raman spectrum of mixture solution, including 1 \( \mu \)M BPA and 10 nM carbendazim. Furthermore, the MN-PCDP demonstrates a superior reusability as shown in Supplementary Fig. 14. Six consecutive BPA adsorption/desorption cycles were performed and the regenerated MN-PCDP exhibited almost no decrease (90.2% to 87.5%) in performance compared to the as-synthesized polymer.
+
+Discussion
+
+In summary, we have developed a robust and rapid sensing strategy based on the MN-PCDP mesoporous nanoponges to capture and enrich organic pollutants from water. In this strategy, the MN-PCDP adsorbent exhibits excellent adsorption capacity for various kinds of pollutants owing to the unique cavity structures. Moreover, the adsorbed pollutant in MN-PCDP can be desorbed in ethanol with a very fast and facile operation. In SERS detection of organic pollutants, i.e. carbendazim and BPA, in this work, the current sensing strategy may significantly increase the sensitivity of plasmonic sensors with 2~3 orders of magnitude. Therefore, the current robust sensing strategy with the ultra-rapid and highly efficient sample pretreatment and molecule enrichment is believed to be applicable to a wider range of sensing devices, such as fluorescent, Raman and infrared spectroscopes for a cost-effective, simple, fast, flexible and portable detection.
+
+Methods
+
+Preparation of magnetite nanoparticles (\( \mathrm{Fe}_3\mathrm{O}_4 \)). The carboxyl-functionalized magnetite nanoparticles (\( \mathrm{Fe}_3\mathrm{O}_4 \)) with highly water-dispersibility were synthesized by a modified solvothermal reaction approach. Typically, FeCl\(_3\)·6H\(_2\)O (1.08 g, 4.0 mmol) and trisodium citrate (0.20 g, 0.68 mmol) were dissolved in ethylene glycol (20 mL) with stirring at 500 rpm. Afterward, sodium acetate trihydrate (2.0 g, 15 mmol) was added and the mixture was stirred for 30 min. Then, the mixture was sealed in a Teflon-lined stainless-steel autoclave (50 mL). The autoclave was heated at 200 °C for 12 h, and then allowed to cool to room temperature. The black products were washed with ethanol and ultrapure water for several times. Finally, the carboxyl-functionalized magnetite nanoparticles (\( \mathrm{Fe}_3\mathrm{O}_4 \)) were separated by magnet, re-dispersed in ethanol and dried in vacuum drying oven at 30°C.
+
+Preparation of magnetic nanoparticles immobilized porous \( \beta \)-CD polymer (MN-PCDP). The MN-PCDP composites were then prepared by modification of nucleophilic aromatic substitution method of hydroxyl groups of \( \beta \)-CD. A dried 100 mL Shrek reaction vial with a magnetic stir bar was charged with \( \beta \)-CD (0.82 g, 0.724 mmol), TFT (0.40 g, 1.03 mmol), and K\(_2\)CO\(_3\) (1.28 g, 9.28 mmol) and dried Fe\(_3\)O\(_4\) (0.041 g). The vial was flushed with N\(_2\) gas for 10 min, then an anhydrous THF/DMF mixture (9:1 v/v, 40 mL) was added and the vial was purged with N\(_2\) for additional 5 min. After that, the N\(_2\) inlet was removed. The mixture was stirred at 500 rpm and refluxed at 85°C for 36 h under nitrogen protection. The brown suspension was cooled to room temperature and magnetically separated the supernatant by magnet. The
+precipitate was washed twice with an appropriate amount of distilled water, THF, ethanol and CH₂Cl₂, respectively. The final precipitate was vacuum dried at 77 K in a liquid nitrogen bath for 24 h and then the magnetic nanoparticles immobilized porous β-CD polymer (MN-PCDP) was obtained.
+
+Batch adsorption kinetic studies. In studies, the dried polymer (MN-PCDP, 20 mg) was initially washed with H₂O for 2 times and then separated by magnet. Adsorption kinetic studies for different pollutants were performed in 30 mL scintillation vials with 20 mL organic pollutant solution and 20 mg adsorbent, at ambient temperature on a hot plate at 25°C. Then the sample was shaken at 250 rpm until the adsorption equilibrium was reached. The mixture was immediately stirred and 1 mL aliquots of the suspension were taken at certain intervals via syringe and filtered immediately by a 0.22 µm PTFE membrane filter. The residual concentration of the pollutant in each sample was determined by UV–vis spectroscopy.
+
+Calculation of removal efficiency. The removal efficiency of pollutant removal by the adsorbent was determined by the following equation:
+
+\[
+\text{Removal efficiency (\%)} = \frac{c_0 - c_t}{c_0} \times 100
+\]
+
+where \( C_0 \) and \( C_t \) are the initial and residual concentration of pollutant in the stock solution and filtrate, respectively.
+
+Flow-through adsorption experiments. Individual pollutants were at high concentrations (mM). 5.0 mg of the MN-PCDP adsorbent was washed with deionized H₂O for 2 times, then the precipitate was pushed by a syringe through a 0.22 µm PTFE membrane filter to form a thin layer of the adsorbent on the filter membrane. 5 mL of the pollutant stock solution was then pushed through the adsorbent in ~30 s (10 mL min⁻¹ flow rate). The filtrate was then measured by UV–vis spectroscopy to determine the pollutant removal efficiency.
+
+MN-PCDP desorption studies. 100.0 mg of the adsorbent was washed with deionized H₂O for 2 times, and then added to the organic pollutant stock solution (0.01 mM) with determine volume (100 mL, 250 mL, 500 mL). The mixture was shaken at 250 rpm for 1 min at 25°C. After separating the supernatant and the adsorbent by an external magnet, the supernatant was filtered through a 0.22 µm filter membrane and determined by UV-vis spectroscopy. Meanwhile the precipitate was evaporated to dryness with a gentle nitrogen stream, then the residue was dissolved in 1mL of ethanol to desorb the adsorbed organic pollutant. The desorption solution was measured by UV-vis spectroscopy and compared with the initial concentration of pollutant in the stock solution.
+
+Calculation of enrichment efficiency. The enrichment efficiency of pollutant adsorbed by the adsorbent was determined by the following equation:
+Enrichment efficiency = \( \frac{c}{c_0} \)
+
+Where \( C_0 \) and \( C \) are the initial and desorbed solution concentration of pollutant, respectively.
+
+Fluorescence measurement. The fluorescence spectra of pure solution were directly measured by fluorescence spectrophotometer.
+
+Preparation of SERS active Au NPs. The Au NPs with different size in diameter were synthesized based on a modified citrate reduction approach. The growth process of gold nanoparticles with different size included three steps. For step 1, 100 mL of ultrapure water was added into a conical flask and heated to boiling. Then, 4ml of 1wt% sodium citrate (SC) solution was injected immediately, and 3.2 mL of 10 mM HAuCl\(_4\) was added after 3 min. Kept the reaction for 25 minutes and made it natural cooling, then the Au seeds were obtained. For step 2, 80 mL of ultrapure water and 20 mL of Au seeds were mixed into the conical flask and heated to boiling. Then, 2 mL of 1wt% sodium citrate solution was injected immediately, and 0.2 mL of HAuCl\(_4\) was added 3 min later. Then additional 0.2 mL × 9 dosage of HAuCl\(_4\) was injected every 8 minutes. After the last precursor was added, the reaction was kept for 25 min, and Au NPs-25 nm were obtained. For step 3, Au NPs prepared in step 2 were used as the seed solution, and the growth process was repeated as growth steps 2, and then Au NPs-55 nm were obtained in this step.
+
+SERS measurement. SERS measurement is based on the hydrophobic slippery surface. Concentrated molecules and Au NPs were prepared on a hydrophobic slippery Teflon membrane as follows: First, a Teflon membrane was attached on a flat glass slide (5 cm × 5 cm) by using a double-sided adhesive. Then, 0.5 mL of perfluorinated fluid was dispersed by spin coating. The low speed was 300 rpm for 30 s, and the high speed was 1500 rpm for 1 min. After the excess lubricating liquid was removed by centrifugal force, and the infused membrane was heated for 30 min. Lastly, 50 μL of probe molecules and 10 μL of Au colloids were simultaneously dropped onto the slippery surface. During drying, the contact line shrunk because of the low friction of the lubricated Teflon surface. As a result, the initial droplet could be concentrated into a small area less than 0.5 mm in diameter.
+
+Declarations
+
+Data availability
+
+The data that support the findings of this study are available within the paper and its Supplementary Information or from the corresponding authors on reasonable request.
+
+Acknowledgements
+
+This work was supported by the programs supported by the National Natural Science Foundation of China (No. 21675122, 21874104, 22074115), the Key Research Program in Shaanxi (2017NY-114), Basic
+Public Welfare Research Project of Zhejiang Province (No. LY20E010007), and Natural Science Foundation of Shaanxi Province (No. 2019JLP-19), the World-Class Universities (Disciplines) and the Characteristic Development Guidance Funds for the Central Universities.
+
+Author contributions
+
+L.L.Z. synthesized the materials, carried out the characterizations and performance, analyzed the data, and wrote the manuscript. R. H., H. N., Y. Z. D. contributed in part of the TEM, Raman and fluorescence characterizations. H.J.Y. and J.X.F, supervised the project, designed the experiments, contributed in discussions, comments and writing of manuscript. All authors discussed the results and commented on the manuscript.
+
+Additional information
+
+Supplementary Information accompanies this paper at
+
+competing of Interest: The authors declare no competing of interest.
+
+Reprints and permission information is available online at
+
+Journal peer review information:
+
+Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
+
+References
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+
+Figures
+Figure 1
+
+Schematic of the current enrichment and detection based on the porous β-CD polymer. a Adsorption and c desorption processes using magnetic nanoparticles immobilized porous β-CD polymer (MN-PCDP) with ~1000 times enrichment. b Optical photograph of MN-PCDP.
+Figure 2
+
+Characterizations of magnetic nanoparticle (MN), porous β-CD polymer (PCDP) and magnetic nanoparticles immobilized porous β-CD polymer (MN-PCDP). TEM images of a MN, b PCDP, and c MN-PCDP. d FT-IR spectra of MN (black), TFT (red), β-CD (blue), PCDP (orange) and MN-PCDP (green). e N2 adsorption isotherms and cumulative pore volume of MN-PCDP.
+Figure 3
+
+MN-PCDP rapidly adsorbs a broad range of organic pollutants. a Structures and of each tested organic pollutant. b Time-dependent adsorption of each pollutant (0.1 mM) by MN-PCDP (1 mg mL-1). c Percentage removal efficiency of each pollutant obtained by stirring NAC (blue), stirring MN-PCDP (red) and rapidly flowing the through a thin MN-PCDP layer (green). The data are reported as the average uptake of triplicate experiments.
+Figure 4
+
+Rapid enrichment performance of MN-PCDP. a Optical photographs of MN-PCDP separation process by magnet in continuous time. b Time-dependent adsorption of BPA (0.1 mM) using MN-PCDP with different dosage (0.1, 0.25, 0.5, 0.75 and 1 mg L-1). c Removal efficiency of BPA (0.01 mM) using MN-PCDP (100 mg) in three methods (100 mL for 10 times, 250 mL for 4 times and 500 mL for 2 times). d Average removal (black) and enrichment (red) efficiency of the three methods in c.
+Figure 5
+
+Application in Raman and fluorescence detection used this enrichment strategy. a Optical photographs about the enrichment process of MN-PCDP in mud water. Fluorescence spectra of carbendazim b before and c after enrichment process of MN-PCDP. Raman spectrum of carbendazim d before and e after enrichment process of MN-PCDP. f Raman spectrum of mixture after the enrichment process of MN-PCDP in real samples.
+
+Supplementary Files
+
+This is a list of supplementary files associated with this preprint. Click to download.
+
+• SupportingInformationNC.docx

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+Peer Review File
+
+Hyperuniformity and phase enrichment in vortex and rotor assemblies
+
+Open Access This file is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. In the cases where the authors are anonymous, such as is the case for the reports of anonymous peer reviewers, author attribution should be to 'Anonymous Referee' followed by a clear attribution to the source work. The images or other third party material in this file are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.
+REVIEWER COMMENTS
+
+Reviewer #2 (Remarks to the Author):
+
+The paper describes simulation results for two related systems of 2D interacting vortices: 1. Simplified point vortices and 2. More realistic rotor assemblies with soft-core steric repulsion and long-range Saffman-Delbruck interaction. The main results are that both systems show hyperuniformity at a range of parameters. In particular, hyperuniformity does not require fine tuning.
+
+This is a well-written, interesting and original paper, of clear interested to researchers in a range of fields, including random-media, Hamiltonian systems, dynamics in membranes and more. Realistic examples demonstrating hyperuniformity are few, thus, the paper is a significant contribution to the field. Accordingly, I recommend the paper is accepted to Nature Communication pending revision and some clarifications as detailed below.
+
+My main concern is regarding the numerical method used to perform the simulation. In particular, I do not understand the dependence of the rate of convergence to the steady state on the step size and the relevance of ref (49). As far as I understand, in (49), the role of the added noise is to break the rotational symmetry in the numerical solution. In contrast, here, the authors claim that conservation of H and M is essential. What happens to fig 2E at long times with added noise? Fig 2E (which can move to the SM) should show the error in H and M for the entire duration of the simulation, not just a few cycles. If the errors (including noise) remain negligible, it may not be necessary to re-do the simulations. However, if errors grow, this may indicate numerical issues. Given the Hamiltonian structure, which is emphasized by the authors but ignored in choosing the appropriate numerical method, it makes more sense to use a symplectic method.
+
+Currently, the results do not exclude the possibility that the hyperuniform steady-state is a numerical artifact. In other words, while a hyperuniform steady state may exist, a dynamical bottleneck may not allow the conservative system to reach it. In this case, initial conditions may also be a factor. To summarize, the authors need to explore the impact of the applied numerical methods on the results and establish their validity.
+
+Minor comments
+
+1. In the subplots showing the 2D S(q), I find the color scheme (black = zero) confusing. I recommend it is inverted
+.
+2. Page 2, 11 lines from the end: typo – extra ‘(`.
+
+3. What happens at low densities? Is the steady state still hyperuniform?
+
+4. The definition of returnity can be clarified.
+
+5. Entropy measurements and Fig 4E: The changes in entropy are very small – about 1-2% with an error of 0.5-1%. This is not surprising given that converting the data into a figure with KxK pixels, estimating the entropy using lossless compression will be severely undersampled unless the number of realizations is of the order of 2^(K^2). As the authors already calculated the structure factor, I suggest applying the method of [43]. Also, it is interesting to plot the entropy as a function of \Gamma_h/\Gamma_l.
+
+Reviewer #3 (Remarks to the Author):
+This manuscript by Oppenheimer et al. "Hyperuniformity and phase enrichment in vortex and rotor assemblies" employs theory and simulations to describe the dynamics of point vortices and finite size rotors in 2-dimensions. The authors show that the 2D rotational flows can lead to ordered states, where hyperuniformity, phase enrichment or hexagonal order can be observed.
+
+By considering Hamiltonian formalism, the authors predict that point vortices should form disordered hyperuniform states due to conservation laws. The authors also recover the exactly the same result for torque driven membrane rotors with a finite size, in the limit of short separations. The theoretical calculations are supported by detailed hydrodynamic simulations, with an excellent agreement between the two. Simulations are then used to consider a 50:50 mixtures of fast and slow spinning point vortices. Here, phase enrichment is observed for both population, while hyperuniformity is observed for fast spinning vortices only. The two populations occupy two different areas, which is shown to maximize the number of available states.
+
+From the point of view of rotational active matter, I do find the presented results interesting. It is fascinating that the conservation laws stemming from the Hamiltonian structure of the rotationally invariant interactions result to the distinct states, as shown by the authors. Especially the phase enrichment in the mixtures is very nice. I am not a theorist nor too familiar with the formalism used, so some details may have escaped from me. The authors make an effort to simplify the mathematics, but at places I was lost what were the basic assumptions vs derived results.
+
+Generally, the results are interesting, nicely presented, and most parts are clear. The article probably deserves publication, but I would encourage the authors to clarify the general presentation/arguments, clearly state what is assumed and what are the corresponding results, and give intuitive explanations if possible. These would render the article more accessible.
+
+Other comments/questions:
+
+1) On the page 3, where the steady state is characterized by 3-distinct ways. The role of perturbations is discussed. It is stated that some amount of perturbations are needed to observe hyperuniformity. While this would not be a problem in an experimental setting, does it imply that if the Hamiltonian and its moments are exactly conserved, hyperuniformity would not be observed for point vortices?
+
+2) The S(q) for rotors (inset in Fig. 3B) shows plateau at small q of all \( \phi > 0.14 \). While in the main text it is said that all the samples showed hyperuniformity. This seems contradictory with the definition of S(q) -> 0 when q -> 0. Also, the rotors probably develop (local) hexatic order before the crystallization observed at \( \phi \sim 0.5 \). It would instructive to plot the local hexatic order parameter as a function of \( \phi \).
+
+3) I was somewhat confused with the returnity. The returnity seems to be close to zero at longtimes. Logically to me this suggests that the particle position has deviated from its original position. However, the definition of the returnity in the caption suggests that zero returnity means no deviation. The calculation/discussion should be clarified.
+
+4) Connected to above, from the main text it seems that the system is not in absorbing state at long times, while it is also said that the ensemble undergoes a solid body rotation, where the particle i returns to its position cyclically. This paragraph should be clarified.
+
+5) For which system is the returnity measured? Would it be expected to be different between point vortices and rotors?
+
+6) The role of fig. 2c is not clear to me. Does this mean that at long separations (low area/volume fractions) the finite size rotors are not expected to have similar steady state as predicted for point
+vortices?
+
+7) Also, if not completely obvious, it would be nice if arguments/simple explanations were given for example for the symmetries for a translation in time, space and rotation corresponding to the conservation laws. This would increase the accessibility of the article. Can these be understood in some simple way, such as conservation of the hamiltonian and 2nd moment kind of fixes the density, while the vanishing first moment corresponds to no center of mass movement? At longtimes this then leads to a steady state with a (close to) solid body rotation, as opposite to the chaotic dynamics at times near the random starting configuration.
+
+8) In the ref 15, for torque driven rotors it is suggested that the steady state is characterized by extrema of a "pseudo kinetic energy". In the formalism presented here, is there an analog to this?
+
+9) The \psi in the Hamiltonian above the equation 5 on page 3 is not defined.
+Below we copy the referee reports in green. Our response is in black below each point.
+
+Report and response to Referee 2:
+
+Referee: The paper describes simulation results for two related systems of 2D interacting vortices: 1. Simplified point vortices and 2. More realistic rotor assemblies with soft-core steric repulsion and long-range Saffman-Delbruck interaction. The main results are that both systems show hyperuniformity at a range of parameters. In particular, hyperuniformity does not require fine tuning.
+
+This is a well-written, interesting and original paper, of clear interested to researchers in a range of fields, including random-media, Hamiltonian systems, dynamics in membranes and more. Realistic examples demonstrating hyperuniformity are few, thus, the paper is a significant contribution to the field. Accordingly, I recommend the paper is accepted to Nature Communication pending revision and some clarifications as detailed below.
+
+Response: We thank the referee for finding our paper well-written, interesting and original! We further appreciate the pertinent questions raised which we hope we properly address in our response below as well as in the revised manuscript. By trying to address the reviewer’s concern we feel that we have not only improved the paper, but also our understanding of the system and its dynamics.
+
+Referee: My main concern is regarding the numerical method used to perform the simulation. In particular, I do not understand the dependence of the rate of convergence to the steady state on the step size and the relevance of ref (49). As far as I understand, in (49), the role of the added noise is to break the rotational symmetry in the numerical solution. In contrast, here, the authors claim that conservation of H and M is essential. What happens to fig 2E at long times with added noise? Fig 2E (which can move to the SM) should show the error in H and M for the entire duration of the simulation, not just a few cycles. If the errors (including noise) remain negligible, it may not be necessary to re-do the simulations. However, if errors grow, this may indicate numerical issues. Given the Hamiltonian structure, which is emphasized by the authors but ignored in choosing the appropriate numerical method, it makes more sense to use a symplectic method.
+
+Currently, the results do not exclude the possibility that the hyperuniform steady-state is a numerical artifact. In other words, while a hyperuniform steady state may exist, a dynamical bottleneck may not allow the conservative system to reach it. In this case, initial conditions may also be a factor. To summarize, the authors need to explore the impact of the applied numerical methods on the results and establish their validity.
+
+Response: The referee raises a valid concern. In fact, we believe that the referee is exactly correct when he states that “while a hyperuniform steady state may exist, a dynamical bottleneck may not allow the conservative system to reach it”. We had written something to that effect in the text, and have now emphasized and refined our phrasing throughout the text. We show theoretically that a system of point vortices should be hyperuniform, but following the simulation results we believe, as the reviewer noted, that a pure system of point vortices may never reach such a state, or may reach it at an infinite time. In other words, some form of perturbation that breaks the rotational symmetry of the Hamiltonian is required to reach hyperuniformity. We have tested a few forms of perturbations to the dynamics. In particular — numerical truncation errors and steric interactions. In both cases the system becomes hyperuniform. In the latter case the rate of convergence to a hyperuniform state does not depend on the stepsize. In the former case it does: as the timestep is reduced, longer times are required to reach hyperuniformity. We therefore believe, as the referee wrote, that a pure system with no numerical noise may never reach hyperuniformity. We have now tested both running a symplectic scheme and adding an additional form of noise as the referee suggested and outline the results below as well as in the text and the SI.
+
+The referee asked about the errors in the conservation of \( \mathcal{H} \) and \( M \) at long times. For 10,000 point vortices, the Hamiltonian is conserved with a relative error of < 0.001 up to 16,000 cycles, the second moment is conserved up to a relative error of \( 4 \times 10^{-4} \). We find these errors to be satisfactory. We have now included in the Methods section details of the conservation of the second moment of vorticity as well. Our reasoning for choosing a Runge-Kutta method with an adaptive time step was two-fold:
+(1) high-order accuracy meant that low truncation errors could be specified and simulations could be run for many cycles in a reasonable wall-time, and (2) since the Hamiltonian and second moments are not explicitly preserved, the conservation of these quantities can be used as a measure of numerical fidelity. In contrast, symplectic schemes, particularly when the Hamiltonian is non-separable (as is the case here), have several associated challenges: (1) to obtain higher than first-order accuracy, careful ordering of computations has to be preserved, making the simulations hard (if not impossible!) to parallelize (and non-amenable to fast algorithms, such as a fast-multipole method), and (2) since the conserved quantities are explicitly conserved, a basic marker of numerical fidelity is lost — meaning that while conservation looks great the actual dynamics could be very wrong.
+
+In particular, the first issue (relating to parallelizability), means that these simulations run far slower: our Runge-Kutta based simulations were run on 128 core nodes using reasonably well optimized code that made effective use of all cores. We have now implemented and run a symplectic integration scheme (see below), but unfortunately, this code is serial (with no clear way to achieve a parallel implementation), and suffers from poor memory access patterns, and hence is slower by orders of magnitude (not to mention less accurate — second order with fixed timesteps, as opposed to fifth or eighth order for the RK schemes, with fixed or adaptive timesteps). We thus had to use a smaller ensemble (1000 particles). When measuring hyperuniformity in an open system, using a smaller system size is problematic. Finally, we cite Min, Mezic and Leonard, (Phys. of Fluids 1996) “Because of the chaotic nature of the vortex motion, error propagation during numerical computation is inevitable. This is a clear manifestation of the ‘sensitive dependence on initial conditions,’ and there is no way around it.”
+
+Although we have not reported every test we have done in the manuscript, we have run many simulations that have explored the effect of initial data. We have typically run experiments using data generated on-the-fly (by rejection sampling a disk of radius R, as explained in the methods section of the paper). For fixed numerical and physical parameters, we have not observed any evidence that the specific realization of this kind of randomly generated data affects the final state of the system nor the timescale that it takes for the system to evolve to that state. We do note that in some cases (e.g. when trying to compare the effect of numerical parameters such as the error tolerance or timestepper), we have purposefully initialized simulations with exactly the same initial data, to eliminate a potential source of variation.
+
+The referee made excellent recommendations which we have tested:
+
+• *White noise*
+We have added random white noise to the simulations. We tested the effect of noise for ensembles of 1,000 particles, with noise levels which are larger than the tolerance of the scheme/the truncation error. We compared results with and without noise by plotting the lowest \( S(q) \) value as a function of time. This is a quick way to estimate the convergence to a steady state. For a noise level with a standard deviation of \( D = 0.001 \) or \( D = 0.0001 \), the rate of convergence to hyperuniformity did not change by the addition of noise. Taking a larger noise, with a standard deviation of \( D = 0.01 \), resulted in no apparent hyperuniformity. We expect that a large diffusion will destroy the conservation laws entirely. We note that this noise was selected completely at random, and was not correlated through the mobility tensor; efficient implementation of such a scheme is nontrivial (see e.g. Sokolov and Diamant, J. Chem. Phys., 2018).
+
+• *Symplectic integration*
+We have used the scheme developed by Zhang and Qin (*Computers. Math. Applic.*, 1993) which incorporates the analytical solution of two point vortices to construct a symplectic scheme. The time to compute single substages of the timestepper is *at least 100 times more costly than a non-symplectic scheme*, as it does not admit parallelization and has poor memory access patterns. We opted instead to test a smaller ensemble of 1,000 particles over \( \sim 10^5 \) cycles. We have tested timesteps of \( 10^{-6} \) for which the Hamiltonian is conserved with a relative error of \( 10^{-4} \), and the second moment is conserved with a relative error of \( 10^{-11} \). In comparison, using ODE853 with a tolerance of \( 10^{-6} \) for 1,000 particles, integrated over the same amount of time, results in conservation with a relative error of \( 2 \times 10^{-3} \) in the Hamiltonian and \( 6 \times 10^{-4} \) in the second moment. The symplectic runs showed little to no signs of hyperuniformity (see figures in the SI) — however, these are smaller ensembles simulated with a low-order, non-adaptive timestepper.
+While the Hamiltonian and second-moment are well conserved, the dynamics are nevertheless not guaranteed to be accurate. We have also tested starting the simulation from a hyperuniform state and running it using the symplectic scheme for a long time (\( \sim 5 \times 10^4 \) cycles). In this case, hyperuniformity persisted. We present the radially averaged structure factor in the SI. Since the symplectic scheme very nearly preserves rotational symmetry of the system, these results reinforce our previous suspicion — that perturbations that break rotational symmetry are needed to overcome the dynamical bottleneck.
+
+• *Other timesteppers*
+In an effort to assess whether the *specific* choice of non-symplectic timestepper might affect the results, we re-implemented the point-vortex portion of our code in Julia, in order to access the large selection of timesteppers implemented in the DifferentialEquations.jl package. We tested several of the high-order adaptive methods, including the “Tsitouras-Papakostas 8/7 Runge-Kutta method” and the “Verner’s ‘Most Efficient’ 9/8 Runge-Kutta method”, as well as this packages implementation of the eighth-order Dormund-Prince scheme used for many of the simulations in the paper. For all timesteppers, the rate at which hyperuniformity appears depends on the size of the truncation error, and those rates are approximately consistent across methods.
+
+Minor comments
+
+1 **Referee:** In the subplots showing the 2D S(q), I find the color scheme (black = zero) confusing. I recommend it is inverted.
+
+**Response:** We understand the confusion and have tested the inverted color scheme. We decided to stay with the current scheme as the features are more observable to the naked eye. This scheme is also in line with typical diffraction scattering experimental plots.
+
+2 **Referee:** Page 2, 11 lines from the end: typo – extra ‘(‘.
+
+**Response:** corrected!
+
+3 **Referee:** What happens at low densities? Is the steady state still hyperuniform?
+
+**Response:** Indeed so it seems. In Fig. 3C we show results for various area fractions, \( \phi \). We have tested down to \( \phi = 0.04 \) and even at that area fraction we see the beginning of hyperuniformity. The lower the density the slower the dynamics is so we have not attempted densities lower than that.
+
+4 **Referee:** The definition of returnity can be clarified.
+
+**Response:** We agree with the referee and have tried to clarify the definition in the revised version. The returnity is now called “the relative deviation” and its meaning redefined in the text and in the caption of the figure.
+
+5 **Referee:** Entropy measurements and Fig 4E: The changes in entropy are very small – about \( 1 - 2\% \) with an error of \( 0.5 - 1\% \). This is not surprising given that converting the data into a figure with KxK pixels, estimating the entropy using lossless compression will be severely undersampled unless the number of realizations is of the order of \( 2^{K^2} \). As the authors already calculated the structure factor, I suggest applying the method of [43]. Also, it is interesting to plot the entropy as a function of \( \Gamma_h / \Gamma_l \).
+
+**Response:** The referee is correct regarding the large errors in the compression plot. We did not attempt a rigorous calculation but merely aimed at showing that the simulations follow the theoretical reasoning — slow vortices expand thereby increasing entropy, fast vortices slightly compress and the entropy of the mixed system increases. Following the referee’s recommendation, we have considered applying the method of Ref. 43 (Ariel and Diamant PRE 2020), but it does not seem to be immediately applicable to a mixture. From Ref. 43: “A key disadvantage of entropy estimation based on density correlations is that it is more particular. While sampling, and especially compression, can be applied ‘blindly’ without prior knowledge of the system, relations such as Eq. (3) are limited to systems of a certain category. For example, Eq. (3) must be modified if it is to be applied to mixtures or to anisotropic particles.”
+Report and response to Referee 3:
+
+Referee: By considering Hamiltonian formalism, the authors predict that point vortices should form disordered hyperuniform states due to conservation laws. The authors also recover the exactly the same result for torque driven membrane rotors with a finite size, in the limit of short separations. The theoretical calculations are supported by detailed hydrodynamic simulations, with an excellent agreement between the two. Simulations are then used to consider a 50:50 mixtures of fast and slow spinning point vortices. Here, phase enrichment is observed for both population, while hyperuniformity is observed for fast spinning vortices only. The two populations occupy two different areas, which is shown to maximize the number of available states.
+
+From the point of view of rotational active matter, I do find the presented results interesting. It is fascinating that the conservation laws stemming from the Hamiltonian structure of the rotationally invariant interactions result to the distinct states, as shown by the authors. Especially the phase enrichment in the mixtures is very nice. I am not a theorist nor too familiar with the formalism used, so some details may have escaped from me. The authors make an effort to simplify the mathematics, but at places I was lost what were the basic assumptions vs derived results.
+
+Response: We thank the referee for stating the results are interesting and nicely presented! We also found it fascinating that there are distinct structural states stemming from the conservation laws. We agree with the reviewer that what we assumed, and what our derived results were, was not always clear in our original manuscript. We have made considerable changes — rewording and reorganization of text — and hope that the resulting revised manuscript is much clearer in this regard.
+
+Let us also summarize here as well what is assumed and what was derived. We start with the equations for vortices in an inviscid fluid. It is known that one can write three conservation laws for point vortices — the Hamiltonian, and the first and second moments of vorticity. We write in Eq. 2 the Stokes equations for membrane rotors and show that the dynamics are exactly the same as for vortices in the limit of \( r \ll \lambda \), where \( \lambda \) is the Saffman-Delbrück length. For rotors, we assume that the density is low such that the main hydrodynamic contribution of a rotor to the flow is of a point torque. We mainly focus on the limit of small distances relative to the Saffman-Delbrück length, but comment on the other limit in the text (e.g. Fig.1B and 2B and C) and in the SI. It is known in Hamiltonian mechanics that symmetries of the Hamiltonian correspond to conservation laws. In our case, the conjugate variables of the Hamiltonian are the actual locations of the particles. Thus, the Hamiltonian is geometric in nature and conservation laws associated with it limit the distribution of the particles. To get a sense of the meaning of the conservation laws:
+
+• The Hamiltonian is analogous to the kinetic energy (for point vortices in an ideal fluid it is, in fact, the actual kinetic energy). Since \( \mathcal{H} \) is a sum of \( -\log \) of the distances between each two vortices, its conservation means that two vortices cannot overlap or be too close since then the Hamiltonian will diverge.
+
+• The second moment of vorticity is also conserved which can be shown from invariance to rotations. The second moment is analogous to the moment of inertia, except that instead of masses the sum over distances squared is weighted by the circulation. Since the second moment is conserved, two particles cannot scatter to large distances, as then the second moment will diverge.
+
+• The first moment of vorticity is analogous to the center of mass. Again, instead of masses the sum is weighted by circulations. Its conservation corresponds to a fixed center of vorticity.
+
+We thus see that particles cannnot be too close to each other nor too far apart, which hints that the system should be hyperuniform. Mind you, hyperuniformity is the suppression of density fluctuations. We go on to show this should be the case: we derive a link between the Hamiltonian and the structure factor, Eq. 1. This integral relation puts a bound on the structure factor. For point vortices, we find that at small wavenumbers \( S(q) \propto q^\alpha \) with \( \alpha > 0 \) which is one of the definitions of a hyperuniform material.
+
+We have revised the manuscript to include the key-points mentioned above.
+Other comments/questions:
+
+1 Referee: On the page 3, where the steady state is characterized by 3-distinct ways. The role of perturbations is discussed. It is stated that some amount of perturbations are needed to observe hyperuniformity. While this would not be a problem in an experimental setting, does it imply that if the Hamiltonian and its moments are exactly conserved, hyperuniformity would not be observed for point vortices?
+
+Response: Yes, we believe the referee is correct. As we show theoretically, a system of point vortices should be hyperuniform from the conservation laws. However, in simulations of point vortices without steric interactions, taking smaller and smaller step sizes results in hyperuniformity emerging at later and later times. It is impossible (or very hard) to show what will happen in a pure system with zero numerical errors, but we suspect that hyperuniformity will not be reached, or perhaps, it will take an infinite time to reach the hyperuniform state. It seems that perturbations that break rotational symmetry are needed. As the referee points out, in any experimental system this will not be a problem. We have now also tested a symplectic integration scheme which by design conserves the rotational symmetry of the Hamiltonian, and do not observe a clear sign of hyperuniformity in it (however, since the scheme is much more computationally expensive, we were only able to test a lower order timestepper and a smaller system of 1,000 particles). We mention the new simulation and its results in the main text and the SI, and clarify the role of perturbations in the main text.
+
+2 Referee: The \( S(q) \) for rotors (inset in Fig. 3B) shows plateau at small q of all \( \phi > 0.14 \). While in the main text it is said that all the samples showed hyperuniformity. This seems contradictory with the definition of \( S(q) \to 0 \) when \( q \to 0 \). Also, the rotors probably develop (local) hexatic order before the crystallization observed at \( \phi \sim 0.5 \). It would instructive to plot the local hexatic order parameter as a function of \( \phi \).
+
+Response: Indeed the referee is correct in that when steric interactions are added local order emerges. We have tested smaller systems of 2,000 particles for the plot in Fig. 3B. The ensemble transitions from a disordered hyperuniform state at low densities to an ordered hyperuniform state in the form of a hexagonal lattice at high ones. In future work we plan to investigate this transition in depth. A plateau in the structure factor does not mean that there is no hyperuniformity. The structure factor of a pure lattice, for example, is what is called ordered hyperuniform. And, for a lattice, the structure factor is zero except for sharp delta peaks. This is what we start to see for the highest concentration \( \phi \sim 0.54 \). For a finite system, the value of the plateau will not be zero but some finite, small, value. The referee made a good suggestion to measure the local hexatic order parameter, which we have now added to the text and the figure.
+
+3 Referee: I was somewhat confused with the returnity. The returnity seems to be close to zero at longtimes. Logically to me this suggests that the particle position has deviated from its original position. However, the definition of the returnity in the caption suggests that zero returnity means no deviation. The calculation/discussion should be clarified.
+
+Response: The referee is correct that the definition was confusing and misleading. We have renamed the returnity and now simply call it the relative deviation. If a particle has returned to its previous position its value will be zero, and its max value is given when the particle has traveled the entire perimeter, whence its value is \( 2\pi \).
+
+4 Referee: Connected to above, from the main text it seems that the system is not in absorbing state at long times, while it is also said that the ensemble undergoes a solid body rotation, where the particle i returns to its position cyclically. This paragraph should be clarified.
+
+Response: The referee is again correct that the writing was confusing. We have changed the manuscript accordingly. The average velocity increases linearly with radius and in that sense we meant it is like a solid body rotation. The system does not appear to reach an absorbing state. Tracking a single particle over long times shows that it still explores the entire phase-space (which
+in our case is equivalent to configurational-space). The relative deviation (previously named “the returnity”) only measures the deviation from the previous position after one cycle. This deviation is initially large on average but is small when the system is at steady state. We now added a clarification to the text as well as a plot of the trajectory of a few particles over many cycles (\( \sim 130 \)). These trajectories show Brownian-like dynamics which will be interesting to further explore, as we hope to do in future work.
+
+5 Referee: For which system is the returnity measured? Would it be expected to be different between point vortices and rotors?
+
+Response: We measured the returnity for a system of point vortices. Following the referee’s comment we have now measured the returnity at a low area fraction \( \phi = 0.1 \) of rotors as well and have gotten a similar plot to Fig. 3D. For rotors, as the concentration is increased, the ensemble crystallizes. Therefore, at higher area fractions the system does reach an absorbing state. We have added a clarification to the text.
+
+6 Referee: The role of fig. 2c is not clear to me. Does this mean that at long separations (low area/volume fractions) the finite size rotors are not expected to have similar steady state as predicted for point vortices?
+
+Response: Indeed there is a difference between cases where the total size of the ensemble is smaller than the Saffman Delbruck length which is a few microns, to cases where the ensemble size is larger than \( \lambda \). For a case where the density is low and the number of particles is large, the scaling of the interaction between faraway rotors is \( 1/r^2 \). That is, lower than the \( 1/r \) for interactions between close rotors. The symmetries of the Hamiltonian are the same and there are still conservation laws bounding the distribution of particles. However, Eq. 1 gives a lower bound of \( S(q) \sim q^\alpha \) with \( \alpha > -1 \) from which we cannot conclude the system should be hyperuniform. Simulation results in this limit indicate that the system is hyperuniform, as we show in the Supplementary Information.
+
+7 Referee: Also, if not completely obvious, it would be nice if arguments/simple explanations were given for example for the symmetries for a translation in time, space and rotation corresponding to the conservation laws. This would increase the accessibility of the article. Can these be understood in some simple way, such as conservation of the hamiltonian and 2nd moment kind of fixes the density, while the vanishing first moment corresponds to no center of mass movement? At longtimes this then leads to a steady state with a (close to) solid body rotation, as opposite to the chaotic dynamics at times near the random starting configuration.
+
+Response: Yes! Exactly as the referee wrote. The conservation of the Hamiltonian and of the 2nd moment of vorticity limit the distribution of particles. The second moment of vorticity is analogous to the conservation of the center of mass. We have now included these comments in the text. We have added further details on the conservation laws in response to the first comment by the referee.
+
+8 Referee: In the ref 15, for torque driven rotors it is suggested that the steady state is characterized by extrema of a ”pseudo kinetic energy”. In the formalism presented here, is there an analog to this?
+
+Response: Yes, the case of torque driven rotors in Ref. 15 is the same as our case, and so here as well, the Hamiltonian could be said to be a pseudo kinetic energy. In Ref. 15 they claim that an hexagonal lattice arises due to minimization of this energy. However, they then show that the hexagonal state is only marginally stable. This is a result of the fact that interactions between the rotors are not repulsive nor attractive. For example, two rotors will orbit around each other at a fixed distance, they will not draw nearer or separate. We show in Ref. 17 that adding steric interactions, this marginally stable state can become stable. The same happens here with steric interactions at sufficiently high concentrations. Due to the marginal stability, we do not expect nor do we see spontaneous crystallization in a system of point vortices.
+9 Referee: The \( \psi \) in the Hamiltonian above the equation 5 on page 3 is not defined.
+
+Response: The referee is correct; this was a typo and now reads \( \Psi \).
+REVIEWERS’ COMMENTS
+
+Reviewer #2 (Remarks to the Author):
+
+Second report on “Hyperuniformity and phase enrichment in vortex and rotor assemblies” by Oppenheimer et al. The authors addressed all my comments. This is an excellent paper. I recommend it is accepted to Nature Communications.
+
+I have two minor comments:
+
+1. This is a matter of style, but I think the abstract can be improved. The revised version is detailed and specialized, which somewhat obscures the main results.
+
+2. It is worth noting that the observed divergence of the relaxation time towards hyperuniformity is consistent with the critical slowing down reported, for example, in [41]. Interestingly, in [41], hyperuniformity is only obtained at critical values of the parameters. Here, it does not require fine tuning. Instead, numerical errors may play an analogues role.
+
+Reviewer #3 (Remarks to the Author):
+
+I would like to thank the authors for the detailed and comprehensive replies. These fully address my queries. Only very minor comment regarding the supplementary fig. 4, which the y-label reads returnity.
+
+I feel that the authors have considerably improved the manuscript, and I am happy to recommend publication in Nature Communications.
+We were very pleased that both referees recommended the paper for publication. As we stated previously, we feel that not only has the manuscript improved by addressing their comments, but also our understanding of the system. The reviewers had additional minor comments which we address below and in the revised text. We also made revisions according to the editorial requests. Below we copy the referee reports in green. Our response is in black below each point.
+
+Report and response to Referee 2:
+
+Referee: Second report on “Hyperuniformity and phase enrichment in vortex and rotor assemblies” by Oppenheimer et al. The authors addressed all my comments. This is an excellent paper. I recommend it is accepted to Nature Communications.
+Referee: I have two minor comments:
+
+1 This is a matter of style, but I think the abstract can be improved. The revised version is detailed and specialized, which somewhat obscures the main results.
+
+Response: We agree with the referee that the new version of the abstract is a bit too specialized. We have changed the abstract back to what it previously was, with much smaller corrections.
+
+2 It is worth noting that the observed divergence of the relaxation time towards hyperuniformity is consistent with the critical slowing down reported, for example, in [41]. Interestingly, in [41], hyperuniformity is only obtained at critical values of the parameters. Here, it does not require fine tuning. Instead, numerical errors may play an analogues role.
+
+Response: We thank the referee for pointing out that our observations are consistent with the critical slowing down towards hyperuniformity in the absorbing states of e.g. [41]. We have now included such a statement:
+“The observed relaxation towards hyperuniformity is consistent with the critical slowing down reported for other systems (e.g. [41])”
+
+Report and response to Referee 3:
+
+Referee: I would like to thank the authors for the detailed and comprehensive replies. These fully address my queries. Only very minor comment regarding the supplementary fig. 4, which the y-label reads returnity.
+I feel that the authors have considerably improved the manuscript, and I am happy to recommend publication in Nature Communication.
+
+Response: We thank the referee for recommending the paper for publication in Nature Communications.
+We have now re-labeled Fig. 4 in the Supplementary Information, and call it the Relative Deviation.

044192f1c210d2b128ea12550aed987a7bd494d2d9c59299caf93d282ac1c77f/peer_review/peer_review.md

@@ -0,0 +1,300 @@
+Reviewers’ Comments:
+
+Reviewer #1:
+Remarks to the Author:
+I have reviewed the manuscript 'Spurious North Tropical Atlantic pre-cursors to ENSO', by W. Zhang et al.
+This is an interesting and well researched study. It clearly shows that the teleconnection from ENSO to the tropical North Atlantic alone may be able to explain observed lead-lag correlations between them, with out a feedback from the North Atlantic to ENSO being necessary. As such this study claims to provide evidence that a previous study by Ham et. al., also in a Nature publishing group, is not valid. It is curious that the Ham paper and this manuscript share a co-author.
+Anyway, I do think that the current study actually does not disprove the findings from Ham et. al., and therefore the language of this paper (including probably title) should be considerably turned down. I recommend a major revision addressing the issues below:
+
+1. The fact that this manuscript shows that ENSO’s teleconnection to the North Atlantic can explain also their lead-lag correlations does not mean that they have shown that a feedback from the North Atlantic to ENSO is also relevant and may also contribute the the lead-lag correlations. This is basic logic.
+
+2. To further support point one, what this manuscript does is essentially only provides evidence for the one-way influence of ENSO on the North Atlantic. However, note that Ham et al., do exactly the opposite, so I guess their results may be complementary. Note that Ham et al, as well as other studies (e.g. Kucharski et. al., Atmosphere 2016, 7(2), 29; https://doi.org/10.3390/atmos7020029) remove the previous winter ENSO statistically to show the feedback on the following year ENSO. You may repeat some of your analysis also removing the previous year's ENSO in order to check the impact of this on your results. Perhaps we see that some of the lead-lag relation could be indeed related to the feedback on the tropical North Atlantic on ENSO.
+
+3. Furhtthermore, the 2 studies mentioned in point 2 also provide pacemaker experiments to show the feedback from the tropical North Atlantic to ENSO, just the opposite of what the present manuscript does. Therefore, these studies are really complementary.
+
+4. In your idealised experiments (e.g. lines 130 - 150), you prescribe a perfectly autocorrelated ENSO cycle. Then your results are almost granted. The correlation for El Nino to the following La Nina or vice versa is in reality much weaker, and the feedback from the North Atlantic may therefore in reality be important to explain the ENSO periodicity.
+
+5. The use of CMIP models gives in no way more confidence tothe main results that the ENSO-North tropical Atlantic interaction is in reality one-way. It has been well noted in many studies that ENSO’s impact may be overestimated in many cmip models, whereas the impact of other ocean basins on ENSO could therefore be underestimated.
+
+Reviewer #2:
+Remarks to the Author:
+Review of “Spurious North Tropical Atlantic pre-cursors to ENSO”
+
+The paper by Wenjun Zhang and his co-authors revisits the linear two-way relationship between ENSO and the Tropical North Atlantic (TNA) sea surface temperature (SST) variability by taking into consideration important aspects of ENSO dynamics, e.g. its strong autocorrelation and irregular cycle. Previous studies have shown that ENSO has a significant impact on the TNA with a lag of 4 months (consistent with the SSTs delayed response). Previous studies suggest that spring TNA SST anomalies
+can be a pre-cursor to ENSO in the next season with a lag of 8 months, although this correlation is only present after the 1990s. Before the 1990s the TNA lags the ENSO response in the Pacific by approximately 20 months, which would be consistent with a quasi-quadrennial cycle, in contrast with the quasi-biennial cycle dominant in the more recent period. The authors use a rich variety of tools (observations, a simple physical model, output from CIMP6 models, and idealized pacemaker experiments) to prove that the suggested impact of the TNA variability on ENSO development is negligible if we account for the internal ENSO cycle. The authors also prove that these conclusions are robust under future climate scenarios.
+
+The results presented in this manuscript are very interesting and relevant for a wide scientific audience. I really enjoyed reading this paper. It is well-written and presents a clear message, which is proved in a very systematic and convincing way. I highly recommend this paper for publication in Nature communications. I just have some small minor comments, which are mostly some clarifications on the methods employed.
+
+Minor comments:
+
+Lines 62-64: The authors describe the mechanism for the warm phase of ENSO. Does La Niña also lead to a similar response on the TNA? From a correlation map, it is difficult to say whether this is the case.
+
+Lines 96-97: How do the authors justify that the complicated irregular ENSO cycle does not affect this relationship? A better reason/explain would be desired.
+
+Line 99-101: I do not understand why a bandpass of 2-3yr is applied to extract the quasi-biennial periodicity and a 3-5yr is used to extract the quasi-quadrennial cycle. Should not they be consistent, i.e. 1-3yr and 3-5yr? I guess this shouldn’t affect the results of the study, but it will be interesting to justify the 2-3yr choice instead of 1-3yr. Is it to remove the seasonal cycle?
+
+Lines 145-146: I think this is a mistake. The quasi-biennial ENSO cycle and 8 months lang between the TNA and the following ENSO phase is after the 1990s.
+
+Lines 161-162: Looking at supplementary Figure 5 it seems that there is a large inter-model spread. It is however impressive how the multi-model mean captures the ENSO-TNA correlation so well. I think the model spread should be mentioned here.
+
+Line 190: I do not understand the term “In-turn linear relationship”. Maybe rewrite this sentence.
+
+Lines 220-221: Do the analysis change when not removing a linear trend? The authors show later that this relationship is still valid even under climate change conditions.
+
+Lines 246-248: What are the parameters that the authors obtain after using the observations to fit this simple model.
+
+Line 248-249: What would be the effect of including this term? What is the reason to not include it?
+
+Line 252: What is the difference between “SSP2-4.5 and SSP5-8.5” and “RCP4.5 and RCP8.5” climate emission scenarios? I think the climate community is more familiar with the RCP scenarios.
+
+Line 277: What SST climatology is used (observations or model, period)?
+
+Figure 1e: I cannot see which lines are dashed and which ones are not in the legend (CP vs EP). This is also not specified in the figure caption.
+Sincerely,
+Bernat Jiménez-Esteve
+MS. NO. NCOMMS-20-41862-T
+
+Response to Reviewers
+
+We would like to thank the reviewers for their constructive comments and suggestions. We have addressed the reviewers’ concerns and implemented the useful suggestions in our revised manuscript. The responses are listed below in blue font.
+
+Response to Reviewer#1
+
+I have reviewed the manuscript 'Spurious North Tropical Atlantic pre-cursors to ENSO', by W. Zhang et al.
+This is an interesting and well researched study. It clearly shows that the teleconnection from ENSO to the tropical North Atlantic alone may be able to explain observed lead-lag correlations between them, without a feedback from the North Atlantic to ENSO being necessary. As such this study claims to provide evidence that a previous study by Ham et. al., also in a Nature publishing group, is not valid. It is curious that the Ham paper and this manuscript share a co-author.
+Anyway, I do think that the current study actually does not disprove the findings from Ham et. al., and therefore the language of this paper (including probably title) should be considerably turned down. I recommend a major revision addressing the issues below:
+
+Response: Thank you for your valuable comments. In this manuscript, we demonstrate that the cross-correlation characteristics between NTA SST and ENSO are consistent with a one-way Pacific to Atlantic forcing. Our work here identified the appropriate way to formulate a physical null hypothesis – that is, by considering the different ENSO regimes – that would need to be falsified by future studies that claim a two-way feedback.
+
+In addition, we present multiple lines of evidence that the NTA SST variability cannot be identified as a statistically significant pre-cursor for ENSO, regardless of whether a feedback from the North Atlantic on ENSO exists based on both observations and a physical model in the manuscript and the following point-to-point responses. Furthermore, we also demonstrate that the results from the previous NTA forced pacemaker experiments by Ham et al. (2013a,b) cannot be used as evidence to reject our null hypothesis of a one-way forcing.
+
+As mentioned by the reviewer, Ham et al. (2013a) and this manuscript shared one co-author (Prof. Fei-fei Jin), who is also one of the corresponding authors here. The concept that the NTA variability has a possible feedback on the following ENSO was first advanced in Ham et al. (2013a). This study was then followed by Wang et al. (2017), which deepened our understanding that this relationship is statistically nonstationary. They attempted to attribute the nonstationarity to the AMO phase transition from negative to positive around the 1990s. However, this hypothesis cannot explain why the correlation between spring NTA SST and following ENSO is also statistically insignificant during the previous positive AMO period (before the
+1960s). Apparently, the previous argument that global warming together with the positive phase of the AMO contribute to the relationship is without substance.
+
+This inspired us (including Prof. Fei-Fei Jin) to revisit the intriguing question. Here, we find that the relationship between NTA SST and ENSO is consistent with a one-way Pacific to Atlantic forcing null hypothesis. This framing by ENSO one-way forcing explains the observed NTA-ENSO linkage variations over the whole observational period in a consistent way. Moreover, the regulation of the ENSO cycle on the NTA-ENSO relationship continues to hold in future warming scenarios, which again disproves the previous assumption on this relationship.
+
+1. The fact that this manuscript shows that ENSO's teleconnection to the North Atlantic can explain also their lead-lag correlations does not mean that they have shown that a feedback from the North Atlantic to ENSO is also relevant and may also contribute the the lead-lag correlations. This is basic logic.
+
+Response: Thank you for your valuable comment. In this manuscript we would like to clarify that the NTA SST cannot be statistically identified as a pre-cursor for ENSO regardless of whether a feedback from the North Atlantic on ENSO exists. This is a crucial point that is of importance to future studies investigating any potential inter-basin feedbacks.
+
+As we have shown in Supplementary Fig. 3 in the manuscript, the residual NTA SST variability – once the ENSO signal is removed – has no preferred interannual spectral peak. This strongly suggests that NTA SST interannual variability could originate from ENSO. In the manuscript, we only consider a simplified ENSO-forced NTA model in which the NTA is treated as a purely deterministic process. From a possible realistic perspective, we could include the stochastic forcing (Eq. (1)) in our original ENSO-forced model (Eq. (2)) (Jin et al. 2007),
+
+\[
+\frac{d\xi(t)}{dt} = -m \xi(t) + w(t),
+\] (1)
+
+\[
+\frac{dT(t)}{dt} = (-\lambda_0 + \lambda_a \cos(\omega_a + \varphi))T(t) + \beta ENSO(t) + \xi(t),
+\] (2)
+
+where \( w(t) \) indicates white noise with a Gaussian distribution and the decorrelation time scale parameter \( m \) is set to 1/2 month here. An ensemble of 500 members of red noise times series \( \xi \) was generated. We integrated Eq. (2) for 60 years to create a 500-member ensemble. The observed NTA SST variability can be sufficiently explained by the reconstructed 500-member ensemble mean NTA with \( \pm 0.5 \) standard deviation spread (Fig. R1). This indicates that the NTA SST variability is fully consistent with an ENSO-forced stochastic dynamical process.
+
+However, does this forced NTA variability in-turn account for any ENSO predictability? This is the major concern from the reviewer and our argument here is that the NTA variability actually adds no additional information in ENSO prediction. We demonstrate this argument from two aspects.
+
+(1) Observational evidence
+The 8-month leading relationship of NTA over ENSO only exists within the
+chain of the ENSO cycle (i.e., ENSO transition from El Niño to La Niña or vice versa) (Fig. R2-R5). To quantify the possible NTA feedback on ENSO, we compare the observed and hindcasted Niño3.4 index by using the previous spring NTA SST. The El Niño and La Niña events in which the hindcasted Niño3.4 amplitudes attain more than 20% of the observed amplitudes are defined as ENSO events with a positive NTA contribution. The results are not sensitive to the criterion of the percentage chosen.
+
+All ENSO years with positive NTA contributions (1970, 1976, 1983, 1986, 1994, 1998, 2005, 2009, 2010, 2016, 2018) have in fact opposite ENSO-related SST anomaly conditions in the previous boreal winter (Fig. R3 and Fig. R4). In other words, the so-called contribution from NTA originates entirely from the previous ENSO conditions. For these ENSO years with positive NTA contributions, we can also hindcast the Niño3.4 index by using the previous winter Niño3.4 index (Red dots in Fig. R5b). In particular, there even appears a significant positive correlation between the previous spring NTA SST and winter ENSO for the second/third year of consecutive ENSO events (1969, 1971, 1974, 1975, 1977, 1984, 1987, 1999, 2000, 2008, 2011, 2017, 2019). The opposite relationship between NTA SST and following ENSO seen in those ENSO years can also be explained by the correlation between the winter Niño3.4 index with previous winter Niño3.4 index (Blue dots in Fig. R5). Importantly, for other ENSO years no evident NTA-ENSO relationship can be detected. This again supports our argument in the manuscript “The notion of NTA serving as precursor for ENSO is therefore equivalent to simply saying that the El Niño is precursor to the next La Niña.”
+
+(2) Simulation insufficiencies
+a) The pacemaker experiments in Ham et al. 2013b lack the key pathway for NTA to impact ENSO, in which the observed SST anomalies in the eastern subtropical and tropical North Pacific are absent (Fig. 1 versus Fig. 4 in Ham et al. 2013b).
+
+b) The pacemaker experiments in Ham et al. 2013b fail to reproduce reasonable ENSO events with realistic phase locking features, which is a fundamental ENSO property. In their experiments, ENSO-related SST anomalies synchronize to the boreal autumn season (Sep-Oct-Nov) and quickly recede in the forthcoming winter (Fig. 4e,g in Ham et al. 2013b).
+
+c) The ENSO-related essential atmospheric processes in those NTA-forced experiments show large model dependency. Strong westerly anomalies in the eastern subtropical and tropical North Pacific shown in Ham et al. 2013b, which is the key physical process, are missing in similar experiments conducted in one review paper mentioned by the reviewer (Kucharski et al. 2016).
+
+Based on the above analyses, the NTA-ENSO relationship is tightly controlled by the ENSO cycle and the interannual NTA SST variability cannot feed back on ENSO in a predictable manner (see also in L15-19 in the manuscript). We have added some analyses and related discussion in the revised manuscript (L210-223). Besides, we also avoid using some absolutized expression to avoid possible confusion (e.g.,
+L23 in the manuscript).
+
+![Time series of observed monthly NTA (black line) and reconstructed monthly ensemble mean NTA (red line). Red shading denotes the ± 0.5 standard deviation spread within the 500-member ensemble.](page_314_370_968_312.png)
+
+Figure R1. Time series of the observed monthly NTA (black line) and reconstructed monthly ensemble mean NTA (red line). Red shading denotes the ± 0.5 standard deviation spread within the 500-member ensemble.
+
+![Observed (red line) and hindcasted (black line) Niño3.4 index (°C) using the previous spring NTA SST. Light and dark grey rectangles indicate the El Niño and La Niña years with hindcasted Niño3.4 index accounting for more than 20% of the observation, respectively. The correlation coefficient between observed and hindcasted Niño3.4 index is 0.28.](page_314_726_968_312.png)
+
+Figure R2. Observed (red line) and hindcasted (black line) Niño3.4 index (°C) using the previous spring NTA SST. Light and dark grey rectangles indicate the El Niño and La Niña years with hindcasted Niño3.4 index accounting for more than 20% of the observation, respectively. The correlation coefficient between observed and hindcasted Niño3.4 index is 0.28.
+Figure R4. a The I
+for more than 20% :
+standard deviation.
+NTA contribution (
+and gray bars the pr
+Figure R5. Scatterplot of winter Niño3.4 index with a previous spring NTA SST anomaly and b previous winter Niño3.4 index. Red dots in (a-b) denote the ENSO years with NTA contribution accounting for more than 20% amplitude, blue dots the second/third years of consecutive ENSO events, orange dots the other ENSO years, and gray dots denote the residual years. The linear fits of red and blue dots are displayed together with the corresponding correlation coefficients (R). The correlation coefficient (R; black) for all dots is also shown.
+
+2. To further support point one, what this manuscript does is essentially only provides evidence for the one-way influence of ENSO on the North Atlantic. However, note that Ham et al., do exactly the opposite, so I guess their results may be complementary. Note that Ham et al, as well as other studies (e.g. Kucharski et. al., Atmosphere 2016, 7(2), 29; https://doi.org/10.3390/atmos7020029) remove the previous winter ENSO statistically to show the feedback on the following year ENSO. You may repeat some of your analysis also removing the previous year's ENSO in order to check the impact of this on your results. Perhaps we see that some of the lead-lag relation could be indeed related to the feedback on the tropical North Atlantic on ENSO.
+
+Response: Thank you for your comment. As we have discussed in our response to Comment#1, the ENSO-forced NTA variability does not account for additional ENSO predictability. Thus, our focus in this manuscript is that the NTA SST cannot be identified as a statistically significant pre-cursor for ENSO regardless of whether a feedback from the North Atlantic on ENSO exists.
+
+It is somewhat accepted by default in many climate studies to exclude ENSO impacts by linearly removing the previous boreal winter ENSO signal, which is unreasonable considering that ENSO is a highly complicated and nonlinear climate phenomenon, considering its amplitude (the asymmetry of El Niño and La Niña episodes), temporal evolution (from weather, annual cycle, interannual to decadal timescales) and spatial pattern (eastern Pacific versus central Pacific El Niño)
+
+Here, we extracted the ENSO signal from the NTA variability by using a simplified ENSO-forced NTA model (Supplementary Fig. 2). As shown in
+Supplementary Fig. 3, the residual variability has no preferred interannual spectral peak.
+
+We also show in our response to Comment#1 the observational evidence and the shortcomings of the previous NTA-forced pacemaker experiments.
+
+3. Furthermore, the 2 studies mentioned in point 2 also provide pacemaker experiments to show the feedback from the tropical North Atlantic to ENSO, just the opposite of what the present manuscript does. Therefore, these studies are really complementary.
+
+Response: Thank you very much for your comment. As shown in response to Comment#1, the NTA SST cannot be identified as the pre-cursor for ENSO regardless of whether a feedback from the North Atlantic on ENSO exists. In this manuscript, we are not intended to rule out the possible feedback of NTA on ENSO.
+
+4. In your idealised experiments (e.g. lines 130 - 150), you prescribe a perfectly autocorrelated ENSO cycle. Then your results are almost granted. The correlation for El Niño to the following La Niña or vice versa is in reality much weaker, and the feedback from the North Atlantic may therefore in reality be important to explain the ENSO periodicity.
+
+Response: Thank you very much for your comment. As shown in our response to Comment#1, the so-called NTA feedback only exists within the chain of the ENSO cycle (i.e., ENSO transition from El Niño to La Niña or vice versa). The NTA variability actually adds no additional information in ENSO prediction (Fig. R2-R5).
+
+Besides, we have discussed in the manuscript (L97-98) that the complexity of the ENSO cycle does not affect the qualitative relationship of NTA SST with following ENSO from a statistical standpoint. This argument can be succinctly proved based on our NTA physical model. Three experiments are performed by using different ENSO cycles as in the case of a 4-yr cycle. A perfectly 4-yr sinusoidal ENSO cycle (similar to the experimental design of the pacemaker experiments in the manuscript) is prescribed in EXP1 for reference. Then a more complicated and realistic 4-yr ENSO cycle comprising 1-yr El Niño and 3-yr La Niña is prescribed in EXP2 (Fig. R6a and b). Besides, the possible interference from the amplitude asymmetry of El Niño and La Niña episodes is also examined in EXP3 by multiplying El Niño amplitude by a factor of 2 in EXP1. Using the parameters estimated in Supplementary table 1, we force the NTA model with different ENSO evolutions for 20 ENSO cycles (960 months) and then derive the respective NTA time series (Fig. R6c). Qualitative ENSO-NTA lead-lag relationships can be obtained under the consideration of these ENSO irregular behaviors including duration and amplitude asymmetries (Fig. R6d), despite slight differences in the respective correlation coefficients.
+Figure R6. a ENSO time series (°C) in EXP1 (black line), EXP2 (red line) and EXP3 (blue line) in two ENSO cycles. b Fast Fourier Transform (FFT) power spectra for ENSO time series. The AR(1) null hypothesis is displayed by a dashed thin line and the 95% confidence level is indicated by a solid thin line. c Derived NTA time series (°C) in one ENSO cycle. d Lead-lagged correlation of the boreal winter ENSO with NTA time series.
+
+5. The use of CMIP models gives in no way more confidence to the main results that the ENSO-North tropical Atlantic interaction is in reality one-way. It has been well noted in many studies that ENSO's impact may be overestimated in many CMIP models, whereas the impact of other ocean basins on ENSO could therefore be underestimated.
+
+Response: Thank you very much for your valuable comment. We agree with your concern regarding biases between the multi-model estimation and the observed ENSO-NTA relationship. In Supplementary Fig. 5 we assess the ability of current climate models to simulate the ENSO-NTA connection. The multi-model ensemble mean and the majority of the individual models can reasonably reproduce the observed ENSO’s impact on NTA SST, although with a certain inter-model spread. Thus, the analysis of the multi-model results again supports our hypothesis that the statistical lead-time of NTA SST anomalies over the subsequent ENSO conditions is tightly regulated by the ENSO periodicity. We have added some related discussion about the model performance in reproducing observed ENSO-NTA connection in the revised manuscript (L165-167).
+Response to Reviewer#2
+
+Review of “Spurious North Tropical Atlantic pre-cursors to ENSO”
+
+The paper by Wenjun Zhang and his co-authors revisits the linear two-way relationship between ENSO and the Tropical North Atlantic (TNA) sea surface temperature (SST) variability by taking into consideration important aspects of ENSO dynamics, e.g. its strong autocorrelation and irregular cycle. Previous studies have shown that ENSO has a significant impact on the TNA with a lag of 4 months (consistent with the SSTs delayed response). Previous studies suggest that spring TNA SST anomalies can be a pre-cursor to ENSO in the next season with a lag of 8 months, although this correlation is only present after the 1990s. Before the 1990s the TNA lags the ENSO response in the Pacific by approximately 20 months, which would be consistent with a quasi-quadrennial cycle, in contrast with the quasi-biennial cycle dominant in the more recent period. The authors use a rich variety of tools (observations, a simple physical model, output from CIMP6 models, and idealized pacemaker experiments) to prove that the suggested impact of the TNA variability on ENSO development is negligible if we account for the internal ENSO cycle. The authors also prove that these conclusions are robust under future climate scenarios. The results presented in this manuscript are very interesting and relevant for a wide scientific audience. I really enjoyed reading this paper. It is well-written and presents a clear message, which is proved in a very systematic and convincing way. I highly recommend this paper for publication in Nature communications. I just have some small minor comments, which are mostly some clarifications on the methods employed.
+
+Minor comments:
+1. Lines 62-64: The authors describe the mechanism for the warm phase of ENSO. Does La Niña also lead to a similar response on the TNA? From a correlation map, it is difficult to say whether this is the case.
+
+Response: Thank you for your valuable comment. La Niña events also lead to a similar response on the NTA SST variability (Fig. R7).
+Figure R7. Cor decaying spring. significant at the
+
+2. Lines 96-97: I does not affect th
+
+Response: Thar argument based ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... 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... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
+Figure R8. a ENSO time series (°C) in EXP1 (black line), EXP2 (red line) and EXP3 (blue line) in two ENSO cycles. b Fast Fourier Transform (FFT) power spectra for ENSO time series. The AR(1) null hypothesis is displayed by a dashed thin line and the 95% confidence level is indicated by a solid thin line. c Derived NTA time series (°C) in one ENSO cycle. d Lead-lagged correlation of the boreal winter ENSO with NTA time series.
+
+3. Line 99-101: I do not understand why a bandpass of 2-3yr is applied to extract the quasi-biennial periodicity and a 3-5yr is used to extract the quasi-quadrennial cycle. Should not they be consistent, i.e. 1-3yr and 3-5yr? I guess this shouldn’t affect the results of the study, but it will be interesting to justify the 2-3yr choice instead of 1-3yr. Is it to remove the seasonal cycle?
+
+Response: In the manuscript, we apply a bandpass of 2-3yr to avoid possible affects by of near-annual variability, such as the ENSO combination mode (C-mode) (Stuecker et al. 2013). Actually, it does not affect our conclusion and qualitative results can be obtained by applying 1-3yr bandpass filtering (Fig. R9).
+![A plot showing NTA leads versus Corr. coef. with several lines labeled 1-3 yr Obs, 3-5 yr Obs, 1-3 yr Rec, and 3-5 yr Rec.](page_420_180_476_377.png)
+
+with the filtering filter. For λ-lag at
+
+and 8
+
+a large
+
+the
+
+mean
+
+observed
+
+have
+
+Maybe
+
+rewrite this sentence.
+
+Response: Thank you for your valuable suggestion. We have modified our related discussion as “In turn, the linear relationship between NTA-lead-time over ENSO and ENSO periodicity continues to hold in the global warming scenarios.”
+
+7. Lines 220-221: Do the analysis change when not removing a linear trend? The authors show later that this relationship is still valid even under climate change conditions.
+
+Response: Thank you for your valuable comment. The analysis does not change
+consider a simplified ENSO-forced NTA model. As we have shown in Supplementary Fig. 3, the residual NTA SST variability – once the ENSO signal is removed – has no preferred interannual spectral peak. This strongly suggests that NTA SST interannual variability could originate from ENSO. In the manuscript, we only consider a simplified ENSO-forced NTA model in which the NTA is treated as a purely deterministic process. From a possible realistic perspective, we could include the stochastic forcing (Eq. (1)) in our original ENSO-forced model (Eq. (2)) (Jin et al. 2007),
+
+\[
+\frac{d\xi(t)}{dt} = -m \xi(t) + w(t),
+\]
+(3)
+
+\[
+\frac{dT(t)}{dt} = (-\lambda_0 + \lambda_a \cos(\omega_a + \varphi))T(t) + \beta ENSO(t) + \xi(t),
+\]
+(4)
+
+where w(t) denotes white noise with a Gaussian distribution and the decorrelation time scale parameter m is set to 0.5 month here. An ensemble of 500 members of red noise times series \( \xi \) was then generated. We integrated the Eq. (4) for 60 years to create a 500-member ensemble. The observed NTA SST variability can be sufficiently explained by the reconstructed 500-member ensemble mean NTA with \( \pm \) 0.5 standard deviation spread (Fig. R11). This also indicates that the NTA SST variability is fully
+consistent with an ENSO-forced stochastic dynamical process. In this manuscript, we neglect this term to emphasize the importance of ENSO forcing on the NTA SST, considering that the predictable part of the NTA SST variability mainly originates from ENSO.
+
+![Time series of the observed monthly NTA (black line) and reconstructed monthly ensemble mean NTA (red line). Red shading denotes the ± 0.5 standard deviation spread within the 500-member ensemble.](page_324_370_1017_384.png)
+
+Figure R11. Time series of the observed monthly NTA (black line) and reconstructed monthly ensemble mean NTA (red line). Red shading denotes the ± 0.5 standard deviation spread within the 500-member ensemble.
+
+10. Line 252: What is the difference between “SSP2-4.5 and SSP5-8.5” and “RCP4.5 and RCP8.5” climate emission scenarios? I think the climate community is more familiar with the RCP scenarios.
+
+Response: Thank you for your comment. Future simulations in CMIP5 were made under a set of four pathways of anthropogenic greenhouse gas and aerosol concentrations resulting in different levels of radiative forcing-the Representative Concentration Pathways (RCPs; Moss et al. 2010; Vuuren et al. 2011). The new scenarios in CMIP6 combine a RCP and a Shared Socioeconomic Pathway (SSP; O’Neill et al. 2016), named for the SSP value then the RCP value. The RCPs, which are defined by the magnitude of radiative forcing at 2100, contain the same values as for CMIP5 and also some new ones: 1.9, 2.6, 3.4, 4.5, 6.0, 7.0, and 8.5 W/m^2. The five SSPs are summarized by the narrative headlines; SSP1-sustainability: taking the green road; SSP2-middle of the road; SSP3-regional rivalry: a rocky road; SSP4-inequality: a road divided; and SSP5-fossil fueled development: taking the highway (O’Neill et al. 2016). The framing in CMIP6 including both SSP and RCP dimensions offers opportunities to examine the future in terms of physical climate change, socioeconomic pathways and their possible interactions.
+
+11. Line 277: What SST climatology is used (observations or model, period)?
+
+Response: Thank you for the comment. The SST anomalies derived from observations are added to the 1960-2019 climatological SSTs. We have added related description in the revised manuscript (L290-291) to make this issue clear.
+
+12. Figure 1e: I cannot see which lines are dashed and which ones are not in the
+legend (CP vs EP). This is also not specified in the figure caption.
+
+Response: Thank you for your suggestion. We have improved Figure 1 for better elucidation. The details of the experimental design are shown in the Methods, so we do not repeat this information in the caption for simplicity.
+
+References
+
+Kucharski, F. et al. The Teleconnection of the Tropical Atlantic to Indo-Pacific Sea Surface Temperatures on Inter-Annual to Centennial Time Scales: A Review of Recent Findings. Atmosphere 7(2), 29 (2016).
+
+Jin, F. F., Lin, L., Timmermann, A. & Zhao, J. Ensemble mean dynamics of the ENSO recharge oscillator under state dependent stochastic forcing. Geophys. Res. Lett. 34, L03807 (2007).
+
+Ham Y.-G., Kug J.-S., Park J.-Y. & Jin F.-F. Sea surface temperature in the north tropical Atlantic as a trigger for El Niño/Southern Oscillation events. Nature Geosci. 6, 112–116 (2013a).
+
+Ham Y.-G., Kug J.-S. & Park J.-Y. Two distinct roles of Atlantic SSTs in ENSO variability: North tropical Atlantic SST and Atlantic Niño. Geophys. Res. Lett. 40, 4012–4017 (2013b).
+
+Moss, R. H. et al. The next generation of scenarios for climate change research and assessment. Nature 463, 747–756 (2010).
+
+O’Neill, B. C. et al. The scenario model intercomparison project (ScenarioMIP) for CMIP6. Geosci. Model Dev. 9, 3461–3482 (2016).
+
+Stuecker, M. F., Timmermann, A., Jin, F.-F., McGregor, S. & Ren, H.-L. A combination mode of the annual cycle and the El Niño/Southern Oscillation. Nat. Geosci. 6, 540–544 (2013).
+
+van Vuuren, D. et al. The representative concentration pathways: An overview. Climatic Change. 109(1 2), 5–31 (2011).
+
+Wang L., Yu J.-Y. & Paek H. Enhanced biennial variability in the Pacific due to Atlantic capacitor effect. Nature Commun. 8, 14887 (2017).
+Reviewers’ Comments:
+
+Reviewer #1:
+Remarks to the Author:
+The authors have addressed all my concerns. Therefore the paper may be accepted.
+
+Reviewer #2:
+Remarks to the Author:
+The revised version of the manuscript by W. Zhang et al. is well written and the results concerning the ENSO-NTA relationship using different methodologies remain the same as the previous version. In general, although the authors have not made any substantial changes in the manuscript, they have put enough effort into answering and clarifying most of my previous comments, as well as the more critical ones by the other reviewer. From my side, I am satisfied with the answers and justifications given to my comments, but I would have appreciated that more of these comments would have been introduced in the manuscript. It would have also helped to have a version with tracked changes, otherwise, I assume not much has been changed. I just have some more specific very minor comments on the text. Apart from those, I am happy to recommend this paper for publication in Nature Communications.
+
+Minor comments:
+
+Line 55: Maybe rephrase the sentence. In my opinion, in this paper, you are not analyzing the underlying mechanisms, but the statistical robustness of the time-varying relationship. You propose a mechanism, but you don’t analyze it dynamically.
+
+Line 64-65: Specify how many months.
+
+Line 75: you might remove “even”
+
+Lines 97-99: I think referring to Figure R6 here, and add it to the supplementary material, would support this claim, which is not obvious that it is true.
+
+Lines 150-155: When comparing in more detail figures 1d and 1e, one can see that whereas the correlation for the 2yr-cycle matches quite well with the 2-3yr filtered observations, the 4yr-cycle experiments show a slightly different evolution than the 3-5yr filtered correlation. This is not mentioned in the manuscript. I wonder if this is due to the simulation setup.
+
+Sincerely,
+Bernat Jiménez-Esteve
+MS. NO. NCOMMS-20-41862A-Z
+
+Response to Reviewers
+
+We would like to thank the reviewers for their constructive comments and suggestions. We have addressed the reviewers’ concerns and implemented the useful suggestions in our revised manuscript. The responses are listed below in blue font.
+
+Response to Reviewer#2
+
+The revised version of the manuscript by W. Zhang et al. is well written and the results concerning the ENSO-NTA relationship using different methodologies remain the same as the previous version. In general, although the authors have not made any substantial changes in the manuscript, they have put enough effort into answering and clarifying most of my previous comments, as well as the more critical ones by the other reviewer. From my side, I am satisfied with the answers and justifications given to my comments, but I would have appreciated that more of these comments would have been introduced in the manuscript. It would have also helped to have a version with tracked changes, otherwise, I assume not much has been changed. I just have some more specific very minor comments on the text. Apart from those, I am happy to recommend this paper for publication in Nature Communications.
+
+Minor comments:
+
+Line 55: Maybe rephrase the sentence. In my opinion, in this paper, you are not analyzing the underlying mechanisms, but the statistical robustness of the time-varying relationship. You propose a mechanism, but you don’t analyze it dynamically.
+
+Response: Thank you for your valuable suggestion. We have rephrased the sentence in L57 in the revised manuscript as “In this study, we use both observations and climate model simulations to interpret this time-varying relationship.”
+
+Line 64-65: Specify how many months.
+
+Response: Thank you for your valuable suggestion. We have specified the months in L67 in the revised manuscript as “Analyzing observed SST anomalies (see Methods), we see that the El Niño remote forcing is felt in the NTA SST 3-5 months later around the spring season.”
+
+Line 75: you might remove “even”
+
+Response: Thank you for your valuable suggestion. We have removed “even” in the revised manuscript (L78).
+
+Lines 97-99: I think referring to Figure R6 here, and add it to the supplementary
+material, would support this claim, which is not obvious that it is true.
+
+Response: Thank you for your valuable suggestion. We have added Figure R6 and some discussion in the supplementary information. Considering that we have not introduced the ENSO-forced NTA model here (L97-99 in the last version), we move the related discussion to L125-130 in the revised manuscript.
+
+Lines 150-155: When comparing in more detail figures 1d and 1e, one can see that whereas the correlation for the 2yr-cycle matches quite well with the 2-3yr filtered observations, the 4yr-cycle experiments show a slightly different evolution than the 3-5yr filtered correlation. This is not mentioned in the manuscript. I wonder if this is due to the simulation setup.
+
+Response: Thank you for your valuable comment. For a 4-yr ENSO-forced experiment, more disturbance from the stochastic forcing would be expected in the relatively longer time evolution of ENSO transition compared to a 2-yr ENSO-forced experiment. As a result, the most obvious difference between 4-yr experiment and 3-5yr filtered correlation appear around the 12-month lead and 12-month lag with respect to ENSO mature winter, when the ENSO condition is near-zero. We have added some discussion about the difference between 4-yr ENSO-forced experiments with 3-5yr filtering correlation in L154-157 in the revised manuscript.

044192f1c210d2b128ea12550aed987a7bd494d2d9c59299caf93d282ac1c77f/preprint/preprint.md

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+Spurious North Tropical Atlantic pre-cursors to ENSO
+
+Wenjun Zhang (zhangwj@nuist.edu.cn)
+Nanjing University of Information Science and Technology   https://orcid.org/0000-0002-6375-8826
+Feng Jiang
+Nanjing University of Information Science and Technology
+Malte Stuecker
+University of Hawai'i at Mānoa
+Fei-Fei Jin
+University of Hawaii at Manoa
+Axel Timmermann
+Pusan National University
+
+Article
+
+Keywords: El Niño-Southern Oscillation (ENSO), North Tropical Atlantic (NTA), sea surface temperature (SST)
+
+Posted Date: February 26th, 2021
+
+DOI: https://doi.org/10.21203/rs.3.rs-85237/v1
+
+License: This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License
+
+Version of Record: A version of this preprint was published at Nature Communications on May 25th, 2021. See the published version at https://doi.org/10.1038/s41467-021-23411-6.
+Spurious North Tropical Atlantic pre-cursors to ENSO
+
+Wenjun Zhang¹, Feng Jiang¹, Malte F. Stuecker², Fei-Fei Jin³, Axel Timmermann⁴,⁵
+
+¹Key Laboratory of Meteorological Disaster of Ministry of Education (KLME), Nanjing University of Information Science and Technology, Nanjing, China
+²Department of Oceanography & International Pacific Research Center (IPRC), SOEST, University of Hawai‘i at Mānoa, Honolulu, HI, USA
+³Department of Atmospheric Sciences, SOEST, University of Hawai‘i at Mānoa, Honolulu, HI, USA
+⁴Institute for Basic Science, Center for Climate Physics, Busan, South Korea
+⁵Pusan National University, Busan, South Korea
+
+Abstract: The El Niño-Southern Oscillation (ENSO), the primary driver of year-to-year global climate variability, is known to influence the North Tropical Atlantic (NTA) sea surface temperature (SST), especially during boreal spring season. Focusing on statistical lead-lag relationships, previous studies have proposed that interannual NTA SST variability can also feed back on ENSO in a predictable manner. However, these studies do not properly account for ENSO’s autocorrelation and the fact that the SST in the Atlantic and Pacific, as well as their atmospheric interaction are seasonally modulated. This can lead to misinterpretations of causality and the spurious identification of Atlantic precursors for ENSO. Revisiting this issue under consideration of seasonality, time-varying ENSO frequency, and greenhouse warming, we demonstrate that the cross-correlation characteristics between NTA SST and ENSO, are fully consistent with a one-way Pacific to Atlantic forcing, even though the interpretation of lead-lag relationships may suggest otherwise.
+
+The El Niño–Southern Oscillation (ENSO) phenomenon is characterized by interannual fluctuations between warm (El Niño) and cold (La Niña) sea surface temperature (SST) conditions in the equatorial Pacific. Its dynamics and associated coupled changes in the atmosphere and ocean have been studied extensively¹,². Conceptual frameworks for ENSO have been proposed to explain the statistical and physical characteristics in terms of a Pacific eigenoscillation that originates from positive air-sea interactions and delayed oceanic negative feedbacks³⁻⁶. ENSO is further
+energized by stochastic atmospheric forcing7 and modulated by the seasonal cycle8-9.
+Counterintuitively, despite significant advances in both ENSO theory and ENSO representation in climate models, the predictability of central-to-eastern tropical Pacific SST anomalies has decreased in the past two decades to only one season10-12. Research over the past years has further revealed that SST anomalies in other ocean basins may also play an important role shaping the evolution of El Niño events and its predictability13-24. In particular, the North Tropical Atlantic (NTA) SST has been highlighted as a potential precursor candidate18,22-24.
+
+The NTA ocean, home to a variety of societally relevant climate phenomena has received widespread attention25-29. Typically, NTA SST warming lags the El Niño mature winter phase, peaking in the following spring (Fig. 1a) and persisting into early summer30. It is caused by El Niño-induced atmospheric forcing that both modulates the Walker Circulation and excites the Pacific-North America teleconnection pattern31-35. In turn, this NTA warming is argued to stimulate a westward-propagating off-equatorial Rossby wave train, conducive to an ensuing La Niña formation18,24. However, this reverse connection, which is characterized by a negative ENSO/NTA cross-correlation with the NTA SST leading by about 8 months (Fig. 1b), is highly variable and especially absent before the 1990s22 (Fig. 1c). Despite some presumptions involved22,36, the mechanisms responsible for the puzzling connection are less appreciated and a comprehensive understanding of the two-way interaction between NTA variability and ENSO is required. In this study, we use both observations and climate model simulations to investigate the underlying mechanisms for the time-varying relationship. We demonstrate that changes in the NTA/ENSO relationship can be explained in terms of changes in ENSO frequency. The proposed mechanism is fully consistent with ENSO forcing NTA, rather than the opposite.
+
+ENSO-NTA SST relationship in observations
+ENSO generally commences its development in boreal summer and peaks in winter, stimulating atmospheric forcing over the NTA through two distinct pathways involving tropical and extra-tropical teleconnections30,34,35. Analyzing observed SST anomalies
+(see Methods), we see that the El Niño remote forcing is felt in the NTA SST a few months later around the spring season (Fig. 1a), possibly due to the local SST adjustment timescale\(^{37}\) and the seasonality of the atmospheric teleconnection to the Atlantic\(^{30,35}\). This robust ENSO/NTA connection can be detected during the entire study period notwithstanding a slight reduction of the correlation coefficient in the recent two decades (red shading in Fig. 1c; see also ref. \(^{38}\)). In turn, the spring NTA warming appears to contribute to the following La Niña development in the Pacific Ocean (and similarly a spring NTA cooling contributing to a following El Niño) (Fig. 1b) with a relatively weak correlation at about 8-month lag. However, we must also emphasize here that an NTA warming in spring following an El Niño will automatically be correlated with La Niña conditions 8 months later, because El Niño conditions are usually followed by La Niña in the following year, without even involving a physical NTA-to-ENSO relationship. Therefore, one needs to be careful in interpreting seasonally modulated teleconnections of ENSO (see for instance discussion in ref. \(^{21}\)). The 8-month leading relationship of NTA over ENSO is observed after the early 1990s while it is absent in the preceding period (blue shading in Fig. 1c; see also ref. \(^{22}\)). Prior to the 1990s we find a much longer characteristic lead of ~20-month (blue shading in Fig. 1c). Interestingly, this decadal change of the NTA-lead-time corresponds well to a shift in ENSO frequency from quasi-quadrennial to quasi-biennial (Supplementary Fig. 1; see also ref. \(^{39}\)). This regime change is also accompanied by more frequent occurrences of Central Pacific (CP) ENSO events (characterized by quasi-biennial timescale) and a reduction of the canonical Eastern Pacific (EP) ENSO events (characterized by quasi-quadrennial timescale)\(^{2,12}\).
+
+Here we hypothesize that the changing ENSO-NTA SST phase-lag relationships can be explained in the context of different ENSO regimes manifested by quasi-biennial and quasi-quadrennial periodicities. An El Niño is typically followed by a La Niña event during the subsequent winter in a quasi-biennial ENSO cycle, whereby the NTA warming in the decaying El Niño spring accompanies a La Niña formation about 8-month later. For a quasi-quadrennial ENSO cycle, it takes around two years for the phase transition on average and correspondingly an El Niño induced NTA warming
+statistically leads the next La Niña mature phase by about 20 months. Observed ENSO cycles are not perfect oscillations with a distinct periodicity, in the case of the quasi-quadrennial cycle in which a strong El Niño event is prone to be followed by consecutive La Niña events. However, the complicated ENSO cycle features do not affect the relationship of NTA SST with following ENSO from a statistical standpoint.
+
+To further illustrate the abovementioned physical linkage between lead time and ENSO frequency, we conduct 2-3- and 3-5-yr bandpass filtering of the observed ENSO and NTA indices to differentiate two-way ENSO-NTA SST connections associated with quasi-biennial and quasi-quadrennial periodicities, respectively. ENSO impacts on boreal spring NTA SST anomalies are clearly displayed in both ENSO frequency bands (Fig. 1d), consistent with the robust relationship derived from the raw data (red shading in Fig. 1c), substantiating ENSO’s physical regulation of the following spring NTA SST.
+
+To understand the distinct statistical relationships of the NTA SST with quasi-biennial and quasi-quadrennial ENSO (negative lags in Fig. 1c), we need to consider first that for these timescales El Niño and La Niña are anticorrelated at a lag of ~12 months and ~24 months, respectively. With El Niño causing robust spring NTA warming, the spring NTA warming will then be automatically anticorrelated with Niño3.4 SST anomalies at lag 8 (=12-4) and lag 20 (=24-4) months, for the quasi-biennial and quasi-quadrennial modes, respectively (Fig. 1d). The decadal shifts in the NTA-ENSO relationship are thus fully consistent with a robust one-way ENSO to NTA forcing relationship combined with a shift of ENSO’s dominant frequency (Supplementary Fig. 1b). The notion of NTA serving as precursor for ENSO is therefore equivalent to simply saying that the El Niño is precursor to the next La Niña.
+
+Next, to understand the role of ENSO forcing in fostering NTA variability when considering its time-varying periodicity change, we use an extension of the original stochastic climate model\(^{40}\) for NTA SST anomalies that includes both remote observed ENSO forcing and a damping rate modulated by the annual cycle (see Methods and ref.\(^{21}\) for the original application of the model). The observed monthly time-varying NTA SST anomaly can be well captured by the ENSO-forced model (R=0.55, statistically significant at the 95% confidence level; Supplementary Fig. 2). Importantly, the
+residual variability has no preferred interannual spectral peak (Supplementary Fig. 3). The reconstructed NTA SST exhibits a very similar lead-lag relationship with ENSO compared to that of the observations (Fig. 1d), further collaborating our hypothesis of a one-way relationship between the tropical Pacific and North Atlantic climate variability.
+
+ENSO-NTA SST relationship in idealized pacemaker experiments
+
+Observed ENSO variability has a broad spectrum in the range of 2-7 years, characterized by quasi-biennial and quasi-quadrennial spectral peaks, which cannot be completely isolated using current linear methods\(^2\). To demonstrate trans-basin relationships that would result from different purely periodic ENSO oscillations, a set of idealized pacemaker experiments is conducted by imposing ENSO SST anomaly forcing with idealized 2- and 4-yr cycles in the tropical Pacific (see Methods). In this modeling set-up only ENSO can force NTA, but not vice versa. Given that there is a shift in the ENSO’s zonal location around the 1990s, we also consider different SST forcing patterns associated with the EP and CP El Niño types in the pacemaker experiments (Supplementary Fig. 4; see Methods), to investigate possible influences of the zonal SST anomaly structure in addition to ENSO timescale changes. The observed robust ENSO effect on the subsequent spring NTA SST can be well reproduced in all ENSO-forced experiments (Fig. 1e). In the experiments with 2-yr ENSO forcing, the NTA SST variability is significantly correlated with subsequent ENSO conditions of opposite sign, having the maximum correlation at an 8-month lead-time of NTA over ENSO regardless of the ENSO SST anomaly patterns. This statistical ENSO/NTA relationship corresponds to what we see in the observations before the 1990s (Fig. 1c). Our results clearly show that the 8-month lead of NTA over ENSO can be obtained, even though the set-up of our model experiments does not allow for NTA to influence ENSO. In the 4-yr ENSO forced experiments, the spring NTA SST anomaly as a response to the preceding ENSO is followed by the subsequent ENSO formation at about 20-month lead time for both EP and CP associated SST forcing. These pacemaker experiments indicate that the statistical ENSO and NTA relationship is largely
+controlled by ENSO periodicity rather than its spatial pattern and that the ENSO auto-correlation itself causes this peculiar phase-relationship.
+
+ENSO-NTA SST relationship in the CMIP6 simulations
+
+Considering the limited sample size of the short observational record though supported by our idealized pacemaker experiments, we further examine the trans-basin relationship between ENSO and NTA SST in 46 coupled models in pre-industrial control (pi-control) simulations participating in Phase 6 of the Coupled Model Inter-comparison Project (CMIP6) (Supplementary Table 1). Almost all coupled models are capable of capturing the robust ENSO forcing on the NTA SST (Supplementary Fig. 5). However, the models exhibit a large diversity in the statistical relationship between boreal spring NTA SST variability and subsequent winter ENSO at ~8-month lead-time, whereas a statistically significant relationship can only be simulated in about a quarter of the CMIP6 models (Fig. 2a). To determine the underlying mechanisms responsible for this, we rank the models based on their correlation between spring NTA SST anomaly and subsequent winter ENSO conditions, and then select the 10 models closest to the observations with the highest negative correlation (left side in Fig. 2a) and the 10 models most different from the observations that show a weakly positive correlation (right side in Fig. 2a).
+
+Although both model groups show a very similar ENSO SST anomaly pattern (Fig. 2b), these two groups exhibit distinct ENSO spectral characteristics (Fig. 2c). The models that have a statistically significant 8-month ENSO/NTA lagged relationship exhibit a relatively shorter ENSO periodicity, analogous to the observations after the 1990s (Fig. 2c). In contrast, the models without a significant relationship at 8-month NTA-lead-time have longer ENSO periodicities resembling the observations before the 1990s (Fig. 2c). In addition, there is a high inter-model linear correlation (R=0.75, statistically significant at the 95% confidence level) between simulated dominant ENSO periodicity and the lead-time of the most pronounced negative correlation of NTA SST leading ENSO (Fig. 2d). This again supports our hypothesis that the statistical
+lead-time of NTA SST anomalies over the subsequent ENSO conditions is tightly controlled by the ENSO periodicity.
+
+There exists considerable uncertainty in the projections of trans-basin interactions and the pan-tropical climate patterns that will emerge in a warming world23. Thus, we next investigate the ENSO/NTA trans-basin interaction in CMIP6 future greenhouse-gas emission scenarios (see Methods). We find that almost all of these models in the SSP2-4.5 (25 of 25) and SSP5-8.5 (26 of 28) simulations are able to simulate the robust ENSO effect on the subsequent spring NTA SST (Supplementary Fig. 6). The in-turn linear relationship between NTA-lead-time over ENSO and ENSO periodicity continues to hold in the global warming scenarios (Figure 3). High correlations can be detected in both warming scenarios (R=0.79 for the SSP2-4.5 scenario and R=0.81 for the SSP5-8.5 scenario, exceeding 95% confidence level). It further supports that the trans-basin ENSO/NTA relationships are predominately determined by ENSO and its internal pacing.
+
+Discussion
+
+In summary, ENSO plays a leading role in generating NTA SST variability in boreal spring following its peak phase via seasonally modulated atmospheric forcing and further influenced by the local SST adjustment timescale in the Atlantic (upper-left quadrant in Fig. 4). In turn, the observed time-varying relationship between these ENSO-induced NTA SST anomalies and the following ENSO conditions (Fig. 1c) can be explained by the ENSO regime shifting from dominantly quasi-quadrennial to dominantly quasi-biennial around the 1990s (upper-right quadrant in Figure 4). We emphasize that the observed ENSO cycles are not perfect oscillations with single frequencies. In nature, stochastic noise and nonlinearities can play important roles in shaping ENSO characteristics41.
+
+Here we demonstrated using observational data, a simple seasonally modulated ENSO-forced model, idealized pacemaker experiments, and CMIP6 simulations that the character of the observed cross correlation between ENSO and NTA is fully consistent with an ENSO forced system. We conclude that previous suggestions about
+possible NTA pre-cursors on ENSO predictability and capacitor arguments remain spurious. We further show that our main results are robust even in a warming world.
+
+Methods
+
+Observation and statistics. The utilized SST datasets are the global sea ice and SST analyses (1960–2019) from the Hadley Centre (HadISST) provided by the Met Office Hadley Centre with the horizontal resolution of 1° longitude × 1° latitude42. Anomalies were derived relative to the monthly mean climatology over the entire study period (1960-2019). A linear trend was removed to avoid possible influences associated with global warming. The Multi-Taper method (MTM), which uses a median smoother to distinguish signals from background noises, is used for spectral estimates43 with 3 (Supplementary Fig. 1b) or 5 tapers (Figs. 2, 3 and Supplementary Fig. 3) in consideration of different sample sizes. We test the spectra against the null hypothesis of an autoregressive model of order one (AR(1)) and calculate the respective 95% confidence levels. A nine-point smoothing is applied in Figs. 1c-e to avoid possible noise disturbance. All statistical significance tests were performed using the two-tailed Student’s t test. El Niño events were identified according to the definition of the Climate Prediction Center based on a threshold of ±0.5 °C of the Niño3.4 index (averaged SST anomaly in the domain of 5°S–5°N, 120°–170°W) for five consecutive months. EP and CP indices (EPI and CPI) are calculated using a mathematic rotation of the Niño3 (averaged SST anomaly in the domain of 5°S to 5°N, 90° to 150°W) and Niño4 (averaged SST anomaly in the domain of 5°S to 5°N, 160°E to 150°W) indices44. El Niño events with EPI greater than CPI were classified as EP events while those with CPI greater than EPI are defined as CP events. Following this criterium, we identified seven EP El Niño events (1965, 1972, 1976, 1982, 1991, 1997, 2015) and twelve CP El Niño events (1963, 1968, 1969, 1977, 1979, 1986, 1994, 2002, 2004, 2006, 2009, 2019).
+
+Simple physical model. We proposed a physically motivated model for the NTA SST anomaly as an extension21 of the stochastic climate model40:
+\[
+\frac{dT(t)}{dt} = (-\lambda_0 + \lambda_a \cos(\omega_a + \varphi))T(t) + \beta ENSO(t) + \xi(t),
+\]
+where T(t) is the monthly NTA SST anomaly, ENSO(t) the monthly Niño 3.4 index, \((- \lambda_0 + \lambda_a \cos(\omega_a + \varphi))\) the seasonally modulated damping rate, in which \( \lambda_0 \) and \( \lambda_a \) denote the mean and annual cycle of the damping coefficient, \( \omega_a \) the frequency of the annual cycle, \( \varphi \) the phase shift, and \( \beta \) a scaling coefficient. The model parameters are estimated by multivariate linear regression using the observed NTA SST anomaly time series and Niño 3.4 index (following ref. 45). The ENSO-independent stochastic forcing term (\( \xi(t) \)) is neglected in the model for simplicity.
+
+CMIP6 simulations. Monthly SST outputs from the CMIP6 pi-control and future (the Shared Socioeconomic Pathways (SSP) 2-4.5 and SSP5-8.5) simulations are utilized. The external forcing (e.g., greenhouse gases and aerosols) is kept constant in the pi-control simulations while the SSP2-4.5 with radiative forcing reaching 4.5 W m\(^{-2}\) and SSP5-8.5 reaching 8.5 W m\(^{-2}\) during 2015-2100\(^{46,47}\). For the pi-control simulations, the last 100 years of 46 available model simulations are used for the analysis, among which 25 models are obtained for the SSP2-4.5 scenario and 28 models for the SSP5-8.5 scenario, respectively (see Table S1). Only one ensemble member for each model is used, mostly r1i1p1f1 with select models using ensemble member f2.
+
+Idealized pacemaker experiments. Numerical experiments are conducted by using the Geophysical Fluid Dynamics Laboratory coupled model, version 2.1 (GFDL-CM2.1), with a horizontal resolution of 2.5° longitude ×2° latitude and 24 vertical levels\(^{48}\). Four sensitivity experiments are performed by using an idealized sinusoidal EP and CP ENSO forcing with 2- and 4-yr periodicities, respectively. Composited EP El Niño SST anomalies over the tropical Pacific (25°S–25°N, 150°E–90°W) are used to derive the SST anomalies forcing patterns for the EXP_2yr_EP experiment with repeated sinusoidal 2-yr periodicity and the EXP_4yr_EP experiment with repeated 4-yr periodicity. The other two experiments (EXP_2yr_CP and EXP_4yr_CP) are the same, except that the SST anomalies are the composites for the observed CP El Niño
+events. SST anomalies outside the forcing area are set to zero and only the positive loading in the forcing region is used. The SSTs are allowed to evolve freely outside of the prescribed regions. ENSO peak phases will occur aligned with the boreal winter season for these idealized 2- and 4-yr periodicities. The simulations are integrated for 100 years and the output from the last 80 years is used for the analyses. Anomalies in GFDL-CM2.1 are relative to a 100-year control simulation (EXP_CTRL) in which the model is forced with seasonal varying climatological SSTs.
+
+Data availability
+
+The data used to reproduce the results of this paper are available online or by contacting the corresponding author. Hadley SST data is publicly available at: https://www.metoffice.gov.uk/hadobs/hadisst/data/download.html. The CMIP6 datasets are available at https://esgf-node.llnl.gov/projects/cmip6/.
+
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+
+Acknowledgements: This work was supported by the National Key Research and Development Program (2018YFC1506002) and the National Nature Science Foundation of China (41675073). This is IPRC publication number X and SOEST contribution number Y.
+
+Author contributions: WZ, FJ, MFS, and FFJ conceived the idea. WZ and FJ conducted the data analyses and prepared the figures. All authors discussed the results and wrote the paper.
+
+Correspondence: Correspondence and requests for materials should be addressed to W. Zhang (email: zhangwj@nuist.edu.cn) and F.-F. Jin (email: jff@hawaii.edu).
+
+Competing financial interests: The authors declare no competing financial interests.
+Figure 1. Relationships between tropical Pacific and North Atlantic climate variability. Regression of a boreal spring (March-May) SST anomalies (shading; °C) upon the preceding winter (November-January) Niño3.4 (black box; 5°S–5°N, 120°–170°W) index and b boreal winter SST anomalies (shading; °C) upon the preceding spring NTA (blue box; 0°–15°N, 90°–0°W) SST anomaly. Dots in (a-b) indicate regression coefficients that are statistically significant at the 95% confidence level. c 15-yr running lead-lagged correlation of the boreal winter Niño3.4 index with the NTA SST anomaly. Solid, dashed, and dotted lines mark the region with values exceeding the 80%, 90% and 95% confidence levels, respectively. d Lead-lagged correlation of the boreal winter Niño3.4 index with the observed (solid) and reconstructed (dashed) NTA SST anomaly for bandpass filtering of 2-3-yr (blue) and 3-5-yr (red) periods by using a Fast Fourier Transform filter. For the y-axis of (c-d), negative and positive values indicate NTA-lead and NTA-lag at monthly scale, respectively. e Lead-lagged correlation of the boreal winter Niño3.4 index with NTA SST anomaly in the idealized pacemaker experiments with different Pacific SST forcing (see Methods). Gray dashed lines in (d-e) indicate the 95% confidence levels.
+Figure 2. Phase relationship of NTA SST anomalies with ENSO in pi-control climate simulations. **a** Lead correlation of boreal spring NTA SST anomaly with the subsequent winter Niño3.4 index for 46 CMIP6 models and observations as a reference. The models are ranked by the NTA/ENSO correlation coefficients in an ascending order. The error bar for the multi-model ensemble (MME) mean corresponds to one standard deviation. The dashed purple lines represent the 80%, 90% and 95% confidence levels. **b** Regression of SST anomalies (\( ^\circ \mathrm{C} \)) upon the Niño3.4 index averaged for the left 10 models with most negative correlation (contours with interval: 0.4 \( ^\circ \mathrm{C} \); models indicated by striped blue bars in panel a) and the right 10 models with most positive correlation (shading; models indicated by striped red bars in panel a). **c** Multi-Taper-Method (MTM) power spectra averaged for the left 10 models with most negative correlation (solid thick blue) and the right 10 models with most positive correlation (solid thick red), superimposed by one standard deviation (blue and red shading). The observed spectral peaks of pre- and post-1990 periods (grey shading) are shown for comparison. The averaged AR(1) null hypothesis is displayed by a dashed thin line and the 95% confidence level is indicated by a solid thin line. **d** Scatterplot of ENSO period and lead-time for which negative correlation coefficients are maximized for boreal spring NTA SST anomaly with the subsequent Niño3.4 index. The linear fit (solid black) is displayed together with the correlation coefficient R and slope.
+Figure 3. Phase relationship of NTA SST anomalies with ENSO in future warming simulations. Scatterplot of ENSO period and lead-time at which negative correlation coefficients are maximized for boreal spring NTA SST anomaly with the subsequent Niño3.4 index for the SSP2-4.5 (red) and SSP5-8.5 (purple) scenarios. The linear fits (solid black) are displayed together with respective correlation coefficient R and slope.
+Figure 4. Schematic trans-basin relationships between tropical Pacific and North Atlantic oceans regulated by the ENSO periodicity. In the quasi-biennial ENSO cycle (red loop), an El Niño condition in boreal winter (left panel) leads to positive NTA warming during subsequent spring (upper panel) at a ~4-month lead time, which in turn can see a La Niña formation (right panel) typically following El Niño in the subsequent winter, showing a statistical ~8-month lead time of the NTA. Likewise, a La Niña condition in boreal winter (right panel) gives rise to the following spring NTA SST cooling (lower panel) with a lag of ~4 months, which is often followed by an El Niño formation (left panel), corresponding to a statistical ~8-month lead time of the NTA. The same applies for the quasi-quadrennial ENSO cycle (blue loop) except for the negative correlation of NTA SST variability with the following ENSO event by ~20 months.
+Figures
+
+![Maps and time series plots showing relationships between tropical Pacific and North Atlantic climate variability](page_120_120_1347_1092.png)
+
+Figure 1
+
+Relationships between tropical Pacific and North Atlantic climate variability. Regression of a boreal spring (March-May) SST anomalies (shading; °C) upon the preceding winter (November-January) Niño3.4 (black box; 5°S–5°N, 120°–170°W) index and b boreal winter SST anomalies (shading; °C) upon the preceding spring NTA (blue box; 0°–15°N, 90°–0°W) SST anomaly. Dots in (a-b) indicate regression coefficients that are statistically significant at the 95% confidence level. c 15-yr running lead-lagged correlation of the boreal winter Niño3.4 index with the NTA SST anomaly. Solid, dashed, and dotted lines mark the region with values exceeding the 80%, 90% and 95% confidence levels, respectively. d Lead-lagged correlation of
+the boreal winter Niño3.4 index with the observed (solid) and reconstructed (dashed) NTA SST anomaly for bandpass filtering of 2-3-yr (blue) and 3-5-yr (red) periods by using a Fast Fourier Transform filter. For the y-axis of (c-d), negative and positive values indicate NTA-lead and NTA-lag at monthly scale, respectively. e Lead-lagged correlation of the boreal winter Niño3.4 index with NTA SST anomaly in the idealized pacemaker experiments with different Pacific SST forcing (see Methods). Gray dashed lines in (d-e) indicate the 95% confidence levels.
+
+![Phase relationship of NTA SST anomalies with ENSO in pi-control climate simulations. a Lead correlation of boreal spring NTA SST anomaly with the subsequent winter Niño3.4 index for 46 CMIP6 models and](page_184_370_1207_1012.png)
+
+Figure 2
+
+Phase relationship of NTA SST anomalies with ENSO in pi-control climate simulations. a Lead correlation of boreal spring NTA SST anomaly with the subsequent winter Niño3.4 index for 46 CMIP6 models and
+observations as a reference. The models are ranked by the NTA/ENSO correlation coefficients in an ascending order. The error bar for the multi-model ensemble (MME) mean corresponds to one standard deviation. The dashed purple lines represent the 80%, 90% and 95% confidence levels. b Regression of SST anomalies (\( ^\circ \mathrm{C} \)) upon the Niño3.4 index averaged for the left 10 models with most negative correlation (contours with interval: 0.4 \( ^\circ \mathrm{C} \); models indicated by striped blue bars in panel a) and the right 10 models with most positive correlation (shading; models indicated by striped red bars in panel a). c Multi-Taper-Method (MTM) power spectra averaged for the left 10 models with most negative correlation (solid thick blue) and the right 10 models with most positive correlation (solid thick red), superimposed by one standard deviation (blue and red shading). The observed spectral peaks of pre- and post-1990 periods (grey shading) are shown for comparison. The averaged AR(1) null hypothesis is displayed by a dashed thin line and the 95% confidence level is indicated by a solid thin line. d Scatterplot of ENSO period and lead-time for which negative correlation coefficients are maximized for boreal spring NTA SST anomaly with the subsequent Niño3.4 index. The linear fit (solid black) is displayed together with the correlation coefficient R and slope.
+Figure 3
+
+Phase relationship of NTA SST anomalies with ENSO in future warming simulations. Scatterplot of ENSO period and lead-time at which negative correlation coefficients are maximized for boreal spring NTA SST anomaly with the subsequent Niño3.4 index for the SSP2-4.5 (red) and SSP5-8.5 (purple) scenarios. The linear fits (solid black) are displayed together with respective correlation coefficient R and slope.
+Figure 4
+
+Schematic trans-basin relationships between tropical Pacific and North Atlantic oceans regulated by the ENSO periodicity. In the quasi-biennial ENSO cycle (red loop), an El Niño condition in boreal winter (left panel) leads to positive NTA warming during subsequent spring (upper panel) at a ~4-month lead time, which in turn can see a La Niña formation (right panel) typically following El Niño in the subsequent winter, showing a statistical ~8-month lead time of the NTA. Likewise, a La Niña condition in boreal winter (right panel) gives rise to the following spring NTA SST cooling (lower panel) with a lag of ~4 months, which is often followed by an El Niño formation (left panel), corresponding to a statistical ~8-month lead time of the NTA. The same applies for the quasi-quadrennial ENSO cycle (blue loop) except for the negative correlation of NTA SST variability with the following ENSO event by ~20 months.
+
+Supplementary Files
+
+This is a list of supplementary files associated with this preprint. Click to download.
+
+• SupplementalINTA20200918final.pdf

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+Peer Review File
+A convolutional neural network STIFMap reveals associations between stromal stiffness and EMT in breast cancer
+
+Open Access This file is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. In the cases where the authors are anonymous, such as is the case for the reports of anonymous peer reviewers, author attribution should be to 'Anonymous Referee' followed by a clear attribution to the source work. The images or other third party material in this file are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.
+Editorial Note: This manuscript has been previously reviewed at another journal that is not operating a transparent peer review scheme. This document only contains reviewer comments and rebuttal letters for versions considered at Nature Communications.
+REVIEWER COMMENTS
+
+Reviewer #1 (Remarks to the Author):
+
+The article by Stashko et al. investigates the possibility of developing an automatized atomic force microscopy (AFM) technique with the intention to obtain reliable spatial information about tissue stiffness. Briefly, they created a motorised stage for AFM, worked with PI-stained samples (to guide imaging and stitch images) and measuring PA gels of defined stiffness before and after each imaging (for calibration). They further overlayed these images with high magnification DAPI stain, used a fluorescent collagen binding protein to stain collagen structures and developed a convolutional neural network expose tissue elasticity onto collagen morphological features.
+
+After validating their system, the authors investigated stiffness associated metastatic potential using human HER2+ PDX samples and further HER2+ or TNBC primary breast cancer samples. Their results suggest the new technique (STIFmap) can predict metastatic potential. Additionally, STIFmaps allowed spatial association of ECM stiffness to EMT gene expression.
+
+This is a well thought and well invested study to make AFM an easy and mainstream technique to measure tissue stiffness. This new technique allows identification of mechanical hotspots where cells interact with collagen rich ECM, therefore will add to spatial gene expression knowledge base in a contextual manner. The article is well written and presented. Figures were informative.
+
+Comments:
+
+- Theoretically, HER2+ tumours should have active Ras pathway and therefore have abundant P-ERK. Is there another and more specific way to assess the effects of ECM stiffness and integrin signalling in PDX modelling? For example, survivin and bcl-2 upregulation or p27 downregulation were shown to be positively regulated by integrin signalling. In addition, YAP/TAZ signalling can be investigated in this context.
+
+- The use of STIFMaps in FFPE is investigated but data provided is limited. I understand morphological features of cryopreserved or FFPE tissues were reflected through CNA collagen staining but to address the problem correctly, tissue stiffness and collagen structure should be assessed before and after FFPE staining and assessing a correlation in a true experimental model.
+
+- Are there any morphological or histopathological differences in mets of PDX tumours embedded in soft or stiff material?
+
+- The authors stained TNBC tissues with ZEB1 and SLUG, quoting an article in melanoma. Breast cancer and melanoma are very different in nature. Nuclear localisation of Twist due upon exposure to stiffer ECM has been reported in breast cancer and accepted as a reason of stiffness associated EMT (Wei et al 2015, Fattet et al. 2020). This aspect of Twist1 (nuclear localisation) cannot be assessed by RNA abundance. It is a good idea to investigate Twist1 expression (rather than SLUG), especially at tumour-stroma interface, along with STIFmap technique in patient materials.
+- Can STIFmap technique determine collagen bundling? There are plenty of reports suggesting collagen bundling can affect or determine metastatic potential.
+
+Please italicize Latin phrases (in situ, etc)
+
+Reviewer #2 (Remarks to the Author):
+
+In this study, the authors estimate tissue stiffness with a microscopic technique. To the reader it is unclear if the main advance is the biological understanding or the method per se. The whole article is a bit confusing at the first read. Only after reading the whole thing the reader realizes that this is actually mostly an engineering article which reports a new AFM protocol with some data analysis. To me it is unclear who the readership of this article would be, apart from people in the AFM field.
+
+The phrasing of the title is odd. The message should focus on the biological finding, and could mention the tool used to make this finding. Please rephrase.
+
+In the abstract, abbreviations such as AFM are not defined. The abstract is confusing to read. It is again unclear what was the state of the art before the study and what's the novelty and the key finding. The last sentence of the abstract does not seem to be substantiated by data.
+
+The introduction is a bit excessive, trying to link many biological concepts, but in my opinion it should focus more on the topic at hand, the mechanical characterization of tissue.
+
+The results report the outcome of a lot of experimental work, which is not directly related to the topics discussed in the introduction. The results have too much technical details which should be moved to the methods section.
+
+The figures have a high visual quality
+Reviewer #3 (Remarks to the Author):
+
+This manuscript proposes an automated AFM system capable of measuring the mechanical distribution of breast cancer tissue slides which combined with other traditional biological and clinical detection and analysis methods, to study the relationship between tissue stiffness heterogeneity and breast cancer tumor aggression behavior. The AFM mechanical measurement data, corresponding CNA and DAPI images are used to train the CNN network to generate the elasticity distribution of tissue sections. The proposed STIFMaps method also has the potential to predict the mechanical distribution of formalin-Fixed paraffin-embedded tissue sections that have lost their intrinsic mechanical information. Experiments show that the STIFMaps obtained by the CNN network is consistent with the information extracted by biological methods and can reveal the relationship between the stromal stiffness of human breast tumor specimens and human breast cancer aggression. This is a very interesting paper and provides a promising way to expand AFM mechanical measurement from cell-scale to tissue-scale. In addition, the STIFMaps solves the problem that traditional AFM cannot perform mechanical mapping of clinical tissue specimens and makes a great contribution to the field of AFM. At the same time, it also provides a versatile tool for clinical to analysis, treat and predict breast cancer. Here are some comments.
+
+1. The accuracy of AFM measurements of mechanical properties of tissue section samples should be considered. The article discussed the case where the cantilever was contaminated. But the tip which is the 5um radius sphere is more easily contaminated and contributes more to the potential bias in the modulus measurement result. The contact area and the tip modulus have a major influence on the modulus calculated from the contact model such as Herts model. If the surface of the sphere is contaminated, the shape and surface area will change. In addition, if the modulus gap between the sphere and the contamination is large, the bias of measurement result should be considered and discussed. It is recommended that the author characterize the microspheres after multiple measurements or perform secondary calibration on the standard sample to eliminate the influence of tip contamination on measurement results.
+
+2. The surface of the thawed tissue slides sample will not be as smooth as that of the single cell sample. If the fluctuation of the sample surface topography is larger than 5 microns which is the diameter of the sphere used in this article, it is likely that the cantilever beam will touch the sample surface first rather than the sphere. In this case, the obtained force curve cannot be applied to the contact model based on sphere to calculate the sample modulus. Therefore, it is necessary to characterize the surface of the sliced tissue to evaluate the validity of the force curves acquired by the sphere of 5um diameters. Maybe the diameter of the sphere should be increased or the flatness of the tissue sample surface should be further improved.
+3. The thickness of the specimens used were 20 \( \mu \)m. The indented depth was 2 \( \mu \)m for each force curve. The substrate effect will affect the accuracy of the Modulus result if the indentation depth is too large. The suitable value of indentation depth is considered as less than 10% of the sample thickness. In this paper, the indentation-thickness ration is 10%, so I suggested that the substrate effect should be considered and studied by decreasing the indentation depth. Besides, the typical force curves in various positions of the specimen should be provided in supplementary information or extended data. The difference in the obtained mechanical properties results can be evaluated from the force curves.
+
+4. Using STIFMaps to predict the tissue mechanical distribution of Formalin-Fixed Paraffin-Embedded Tissue is one of the contributions in this paper, which will also provide potential contribution to the pathology and clinical medicine. But the authors didn’t provide further experimental results to prove the feasibility of this method. It is suggested that the comparison of the modulus between the measured fresh sample and the predicted FFPE sample should be added. This will significantly improve the quality of the article.
+
+5. For the CNN used in this paper, it is mentioned that Alexnet has a better effect than other networks. However, the performance of neural network ResNet and DenseNet in images classification is better than that of AlexNet proposed in 2012. So my question is why AlexNet has better effect than other networks on your task? Regarding the use of AlexNet in the pytorch library, whether a pre-trained model is used (the parameters trained by AlexNet on a large data set are loaded during initialization), and how many images are used during training, and whether there is any overfitting during the training process? (The performance on the train set is much better than the test set).
+
+-----------
+Rebuttal Comments:
+
+We thank the reviewers for their constructive comments. We have addressed each of their critiques by conducting additional experiments, validations and analysis. We comprehensively revised the text of the manuscript and included additional panels in the figures and updated main and supplemental figures. We include below a detailed point by point response to each of the reviewer’s comments. We are confident that the editors and reviewers will be satisfied with our revised manuscript and accept our manuscript for publication in Nature Communications.
+
+Reviewer Comments:
+
+Reviewer #1 (Remarks to the Author):
+
+The article by Stashko et al. investigates the possibility of developing an automatized atomic force microscopy (AFM) technique with the intention to obtain reliable spatial information about tissue stiffness. Briefly, they created a motorised stage for AFM, worked with PI-stained samples (to guide imaging and stitch images) and measuring PA gels of defined stiffness before and after each imaging (for calibration). They further overlayed these images with high magnification DAPI stain, used a fluorescent collagen binding protein to stain collagen structures and developed a convolutional neural network expose tissue elasticity onto collagen morphological features. After validating their system, the authors investigated stiffness associated metastatic potential using human HER2+ PDX samples and further HER2+ or TNBC primary breast cancer samples. Their results suggest the new technique (STIFmap) can predict metastatic potential. Additionally, STIFmaps allowed spatial association of ECM stiffness to EMT gene expression. This is a well thought and well invested study to make AFM an easy and mainstream technique to measure tissue stiffness. This new technique allows identification of mechanical hotspots where cells interact with collagen rich ECM, therefore will add to spatial gene expression knowledge base in a contextual manner. The article is well written and presented. Figures were informative.
+
+Comments:
+
+1. Theoretically, HER2+ tumours should have active Ras pathway and therefore have abundant P-ERK. Is there another and more specific way to assess the effects of ECM stiffness and integrin signalling in PDX modelling? For example, survivin and bcl-2 upregulation or p27 downregulation were shown to be positively regulated by integrin signalling. In addition, YAP/TAZ signalling can be investigated in this context.
+
+We agree that HER2+ tumors exhibit activated Ras signaling and elevated phospho-ERK. However, we and others showed that a stiff ECM further increases phospho-ERK activity by enhancing growth factor receptor signaling. Nevertheless, to address the reviewers concerns, in our revised manuscript we incorporated additional markers indicating elevated mechanosignaling including staining for and quantification of nuclear YAP localization. These new data are included in a revised figure 4.
+
+2. The use of STIFMaps in FFPE is investigated but data provided is limited. I understand morphological features of cryopreserved or FFPE tissues were reflected through CNA collagen staining but to address the problem correctly, tissue stiffness and collagen structure should be assessed before and after FFPE staining and assessing a correlation in a true experimental model.
+
+The reviewer raises an interesting point. We would like to respectfully point out that a pathologist evaluated collagen morphology in a patient-matched cryopreserved and FFPE sample and did not
+discern any morphological or pathological differences (Fig S5). Additionally, in our study we utilized pathology-archived FFPE tissues, thus it is impossible to conduct staining within the same tissue before and after formalin-fixation. However, in an effort to address the reviewer’s comment, we did image collagen with CNA-35 staining in cryopreserved tissues before and after 10% formalin fixation for 1 hour. Importantly, we did not observe any significant morphological differences following image overlay (red; pre-fixation and blue; post-fixation; see images below).
+
+b    Pre-fixation    Post-fixation
+
+![Collagen staining images showing pre-fixation and post-fixation](page_246_370_1092_384.png)
+
+We further confirmed that antigen retrieval (AR) does not disrupt collagen morphology. We stained collagen with Picrosirius Red staining in FFPE tissues before and after antigen retrieval (red; pre-AR and blue; post-AR; see figure inserted below). We incorporated these images into our revised manuscript, as extended data figure 5 (panel b and c) and discussed the results in the main text.
+
+c    Pre-AR    Post-AR    Merged
+
+![Collagen staining images showing pre-AR, post-AR, and merged images](page_246_820_1092_384.png)
+
+3. Are there any morphological or histopathological differences in mets of PDX tumours embedded in soft or stiff material?
+While this question is intriguing we respectfully contend that this question falls well beyond the scope of the current manuscript. Indeed, we already presented detailed data quantifying the frequency of mice with lung metastasis, and reported on the number and size of metastatic lesions in the HER2+ PDX tumors. The presence of metastasis is clinically an independent poor prognostic indicator. Moreover, the morphology of lung metastasis has no bearing on clinical outcome. Nevertheless, to address the current reviewers concerns, in our revised manuscript we incorporated histopathological assessment of the primary HER2+ PDX tumor samples into the main text. Our histopathological analysis identified all HER2+ PDX tumors to be of high histological grade. However and importantly, we did note that there was more extensive necrosis in the STIFF ECM tumors, which further supports that stromal stiffness drives tumor aggression. Finally, given metastatic lesions are thought to undergo mesenchymal-to-epithelial transition, investigating EMT markers histologically may yield non interpretable results that would require extensive studies to address and would go well beyond the scope of the current manuscript (reviewed in doi.org/10.1084/jem.20181827).
+
+4. The authors stained TNBC tissues with ZEB1 and SLUG, quoting an article in melanoma. Breast cancer and melanoma are very different in nature. Nuclear localisation of Twist due upon exposure to stiffer ECM has been reported in breast cancer and accepted as a reason of stiffness associated EMT (Wei et al 2015, Fattet et al. 2020). This aspect of Twist1 (nuclear localisation) cannot be assessed by RNA abundance. It is a good idea to investigate Twist1 expression (rather than SLUG), especially at tumour-stroma interface, along with STIFmap technique in patient materials.
+
+We now include additional references describing EMT in breast cancer. We acknowledge that RNA abundance does not necessarily reflect protein abundance nor can it assess protein nuclear localization. To address this concern in our revised manuscript we performed Twist1 staining and combined this with our STIFMap method. The new data clearly demonstrates that elevated total and nuclear Twist1 associates with stromal stiffness in TNBC tissues (**P<10^{-5}). We respectfully contend that the elevated expression we previously quantified using RT-PCR and reported in our original submitted manuscript does in fact support our finding that STIFF ECM tumors correlate with markers of a mesenchymal phenotype.
+
+5. Can STIFmap technique determine collagen bundling? There are plenty of reports suggesting collagen bundling can affect or determine metastatic potential.
+
+The reviewer raises a very interesting question. Identifying collagen bundling with STIFMap still requires further work, but we do believe that the model can be trained to predict collagen bundling. Indeed, we are currently considering this option, however, to decouple collagen stiffness and collagen bundling is not trivial. A recent article (https://doi.org/10.1038/s41388-022-02258-1) using organotypic models from mice, has been able to decouple bundling and stiffness in vivo, which would provide an elegant way to validate the trained model. We are exploring the use of in vitro systems for collagen bundling to test it experimentally (E.g. https://doi.org/10.1021/acsomega.9b03704).
+
+6. Please italicize Latin phrases (in situ, etc)
+
+In our revised manuscript we italicized all latin phrases.
+
+Reviewer #2 (Remarks to the Author):
+
+In this study, the authors estimate tissue stiffness with a microscopic technique. To the reader it is unclear if the main advance is the biological understanding or the method per se. The whole article is a bit confusing at the first read. Only after reading the whole thing the reader realizes that this is actually
+mostly an engineering article which reports a new AFM protocol with some data analysis. To me it is unclear who the readership of this article would be, apart from people in the AFM field.
+
+Comments:
+
+1. The phrasing of the title is odd. The message should focus on the biological finding, and could mention the tool used to make this finding. Please rephrase.
+
+We retain that the title our of manuscript is clear and concise, highlighting the utility of our STIFMap tool in identifying mechanical heterogeneity spatially within tissues. We thereafter used our STIFMap tool to reveal a direct association between stromal stiffness and EMT in human breast tumors.
+
+2. In the abstract, abbreviations such as AFM are not defined. The abstract is confusing to read. It is again unclear what was the state of the art before the study and what's the novelty and the key finding. The last sentence of the abstract does not seem to be substantiated by data.
+
+We revised our manuscript text and carefully defined all abbreviations used within the abstract and throughout the main text. Within our revised abstract, we highlighted the utility of STIFMaps to enable spatially resolved forced maps across whole tissue sections which we were able to integrate with biomarker staining to identify the novel association between stromal stiffness and EMT, which has not been shown before. In our revised introduction, we now restrict our discussion of previous methods towards work done by prior investigators to quantify tissue rheology.
+
+3. The introduction is a bit excessive, trying to link many biological concepts, but in my opinion it should focus more on the topic at hand, the mechanical characterization of tissue.
+
+We maintain that our introduction provides a cohesive summary regarding tumor heterogeneity, stromal stiffness and EMT in driving breast cancer aggression and poor patient outcome. We also provide a background of current state of the art methods to study spatial tumor heterogeneity and tissue rheology. We include this information to prime a broad range of readers to understand the methodology and experimental findings presented within our manuscript.
+
+4. The results report the outcome of a lot of experimental work, which is not directly related to the topics discussed in the introduction. The results have too much technical details which should be moved to the methods section.
+
+We provide only essential technical detail within the results so that we can provide the reader with an understanding of all of the data presented in the results.
+
+5. The figures have a high visual quality.
+
+We thank the reviewer for this comment.
+
+Reviewer #3 (Remarks to the Author):
+
+This manuscript proposes an automated AFM system capable of measuring the mechanical distribution of breast cancer tissue slides which combined with other traditional biological and clinical detection and analysis methods, to study the relationship between tissue stiffness heterogeneity and breast cancer tumor aggression behavior. The AFM mechanical measurement data, corresponding CNA and DAPI images are used to train the CNN network to generate the elasticity distribution of tissue sections. The proposed STIFMaps method also has the potential to predict the mechanical distribution of formalin-Fixed paraffin-embedded tissue sections that have lost their intrinsic mechanical information.
+Experiments show that the STIFMaps obtained by the CNN network is consistent with the information extracted by biological methods and can reveal the relationship between the stromal stiffness of human breast tumor specimens and human breast cancer aggression. This is a very interesting paper and provides a promising way to expand AFM mechanical measurement from cell-scale to tissue-scale. In addition, the STIFMaps solves the problem that traditional AFM cannot perform mechanical mapping of clinical tissue specimens and makes a great contribution to the field of AFM. At the same time, it also provides a versatile tool for clinical to analysis, treat and predict breast cancer. Here are some comments.
+
+1. The accuracy of AFM measurements of mechanical properties of tissue section samples should be considered. The article discussed the case where the cantilever was contaminated. But the tip which is the 5um radius sphere is more easily contaminated and contributes more to the potential bias in the modulus measurement result. The contact area and the tip modulus have a major influence on the modulus calculated from the contact model such as Herts model. If the surface of the sphere is contaminated, the shape and surface area will change. In addition, if the modulus gap between the sphere and the contamination is large, the bias of measurement result should be considered and discussed. It is recommended that the author characterize the microspheres after multiple measurements or perform secondary calibration on the standard sample to eliminate the influence of tip contamination on measurement results.
+
+We agree with the reviewer that the tip can become contaminated. Accordingly, to assess the integrity and consistency of the tip in our studies, we utilized polyacrylamide gels across a range of known (and measured) stiffnesses as reference samples. We evaluated the stiffness of the polyacrylamide gels both before and after each day of AFM experimental measurement. By comparing the stiffnesses pre- and post-sampling, we observed a 1:1 relationship (see attached figure), indicating no changes in stiffness were observed. If the tip was contaminated, we would expect the data to be consistently above/below the 1:1 line (140 Pa gels p-value = 0.551 and 1 kPa gels p-value = 0.970. Wilcoxon Rank-Sum Test. Normality was checked using Shapiro-Wilks Normality Test). Therefore, we conclude that the tip was not contaminated in our studies, and that the data shown in our manuscript is not affected by tip contamination. We have incorporated this figure into the revised manuscript, in an extended data figure 2 and discussed these controls in the main text.
+
+![Scatter plot showing pre-calibration stiffness vs post-calibration stiffness for 1 kPa and 140 Pa gels, with a 1:1 line](page_682_1042_430_312.png)
+
+2. The surface of the thawed tissue slides sample will not be as smooth as that of the single cell sample. If the fluctuation of the sample surface topography is larger than 5 microns which is the diameter of the sphere used in this article, it is likely that the cantilever beam will touch the sample surface first rather than the sphere. In this case, the obtained force curve cannot be applied to the contact model based on sphere to calculate the sample modulus. Therefore, it is necessary to
+characterize the surface of the sliced tissue to evaluate the validity of the force curves acquired by the sphere of 5um diameters. Maybe the diameter of the sphere should be increased or the flatness of the tissue sample surface should be further improved.
+
+We appreciate the reviewer’s comment, however, we do not believe that the beam is touching the sample prior to the sphere. To support this assertion, we maintain that the cantilevers are tilted between 10-20 degrees (https://doi.org/10.1021/la036128m). We measured the cantilevers used for the measurement we reported in this work, whereby the distance between the sphere and the beam is around 45 um (see attached figure, scale bar; 50 um).
+
+![AFM image showing the cantilever tip and the tissue surface](page_370_370_808_370.png)
+
+In the worst case scenario, when the cantilever is tilted 10 degrees, we can still obtain the clearance of the z-axis, which would result in C = sin (10)*45 = 7.8 um, therefore providing even a higher distance that avoids touching with the beam. We experimentally tested this assumption. To do so, we did AFM measurements in a PRIMO PDMS system, indenting with the sphere and with the beam. We found that the sphere is 5.5 um lower than the tip of the cantilever beam, in agreement with our analytical solution. We don’t expect a local variation in height of 5.5 um (27.5% of the section height)
+
+Sphere        Beam
+
+![AFM images comparing sphere and beam indentation](page_370_1090_808_120.png)
+Furthermore, when using the Hertz model for the calculation of the stiffness, the stiffness is given by the following equation:
+
+\[
+E = \frac{k \Delta d \ 3 \ (1 - \nu^2)}{4 \ R^{1/2} \delta^{3/2}}
+\]
+
+Where k is the spring constant of the cantilever, \( \Delta d \) is the cantilever deflection, \( \nu \) is the Poisson ratio of the sample, R is the radius of the tip and \( \delta \) is the indentation. Therefore, the stiffness is inversely proportional to the radius of the tip (R) and directly proportional to the ratio of \( \Delta d / \delta^{(3/2)} \).
+
+If the sample is touched with the beam, we can assume that the radius of the tip is either at least one order of magnitude higher (width of the beam ~ 30 um) or tends to infinity (https://doi.org/10.1038/ncomms11566), therefore the stiffness of the tissue would significantly drop, or to keep reasonable values for the stiffness, the ratio of \( \Delta d / \delta^{(3/2)} \) would significantly increase. We did not observe any of these situations in our measurements.
+
+3. The thickness of the specimens used were 20 \( \mu \)m. The indented depth was 2 \( \mu \)m for each force curve. The substrate effect will affect the accuracy of the Modulus result if the indentation depth is too large. The suitable value of indentation depth is considered as less than 10% of the sample thickness. In this paper, the indentation-thickness ration is 10%, so I suggested that the substrate effect should be considered and studied by decreasing the indentation depth. Besides, the typical force curves in various positions of the specimen should be provided in supplementary information or extended data. The difference in the obtained mechanical properties results can be evaluated from the force curves.
+
+We would like to highlight that all the curves are available in https://data.mendeley.com/datasets/vw2bb5jy99/2, we clarified that in the revised manuscript (DATA AVAILABILITY).
+
+We respectfully point out that according to Buckle’s rule, **the indentation should not exceed 10%, which is the criteria we used for our measurements**. Nevertheless, to rigorously address reviewer’s comment, we reassessed all of our AFM curves and found that for 95.4% of the samples, the indentation was less than 10%.
+For the remaining 4.6% of the data, we reanalyzed the data fitting 2 microns to adhere to Buckle’s rule. This analysis yielded virtually the same results as the existing stiffnesses (Pearson's r = 0.995).
+
+Finally, we compared all the data limiting the maximum indentation to 1 um after the contact point vs 2 um after the contact point (5% and 10% sample thickness, respectively). Once again we saw that the choice of maximum indentation depth made little difference on the resulting stiffness measurements (Pearson's r = 0.998). Altogether, these data indicate that our results are not affected by the substrate effect. We have included this information the Methods (Atomic Force Microscopy)
+4. Using STIFMaps to predict the tissue mechanical distribution of Formalin-Fixed Paraffin-Embedded Tissue is one of the contributions in this paper, which will also provide potential contribution to the pathology and clinical medicine. But the authors didn’t provide further experimental results to prove the feasibility of this method. It is suggested that the comparison of the modulus between the measured fresh sample and the predicted FFPE sample should be added. This will significantly improve the quality of the article.
+
+As reported in our manuscript the utility of STIFMaps was used to assess mechanical heterogeneity across whole-slide images of human FFPE clinical specimens. We were then able to link stiffness measurements to register with EMT marker analysis that supported a significant correlation between regions of elevated ECM stiffness and indicators of an epithelial to mesenchymal transition phenotype. While it would be interesting to understand how formalin-fixation alters the mechanical properties of the tissue, we are unable to compare the stiffness measurements of these samples pre- and post-fixation since we utilize pathology-archived FFPE tissues. Instead, we carefully addressed the modifications we incorporated into our revised manuscript similar to our response to reviewer ones comments on this same topic – see reviewer #1 comment #2 and associated rebuttal.
+
+5. For the CNN used in this paper, it is mentioned that Alexnet has a better effect than other networks. However, the performance of neural network ResNet and DenseNet in images classification is better than that of AlexNet proposed in 2012. So my question is why AlexNet has better effect than other networks on your task? Regarding the use of AlexNet in the pytorch library, whether a pre-trained model is used (the parameters trained by AlexNet on a large data set are loaded during initialization), and how many images are used during training, and whether there is any overfitting during the training process? (The performance on the train set is much better than the test set).
+
+While it is true that DenseNet and ResNet perform better on image classification tasks, to our knowledge they have not been applied to regression tasks and therefore it is unknown if they perform better at this style of problem than AlexNet. The AlexNet utilized in these studies is a simpler model with fewer parameters than DenseNet or ResNet, making it more straightforward to tune hyperparameters and visualize intermediate layer activations. Moreover, the added complexities of DenseNet and ResNet also entail longer training times and greater computational power, making
+AlexNet faster to optimize. Nevertheless, we did experiment with DenseNet and ResNet architectures, though these models each took several days to train, preventing us from optimizing further:
+
+![Two line plots comparing training, validation, and MV Regression correlation over epochs for ResNet and DenseNet](page_120_180_1347_393.png)
+
+The applied AlexNet was not pre-trained. Weights and biases are initialized using Xavier initialization, which is the PyTorch default. The model performs better on the validation set than the training set (Fig. 2c) due to the transformation that are applied to the training set to avoid overfitting (Fig. 2a). All data is available via https://data.mendeley.com/datasets/vw2bb5jy99/2 (refer to DATA AVAILABILITY STATEMENT in manuscript) for training, validating, and reproducing the exact model architecture used in these studies for users interested in experimenting with different models such as DenseNet and ResNet.
+REVIEWER COMMENTS
+
+Reviewer #1 (Remarks to the Author):
+
+The article by Stashko et al. has been mostly revised according to my recommendations. However, I should say that I am disappointed with the revised manuscript for 2 reasons.
+
+1- The authors provided very little or no guidance as to how the manuscript was revised or where in text the revision has taken place. In the rebuttal letter they were using vague language to suggest they made changes but it is impossible to identify what was done. For example they say “in our revised manuscript we incorporated additional markers indicating elevated mechanosignaling including staining for and quantification of nuclear YAP localization”. I have no guidance which additional markers were added and in which panels?
+
+Overall, the changes were not highlighted, there was no guidance to identify the revision in text and figures. I trust the authors have clarified certain issues in the revised version of the manuscript but the whole meaning of review process goes away if I cannot find what I am looking for.
+
+2- Two referees, (me and ref 3) highlighted the fact that the new technique has not been empirically tested in FFPE tissues (my comment 2 and referee 3 comment 4) although the authors specifically claim their approach will "advance current stiffness measurement techniques which preclude FFPE samples". The novelty aspect of the paper is the possibility that one can measure the stiffness of an FFPE fixed tissue and identify its stiffness before fixation. This will allow a clinical use for AFM and retrospective studies.
+
+I believe there has been a misunderstanding between the authors and me (and referee 3). To address our concerns, the authors compared the ECM morphology of FFPE tissue with ECM staining and AFM imaging as analysed by a pathologist. We all know that FFPE preserves the structural identity of the tumour so I do not dispute their findings on morphology front. But there is no data in the manuscript about tissue stiffness before and after fixation. Therefore their answer is not addressing my question or justifying their claim. This question could only be empirically addressed by analysing the same tissue, before and after formalin fixation, using conventional pathology and with AFM. I believe duration of fixation and age of the FFPE block are also variables in this equation which should be tested. I would expect formalin fixation would increase the stiffness of the tissue as it is a cross linking agent. In that regard maybe a correlation (e.g. fold increase) can be found between post and pre fixation stiffness.
+
+Reviewer #2 (Remarks to the Author):
+The authors did not make substantial changes in response to my comments. They just argued that they do not agree with my comments. It is OK to have different opinions on scientific questions. However, I maintain that the article would benefit from the clarifications I suggested.
+
+Reviewer #3 (Remarks to the Author):
+
+The reviewer's comments were seriously considered by the authors. The paper was revised accordingly. The contributions of the paper is clear and the paper is well written and organized.
+We thank the reviewers for their re-assessment of our revised manuscript. We have responded to each of the newly raised issues in a point by point rebuttal listed below. We are confident the reviewers will be satisfied with our updated manuscript revisions and will agree that our article is now suitable for publication in Nature Communications.
+
+Reviewer Comments:
+
+Reviewer #1 (Remarks to the Author):
+
+The article by Stashko et al. has been mostly revised according to my recommendations. However, I should say that I am disappointed with the revised manuscript for 2 reasons.
+
+1. The authors provided very little or no guidance as to how the manuscript was revised or where in text the revision has taken place. In the rebuttal letter they were using vague language to suggest they made changes but it is impossible to identify what was done. For example they say “in our revised manuscript we incorporated additional markers indicating elevated mechanosignaling including staining for and quantification of nuclear YAP localization”. I have no guidance which additional markers were added and in which panels? Overall, the changes were not highlighted, there was no guidance to identify the revision in text and figures. I trust the authors have clarified certain issues in the revised version of the manuscript but the whole meaning of review process goes away if I cannot find what I am looking for.
+
+We apologize for not providing a version of our revised manuscript text file with tracked changes. We have now color highlighted all of the changes that were made in the text of our revised manuscript. Within our original point-by-point response to each of the reviewer’s comments, where possible we referenced the Figure that included modifications to the data. With respect to reviewer #1s original comments, in our newly revised manuscript as requested we now list where significant modifications occur to the Figures and/or lines of text in response to major comments:
+
+Comment 1: These new data are included in revised Figure 4, and text modifications occur within the results section on lines 307-310 and materials and methods section on lines 651-652.
+
+Comment 2: These new data are included in revised Extended Data Figure 5, and text modifications occur within the results section on lines 284-291.
+
+Comment 3: Text modifications occur within the results section on lines 314-316.
+
+Comment 4: These new data are included in revised Figure 5, and text modifications occur within the results section on lines 337-339 and materials and methods section on lines 653-654.
+
+2. Two referees, (me and ref 3) highlighted the fact that the new technique has not been empirically tested in FFPE tissues (my comment 2 and referee 3 comment 4) although
+the authors specifically claim their approach will "advance current stiffness measurement techniques which preclude FFPE samples". The novelty aspect of the paper is the possibility that one can measure the stiffness of an FFPE fixed tissue and identify its stiffness before fixation. This will allow a clinical use for AFM and retrospective studies. I believe there has been a misunderstanding between the authors and me (and referee 3). To address our concerns, the authors compared the ECM morphology of FFPE tissue with ECM staining and AFM imaging as analysed by a pathologist. We all know that FFPE preserves the structural identity of the tumour so I do not dispute their findings on morphology front. But there is no data in the manuscript about tissue stiffness before and after fixation. Therefore, their answer is not addressing my question or justifying their claim. This question could only be empirically addressed by analysing the same tissue, before and after formalin fixation, using conventional pathology and with AFM. I believe duration of fixation and age of the FFPE block are also variables in this equation which should be tested. I would expect formalin fixation would increase the stiffness of the tissue as it is a cross linking agent. In that regard maybe a correlation (e.g. fold increase) can be found between post and pre fixation stiffness.
+
+Within the original reviewer comments, this reviewer requested that we “assess tissue stiffness and collagen structure before and after formalin-fixation paraffin-embedding (FFPE)”. We agree with the reviewer that FFPE processing preserves collagen morphology, which we demonstrate in Extended Data Figure S5 through pathological assessment of collagen morphology between patient-matched cryopreserved and FFPE samples, as well as pre- and post-formalin-fixation in cryopreserved samples. However, with all due respect, in our newly revised manuscript, as requested by this reviewer, we did not assess tissue stiffness pre- and post-formalin-fixation. May we respectfully point out that formalin fixation crosslinks the tissue thereby dramatically increasing the stiffness of the tissue to such a degree that it would be near impossible to distinguish differential regions of stiffness versus compliance in any given tissue. For instance, it has been shown that physiological differences in the stiffness of fresh tissue are lost upon formalin-fixation (Calò, A., Romin, Y., Srouji, R. et al. Spatial mapping of the collagen distribution in human and mouse tissues by force volume atomic force microscopy. Sci Rep 10, 15664 (2020). https://doi.org/10.1038/s41598-020-72564-9, Fig. 2). Moreover, as requested by the current reviewer, we also respectfully point out that post-formalin fixation stiffness depends upon many variables: tissue content, tissue age, fixation method, fixation duration, among other factors. These are all highly variable across various clinical pathology settings. This has led us to conclude that executing the measurements as requested by the current reviewer would fail to address their main concerns and moreover, would not add any physiological relevance to the findings of our study. We suggest that this very issue regarding FFPE processing actually highlights the utility of our STIFMap method, which preserves the integrity of the collagen morphology, and thereby permits the prediction of the mechanical properties of these clinical tissues. Indeed, the very rationale for developing the STIFMaps method is to overcome these stated technical issues and to permit analysis of FFPE clinical tissues including assessing the mechanical heterogeneity of the specimen across whole-slide images of FFPE clinical specimens.
+The current correctly pointed out that reviewer 3 raised similar points pertaining to the fidelity of the collagen architecture and our AFM measurements. Accordingly, we addressed the similar issue raised by reviewer 3 and include our rebuttal to reviewer 3 for this reviewer’s assessment, and their acknowledgement that we comprehensively addressed the points they raised.
+
+“As reported in our manuscript the utility of STIFMaps was used to assess mechanical heterogeneity across whole-slide images of human FFPE clinical specimens. We were then able to link stiffness measurements to register with EMT marker analysis that supported a significant correlation between regions of elevated ECM stiffness and indicators of an epithelial to mesenchymal transition phenotype. While it would be interesting to understand how formalin-fixation alters the mechanical properties of the tissue, we are unable to compare the stiffness measurements of these samples pre- and post-fixation since we utilize pathology-archived FFPE tissues. Instead, we carefully addressed the modifications we incorporated into our revised manuscript similar to our response to reviewer ones comments on this same topic – see reviewer #1 comment #2 and associated rebuttal.”
+
+We respectfully point out that reviewer 3 agreed and acknowledged our rebuttal to their query and stated that we had comprehensively addressed the points they had raised including the fidelity of the collagen architecture and our AFM measurements as similarly raised by this current reviewer.
+
+Reviewer #2 (Remarks to the Author):
+
+The authors did not make substantial changes in response to my comments. They just argued that they do not agree with my comments. It is OK to have different opinions on scientific questions. However, I maintain that the article would benefit from the clarifications I suggested.
+
+We are in the process of carefully editing the manuscript to clarify the “general” points raised by reviewer 2.
+
+Reviewer #3 (Remarks to the Author):
+
+The reviewer's comments were seriously considered by the authors. The paper was revised accordingly. The contributions of the paper are clear and the paper is well written and organized.

0a57595338b1390798459ee5d63f40d3108931b635b32aecd97babb2ece11f54/peer_review/peer_review.md

@@ -0,0 +1,132 @@
+Peer Review File
+
+An ancestral interaction module promotes oligomerization in divergent mitochondrial ATP synthases
+REVIEWER COMMENTS
+
+Reviewer #1 (Remarks to the Author):
+
+To generate mitochondrial inner membrane curvature and maintain high level of ATP production, the mitochondrial ATP synthase forms dimers which further arrange into oligomers. In this work, Gahura et al. determined the cryo-EM structure of the ATP synthase dimer from Trypanosoma brucei, identified both protein and lipid components, revealed a set of rotational states, and proposed subunit-e/g module as an ancestral oligomerization motif of ATP synthases. The functional importance of subunit-g was supported by their RNAi knockdown, mitochondrial ultrastructure, membrane polarization measurement, and ATP production assay. This manuscript is well written with clearly presented figures, and most results are properly interpreted. The results are interesting to the community of ATP synthase research as well as broader membrane protein biology.
+
+I have a few comments and questions listed below.
+
+For the assignment of cardiolipin molecules, particularly those in Fig. 1c, the author should discuss the possibility of other lipids. The densities (Fig. 1c and Ext Data Fig. 4) are not complete or high enough resolution to conclude the lipid identity. In addition, it would be helpful to indicate contour (sigma) levels when showing the lipid densities.
+Similarly, how was the ordered PC1 lipid in Fig. 4 assigned as PC, but not other lipids? Please discuss if other lipids can contribute to this density.
+It is interesting that cryo-EM analysis separated several classes within rotational states 1 and 2. However, only the differences between 1a, 2a and 3 are presented. Can the authors describe the distinct features of all classes?
+In all 10 classes representing different rotational states, what are the F1 conformations? Do they represent the same functional/nucleotide state of F1?
+In Fig. 3b, “su-β” label is difficult to see. Consider moving the label?
+Please show local resolution maps for all final cryo-EM maps. To demonstrate sufficiently high resolution to visualize ordered water molecule around proton channel, FSC curves focusing on relevant regions should be helpful.
+Please clarify exactly which gel filtration fractions in Ext Data Fig. 1a were pooled together for cryo-EM study.
+
+Reviewer #2 (Remarks to the Author):
+
+The manuscript by Gahura et al., describes the structure of the ATP synthase from T. Brucei as determined by cryo-EM. They identified 10 rotational states that were assembled into a rotational mechanism. They identified localized water molecules in the lumen half-channel, and proximal to the key Arginine residue of subunit a. They discovered structures of subunits b, e, and g that were different from other species. In particular e and g were a key part of an oligomerization interface that was different from other studied ATP synthase from various species. RNAi knockdowns revealed that disrupting the interface affected dimerization and cristae formation in the mitochondria, while the enzyme retained some activity.
+
+This is an important and interesting paper regarding the role of the ATP synthase in cristae formation, and its place in evolutionary schemes. It also provides further insights into mechanisms of ATP synthesis.
+
+There were several features of the structure that were not clearly explained or illustrated:
+
+1. Subunit b is found in all ATP synthases (while being rather divergent), and was discussed here
+(para 3 of the Results). But no image illustrates the differences with other b subunits: the N-terminal transmembrane domains and the shortened C-terminus.
+
+2. The unusual beta-barrel of the ring of subunits c was illustrated, but not discussed very much. Apparently it is the N-terminus, but not clear if it is the entire N-terminus, or is there another segment not resolved? What species have this feature? It would seem to create a significant cavity. The authors speculated that subunit e, C-terminus, interacted there. (But for what purpose?)
+
+3. The rotary mechanism was discussed on p.5 of the Results, but was not entirely clear to me. The angles of 117, 136, and 107 would appear to be related to the positions of gamma relative to alpha/beta. The description of c-ring station relative to F1 does not seem complete
+
+Reviewer #3 (Remarks to the Author):
+
+The studies in the manuscript can be divided into 2 related, but distinct areas. In the first part, the studies investigate the structure of the dimer form of the ATP synthase from Trypanosoma brucei. In the second part, the studies concentrate on the role of subunits e and g on the formation of the dimer and their role in forming an active enzyme. The first part reports on the high-resolution structure of the dimer form of the ATP synthase – which consists of 25 subunits and 36 lipid molecules. They also report on the presence of 5 ordered water molecules which likely participate in the proton conduction pathway in Fo. The dimerization interface is formed by subunits e and g. The authors report on 10 distinct rotamer structures of the enzyme with a resolution from 3.5-4.3Å resolution. Overall, these structures, and are very good and add to the understanding of the structure, function, and evolution of the enzyme.
+
+The second part of the study looks more specifically at the roles of subunits e and g in the dimerization interface. Here a number of biochemical studies are used to investigate their role in activity and dimerization. The studies also revealed that dimerization is critical when it is the primary source of cellular ATP.
+
+The results in this study are clear and unambiguous. The structures are very good and provide some new insights into the structure and function of the ATP synthase and the mechanism of ATP synthesis.
+
+There is just one suggestion. The authors identify cryo density in the cavity of the c-ring as UTP. I understand the rationale for the assignment, but the density does not seem to be good enough to make the assignment. It would have been good to do analysis on the sample to determine if UTP is bound to the enzyme. But I understand that the assignment is made with an understanding that the identity is not certain.
+Gahura et al. Response to Reviewer comments
+
+We warmly thank the Reviewers for their constructive feedback, which has helped to significantly improve the manuscript. Before responding to the Reviewer comments below, we would like to briefly outline the major additions and changes to our revised manuscript. We included a more detailed description of the rotary cycle, and extended Figures 2, ED3 and ED5 with additional panels, as requested. We also performed mass-spectrometry analysis to identify the pyrimidine nucleotide residing in the cavity of the \( c_{10} \)-ring that has been modeled based on the density, but unfortunately, the compound hasn’t been experimentally detected. All panels containing bar graphs were modified and now show all individual data points, to meet the journal’s requirements.
+
+Reviewer #1 (Remarks to the Author):
+
+To generate mitochondrial inner membrane curvature and maintain high level of ATP production, the mitochondrial ATP synthase forms dimers which further arrange into oligomers. In this work, Gahura et al. determined the cryo-EM structure of the ATP synthase dimer from Trypanosoma brucei, identified both protein and lipid components, revealed a set of rotational states, and proposed subunit-e/g module as an ancestral oligomerization motif of ATP synthases. The functional importance of subunit-g was supported by their RNAi knockdown, mitochondrial ultrastructure, membrane polarization measurement, and ATP production assay. This manuscript is well written with clearly presented figures, and most results are properly interpreted. The results are interesting to the community of ATP synthase research as well as broader membrane protein biology.
+
+I have a few comments and questions listed below.
+
+For the assignment of cardiolipin molecules, particularly those in Fig. 1c, the author should discuss the possibility of other lipids. The densities (Fig. 1c and Ext Data Fig. 4) are not complete or high enough resolution to conclude the lipid identity. In addition, it would be helpful to indicate contour (sigma) levels when showing the lipid densities. Similarly, how was the ordered PC1 lipid in Fig. 4 assigned as PC, but not other lipids? Please discuss if other lipids can contribute to this density.
+- This information has now been added to Fig ED5 and Methods section on model building. Particularly, cardiolipins were assigned based on the presence of a characteristic elongated density branched on both termini, corresponding to two phosphatidyl groups linked by a central glycerol bridge. The assignment of the negative phosphate groups is supported by coordination of positively charged residues, mostly arginines. Monophosphatidyl lipids can be distinguished based on the shape of their headgroups. In PC, the three methyl groups of choline moiety generate a distinct tetrahedral density, which is not observed in the case of amine in PE. None of the headgroup
+densities is compatible with other monophosphatidyl lipids possibly present in the inner mitochondrial membrane (phosphatidylserine, phosphatidylinositol).
+
+It is interesting that cryo-EM analysis separated several classes within rotational states 1 and 2. However, only the differences between 1a, 2a and 3 are presented. Can the authors describe the distinct features of all classes?
+- We thank the reviewer for the opportunity to discuss our data more extensively, and now added the additional information on page 6 with a reference to Sobti et al., 2020, Nat Comm. In the original version of our manuscript we focused on the most populated main rotational state 1 (5 classes/substates), in which we described (i) counter-directional torque of the \( \alpha_3\beta_3 \) hexamer (Fig. 2c,d), (ii) bending of F1 (Fig. 2e), and (iii) twisting of the peripheral stalk (Fig. 2f). We reason that the motions observed in the main state 1 likely occur also in the remaining states, but could not be observed due to the lower number of detectable substeps (four and one substeps for the states 2 and 3, respectively). Unequal representation of individual main steps is most likely caused by a symmetry mismatch between the decameric c-ring and the \( \alpha_3\beta_3 \) hexamer (tenfold vs threefold symmetry), as revealed in bacterial ATP synthase (Sobti et al., 2020, Nat Comm), and observed also in *Polytomella* (Murphy et al., 2019, Science).
+
+In all 10 classes representing different rotational states, what are the F1 conformations? Do they represent the same functional/nucleotide state of F1?
+- We added a clarification on page 6. The conformation of F1 in all 10 classes corresponds to the catalytic dwell, in which the three \( \alpha\beta \) dimers attain typical tight closed (TP), loose closed (DP) and open (E) conformation, alternating during transitions between individual rotational states. The catalytic interfaces in TP, DP and E conformations bind ATP, ADP, and no nucleotides, consistently with previous studies in similar settings, including the T. brucei F1 crystal structure. As no fresh nucleotides were added shortly before freezing, this is the expected functional state of the enzyme.
+
+In Fig. 3b, “su-\( \beta \)” label is difficult to see. Consider moving the label?
+- The label was highlighted, thank you.
+
+Please show local resolution maps for all final cryo-EM maps. To demonstrate sufficiently high resolution to visualize ordered water molecule around proton channel, FSC curves focusing on relevant regions should be helpful.
+- We have added new Extended Data Fig. 3, showing all local resolution maps (which are based on FSC curves of overlapping spheres). The highest resolution of 2.55 Å was observed in the membrane region that includes the half channel with the ordered water molecules. To illustrate that the modeled water molecules are part or the highest resolved region, the new figure includes a
+closeup view of the lumenal proton channel. The information about the local resolution was also added on page 8.
+
+Please clarify exactly which gel filtration fractions in Ext Data Fig. 1a were pooled together for cryo-EM study.
+- The figure was modified as requested, thank you.
+
+Reviewer #2 (Remarks to the Author):
+
+The manuscript by Gahura et al., describes the structure of the ATP synthase from T. Brucei as determined by cryo-EM. They identified 10 rotational states that were assembled into a rotational mechanism. They identified localized water molecules in the lumen half-channel, and proximal to the key Arginine residue of subunit a. They discovered structures of subunits b, e, and g that were different from other species. In particular e and g were a key part of an oligomerization interface that was different from other studied ATP synthase from various species. RNAi knockdowns revealed that disrupting the interface affected dimerization and cristae formation in the mitochondria, while the enzyme retained some activity.
+
+This is an important and interesting paper regarding the role of the ATP synthase in cristae formation, and its place in evolutionary schemes. It also provides further insights into mechanisms of ATP synthesis.
+
+There were several features of the structure that were not clearly explained or illustrated:
+
+1. Subunit b is found in all ATP synthases (while being rather divergent), and was discussed here (para 3 of the Results). But no image illustrates the differences with other b subunits: the N-terminal transmembrane domains and the shortened C-terminus.
+- We added the requested illustration in Fig 2c. Particularly, to illustrate the divergence of subunit-b, we added a schematic figure comparing the arrangement of transmembrane helices of subunit-b and adjacent structural elements in T. brucei with another type IV ATP synthase of Euglena and the type I ATP synthase represented by S. cerevisiae. Accordingly, we also elaborated on the conservancy of subunit-b transmembrane helices and their context in different types of ATP synthases in the Discussion section.
+
+2. The unusual beta-barrel of the ring of subunits c was illustrated, but not discussed very much. Apparently it is the N-terminus, but not clear if it is the entire N-terminus, or is there another segment not resolved? What species have this feature? It would seem to create a significant cavity. The authors speculated that subunit e, C-terminus, interacted there. (But for what purpose?)
+- We added an expansion in the text with a reference to Pinke et al., 2020. Our mass-spec data indicate that only a single N-terminal residue of mature subunit-c has not been built in our model, which is likely due to flexibility. Thus, there is no unresolved segment and the \( c_{10} \)-ring beta-barrel is constituted by N-termini of the ten copies of subunit-c. The same beta-barrel has been so far reported in the structure of type IV ATP synthase from Euglena (Mühleip et al., 2019, *eLife*). Sequence comparison and secondary structure prediction upstream of the highly conserved first transmembrane helix of subunit-c from species across eukaryotes suggest that the N-terminal beta-barrel is not found outside of Euglenozoa. However, the analysis has limitations, because the presence of mitochondrial targeting sequences prevents reliable prediction of mature N-termini. Therefore, we added a conservative statement “*The β-barrel has been previously reported also in other type IV ATP synthase from E. gracilis (Mühleip et al., 2019)*” on page 3.
+The function of the interaction of subunit-e with the beta-barrel or its lipid plug is unclear from our structure. A model, in which retraction of subunit-e upon calcium exposure pulls out the lipid plug, which induces disassembly of the c-ring and triggers permeability transition pore (PTP) opening, has been proposed (Pinke et al., 2020). We added this information to the revised manuscript. However, because cyclophilin D, the key component of mitochondrial permeability transition, has not been found in *T. brucei* (Bustos et al., 2017, PMID 28933785) a putative function remains unclear in our study.
+
+3. The rotary mechanism was discussed on p.5 of the Results, but was not entirely clear to me. The angles of 117, 136, and 107 would appear to be related to the positions of gamma relative to alpha/beta. The description of c-ring station relative to F1 does not seem complete
+- To describe rotary motion, the rotor (the \( c_{10,\gamma\delta\epsilon} \) subcomplex) is viewed as a rigid body rotating against static F₀. The angles are the rotor step size between classes 1a, 2a and 3 relative to the static F₀ subunit-a. We specified this information in the revised manuscript on page 6. We also expanded the text describing the F₁ movement relative to \( c_{10} \)-ring throughout the rotary cycle, and complementary information is found in the corresponding supplementary movie.
+
+Reviewer #3 (Remarks to the Author):
+
+The studies in the manuscript can be divided into 2 related, but distinct areas. In the first part, the studies investigate the structure of the dimer form of the ATP synthase from Trypanosoma brucei. In the second part, the studies concentrate on the role of subunits e and g on the formation of the dimer and their role in forming an active enzyme. The first part reports on the high-resolution structure of the dimer form of the ATP synthase – which consists of 25 subunits and 36 lipid molecules. They also report on the presence of 5 ordered water molecules which likely participate in the proton conduction pathway in Fo. The dimerization interface is formed by subunits e and g. The authors report on 10 distinct rotamer structures of the enzyme with a resolution from 3.5-4.3Å
+resolution. Overall, these structures, and are very good and add to the understanding of the structure, function, and evolution of the enzyme.
+
+The second part of the study looks more specifically at the roles of subunits e and g in the dimerization interface. Here a number of biochemical studies are used to investigate their role in activity and dimerization. The studies also revealed that dimerization is critical when it is the primary source of cellular ATP.
+
+The results in this study are clear and unambiguous. The structures are very good and provide some new insights into the structure and function of the ATP synthase and the mechanism of ATP synthesis.
+
+There is just one suggestion. The authors identify cryo density in the cavity of the c-ring as UTP. I understand the rationale for the assignment, but the density does not seem to be good enough to make the assignment. But I understand that the assignment is made with an understanding that the identity is not certain.
+
+- Thank you. We made a dedicated large-scale preparation of the ATP synthase from the parasites, as well as a control sample from bacterial cells with the aim of the compound detection by mass-spectrometry. The analysis was performed at the Swedish Metabolomics Centre in Umeå University, on UHPLC-QqQ MRM mode for highest sensitivity method set to detect possible nucleotides. 330 ul of the sample was used, which is more than the total amount required for cryo-EM structure determination. Unfortunately, no signal has been detected.
+We thus added in the text “assigned as UTP, although not experimentally detected.”
+
+![Chromatogram showing UTP peak should be present here](page_184_1207_1207_393.png)
+REVIEWERS’ COMMENTS
+
+Reviewer #1 (Remarks to the Author):
+
+The authors have adequately addressed my comments. I support the publication of this manuscript in Nature Communications.
+
+Reviewer #2 (Remarks to the Author):
+
+No further comments. Thank you
+
+Reviewer #3 (Remarks to the Author):
+
+This is a revised version of the manuscript with the same title. The authors have addressed well each of the comments in the review. Overall, this is a very solid study that brings novel and significant information on the structure, function, and evolution of the ATP synthase. This will have appeal to a broad audience.
+REVIEWERS’ COMMENTS
+
+Reviewer #1 (Remarks to the Author):
+
+The authors have adequately addressed my comments. I support the publication of this manuscript in Nature Communications.
+
+Reviewer #2 (Remarks to the Author):
+
+No further comments. Thank you
+
+Reviewer #3 (Remarks to the Author):
+
+This is a revised version of the manuscript with the same title. The authors have addressed well each of the comments in the review. Overall, this is a very solid study that brings novel and significant information on the structure, function, and evolution of the ATP synthase. This will have appeal to a broad audience.

0a57595338b1390798459ee5d63f40d3108931b635b32aecd97babb2ece11f54/preprint/preprint.md

@@ -0,0 +1,1170 @@
+An ancestral interaction module promotes oligomerization in divergent mitochondrial ATP synthases
+
+Alexey Amunts (amunts@scilifelab.se)
+Stockholm University https://orcid.org/0000-0002-5302-1740
+
+Ondrej Gahura
+Institute of Parasitology, Biology Centre CAS https://orcid.org/0000-0002-2925-4763
+
+Alexander Muhleip
+Stockholm University https://orcid.org/0000-0002-1877-2282
+
+Carolina Hierro-Yap
+Institute of Parasitology, Biology Centre CAS
+
+Brian Panicucci
+Biology Centre
+
+Minal Jain
+Institute of Parasitology, Biology Centre CAS
+
+David Hollaus
+Institute of Parasitology, Biology Centre CAS https://orcid.org/0000-0001-7403-6434
+
+Martina Slapničková
+Institute of Parasitology, Biology Centre CAS
+
+Alena Zikova
+Biology Centre https://orcid.org/0000-0002-8686-0225
+
+Article
+
+Keywords:
+
+Posted Date: December 30th, 2021
+
+DOI: https://doi.org/10.21203/rs.3.rs-1196040/v1
+
+License: This work is licensed under a Creative Commons Attribution 4.0 International License.
+Read Full License
+
+Version of Record: A version of this preprint was published at Nature Communications on October 11th, 2022. See the published version at https://doi.org/10.1038/s41467-022-33588-z.
+An ancestral interaction module promotes oligomerization in divergent mitochondrial ATP synthases
+
+Ondřej Gahura1,†, Alexander Mühleip2,†, Carolina Hierro-Yap1,3, Brian Panicucci1, Minal Jain1,3, David Hollaus3, Martina Slapničková1, Alena Zíková1,3,*, Alexey Amunts2,4*
+
+1Institute of Parasitology, Biology Centre CAS, Ceske Budejovice, Czech Republic
+2Science for Life Laboratory, Department of Biochemistry and Biophysics, Stockholm University, 17165 Solna, Sweden
+3Faculty of Science, University of South Bohemia, Ceske Budejovice, Czech Republic
+4Department of Physiology and Pharmacology, Karolinska Institutet, Stockholm, Sweden
+
+*Correspondence to: azikova@paru.cas.cz; amunts@scilifelab.se
+†These authors contributed equally to this work.
+
+Abstract
+Mitochondrial ATP synthase forms stable dimers arranged into oligomeric assemblies that generate the inner-membrane curvature essential for efficient energy conversion. Here, we report cryo-EM structures of the intact ATP synthase dimer from Trypanosoma brucei in ten different rotational states. The model consists of 25 subunits, including nine lineage-specific, as well as 36 lipids. The rotary mechanism is influenced by the divergent peripheral stalk, conferring a greater conformational flexibility. Proton transfer in the luminal half-channel occurs via a chain of five ordered water molecules. The dimerization interface is formed by subunit-g that is critical for interactions but not for the catalytic activity. Although overall dimer architecture varies among eukaryotes, we find that subunit-g together with subunit-e form an ancestral oligomerization motif, which is shared between the trypanosomal and mammalian lineages. Therefore, our data defines the subunit-g/e module as a structural component determining ATP synthase oligomeric assemblies.
+Mitochondrial ATP synthase consists of the soluble F₁ and membrane-bound F₀ subcomplexes, and occurs in dimers that assemble into oligomers to induce the formation of inner-membrane folds, called cristae. The cristae are the sites for oxidative phosphorylation and energy conversion in eukaryotic cells. Dissociation of ATP synthase dimers into monomers results in the loss of native cristae architecture and impairs mitochondrial function¹². While cristae morphology varies substantially between organisms from different lineages, ranging from flat lamellar in opisthokonts to coiled tubular in ciliates and discoidal in euglenozoans³, the mitochondrial ATP synthase dimers represent a universal occurrence to maintain the membrane shape⁴.
+
+ATP synthase dimers of variable size and architecture, classified into types I to IV have recently been resolved by high-resolution cryo-EM studies. In the structure of the type-I ATP synthase dimer from mammals, the monomers are only weakly associated⁵,⁶, and in yeast insertions in the membrane subunits form tighter contacts⁷. The structure of the type-II ATP synthase dimer from the alga Polytomella sp. showed that the dimer interface is formed by phylum-specific components⁸. The type-III ATP synthase dimer from the ciliate Tetrahymena thermophila is characterized by parallel rotary axes, and a substoichiometric subunit, as well as multiple lipids were identified at the dimer interface, while additional protein components that tie the monomers together are distributed between the matrix, transmembrane, and luminal regions⁹. The structure of the type-IV ATP synthase with native lipids from Euglena gracilis also showed that specific protein-lipid interactions contribute to the dimerization, and that the central and peripheral stalks interact with each other directly¹⁰. Finally, a unique apicomplexan ATP synthase dimerizes via 11 parasite-specific components that contribute ~7000 Ų buried surface area¹¹, and unlike all other ATP synthases, that assemble into rows, it associates in higher oligomeric states of pentagonal pyramids in the curved apical membrane regions. Together, the available structural data suggest a diversity of oligomerization, and it remains unknown whether common elements mediating these interactions exist or whether dimerization of ATP synthase occurred independently and multiple times in evolution⁴.
+
+The ATP synthase of Trypanosoma brucei, a representative of kinetoplastids and an established medically important model organism causing the sleeping sickness, is highly divergent, exemplified by the pyramid-shaped F₁ head containing a phylum specific subunit¹²,¹³. The dimers are sensitive to the lack of cardiolipin¹⁴ and form short left-handed helical segments that extend across the membrane ridge of the discoidal cristae¹⁵. Uniquely among aerobic eukaryotes, the mammalian life cycle stage of T. brucei utilizes the reverse mode of ATP synthase, using the enzyme as a proton pump to maintain mitochondrial membrane potential at the expense of ATP¹⁶,¹⁷. In contrast, the insect stages of the parasite employ the ATP-producing forward mode of the enzyme¹⁸,¹⁹.
+
+Given the conservation of the core subunits, the different nature of oligomerization and the ability to test structural hypotheses biochemically, we reasoned that investigation of the T. brucei ATP synthase structure and function would provide the missing evolutionary link to understand how the monomers interact to form physiological dimers. Here, we address this question by combining structural, functional and evolutionary analysis of the T. brucei ATP synthase dimer.
+Results
+
+Cryo-EM structure of the T. brucei ATP synthase
+
+We purified ATP synthase dimers from cultured T. brucei procyclic trypomastigotes by affinity chromatography with a recombinant natural protein inhibitor TbIF1^{20}, and subjected the sample to cryo-EM analysis (Extended Data Fig. 1 and 2). Using masked refinements, maps were obtained for the membrane region, the rotor, and the peripheral stalk. To describe the conformational space of the T. brucei ATP synthase, we resolved ten distinct rotary substates, which were refined to 3.5–4.3 Å resolution. Finally, particles with both monomers in rotational state 1 were selected, and the consensus structure of the dimer was refined to 3.2 Å resolution (Extended Data Table 1, Extended Data Fig. 2).
+
+Unlike the wide-angle architecture of dimers found in animals and fungi, the T. brucei ATP synthase displays an angle of 60° between the two F_{1}/c-ring subcomplexes. The model of the T. brucei ATP synthase includes all 25 different subunits, nine of which are lineage-specific (Fig. 1a, Supplementary Video 1, Extended Data Fig. 3). We named the subunits according to the previously proposed nomenclature^{21-23} (Extended Data Table 2). In addition, we identified and modeled 36 bound phospholipids, including 24 cardiolipins (Extended Data Fig. 4). Both detergents used during purification, n-dodecyl β-D-maltoside (β-DDM) and glyco-diosgenin (GDN) are also resolved in the periphery of the membrane region (Extended Data Fig. 5).
+
+In the catalytic region, F_{1} is augmented by three copies of subunit p18, each bound to subunit-\alpha^{12,13}. Our structure shows that p18 is involved in the unusual attachment of F_{1} to the peripheral stalk. The membrane region includes eight conserved F_{0} subunits (b, d, f, 8, i/j, k, e, and g) arranged around the central proton translocator subunit-\alpha. We identified those subunits based on the structural similarity and matching topology to their yeast counterparts (Fig 2). For subunit-b, a single transmembrane helix superimposes well with bH1 from yeast and anchors the newly identified subunit-e and -g to the F_{0} (Fig 2a); a long helix bH2, which constitutes the central part of the peripheral stalk in other organisms is absent in T. brucei. The sequence of this highly reduced subunit-b shows 18% identity and 40% similarity to E. gracilis subunit-b^{10}, representing a diverged homolog (Extended Data Fig. 6). No alternative subunit-b^{24} is found in our structure.
+
+The membrane region contains a peripheral subcomplex, formed primarily by the phylum-specific ATPTB1,6,12 and ATPEG3 (Fig. 1b). It is separated from the conserved core by a membrane-intrinsic cavity, in which nine bound cardiolipins are resolved (Fig. 1c), and the C-terminus of ATPTB12 interacts with the luminal β-barrel of the c_{10}-ring. In the cavity of the decameric c-ring near the matrix side, 10 Arg66_{c} residues coordinate a ligand density, which is consistent with a pyrimidine ribonucleoside triphosphate (Fig. 1d). We assign this density as uridine-triphosphate (UTP), due to its large requirement in the mitochondrial RNA metabolism of African trypanosomes being a substrate for post-transcriptional RNA editing^{25}, and addition of poly-uridine tails to gRNAs and rRNAs^{26,27}, as well as due to low abundance of cytidine triphosphate (CTP)^{28}. The nucleotide base is inserted between two Arg82_{c} residues, whereas the triphosphate region is coordinated by another five Arg82_{c} residues, with Tyr79_{c} and Asn76_{c} providing asymmetric coordination contacts. The presence of a nucleotide inside the c-ring is
+surprising, given the recent reports of phospholipids inside the c-rings in mammals\(^{5,6}\) and ciliates\(^9\), indicating that a range of different ligands can provide structural scaffolding.
+
+![Front and side views of the composite model with both monomers in rotational state 1. The two F_1/c_{10}-ring complexes, each augmented by three copies of the phylum-specific p18 subunit, are tied together at a 60°-angle. The membrane-bound F_o region displays a unique architecture and is composed of both conserved and phylum-specific subunits. Side view of the F_o region showing the luminal interaction of the ten-stranded β-barrel of the c-ring (grey) with ATPTB12 (pale blue). The lipid-filled peripheral F_o cavity is indicated. Close-up view of the bound lipids within the peripheral F_o cavity with cryo-EM density shown. Top view into the decameric c-ring with a bound pyrimidine ribonucleoside triphosphate, assigned as UTP. Map density shown in transparent blue, interacting residues shown.](page_172_340_1097_627.png)
+
+Fig. 1: The *T. brucei* ATP synthase structure with lipids and ligands.
+
+a, Front and side views of the composite model with both monomers in rotational state 1. The two F_1/c_{10}-ring complexes, each augmented by three copies of the phylum-specific p18 subunit, are tied together at a 60°-angle. The membrane-bound F_o region displays a unique architecture and is composed of both conserved and phylum-specific subunits. b, Side view of the F_o region showing the luminal interaction of the ten-stranded β-barrel of the c-ring (grey) with ATPTB12 (pale blue). The lipid-filled peripheral F_o cavity is indicated. c, Close-up view of the bound lipids within the peripheral F_o cavity with cryo-EM density shown. d, Top view into the decameric c-ring with a bound pyrimidine ribonucleoside triphosphate, assigned as UTP. Map density shown in transparent blue, interacting residues shown.
+Fig. 2: Identification of conserved F_o subunits.
+
+a, Top view of the membrane region with T. brucei subunits (colored) overlaid with S. cerevisiae structure (gray transparent). Close structural superposition and matching topology allowed the assignment of conserved subunits based on matching topology and location.
+b, Superposition of subunits-e and -g with their S. cerevisiae counterparts (PDB 6B2Z) confirms their identity.
+
+Peripheral stalk flexibility and distinct rotational states
+
+The trypanosomal peripheral stalk displays a markedly different architecture compared to its yeast and mammalian counterparts. In the opisthokont complexes, the peripheral stalk is organized around the long bH2, which extends from the membrane ~15 nm into the matrix and attaches to OSCP at the top of F_1^{5,7}. By contrast, T. brucei lacks the canonical bH2 and instead, helices 5-7 of divergent subunit-d and the C-terminal helix of extended subunit-8 bind to a C-terminal extension of OSCP at the apical part of the peripheral stalk (Fig. 3a). The interaction between OSCP and subunit-d and -8 is stabilized by soluble ATPTB3 and ATPTB4. The peripheral stalk is rooted to the membrane subcomplex by a transmembrane helix of subunit-8, wrapped on the matrix side by helices 8-11 of subunit-d. Apart from the canonical contacts at the top of F_1, the peripheral stalk is attached to the F_1 via a euglenozoa-specific C-terminal extension of OSCP, which contains a disordered linker and a terminal helix hairpin extending between the F_1-bound p18 and subunits -d and -8 of the peripheral stalk (Fig. 3a, Supplementary Videos 2,3). Another interaction of F_1 with the peripheral stalk occurs between the stacked C-terminal helices of subunit-β and -d (Fig. 3b), the latter of which structurally belongs to F_1 and is connected to the peripheral stalk via a flexible linker.
+
+To assess whether the unusual peripheral stalk architecture influences the rotary mechanism, we analysed 10 classes representing different rotational states. The three main states (1-3) result from a ~120° rotation of the central stalk subunit-γ, and we identified five (1a-1e), four (2a-2d) and one (3) classes of the respective main states. The rotor positions of the rotational states 1a, 2a and 3 are related by steps of 117°, 136° and 107°, respectively. Throughout all the identified substeps of the rotational state 1 (classes 1a to 1e) the rotor turns by ~33°, which corresponds approximately to the advancement by one subunit-c of the c_{10}-ring. While rotating along with the rotor, the F_1 headpiece lags behind, advancing by only ~13°. During the following transition from 1e to 2a, the rotor advances by ~84°, whereas the F_1 headpiece rotates ~22° in the opposite direction (Fig. 3c,d). This generates a counter-directional torque between the two motors,
+which is consistent with a power-stroke mechanism. Albeit with small differences in step size, this mechanism is consistent with a previous observation in the Polytomella ATP synthase8. However, due to its large, rigid peripheral stalk, the Polytomella ATP synthase mainly displays rotational substeps, whereas the Trypanosoma F₁ also displays a tilting motion of ~8° revealed by rotary states 1 and 2 (Fig. 3e, Supplementary Video 2). The previously reported hinge motion between the N- and C-terminal domains of OSCP8 is not found in our structures, instead, the conformational changes of the F₁/c₁₀-ring subcomplex are accommodated by a 5° bending of the apical part of the peripheral stalk. (Fig. 3e, Supplementary Videos 2,3). Together, the structural data indicate that the divergent peripheral stalk attachment confers greater conformational flexibility to the T. brucei ATP synthase.
+
+![A divergent peripheral stalk allows high flexibility during rotary catalysis.](page_176_495_1092_670.png)
+
+Fig. 3: A divergent peripheral stalk allows high flexibility during rotary catalysis. a, N-terminal OSCP extension provides a permanent central stalk attachment, while the C-terminal extension provides a phylum-specific attachment to the divergent peripheral stalk. b, The C-terminal helices of subunits -β and -d provide a permanent F₁ attachment. c, Substeps of the c-ring during transition from rotational state 1 to 2. d, F₁ motion accommodating steps shown in (c). After advancing along with the rotor to state 1e, the F₁ rotates in the opposite direction when transitioning to state 2a. e, Tilting motion of F₁ and accommodating bending of the peripheral stalk.
+Luminal proton half-channel is insulated by a lipid and contains ordered water molecules
+
+The mechanism of proton translocation involves sequential protonation of E102 of subunits-c, rotation of the c10-ring with neutralized E102c exposed to the phospholipid bilayer, and release of protons on the other side of the membrane. The sites of proton binding and release are separated by the conserved R146 contributed by the horizontal helix H5 of subunit-a and are accessible from the cristae lumen and mitochondrial matrix by aqueous half-channels (Fig. 4a). Together, R146 and the adjacent N209 coordinate a pair of water molecules in between helices H5 and H6 (Fig. 4b). A similar coordination has been observed in the Polytomella ATP synthase8. The coordination of water likely restricts the R146 to rotamers that extend towards the c-ring, with which it is thought to interact.
+
+In our structure, the luminal half-channel is filled with a network of resolved water densities, ending in a chain of five ordered water molecules (W1-W5; Fig. 4c,d,e). The presence of ordered water molecules in the aqueous channel is consistent with a Grotthuss-type mechanism for proton transfer, which would not require long-distance diffusion of water molecules5. However, because some distances between the observed water molecules are too large for direct hydrogen bonding, proton transfer may involve both coordinated and disordered water molecules. The distance of 7 Å between the last resolved water (W1) and D202a, the conserved residue that is thought to transfer protons to the c-ring, is too long for direct proton transfer. Instead, it may occur via the adjacent H155a. Therefore, our structure resolves individual elements participating in proton transport (Fig. 4d,e).
+
+The luminal proton half-channel in the mammalian5,6 and apicomplexan11 ATP synthase is lined by the transmembrane part of bH2, which is absent in T. brucei. Instead, the position of bH2 is occupied by a fully ordered phosphatidylcholine in our structure (PC1; Fig. 4a,c). Therefore, a bound lipid replaces a proteinaceous element in the proton path.
+Fig. 4: The lumenal half-channel contains ordered water molecules and is confined by an F_o-bound lipid. a, Subunit-a (green) with the matrix (orange) and lumenal (light blue) channels, and an ordered phosphatidylcholine (PC1; blue). E102 of the c10-ring shown in grey. b, Close-up view of the highly conserved R146_a and N209_a, which coordinate two water molecules between helices H5-6_a. c, Sideview of the lumenal channel with proton pathway (light blue) and confining phosphatidylcholine (blue). d, Chain of ordered water molecules in the lumenal channel. Distances between the W1-W5 (red) are 5.2, 3.9, 7.3 and 4.8 Å, respectively. e, The ordered waters extend to H155_a, which likely mediates the transfer of protons to D202_a.
+
+Subunit-g facilitates assembly of different ATP synthase oligomers
+
+Despite sharing a set of conserved F_o subunits, the T. brucei ATP synthase dimer displays a markedly different dimer architecture compared to previously determined structures. First, its dimerization interface of 3,600 Å^2 is smaller than that of the E. gracilis type-IV (10,000 Å^2) and the T. thermophila type-III ATP synthases (16,000 Å^2). Second, unlike mammalian and fungal ATP synthase, in which the peripheral stalks extend in the plane defined by the two rotary axes, in our structure the monomers are rotated such that the peripheral stalks are offset laterally on the opposite sides of the plane. Due to the rotated monomers, this architecture is associated with a specific dimerization interface, where two subunit-g copies interact homotypically on the C_2 symmetry axis (Fig. 5a, Supplementary Video 1). Both copies of H1-2_g extend horizontally along the matrix side of the membrane, clamping against each other (Fig. 5c,e). This facilitates formation of contacts between an associated transmembrane helix
+of subunit-e with the neighbouring monomer via subunit-a' in the membrane, and -f' in the lumen, thereby further contributing to the interface (Fig. 5b). Thus, the ATP synthase dimer is assembled via the subunit-e/g module. The C-terminal part of the subunit-e helix extends into the lumen, towards the ten-stranded β-barrel of the c-ring (Extended Data Fig. 7a). The terminal 23 residues are disordered with poorly resolved density connecting to the detergent plug of the c-ring β-barrel (Extended Data Fig. 7b). This resembles the luminal C-terminus of subunit-e in the bovine structure5, indicating a conserved interaction with the c-ring.
+
+The e/g module is held together by four bound cardiolipins in the matrix leaflet, anchoring it to the remaining F_o region (Fig. 5c). The head groups of the lipids are coordinated by polar and charged residues with their acyl chains filling a central cavity in the membrane region at the dimer interface (Fig 5c, Extended Data Fig. 4f). Cardiolipin binding has previously been reported to be obligatory for dimerization in secondary transporters29 and the depletion of cardiolipin synthase resulted in reduced levels of ATP synthase in bloodstream trypanosomes14.
+
+Interestingly, for yeasts, early blue native gel electrophoresis30 and subtomogram averaging studies2 suggested subunit-g as potentially dimer-mediating, however the e/g modules are located laterally opposed on either side of the dimer long axis, in the periphery of the complex, ~8.5 nm apart from each other. Because the e/g modules do not interact directly within the yeast ATP synthase dimer, they have been proposed to serve as membrane-bending elements, whereas the major dimer contacts are formed by subunit-a and -i/f'. In mammals, the e/g module occupies the same position as in yeasts, forming the interaction between two diagonal monomers in a tetramer5,6,31, as well as between parallel dimers32. The comparison with our structure shows that the overall organization of the intra-dimeric trypanosomal and inter-dimeric mammalian e/g module is structurally similar (Fig. 5d). Furthermore, kinetoplastid parasites and mammals share conserved GXXXXG motifs in subunit-e33 and -g (Extended Data Fig. 8), which allow close interaction of their transmembrane helices (Fig. 5e), providing further evidence for subunit homology. However, while the mammalian ATP synthase dimers are arranged perpendicularly to the long axis of their rows along the edge of cristae34, the T. brucei dimers on the rims of discoidal cristae are inclined ~45° to the row axis15. Therefore, the e/g module occupies equivalent positions in the rows of both evolutionary distant groups (Fig. 5f and reference 32).
+Fig. 5: The homotypic dimerization motif of subunit-g generates a conserved oligomerization module. a, Side view with dimerising subunits colored. b,c, The dimer interface is constituted by (b) subunit-e’ contacting subunit-a in the membrane and subunit-f in the lumen, (c) subunits e and g from both monomers forming a subcomplex with bound lipids. d, Subunit-g and -e form a dimerization motif in the trypanosomal (type-IV) ATP synthase dimer (this study), the same structural element forms the oligomerization motif in the porcine ATP synthase tetramer. The structural similarity of the pseudo-dimer (i.e., two diagonal monomers from adjacent dimers) in the porcine structure with the trypanosomal dimer suggests that type I and IV ATP synthase dimers have evolved through divergence from a common ancestor. e, The dimeric subunit-e/g structures are conserved in pig (PDB 6ZNA) and T. brucei (this work) and contain a conserved GXXXG motif (orange) mediating interaction of transmembrane helices. f, Models of the ATP synthase dimers fitted into subtomogram averages of short oligomers15: matrix view, left; cut-through, middle, lumenal view, right (EMD-3560).
+Fig. 6: RNAi knockdown of subunit-g results in monomerization of ATP synthase. a, Growth curves of non-induced (solid lines) and tetracycline-induced (dashed lines) RNAi cell lines grown in the presence (black) or absence (brown) of glucose. The insets show relative levels of the respective target mRNA at indicated days post-induction (DPI) normalized to the levels of 18S rRNA (black bars) or β-tubulin (white bars). b, Immunoblots of mitochondrial lysates from indicated RNAi cell lines resolved by BN-PAGE probed with antibodies against indicated ATP synthase subunits. c, Representative immunoblots of whole cell lysates from indicated RNAi cell lines probed with indicated antibodies. d, Quantification of three replicates of immunoblots in (c). Values were normalized to the signal of the loading control Hsp70 and to non-induced cells. Plots show means with standard deviations (SD).
+Subunit-g retains the dimer but is not essential for the catalytic monomer
+
+To validate structural insights, we knocked down each individual F_o subunit by inducible RNA interference (RNAi). All target mRNAs dropped to 5-20 % of their original levels after two and four days of induction (Fig. 6a and Extended Data Fig. 9a). Western blot analysis of whole-cell lysates resolved by denaturing electrophoresis revealed decreased levels of F_o subunits ATPB1 and -d suggesting that the integrity of the F_o moiety depends on the presence of other F_o subunits (Fig. 6c,d). Immunoblotting of mitochondrial complexes resolved by blue native polyacrylamide gel electrophoresis (BN-PAGE) with antibodies against F_1 and F_o subunits revealed a strong decrease or nearly complete loss of dimeric and monomeric forms of ATP synthases four days after induction of RNAi of most subunits (b, e, f, i/j, k, 8, ATPTB3, ATPTB4, ATPTB6, ATPTB11, ATPTB12, ATPEG3 and ATPEG4), documenting an increased instability of the enzyme or defects in its assembly. Simultaneous accumulation in F_1-ATPase, as observed by BN-PAGE, demonstrated that the catalytic moiety remains intact after the disruption of the peripheral stalk or the membrane subcomplex (Fig. 6b,c,d and Extended Data Fig. 9b).
+
+In contrast to the other targeted F_o subunits, the downregulation of subunit-g with RNAi resulted in a specific loss of dimeric complexes with concomitant accumulation of monomers (Fig. 6b), indicating that it is required for dimerization, but not for the assembly and stability of the monomeric F_1F_o ATP synthase units. Transmission electron microscopy of thin cell sections revealed that the ATP synthase monomerization in the subunit-g^{RNAi} cell line had the same effect on mitochondrial ultrastructure as nearly complete loss of monomers and dimers upon knockdown of subunit-8. Both cell lines exhibited decreased cristae counts and aberrant cristae morphology (Fig. 7a,b), including the appearance of round shapes reminiscent of structures detected upon deletion of subunit-g or -e in Saccharomyces cerevisiae^1. These results indicate that monomerization prevents the trypanosomal ATP synthase from assembling into short helical rows on the rims of the discoidal cristae^15, as has been reported for impaired oligomerization in counterparts from other eukaryotes^2,35.
+
+Despite the altered mitochondrial ultrastructure, the subunit-g^{RNAi} cells showed only a very mild growth phenotype, in contrast to all other RNAi cell lines that exhibited steadily slowed growth from day three to four after the RNAi induction (Fig. 7a, Extended Data Fig. 9a). This is consistent with the growth defects observed after the ablation of F_o subunit ATPTB1^19 and F_1 subunits-α and p18^12. Thus, the monomerization of ATP synthase upon subunit-g ablation had only a negligible effect on the fitness of trypanosomes cultured in glucose-rich medium, in which ATP production by substrate level phosphorylation partially compensates for compromised oxidative phosphorylation^36.
+
+Measurement of oligomycin-sensitive ATP-dependent mitochondrial membrane polarization by safranin O assay in permeabilized cells showed that the proton pumping activity of the ATP synthase in the induced subunit-g^{RNAi} cells is negligibly affected, demonstrating that the monomerized enzyme is catalytically functional. By contrast, RNAi downregulation of subunit-8, ATPTB4 and ATPTB11, and ATPTB1 resulted in a strong decline of the mitochondrial membrane polarization capacity, consistent with the loss of both monomeric and dimeric ATP synthase forms (Fig. 7c). Accordingly, knockdown of the same subunits resulted in inability to produce ATP by oxidative phosphorylation (Fig. 7d). However, upon subunit-g
+ablation the ATP production was affected only partially, confirming that the monomerized ATP synthase remains catalytically active. The ~50% drop in ATP production of subunit-gRNAi cells can be attributed to the decreased oxidative phosphorylation efficiency due to the impaired cristae morphology. Indeed, when cells were cultured in the absence of glucose, enforcing the need for oxidative phosphorylation, knockdown of subunit-g results in a growth arrest, albeit one to two days later than knockdown of all other tested subunits (Fig. 6a). The data show that dimerization is critical when oxidative phosphorylation is the predominant source of ATP.
+
+![Transmission electron micrographs and quantification of mitochondrial ultrastructure and ATP production](page_324_613_1097_484.png)
+
+Fig. 7: Monomerization of ATP synthase by subunit-g knockdown results in aberrant mitochondrial ultrastructure but does not abolish catalytic activity. a, Transmission electron micrographs of sections of non-induced or 4 days induced RNAi cell lines. Mitochondrial membranes and cristae are marked with blue and red arrowheads, respectively. Top panel shows examples of irregular, elongated and round cross-sections of mitochondria quantified in (b). b, Cristae numbers per vesicle from indicated induced (IND) or non-induced (NON) cell lines counted separately in irregular, elongated and round mitochondrial cross-section. Boxes and whiskers show 25th to 75th and 5th to 95th percentiles, respectively. The numbers of analysed cross-sections are indicated for each data point. Unpaired t-test, p-values are shown. c, Mitochondrial membrane polarization capacity of non-induced or RNAi-induced cell lines two and four DPI measured by Safranine O. Black and gray arrow indicate addition of ATP and oligomycin, respectively. d, ATP production in permeabilized non-induced (0) or RNAi-induced cells 2 and 4 DPI in the presence of indicated substrates and inhibitors. Error bars represent SD of three replicates. Gly3P, DL-glycerol phosphate; KCN, potassium cyanide; CATR, carboxyatractyloside
+Discussion
+Our structure of the mitochondrial ATP synthase dimer from the mammalian parasite T. brucei offers new insight into the mechanism of membrane shaping, rotary catalysis, and proton transfer. Considering that trypanosomes belong to an evolutionarily divergent group of Kinetoplastida, the ATP synthase dimer has several interesting features that differ from other dimer structures. The subunit-b found in bacterial and other mitochondrial F-type ATP synthases appears to be highly reduced to a single transmembrane helix bH1. The long bH2, which constitutes the central part of the peripheral stalk in other organisms, and is also involved in the composition of the luminal proton half-channel, is completely absent in T. brucei. Interestingly, the position of bH2 in the proton half channel is occupied by a fully ordered phosphatidylcholine molecule that replaces a well-conserved proteinaceous element in the proton path. Lack of the canonical bH2 also affects composition of the peripheral stalk in which the divergent subunit-d and subunit-8 binds directly to a C-terminal extension of OSCP, indicating a remodeled peripheral stalk architecture. The peripheral stalk contacts the F₁ headpiece at several positions conferring greater conformational flexibility to the ATP synthase.
+
+Using the structural and functional data, we also identified a conserved structural element of the ATP synthase that is responsible for its multimerization. Particularly, subunit-g is required for the dimerization, but dispensable for the assembly of the F₁F₀ monomers. Although the monomerized enzyme is catalytically competent, the inability to form dimers results in defective cristae structure, and consequently leads to compromised oxidative phosphorylation and cease of proliferation. The cristae-shaping properties of mitochondrial ATP synthase dimers are critical for sufficient ATP production by oxidative phosphorylation, but not for other mitochondrial functions, as demonstrated by the lack of growth phenotype of subunit-gRNAi cells in the presence of glucose. Thus, trypanosomal subunit-g depletion strain represents an experimental tool to assess the roles of the enzyme’s primary catalytic function and mitochondria-specific membrane-shaping activity, highlighting the importance of the latter for oxidative phosphorylation.
+
+Based on our data and previously published structures, we propose an ancestral state with double rows of ATP synthase monomers connected by e/g modules longitudinally and by other F₀ subunits transversally. During the course of evolution, different pairs of adjacent ATP synthase monomer units formed stable dimers in individual lineages (Fig. 8). This gave rise to the highly divergent type-I and type-IV ATP synthase dimers with subunit-e/g modules serving either as oligomerization or dimerization motives, respectively. Because trypanosomes belong to the deep-branching eukaryotic supergroup Discoba, the proposed arrangement might have been present in the last eukaryotic common ancestor. Although sequence similarity of subunit-g is low and restricted to the single transmembrane helix, we found homologs of subunit-g in addition to Opisthokonta and Discoba also in Archaeplastida and Amoebozoa, which represent other eukaryotic supergroups, thus supporting the ancestral role in oligomerization (Extended Data Fig. 8). Taken together, our analysis reveals that mitochondrial ATP synthases that display markedly diverged architecture share the ancestral structural module that promotes oligomerization.
+Fig. 8: The subunit-e/g module is an ancestral oligomerization motif of ATP synthase.
+Schematic model of the evolution of type-I and IV ATP synthases. Mitochondrial ATP synthases are derived from a monomeric complex of proteobacterial origin. In a mitochondrial ancestor, acquisition of mitochondria-specific subunits, including the subunit-e/g module resulted in the assembly of ATP synthase double rows, the structural basis for cristae biogenesis. Through divergence, different ATP synthase architectures evolved, with the subunit-e/g module functioning as an oligomerization (type I) or dimerization (type IV) motif, resulting in distinct row assemblies between mitochondrial lineages.
+
+Materials and Methods
+
+Cell culture and isolation of mitochondria
+T. brucei procyclic strains were cultured in SDM-79 medium supplemented with 10% (v/v) fetal bovine serum. For growth curves in glucose-free conditions, cells were grown in SDM-80 medium with 10 % dialysed FBS. RNAi cell lines were grown in presence of 2.5 μg/ml phleomycin and 1 μg/ml puromycin. For ATP synthase purification, mitochondria were isolated from the Lister strain 427. Typically, 1.5×10^11 cells were harvested, washed in 20 mM sodium phosphate buffer pH 7.9 with 150 mM NaCl and 20 mM glucose, resuspended in hypotonic buffer 1 mM Tris-HCl pH 8.0, 1 mM EDTA, and disrupted by 10 strokes in a 40-ml Dounce homogenizer. The lysis was stopped by immediate addition of sucrose to 0.25 M. Crude mitochondria were pelleted (15 min at 16,000 xg, 4°C), resuspended in 20 mM Tris-HCl pH 8.0, 250 mM sucrose, 5 mM MgCl2, 0.3 mM CaCl2 and treated with 5 μg/ml DNase I. After 60 min on ice, one volume of the STE buffer (20 mM Tris-HCl pH 8.0, 250 mM sucrose, 2 mM EDTA) was added and mitochondria were pelleted (15 min at 16000 xg, 4°C). The pellet was resuspended in 60% (v/v) Percoll in STE and loaded on six linear 10-35% Percoll gradients in STE in polycarbonate tubes for SW28 rotor (Beckman). Gradients were centrifuged for 1 h at 24,000 rpm, 4°C. The middle phase containing mitochondrial vesicles (15-20 ml per tube) was collected, washed four times in the STE buffer, and pellets were snap-frozen in liquid nitrogen and stored at -80°C.
+
+Plasmid construction and generation of RNAi cell lines
+To downregulate ATP synthase subunits by RNAi, DNA fragments corresponding to individual target sequences were amplified by PCR from Lister 427 strain genomic DNA using
+forward and reverse primers extended with restriction sites XhoI&KpnI and XbaI&BamHI, respectively (Extended Data Table 3). Each fragment was inserted into the multiple cloning sites 1 and 2 of pAZ0055 vector, derived from pRHIVG-SSL (courtesy of Sam Alsford) by replacement of hygromycin resistance gene with phleomycin resistance gene, with restriction enzymes KpnI/BamHI and XhoI/XbaI, respectively. Resulting constructs with tetracycline inducible T7 polymerase driven RNAi cassettes were linearized with NotI and transfected into a cell line derived from the Lister strain 427 by integration of the SmOx construct for expression of T7 polymerase and the tetracycline repressor37 into the β-tubulin locus. RNAi was induced in selected semi-clonal populations by addition of 1 μg/ml tetracycline and the downregulation of target mRNAs was verified by quantitative RT-PCR 2 and 4 days post induction. The total RNA isolated by an RNeasy Mini Kit (Qiagen) was treated with 2 μg of DNase I, and then reverse transcribed to cDNA with TaqMan Reverse Transcription kit (Applied Biosciences). qPCR reactions were set with Light Cycler 480 SYBR Green I Master mix (Roche), 2 μl of cDNA and 0.3 μM primers (Extended Data Table 3), and run on LightCycler 480 (Roche). Relative expression of target genes was calculated using - ΔΔCt method with 18S rRNA or β-tubulin as endogenous reference genes and normalized to noninduced cells.
+
+Denaturing and blue native polyacrylamide electrophoresis and immunoblotting
+
+Whole cell lysates for denaturing sodium dodecyl sulphate polyacrylamide electrophoresis (SDS-PAGE) were prepared from cells resuspended in PBS buffer (10 mM phosphate buffer, 130 mM NaCl, pH 7.3) by addition of 3x Laemmli buffer (150 mM Tris pH 6.8, 300 mM 1,4-dithiothreitol, 6% (w/v) SDS, 30% (w/v) glycerol, 0.02% (w/v) bromophenol blue) to final concentration of 1×10^7 cells in 30 μl. The lysates were boiled at 97°C for 10 min and stored at -20°C. For immunoblotting, lysates from 3×10^6 cells were separated on 4-20 % gradient Tris-glycine polyacrylamide gels (BioRad 4568094), electroblotted onto a PVDF membrane (Pierce 88518), and probed with respective antibodies (Extended Data Table 4). Membranes were incubated with the Clarity Western ECL substrate (BioRad 1705060EM) and chemiluminescence was detected on a ChemiDoc instrument (BioRad). Band intensities were quantified densitometrically using the ImageLab software. The levels of individual subunits were normalized to the signal of mtHsp70.
+
+Blue native PAGE (BN-PAGE) was performed as described earlier12 with following modifications. Crude mitochondrial vesicles from 2.5 × 10^8 cells were resuspended in 40 μl of Solubilization buffer A (2 mM ε-aminocaproic acid (ACA), 1 mM EDTA, 50 mM NaCl, 50 mM Bis-Tris/HCl, pH 7.0) and solubilized with 2% (w/v) dodecylmaltoside (β-DDM) for 1 h on ice. Lysates were cleared at 16,000 g for 30 min at 4°C and their protein concentration was estimated using bicinchoninic acid assay. For each time point, a volume of mitochondrial lysate corresponding to 4 μg of total protein was mixed with 1.5 μl of loading dye (500 mM ACA, 5% (w/v) Coomassie Brilliant Blue G-250) and 5% (w/v) glycerol and with 1 M ACA until a final volume of 20 μl/well, and resolved on a native PAGE 3-12% Bis-Tris gel (Invitrogen). After the electrophoresis (3 h, 140 V, 4°C), proteins were transferred by electroblotting onto a
+PVDF membrane (2 h, 100 V, 4°C, stirring), followed by immunodetection with an appropriate antibody (Extended Data Table 4).
+
+Mitochondrial membrane polarization measurement
+
+The capacity to polarize mitochondrial membrane was determined fluorometrically employing safranin O dye (Sigma S2255) in permeabilized cells. For each sample, 2×10^7 cells were harvested and washed with ANT buffer (8 mM KCl, 110 mM K-gluconate, 10 mM NaCl, 10 mM free-acid Hepes, 10 mM K_2HPO_4, 0.015 mM EGTA potassium salt, 10 mM mannitol, 0.5 mg/ml fatty acid-free BSA, 1.5 mM MgCl_2, pH 7.25). The cells were permeabilized by 8 μM digitonin in 2 ml of ANT buffer containing 5 μM safranin O. Fluorescence was recorded for 700 s in a Hitachi F-7100 spectrofluorimeter (Hitachi High Technologies) at a 5-Hz acquisition rate, using 495 nm and 585 nm excitation and emission wavelengths, respectively. 1 mM ATP (PanReac AppliChem A1348,0025) and 10 μg/ml oligomycin (Sigma O4876) were added after 230 s and 500 s, respectively. Final addition of the uncoupler SF 6847 (250 nM; Enzo Life Sciences BML-EI215-0050) served as a control for maximal depolarization. All experiments were performed at room temperature and constant stirring.
+
+ATP production assay
+
+ATP production in digitonin-isolated mitochondria was performed as described previously38. Briefly, 1×10^8 cells per time point were lysed in SoTE buffer (600 mM sorbitol, 2 mM EDTA, 20 mM Tris-HCl, pH 7.75) containing 0.015% (w/v) digitonin for 5 min on ice. After centrifugation (3 min, 4,000 g, 4°C), the soluble cytosolic fraction was discarded and the organellar pellet was resuspended in 75 μl of ATP production assay buffer (600 mM sorbitol, 10 mM MgSO_4, 15 mM potassium phosphate buffer pH 7.4, 20 mM Tris-HCl pH 7.4, 2.5 mg/ml fatty acid-free BSA). ATP production was induced by addition of 20 mM DL-glycerol phosphate (sodium salt) and 67 μM ADP. Control samples were preincubated with the inhibitors potassium cyanide (1 mM) and carboxyatractyloside (6.5 μM) for 10 min at room temperature. After 30 min at room temperature, the reaction was stopped by addition of 1.5 μl of 70% perchloric acid. The concentration of ATP was estimated using the Roche ATP Bioluminescence Assay Kit HS II in a Tecan Spark plate reader. The luminescence values of the RNAi induced samples were normalized to that of the corresponding noninduced sample.
+
+Thin sectioning and transmission electron microscopy
+
+The samples were centrifuged and pellet was transferred to the specimen carriers which were completed with 20% BSA and immediately frozen using high pressure freezer Leica EM ICE (Leica Microsystems). Freeze substitution was performed in the presence of 2% osmium tetroxide diluted in 100% acetone at -90°C. After 96 h, specimens were warmed to -20°C at a slope 5 °C/h. After the next 24 h, the temperature was increased to 3°C (3°C/h). At room temperature, samples were washed in acetone and infiltrated with 25%, 50%, 75% acetone/resin EMbed 812 (EMS) mixture 1 h at each step. Finally, samples were infiltrated in 100% resin and polymerized at 60°C for 48h. Ultrathin sections (70 nm) were cut using a
+diamond knife, placed on copper grids and stained with uranyl acetate and lead citrate. TEM micrographs were taken with Mega View III camera (SIS) using a JEOL 1010 TEM operating at an accelerating voltage of 80 kV.
+
+Purification of T. brucei ATP synthase dimers
+
+Mitochondria from 3×10^{11} cells were lysed by 1 % (w/v) β-DDM in 60 ml of 20 mM Bis-tris propane pH 8.0 with 10 % glycerol and EDTA-free Complete protease inhibitors (Roche) for 20 min at 4°C. The lysate was cleared by centrifugation at 30,000 xg for 20 min at 4°C and adjusted to pH 6.8 by drop-wise addition of 1 M 3-(N-morpholino) propanesulfonic acid pH 5.9. Recombinant TblF_1 without dimerization region, whose affinity to F_1-ATPase was increased by N-terminal truncation and substitution of tyrosine 36 with tryptophan^{20}, with a C-terminal glutathione S-transferase (GST) tag (TblF_1(9-64)-Y36W-GST) was added in approximately 10-fold molar excess over the estimated content of ATP synthase. Binding of TblF_1 was facilitated by addition of neutralized 2 mM ATP with 4 mM magnesium sulphate. After 5 min, sodium chloride was added to 100 mM, the lysate was filtered through a 0.2 μm syringe filter and immediately loaded on 5 ml GSTrap HP column (Cytiva) equilibrated in 20 mM Bis-Tris-Propane pH 6.8 binding buffer containing 0.1 % (w/v) glyco-diosgenin (GDN; Avanti Polar Lipids), 10 % (v/v) glycerol, 100 mM sodium chloride, 1 mM tris(2-carboxyethyl)phosphine (TCEP), 1 mM ATP, 2 mM magnesium sulphate, 15 μg/ml cardiolipin, 50 μg/ml 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC), 25 μg/ml 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphoethanolamine (POPE) and 10 μg/ml 1-palmitoyl-2-oleoyl-sn-glycero-3-[phospho-rac-(1-glycerol)] (POPG). All phospholipids were purchased from Avanti Polar Lipids (catalog numbers 840012C, 850457C, 850757C and 840757, respectively). ATP synthase was eluted with a gradient of 20 mM reduced glutathione in Tris pH 8.0 buffer containing the same components as the binding buffer. Fractions containing ATP synthase were pooled and concentrated to 150 μl on Vivaspin centrifugal concentrator with 30 kDa molecular weight cut-off. The sample was fractionated by size exclusion chromatography on a Superose 6 Increase 3.2/300 GL column (Cytiva) equilibrated in a buffer containing 20 mM Tris pH 8.0, 100 mM sodium chloride, 2 mM magnesium chloride, 0.1 % (w/v) GDN, 3.75 μg/ml cardiolipin, 12.5 μg/ml POPC, 6.25 μg/ml POPE and 2.5 μg/ml POPG at 0.03 ml/min. Fractions corresponding to ATP synthase were pooled, supplemented with 0.05% (w/v) β-DDM that we and others experimentally found to better preserve dimer assemblies in cryo-EM^{39}, and concentrated to 50 μl.
+
+Preparation of cryo-EM grids and data collection
+
+Samples were vitrified on glow-discharged Quantifoil R1.2/1.3 Au 300-mesh grids after blotting for 3 sec, followed by plunging into liquid ethane using a Vitrobot Mark IV. 5,199 movies were collected using EPU 1.9 on a Titan Krios (ThermoFisher Scientific) operated at 300 kV at a nominal magnification of 165 kx (0.83 Å/pixel) with a Quantum K2 camera (Gatan) using a slit width of 20 eV. Data was collected with an exposure rate of 3.6 electrons/px/s, a total exposure of 33 electrons/Å^2 and 20 frames per movie.
+Image processing
+
+Image processing was performed within the Scipion 2 framework40, using RELION-3.0 unless specified otherwise. Movies were motion-corrected using the RELION implementation of the MotionCor2. 294,054 particles were initially picked using reference-based picking in Gautomatch (http://www.mrc-lmb.cam.ac.uk/kzhang/Gautomatch) and Contrast-transfer function parameters were using GCTF41. Subsequent image processing was performed in RELION-3.0 and 2D and 3D classification was used to select 100,605 particles, which were then extracted in an unbinned 560-pixel box (Fig. S1). An initial model of the ATP synthase dimer was obtained using de novo 3D model generation. Using masked refinement with applied C2 symmetry, a 2.7-Å structure of the membrane region was obtained following per-particle CTF refinement and Bayesian polishing. Following C2-symmetry expansion and signal subtraction of one monomer, a 3.7 Å map of the peripheral stalk was obtained. Using 3D classification (T=100) of aligned particles, with a mask on the F1/c-ring region, 10 different rotational substates were then separated and maps at 3.5-4.3 Å resolution were obtained using 3D refinement. The authors note that the number of classes identified in this study likely reflects the limited number of particles, rather than the complete conformational space of the complex. By combining particles from all states belonging to main rotational state 1, a 3.7-Å map of the rotor and a 3.2-Å consensus map of the complete ATP synthase dimer with both rotors in main rotational state 1 were obtained.
+
+Model building, refinement and data visualization
+
+An initial atomic model of the static F0 membrane region was built automatically using Bucaneer42. Subunits were subsequently assigned directly from the cryo-EM map, 15 of them corresponding to previously identified T. brucei ATP synthase subunits21, while three subunits (ATPTB14, ATPEG3, ATPEG4) were newly identified using BLAST searches. Manual model building was performed in Coot using the T. brucei F1 (PDB 6F5D)13 and homology models43 of the E. gracilis OSCP and c-ring (PDB 6TDU)10 as starting models. Ligands were manually fitted to the map and restraints were generated by the GRADE server (http://grade.globalphasing.org). Real-space refinement was performed in PHENIX using auto-sharpened, local-resolution-filtered maps of the membrane region, peripheral stalk tip, c-ring/central stalk and F1F0 monomers in different rotational states, respectively, using secondary structure restraints. Model statistics were generated using MolProbity44 and EMRinger45 Finally, the respective refined models were combined into a composite ATP synthase dimer model and real-space refined against the local-resolution-filtered consensus ATP synthase dimer map with both monomers in rotational state 1, applying reference restraints. Figures of the structures were prepared using ChimeraX46, the proton half-channels were traced using HOLLOW47.
+
+Data availability
+
+The atomic coordinates have been deposited in the Protein Data Bank (PDB) and are available under the accession codes: XXXX (membrane-region), XXXX (peripheral stalk), XXXX (rotor), XXXX (F1Fo dimer), XXXX (rotational state 1a), XXXX (rotational state 1b), XXXX
+(rotational state 1c), XXXX (rotational state 1d), XXXX (rotational state 1e), XXXX (rotational state 2a), XXXX (rotational state 2b), XXXX (rotational state 2c), XXXX (rotational state 2d), XXXX (rotational state 3). The local resolution filtered cryo-EM maps, half maps, masks and FSC-curves have been deposited in the Electron Microscopy Data Bank with the accession codes: EMD-XXXX (membrane-region), EMD-XXXX (peripheral stalk), EMD-XXXX (rotor), EMD-XXXX (F₁F₀ dimer), EMD-XXXX (rotational state 1a), EMD-XXXX (rotational state 1b), EMD-XXXX (rotational state 1c), EMD-XXXX (rotational state 1d), EMD-XXXX (rotational state 1e), EMD-XXXX (rotational state 2a), EMD-XXXX (rotational state 2b), EMD-XXXX (rotational state 2c), EMD-XXXX (rotational state 2d), EMD-XXXX (rotational state 3).
+
+Acknowledgements
+
+We are grateful to Sir John E. Walker and Martin Montgomery for invaluable assistance with ATP synthase purification in the initial stage of the project. We acknowledge cryo-electron microscopy and tomography core facility of CIISB, Instruct-CZ Centre, supported by MEYS CR (LM2018127). This work was supported by the Czech Science Foundation grants number 18-17529S to A.Z. and 20-04150Y to O.G. and by European Regional Development Fund (ERDF) and Ministry of Education, Youth and Sport (MEYS) project CZ.02.1.01/0.0/0.0/16_019/0000759 to A.Z., Swedish Foundation for Strategic Research (FFL15:0325), Ragnar Söderberg Foundation (M44/16), European Research Council (ERC-2018-StG-805230), Knut and Alice Wallenberg Foundation (2018.0080), and EMBO Young Investigator Programme to A.A.
+
+Author contributions
+
+A.Z. and A.A. conceived and designed the work. O.G. prepared the sample for cryo-EM. O.G. and A.M. performed initial screening. A.M. processed the cryo-EM data and built the model. O.G., A.M. and A.A. analyzed the structure. B.P., C.H.Y., M.J., M.S., O.G. and A.Z. performed biochemical analysis. O.G., A.M., A.A. and A.Z. interpreted the data. O.G., A.M., A.A. and A.Z. wrote and revised the manuscript. All authors contributed to the analysis and approved the final version of the manuscript.
+
+Competing interests
+
+The authors declare no competing interests.
+
+References
+
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+12. Gahura, O. et al. The F_1-ATPase from Trypanosoma brucei is elaborated by three copies of an additional p18-subunit. FEBS J 285, 614-628 (2018).
+13. Montgomery, M.G., Gahura, O., Leslie, A.G.W., Zikova, A. & Walker, J.E. ATP synthase from Trypanosoma brucei has an elaborated canonical F_1-domain and conventional catalytic sites. Proc Natl Acad Sci U S A 115, 2102-2107 (2018).
+14. Serricchio, M. et al. Depletion of cardiolipin induces major changes in energy metabolism in Trypanosoma brucei bloodstream forms. FASEB J 35, 21176 (2020).
+15. Muhleip, A.W., Dewar, C.E., Schnaufer, A., Kuhlbrandt, W. & Davies, K.M. In situ structure of trypanosomal ATP synthase dimer reveals a unique arrangement of catalytic subunits. Proc Natl Acad Sci U S A 114, 992-997 (2017).
+16. Schnaufer, A., Clark-Walker, G.D., Steinberg, A.G. & Stuart, K. The F_1-ATP synthase complex in bloodstream stage trypanosomes has an unusual and essential function. EMBO J 24, 4029-40 (2005).
+17. Brown, S.V., Hosking, P., Li, J. & Williams, N. ATP synthase is responsible for maintaining mitochondrial membrane potential in bloodstream form Trypanosoma brucei. Eukaryot Cell 5, 45-53 (2006).
+18. Gahura, O., Hierro-Yap, C. & Zikova, A. Redesigned and reversed: Architectural and functional oddities of the trypanosomal ATP synthase. Parasitology 148, 1151-1160 (2021).
+19. Hierro-Yap, C. et al. Bioenergetic consequences of F_oF_1-ATP synthase/ATPase deficiency in two life cycle stages of Trypanosoma brucei. J Biol Chem 296, 100357 (2021).
+20. Gahura, O., Panicucci, B., Vachova, H., Walker, J.E. & Zikova, A. Inhibition of F₁-ATPase from Trypanosoma brucei by its regulatory protein inhibitor TbIF1. FEBS J 285, 4413-4423 (2018).
+21. Zikova, A., Schnaufer, A., Dalley, R.A., Panigrahi, A.K. & Stuart, K.D. The F(0)F(1)-ATP synthase complex contains novel subunits and is essential for procyclic Trypanosoma brucei. PLoS Pathog 5, e1000436 (2009).
+22. Perez, E. et al. The mitochondrial respiratory chain of the secondary green alga Euglena gracilis shares many additional subunits with parasitic Trypanosomatidae. Mitochondrion 19 Pt B, 338-49 (2014).
+23. Sathish Yadav, K.N. et al. Atypical composition and structure of the mitochondrial dimeric ATP synthase from Euglena gracilis. Biochim Biophys Acta 1858, 267-275 (2017).
+24. Dewar, C.E., Oeljeklaus, S., Warscheid, B. and Schneider, A. Characterisation of a highly diverged mitochondrial ATP synthase peripheral stalk subunit b in Trypanosoma brucei (2021). https://www.biorxiv.org/content/10.1101/2021.10.13.464200v1
+25. Aphasiszheva, I. et al. Lexis and Grammar of Mitochondrial RNA Processing in Trypanosomes. Trends Parasitol 36, 337-355 (2020).
+26. Blum, B., Bakalara, N. & Simpson, L. A model for RNA editing in kinetoplastid mitochondria: "guide" RNA molecules transcribed from maxicircle DNA provide the edited information. Cell 60, 189-98 (1990).
+27. Adler, B.K., Harris, M.E., Bertrand, K.I. & Hajduk, S.L. Modification of Trypanosoma brucei mitochondrial rRNA by posttranscriptional 3' polyuridine tail formation. Mol Cell Biol 11, 5878-84 (1991).
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+29. Gupta, K. et al. The role of interfacial lipids in stabilizing membrane protein oligomers. Nature 541, 421-424 (2017).
+30. Arnold, I., Pfeiffer, K., Neupert, W., Stuart, R.A. & Schagger, H. Yeast mitochondrial F₁F₀-ATP synthase exists as a dimer: identification of three dimer-specific subunits. EMBO J 17, 7170-8 (1998).
+31. Gu, J. et al. Cryo-EM structure of the mammalian ATP synthase tetramer bound with inhibitory protein IF1. Science 364, 1068-1075 (2019).
+32. Spikes, T.E., Montgomery, M.G. & Walker, J.E. Interface mobility between monomers in dimeric bovine ATP synthase participates in the ultrastructure of inner mitochondrial membranes. Proc Natl Acad Sci U S A 118, e2021012118 (2021).
+33. Cadena, L.R. et al. Mitochondrial contact site and cristae organization system and F₁F₀-ATP synthase crosstalk is a fundamental property of mitochondrial cristae. mSphere 6, e0032721 (2021).
+34. Davies, K.M. et al. Macromolecular organization of ATP synthase and complex I in whole mitochondria. Proc Natl Acad Sci U S A 108, 14121-6 (2011).
+35. Blum, T.B., Hahn, A., Meier, T., Davies, K.M. & Kühlbrandt, W. Dimers of mitochondrial ATP synthase induce membrane curvature and self-assemble into rows. Proc Natl Acad Sci U S A **116**, 4250-4255 (2019).
+36. Bochud-Allemann, N. & Schneider, A. Mitochondrial substrate level phosphorylation is essential for growth of procyclic *Trypanosoma brucei*. *J Biol Chem* **277**, 32849-54 (2002).
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+38. Allemann, N. & Schneider, A. ATP production in isolated mitochondria of procyclic Trypanosoma brucei. *Mol Biochem Parasitol* **111**, 87-94 (2000).
+39. Aibara, S., Dienemann, C., & Cramer, P.. Structure of an inactive RNA polymerase II dimer. *Nucleic Acids Research*, gkab783 (2021).
+40. de la Rosa-Trevin, J.M. et al. Scipion: A software framework toward integration, reproducibility and validation in 3D electron microscopy. *J Struct Biol* **195**, 93-9 (2016).
+41. Zhang, K. Gctf: Real-time CTF determination and correction. *J Struct Biol* **193**, 1-12 (2016).
+42. Cowtan, K. The Buccaneer software for automated model building. 1. Tracing protein chains. *Acta Crystallogr D Biol Crystallogr* **62**, 1002-11 (2006).
+43. Waterhouse, A. et al. SWISS-MODEL: homology modelling of protein structures and complexes. *Nucleic Acids Res* **46**, W296-W303 (2018).
+44. Williams, C.J., Headd, J.J., Moriarty, N.W., Prisant, M.G., Videau, L.L., Deis, L.N., Verma, V., Keedy, D.A., Hintze, B.J., Chen, V.B. and Jain, S. MolProbity: More and better reference data for improved all-atom structure validation. *Protein Science*, **27**, 293-315 (2018).
+45. Barad, B.A., Echols, N., Wang, R.Y.R., Cheng, Y., DiMaio, F., Adams, P.D. and Fraser, J.S. EMRinger: side chain–directed model and map validation for 3D cryo-electron microscopy. *Nature methods*, **12**, 943-946 (2015).
+46. Goddard, T.D. et al. UCSF ChimeraX: Meeting modern challenges in visualization and analysis. *Protein Sci* **27**, 14-25 (2018).
+47. Ho, B.K. & Gruswitz, F. HOLLOW: generating accurate representations of channel and interior surfaces in molecular structures. *BMC Struct Biol* **8**, 49 (2008).
+Extended Data Fig. 1 Purification of the T. brucei ATP synthase dimer.
+a, Size exclusion chromatography trace with peaks enriched with ATP synthase dimers (D), monomers (M) and F_1-ATPase (F_1) labelled. b, Fractions from size exclusion chromatography marked with green bar in (a) resolved by native BN-PAGE. c, Dimer-enriched fraction resolved by SDS-PAGE stained by Coomassie blue dye. Bands are annotated based on mass spectrometry identification from excised gel pieces.
+Extended Data Fig. 2 Cryo-EM data processing of the T. brucei ATP synthase dimer.
+a, Representative micrograph. b, 2D class averages. c, Fourier Shell Correlation (FSC) curves showing the estimated resolutions of ATP synthase maps according to the gold standard 0.143 criterion. d, Data processing scheme resulting in maps covering all regions of the complex, as well as 10 rotational states.
+Extended Data Fig. 3 Conserved and phylum specific elements generate the T. brucei ATP synthase architecture.
+The canonical OSCP/F₁/c-ring monomers (dark grey) are tied together by both conserved F₀ subunits and extensions of lineage-specific subunits (red). The F₀ periphery and peripheral stalk attachment are composed of lineage specific subunits (blue).
+
+![Conserved and phylum specific elements generate the T. brucei ATP synthase architecture.](page_186_120_1077_349.png)
+Extended Data Fig. 4 The F_o region coordinates numerous bound lipids.
+a, F_o top view, cardiolipin (CDL), phosphatidylcholine (PC) and phosphatidylethanolamine (PE) are bound at the dimer interface, the luminal proton half-channel and the peripheral F_o cavity. b, The 60°-dimer angle generates a curved F_o region with phospholipids bound in an arc-shaped bilayer. c-f, Bound lipids with cryo-EM density and coordinating residues.
+Extended Data Fig. 5 Bound detergents of the F_o region.
+GDN (a,b) and β-DDM (c,d) molecules bound in the periphery of the membrane region with cryo-EM map densities shown (transparent), indicating that both glycosides are retained in the detergent micelle.
+PDB_6TDV_su-b_E.gracilis tr|Q580A0|Q580A0_TRYB2    DKDVPMISLHTHGLSYVNWCMSLAPGLLVFEGFRARYYRSRVPEPSRTVL RRLVPVRVMAMPGGA-TALCTSRYGNMLVFRDPK----------RRPQL : ** :: * : . * * . .:***.. * . *
+
+PDB_6TDV_su-b_E.gracilis tr|Q580A0|Q580A0_TRYB2    MNGLKMRMFSLARQQAPKIVHK----------PVLSP1PEHLRLVKNVASDEE----------RAKVVVNQAEWPEEFKDFDPDPYKNSPEIIGMS : .*:* : * : .::*::
+
+PDB_6TDV_su-b_E.gracilis tr|Q580A0|Q580A0_TRYB2    QVQIDMLKLNNQAQAK SWNLFLWGVECAFIYQ . :: : : * :
+
+Extended Data Fig. 6 Sequence alignment of subunit-b with E. gracilis.
+The E. gracilis sequence was retrieved from the PDB ID 6TDV\(^1\) and aligned with the current work using ClustalW\(^2\). Both sequences represent reduced versions of subunit-b that are structurally conserved and occupy similar positions in the models. Termini were removed.
+Extended Data Fig. 7 The C-terminal tail of subunit-e interacts with the c_{10}-ring.
+a, The cryo-EM map reveals disordered detergent density of the detergent belt surrounding the membrane region as well as a detergent plug on the luminal side of the c-ring. b, The helical C-terminus of subunit-e extends into the lumen towards the c-ring. The terminal 23 residues are disordered and likely interact with the β-barrel.
+
+![Cryo-EM map showing the interaction between the C-terminal tail of subunit-e and the c_{10}-ring](page_186_154_1077_393.png)
+Extended Data Fig. 8 Phylogenetic distribution and sequence conservancy of subunit-e and -g.
+
+a. Distribution of subunits e and g mapped on the phylogenetic tree of eukaryotes3. Homologs of subunits e and g were searched in non-redundant GenBank and UniprotKB protein databases by PSI-BLAST, and phmmmer and hmmsearch4, respectively, using individual sequences of representatives from H. sapiens and T. brucei, and in the case of hmmsearch a multiple sequence alignment (MSA) of representatives from Homo sapiens, Saccharomyces cerevisiae, Arabidopsis thaliana and T. brucei, as queries. Groups, in which at least one structure of ATP synthase is available, are marked. Abbreviations of species used in MSA in panels (c) and (d) are shown. b. Sequence logo of GXXXXG motifs and flanking regions of subunits e and g. Hits from hmmsearch were clustered by CD-HIT Suite5 to 50% sequence identity and MSA of representative sequences of each cluster was generated by Clustal Omega46. The sequence logos were created from MSA in Geneious Prime (Biomatters Ltd.). c,d, MSA of sequences of subunits g (c) and e (d) from species representing major groups shown in (a) generated by MUSCLE7 and visualized in Geneious Prime. The experimentally determined or predicted transmembrane regions are highlighted in yellow. Species abbreviations: Tb – T. brucei, Hs – H. sapiens, Sc – S. cerevisiae, Sr – Salpingoeca rosetta, Tt – Thecamonas trahens, Dd – Dictyostelium discoideum, Cm – Cyanidioschyzon merolae, Cv – Chlorella vulgaris, At – Arabidopsis thaliana, Os – Oryza sativa.
+a
+su-e RNAi
+
+su-f RNAi
+
+su-i/j RNAi
+
+su-k RNAi
+
+ATPTB3 RNAi
+
+b
+
+DPI 0 2 4
+su-β   ATPTB1   su-d
+
+c
+
+DPI 0 2 4
+su-β   p18   ATPTB1   su-d   Hsp70
+Extended Data Fig. 9 Effects of RNAi knock-down of ATP synthase subunits on viability and stability and dimerization of ATP synthase.
+
+a, Growth curves of indicated non-induced (solid lines) and tetracycline induced (dashed lines) RNAi cells lines in the presence (black) or absence (brown) of glucose. The insets show relative levels of the respective target mRNA at indicated days post induction (DPI) normalized to the levels of 18S rRNA (black bars) or β-tubulin (white bars). b, Immunoblots of mitochondrial lysates from indicated RNAi cell lines resolved by BN-PAGE probed by antibodies against indicated ATP synthase subunits. c, Immunoblots of whole cell lysates from indicated RNAi cell lines probed with indicated antibodies.
+<table>
+  <tr>
+    <th>Membrane region</th>
+    <th>Rotor</th>
+    <th>Peripheral stalk</th>
+    <th>F1/F0 dimer</th>
+    <th>Rot. 1a</th>
+    <th>Rot. 1b</th>
+    <th>Rot. 1c</th>
+    <th>Rot. 1d</th>
+    <th>Rot. 1e</th>
+    <th>Rot. 2a</th>
+    <th>Rot. 2b</th>
+    <th>Rot. 2c</th>
+    <th>Rot. 2d</th>
+    <th>Rot. 3</th>
+  </tr>
+  <tr>
+    <th colspan="15">Data collection</th>
+  </tr>
+  <tr>
+    <td>Microscope</td>
+    <td colspan="14">Titan Krios</td>
+  </tr>
+  <tr>
+    <td>Voltage (kV)</td>
+    <td colspan="14">300</td>
+  </tr>
+  <tr>
+    <td>Camera</td>
+    <td colspan="14">K2 Summit</td>
+  </tr>
+  <tr>
+    <td>Magnification</td>
+    <td colspan="14">165 kx</td>
+  </tr>
+  <tr>
+    <td>Exposure (e/Å<sup>2</sup>)</td>
+    <td colspan="14">33</td>
+  </tr>
+  <tr>
+    <td>Defocus range (μm)</td>
+    <td colspan="14">-1.6 to -3.2</td>
+  </tr>
+  <tr>
+    <td>Pixel size (Å)</td>
+    <td colspan="14">0.83</td>
+  </tr>
+  <tr>
+    <td>Movies collected</td>
+    <td colspan="14">5,199</td>
+  </tr>
+  <tr>
+    <td>Frames per movie</td>
+    <td colspan="14">20</td>
+  </tr>
+  <tr>
+    <th colspan="15">Data processing</th>
+  </tr>
+  <tr>
+    <th>Initial particles</th>
+    <td colspan="14">100,605 (C<sub>2</sub> symmetry-expanded: 201,210)</td>
+  </tr>
+  <tr>
+    <td>Symmetry</td>
+    <td>C<sub>2</sub></td>
+    <td>C<sub>1</sub></td>
+    <td>C<sub>1</sub></td>
+    <td>C<sub>2</sub></td>
+    <td>C<sub>1</sub></td>
+    <td>C<sub>1</sub></td>
+    <td>C<sub>1</sub></td>
+    <td>C<sub>1</sub></td>
+    <td>C<sub>1</sub></td>
+    <td>C<sub>1</sub></td>
+    <td>C<sub>1</sub></td>
+    <td>C<sub>1</sub></td>
+    <td>C<sub>1</sub></td>
+    <td>C<sub>1</sub></td>
+  </tr>
+  <tr>
+    <td>Map resolution (Å)</td>
+    <td>2.7</td>
+    <td>3.7</td>
+    <td>3.7</td>
+    <td>3.2</td>
+    <td>3.7</td>
+    <td>3.5</td>
+    <td>3.7</td>
+    <td>3.8</td>
+    <td>3.7</td>
+    <td>4.3</td>
+    <td>3.5</td>
+    <td>3.8</td>
+    <td>3.8</td>
+    <td>3.7</td>
+    <td>3.7</td>
+  </tr>
+  <tr>
+    <td>Sharpening B factor</td>
+    <td>-46.2</td>
+    <td>-74.4</td>
+    <td>-92.5</td>
+    <td>-49.8</td>
+    <td>-61.8</td>
+    <td>-61.1</td>
+    <td>-57.6</td>
+    <td>-45.6</td>
+    <td>-58.0</td>
+    <td>-73.8</td>
+    <td>-54.5</td>
+    <td>-65.2</td>
+    <td>-54.9</td>
+    <td>-61.7</td>
+  </tr>
+  <tr>
+    <th>EMD ID</th>
+    <td colspan="14"></td>
+  </tr>
+  <tr>
+    <th colspan="15">Model refinement statistics</th>
+  </tr>
+  <tr>
+    <td>CC (map/model)</td>
+    <td>0.86</td>
+    <td>0.83</td>
+    <td>0.82</td>
+    <td>0.71</td>
+    <td>0.79</td>
+    <td>0.79</td>
+    <td>0.82</td>
+    <td>0.79</td>
+    <td>0.69</td>
+    <td>0.71</td>
+    <td>0.81</td>
+    <td>0.77</td>
+    <td>0.77</td>
+    <td>0.79</td>
+  </tr>
+  <tr>
+    <td>Resolution (map/model)</td>
+    <td>2.65</td>
+    <td>3.4</td>
+    <td>3.68</td>
+    <td>3.13</td>
+    <td>3.48</td>
+    <td>3.36</td>
+    <td>3.36</td>
+    <td>3.55</td>
+    <td>3.57</td>
+    <td>3.94</td>
+    <td>3.39</td>
+    <td>3.73</td>
+    <td>3.64</td>
+    <td>3.58</td>
+  </tr>
+  <tr>
+    <td>No. of atoms</td>
+    <td>76,690</td>
+    <td>19,669</td>
+    <td>12,083</td>
+    <td>251,552</td>
+    <td>129,568</td>
+    <td>129,568</td>
+    <td>129,568</td>
+    <td>129,568</td>
+    <td>129,568</td>
+    <td>129,563</td>
+    <td>129,563</td>
+    <td>129,563</td>
+    <td>129,563</td>
+    <td>129,566</td>
+  </tr>
+  <tr>
+    <td>No. of residues</td>
+    <td>4074</td>
+    <td>1285</td>
+    <td>767</td>
+    <td>15,356</td>
+    <td>7872</td>
+    <td>7872</td>
+    <td>7872</td>
+    <td>7872</td>
+    <td>7872</td>
+    <td>7872</td>
+    <td>7872</td>
+    <td>7872</td>
+    <td>7872</td>
+    <td>7872</td>
+  </tr>
+  <tr>
+    <td>No. of ligands</td>
+    <td>36</td>
+    <td>0</td>
+    <td>0</td>
+    <td>36</td>
+    <td>21</td>
+    <td>21</td>
+    <td>21</td>
+    <td>21</td>
+    <td>21</td>
+    <td>21</td>
+    <td>21</td>
+    <td>21</td>
+    <td>21</td>
+    <td>21</td>
+    <td>21</td>
+  </tr>
+  <tr>
+    <td>No. of ATP/ADP</td>
+    <td>0</td>
+    <td>0</td>
+    <td>0</td>
+    <td>10</td>
+    <td>5</td>
+    <td>5</td>
+    <td>5</td>
+    <td>5</td>
+    <td>5</td>
+    <td>5</td>
+    <td>5</td>
+    <td>5</td>
+    <td>5</td>
+    <td>5</td>
+    <td>5</td>
+  </tr>
+  <tr>
+    <td>No. of Mg ions</td>
+    <td>0</td>
+    <td>0</td>
+    <td>0</td>
+    <td>10</td>
+    <td>5</td>
+    <td>5</td>
+    <td>5</td>
+    <td>5</td>
+    <td>5</td>
+    <td>5</td>
+    <td>5</td>
+    <td>5</td>
+    <td>5</td>
+    <td>5</td>
+    <td>5</td>
+  </tr>
+  <tr>
+    <td>B-factor (Å<sup>2</sup>)</td>
+    <td colspan="15"></td>
+  </tr>
+  <tr>
+    <td>- protein</td>
+    <td>54.05</td>
+    <td>36.13</td>
+    <td>77.88</td>
+    <td>84.48</td>
+    <td>55.65</td>
+    <td>70.37</td>
+    <td>80.22</td>
+    <td>83.27</td>
+    <td>70.70</td>
+    <td>112.72</td>
+    <td>79.93</td>
+    <td>65.52</td>
+    <td>66.49</td>
+    <td>101.5</td>
+  </tr>
+  <tr>
+    <td>- ligands</td>
+    <td>50.57</td>
+    <td>58.25</td>
+    <td>-</td>
+    <td>69.94</td>
+    <td>40.99</td>
+    <td>72.29</td>
+    <td>63.18</td>
+    <td>78.43</td>
+    <td>63.76</td>
+    <td>75.25</td>
+    <td>74.47</td>
+    <td>61.79</td>
+    <td>46.55</td>
+    <td>83.68</td>
+  </tr>
+  <tr>
+    <td>Rotamer outliers (%)</td>
+    <td>0.44</td>
+    <td>0.40</td>
+    <td>0.31</td>
+    <td>0.22</td>
+    <td>0.42</td>
+    <td>0.09</td>
+    <td>0.18</td>
+    <td>0.26</td>
+    <td>0.58</td>
+    <td>0.18</td>
+    <td>0.27</td>
+    <td>0.48</td>
+    <td>0.42</td>
+    <td>0.39</td>
+  </tr>
+  <tr>
+    <td>Ramachandran (%)</td>
+    <td colspan="15"></td>
+  </tr>
+  <tr>
+    <td>- outliers</td>
+    <td>0.00</td>
+    <td>0.00</td>
+    <td>0.00</td>
+    <td>0.01</td>
+    <td>0.001</td>
+    <td>0.003</td>
+    <td>0.004</td>
+    <td>0.01</td>
+    <td>0.003</td>
+    <td>0.01</td>
+    <td>0.00</td>
+    <td>0.04</td>
+    <td>0.04</td>
+    <td>0.04</td>
+  </tr>
+  <tr>
+    <td>- allowed</td>
+    <td>1.37</td>
+    <td>1.91</td>
+    <td>1.59</td>
+    <td>1.56</td>
+    <td>1.52</td>
+    <td>1.65</td>
+    <td>1.44</td>
+    <td>1.49</td>
+    <td>1.49</td>
+    <td>1.67</td>
+    <td>1.58</td>
+    <td>1.47</td>
+    <td>1.65</td>
+    <td>1.79</td>
+  </tr>
+  <tr>
+    <td>- favored</td>
+    <td>98.43</td>
+    <td>98.08</td>
+    <td>98.41</td>
+    <td>98.42</td>
+    <td>98.47</td>
+    <td>98.34</td>
+    <td>98.36</td>
+    <td>98.49</td>
+    <td>98.48</td>
+    <td>98.31</td>
+    <td>98.42</td>
+    <td>98.49</td>
+    <td>98.31</td>
+    <td>98.17</td>
+  </tr>
+  <tr>
+    <td>Clash score</td>
+    <td>1.66</td>
+    <td>2.44</td>
+    <td>2.32</td>
+    <td>2.26</td>
+    <td>2.60</td>
+    <td>2.65</td>
+    <td>2.33</td>
+    <td>2.67</td>
+    <td>2.99</td>
+    <td>2.38</td>
+    <td>2.30</td>
+    <td>2.32</td>
+    <td>2.38</td>
+    <td>3.57</td>
+  </tr>
+  <tr>
+    <td>MolProbity score</td>
+    <td>0.92</td>
+    <td>1.03</td>
+    <td>1.01</td>
+    <td>1.00</td>
+    <td>1.05</td>
+    <td>1.05</td>
+    <td>1.04</td>
+    <td>1.05</td>
+    <td>1.09</td>
+    <td>1.02</td>
+    <td>1.01</td>
+    <td>1.04</td>
+    <td>1.02</td>
+    <td>1.15</td>
+  </tr>
+  <tr>
+    <th>RMSD</th>
+    <td colspan="15"></td>
+  </tr>
+  <tr>
+    <td>- bonds (Å)</td>
+    <td>0.004</td>
+    <td>0.004</td>
+    <td>0.02</td>
+    <td>0.003</td>
+    <td>0.003</td>
+    <td>0.004</td>
+    <td>0.003</td>
+    <td>0.003</td>
+    <td>0.002</td>
+    <td>0.003</td>
+    <td>0.003</td>
+    <td>0.003</td>
+    <td>0.003</td>
+    <td>0.003</td>
+  </tr>
+  <tr>
+    <td>- angles (°)</td>
+    <td>0.455</td>
+    <td>0.416</td>
+    <td>0.386</td>
+    <td>0.407</td>
+    <td>0.414</td>
+    <td>0.424</td>
+    <td>0.417</td>
+    <td>0.407</td>
+    <td>0.412</td>
+    <td>0.410</td>
+    <td>0.416</td>
+    <td>0.419</td>
+    <td>0.428</td>
+    <td>0.421</td>
+  </tr>
+  <tr>
+    <td>EMRinger score</td>
+    <td>5.11</td>
+    <td>3.96</td>
+    <td>1.61</td>
+    <td>2.56</td>
+    <td>3.24</td>
+    <td>2.95</td>
+    <td>3.32</td>
+    <td>2.85</td>
+    <td>3.32</td>
+    <td>1.35</td>
+    <td>2.89</td>
+    <td>2.32</td>
+    <td>2.49</td>
+    <td>2.8</td>
+  </tr>
+  <tr>
+    <th>PDB ID</th>
+    <td colspan="14"></td>
+  </tr>
+</table>
+
+Extended Data Table 1. Data collection, processing, model refinement and validation statistics.
+<table>
+  <tr>
+    <th>Subunit name</th>
+    <th>TriTrypDB Lister strain 427 ID</th>
+    <th>TriTrypDB TREU927 strain ID</th>
+    <th>Uniprot TREU927 strain ID</th>
+    <th>Residues</th>
+    <th>Residues built</th>
+  </tr>
+  <tr>
+    <th colspan="6">F₁ subcomplex</th>
+  </tr>
+  <tr>
+    <td><i>α</i></td>
+    <td>Tb427_070081800<br>Tb427_070081900</td>
+    <td>Tb927.7.7420<br>Tb927.7.7430</td>
+    <td>Q57TX9</td>
+    <td>584</td>
+    <td>45-151,<br>161-584</td>
+  </tr>
+  <tr>
+    <td><i>β</i></td>
+    <td>Tb427_030013500</td>
+    <td>Tb927.3.1380</td>
+    <td>Q57XX1</td>
+    <td>519</td>
+    <td>26-514</td>
+  </tr>
+  <tr>
+    <td><i>γ</i></td>
+    <td>Tb427_100005200</td>
+    <td>Tb927.10.180</td>
+    <td>B0Z0F6</td>
+    <td>305</td>
+    <td>2-301</td>
+  </tr>
+  <tr>
+    <td><i>δ</i></td>
+    <td>Tb427_060054900</td>
+    <td>Tb927.6.4990</td>
+    <td>Q586H1</td>
+    <td>182</td>
+    <td>22-182</td>
+  </tr>
+  <tr>
+    <td><i>ε</i></td>
+    <td>Tb427_100054600</td>
+    <td>Tb427.10.5050</td>
+    <td>N/A</td>
+    <td>75</td>
+    <td>11-75</td>
+  </tr>
+  <tr>
+    <td>p18</td>
+    <td>Tb427_050022900</td>
+    <td>Tb927.5.1710</td>
+    <td>Q57ZP0</td>
+    <td>188</td>
+    <td>23-188</td>
+  </tr>
+  <tr>
+    <th colspan="6">F₀ subcomplex</th>
+  </tr>
+  <tr>
+    <td>OSCP</td>
+    <td>Tb427_100087100</td>
+    <td>Tb927.10.8030</td>
+    <td>Q38AG1</td>
+    <td>255</td>
+    <td>18-202,<br>208-255</td>
+  </tr>
+  <tr>
+    <td><i>a</i></td>
+    <td>mt encoded</td>
+    <td>mt encoded</td>
+    <td>N/A</td>
+    <td>231</td>
+    <td>1-231</td>
+  </tr>
+  <tr>
+    <td><i>b</i></td>
+    <td>Tb427_040009100</td>
+    <td>Tb927.4.720</td>
+    <td>Q580A0</td>
+    <td>105</td>
+    <td>26-105</td>
+  </tr>
+  <tr>
+    <td><i>c</i></td>
+    <td>Tb427_100018700<br>Tb427_110057900<br>Tb427_070019000</td>
+    <td>Tb927.10.1570<br>Tb927.11.5280<br>Tb927.7.1470</td>
+    <td>Q38C84<br>Q385P0<br>Q57WQ3</td>
+    <td>118</td>
+    <td>41-118</td>
+  </tr>
+  <tr>
+    <td><i>d</i></td>
+    <td>Tb427_050035800</td>
+    <td>Tb927.5.2930</td>
+    <td>Q57ZW9</td>
+    <td>370</td>
+    <td>17-325,<br>332-354</td>
+  </tr>
+  <tr>
+    <td><i>e</i></td>
+    <td>Tb427_110010200</td>
+    <td>Tb927.11.600</td>
+    <td>N/A</td>
+    <td>92</td>
+    <td>1-383</td>
+  </tr>
+  <tr>
+    <td><i>f</i></td>
+    <td>Tb427_030016600</td>
+    <td>Tb927.3.1690</td>
+    <td>Q57ZE2</td>
+    <td>145</td>
+    <td>2-136</td>
+  </tr>
+  <tr>
+    <td><i>g</i></td>
+    <td>Tb427_020016900</td>
+    <td>Tb927.2.3610</td>
+    <td>Q586X8</td>
+    <td>144</td>
+    <td>16-144</td>
+  </tr>
+  <tr>
+    <td><i>ij</i></td>
+    <td>Tb427_030029400</td>
+    <td>Tb927.3.2880</td>
+    <td>Q57ZM4</td>
+    <td>104</td>
+    <td>2-104</td>
+  </tr>
+  <tr>
+    <td><i>k</i></td>
+    <td>Tb427_070011800</td>
+    <td>Tb927.7.840</td>
+    <td>Q57VT0</td>
+    <td>124</td>
+    <td>20-124</td>
+  </tr>
+  <tr>
+    <td>8</td>
+    <td>Tb427_040037300</td>
+    <td>Tb927.4.3450</td>
+    <td>Q585K5</td>
+    <td>114</td>
+    <td>29-114</td>
+  </tr>
+  <tr>
+    <td>ATPTB1</td>
+    <td>Tb427_100008400</td>
+    <td>Tb927.10.520</td>
+    <td>Q38CI8</td>
+    <td>396</td>
+    <td>1-383</td>
+  </tr>
+  <tr>
+    <td>ATPTB3</td>
+    <td>Tb427_110067400</td>
+    <td>Tb927.11.6250</td>
+    <td>Q385E4</td>
+    <td>269</td>
+    <td>2-269</td>
+  </tr>
+  <tr>
+    <td>ATPTB4</td>
+    <td>Tb427_100105100</td>
+    <td>Tb927.10.9830</td>
+    <td>Q389Z3</td>
+    <td>157</td>
+    <td>21-157</td>
+  </tr>
+  <tr>
+    <td>ATPTB6</td>
+    <td>Tb427_110017200</td>
+    <td>Tb927.11.1270</td>
+    <td>Q387C5</td>
+    <td>169</td>
+    <td>2-169</td>
+  </tr>
+  <tr>
+    <td>ATPTB11</td>
+    <td>Tb427_030021500</td>
+    <td>Tb927.3.2180</td>
+    <td>Q582T1</td>
+    <td>156</td>
+    <td>18-156</td>
+  </tr>
+  <tr>
+    <td>ATPTB12</td>
+    <td>Tb427_050037400</td>
+    <td>Tb927.5.3090</td>
+    <td>Q57Z84</td>
+    <td>101</td>
+    <td>5-100</td>
+  </tr>
+  <tr>
+    <td>ATPEG3</td>
+    <td>Tb427_060009300</td>
+    <td>Tb927.6.590</td>
+    <td>Q583U4</td>
+    <td>98</td>
+    <td>14-98</td>
+  </tr>
+  <tr>
+    <td>ATPEG4</td>
+    <td>N/A</td>
+    <td>Tb927.11.2245</td>
+    <td>N/A</td>
+    <td>62</td>
+    <td>1-62</td>
+  </tr>
+</table>
+
+Extended Data Table 2. Composition of <i>T. brucei</i> ATP synthase dimer.
+<table>
+  <tr>
+    <th>Subunit</th>
+    <th>Primer pair sequences</th>
+  </tr>
+  <tr>
+    <th colspan="2">Primers for amplification of RNAi cassettes</th>
+  </tr>
+  <tr>
+    <td><i>b</i></td>
+    <td>TAATCTCGAGGGTACCGTTGAGTGAGGAGGAACGGG<br>GCAGTCTAGAGGATCCCTATCCCTTCCACCCACACT</td>
+  </tr>
+  <tr>
+    <td><i>e</i></td>
+    <td>TAATCTCGAGGGTACCGGGAGTACAGAAGGGCTACA<br>TAGATCTAGAGGATCCCGTGCACACCATCAGCTG</td>
+  </tr>
+  <tr>
+    <td><i>f</i></td>
+    <td>ATATCTCGAGGGTACCGTGAGTGACCGCCTTTACGC<br>GCGTCTAGAGGATCCACGACTGATCACCAAATCAGC</td>
+  </tr>
+  <tr>
+    <td><i>g</i></td>
+    <td>ACTGCTCGAGGGTACCCACCGGGAATTCAAAAAGACC<br>GCGGTCTAGAGGATCCCGTTGCCGTGCTTGTCTATTA</td>
+  </tr>
+  <tr>
+    <td><i>ij</i></td>
+    <td>TAATCTCGAGGGTACCGAATATCCGATGCGATGCCGC<br>GCCGTCTAGAGGATCCACTTCGCTCTACTGCGATGCA</td>
+  </tr>
+  <tr>
+    <td><i>k</i></td>
+    <td>ATTACTCGAGCCGGGCGATCAGTGCGAGGGGATTTT<br>GCCGTCTAGAGGATCCTTTCCTCGAAAACGCACACA</td>
+  </tr>
+  <tr>
+    <td><b>8</b></td>
+    <td>ATGACTCGAGGGTACCGGGCTATGGGTGGTATTATGC<br>GACGTCTAGAGGATCCGCAGAAACTCCCAACGACA</td>
+  </tr>
+  <tr>
+    <td>ATPTB3</td>
+    <td>ACTGCTCGAGGGTACCAAAGAGGAGGTTGAGGCTTCGC<br>GCAGTCTAGAGGATCCCCCTAGGGTTCTTTCGAAGCA</td>
+  </tr>
+  <tr>
+    <td>ATPTB4</td>
+    <td>CTGACTCGAGGGTACCTTCCCTTTTCTGCTGATCGG<br>GCAGTCTAGAGGATCCCTCCTCGGGCTTCCAATTTG</td>
+  </tr>
+  <tr>
+    <td>ATPTB6</td>
+    <td>ACTGCTCGAGGGTACCCAACATGGCAGTATCCGGTG<br>GCAGTCTAGAGGATCCTTATTAGTGGCGGTGGTGGT</td>
+  </tr>
+  <tr>
+    <td>ATPTB11</td>
+    <td>ACTGCTCGAGGGTACCGCGCTGCTTCTCCCATTTTC<br>GCAGAAAGTGGATCCAGGTGGGGTGTTTAGGGAG</td>
+  </tr>
+  <tr>
+    <td>ATPTB12</td>
+    <td>TAATCTCGAGGGTACCGACGCCATCAAAGGAATGCC<br>GCCGTCTAGAGGATCCAGCAGCCAACAAACAGACAA</td>
+  </tr>
+  <tr>
+    <td>ATPEG3</td>
+    <td>TACACTCGAGGGTACCAAACCTGAAGGCCCTCACAC<br>GCAGTCTAGAGGATCCCTTTCGTGCCGCCCTGATA</td>
+  </tr>
+  <tr>
+    <th colspan="2">Primers for quantification of mRNA levels by qPCR</th>
+  </tr>
+  <tr>
+    <td><i>b</i></td>
+    <td>CCAAGAGTGATGATGGCCCC<br>CGTTTAGGGTCCGGGAAAAAC</td>
+  </tr>
+  <tr>
+    <td><i>e</i></td>
+    <td>CAAGCCTTGACACACTTTATG<br>CCGCAAAGAAGTACGCCAC</td>
+  </tr>
+  <tr>
+    <td><i>f</i></td>
+    <td>TTTTCTACATACCGCAGCAGT<br>TACCATTCCATGCCGCTTG</td>
+  </tr>
+  <tr>
+    <td><i>g</i></td>
+    <td>GCAATTGTGTGAGCTGAACG<br>TACTGGCCGATTCGATAAC</td>
+  </tr>
+  <tr>
+    <td><i>ij</i></td>
+    <td>AGAGTAAAAGCGCGCCTACG</td>
+  </tr>
+</table>
+<table>
+  <tr>
+    <th></th>
+    <th>CAGTTGGAAAACCGGTAGCC</th>
+  </tr>
+  <tr>
+    <td><i>k</i></td>
+    <td>ACACAAAAACCTTCCAGCAGA<br>CGCTATGACGGACAGGTGT</td>
+  </tr>
+  <tr>
+    <td>8</td>
+    <td>GCTACGGCGACTTGGTGCG<br>CGTCACCACGGTATTGTGTTCA</td>
+  </tr>
+  <tr>
+    <td>ATPTB3</td>
+    <td>AACGTTTATATCAGCGGGCG<br>CTGTTTTTGGTCTGCACACGA</td>
+  </tr>
+  <tr>
+    <td>ATPTB4</td>
+    <td>CCAAACTTTGAAGCAGCGGA<br>ATTCCCTTGGATCCGCACCTT</td>
+  </tr>
+  <tr>
+    <td>ATPTB6</td>
+    <td>TCGGCATAGGAGAAGTAACGA<br>GATTCGGTTTGGAACTTGCG</td>
+  </tr>
+  <tr>
+    <td>ATPTB11</td>
+    <td>CAACGGCCCCCACATTCTC<br>ACACCGCGGTCAATTCATTG</td>
+  </tr>
+  <tr>
+    <td>ATPTB12</td>
+    <td>GCACTTCATTCTCCCGACTG<br>ACATGATGTAACACCTCCGC</td>
+  </tr>
+  <tr>
+    <td>ATPEG3</td>
+    <td>TGGCCCCACATGACTGAAAA<br>GGAAAGTGATCCGCCGGGATTT</td>
+  </tr>
+</table>
+
+Extended Data Table 3. List of primers used in the study.
+<table>
+  <tr>
+    <th>Target</th>
+    <th>Type</th>
+    <th>Reference</th>
+    <th>Dilution SDS-PAGE</th>
+    <th>Dilution BN-PAGE</th>
+  </tr>
+  <tr>
+    <th colspan="5">Primary antibodies</th>
+  </tr>
+  <tr>
+    <td><b>subunit-β</b></td>
+    <td>rabbit polyclonal</td>
+    <td>1</td>
+    <td>1:2000</td>
+    <td>1:2000</td>
+  </tr>
+  <tr>
+    <td>p18</td>
+    <td>rabbit polyclonal</td>
+    <td>1</td>
+    <td>1:1000</td>
+    <td>-</td>
+  </tr>
+  <tr>
+    <td><b>ATPTB1</b></td>
+    <td>rabbit polyclonal</td>
+    <td>1</td>
+    <td>1:1000</td>
+    <td>1:1000</td>
+  </tr>
+  <tr>
+    <td><b>subunit-d</b></td>
+    <td>rabbit polyclonal</td>
+    <td>1</td>
+    <td>1:1000</td>
+    <td>1:500</td>
+  </tr>
+  <tr>
+    <td>mtHsp70</td>
+    <td>mouse monoclonal</td>
+    <td>2</td>
+    <td>1:5000</td>
+    <td>-</td>
+  </tr>
+  <tr>
+    <th colspan="5">Secondary antibodies</th>
+  </tr>
+  <tr>
+    <td>goat anti-rabbit IgG HRP conjugate</td>
+    <td>BioRad 1721019</td>
+    <td></td>
+    <td>1:2000</td>
+    <td>1:2000</td>
+  </tr>
+  <tr>
+    <td>goat anti-mouse IgG HRP conjugate</td>
+    <td>BioRad 1721011</td>
+    <td></td>
+    <td>1:2000</td>
+    <td>1:2000</td>
+  </tr>
+</table>
+
+Extended Data Table 4. List of antibodies used in the study.
+Extended Data references:
+1. Muhleip, A., McComas, S.E. & Amunts, A. Structure of a mitochondrial ATP synthase with bound native cardiolipin. Elife **8**, e51179 (2019).
+2. Larkin, M.A. et al. (2007). Clustal W and Clustal X version 2.0. *Bioinformatics*, **23**, 2947-2948 (2007).
+3. Burki, F., Roger, A.J., Brown, M.W. & Simpson, A.G.B. The New Tree of Eukaryotes. *Trends Ecol Evol* **35**, 43-55 (2020).
+4. Protein Sequence Similarity Search. *Curr Protoc Bioinformatics* **60**, 3151-31523 (2017).
+5. Huang, Y., Niu, B., Gao, Y., Fu, L. & Li, W. CD-HIT Suite: a web server for clustering and comparing biological sequences. *Bioinformatics* **26**, 680-2 (2010).
+6. Sievers, F. et al. Fast, scalable generation of high-quality protein multiple sequence alignments using Clustal Omega. *Mol Syst Biol* **7**, 539 (2011).
+7. Edgar, R.C. MUSCLE: multiple sequence alignment with high accuracy and high throughput. *Nucleic Acids Res* **32**, 1792-7 (2004).
+Supplementary Files
+
+This is a list of supplementary files associated with this preprint. Click to download.
+
+• Video1.mp4
+• Video2.mp4
+• Video3.mp4

0a6508a983f37e141aa8dd5412d3637dcad95223e127d307f2bb548398049c6f/peer_review/peer_review.md

@@ -0,0 +1,252 @@
+Peer Review File
+
+A New Gene Set Identifies Senescent Cells and Predicts Senescence-Associated Pathways Across Tissues
+Reviewers’ Comments:
+
+Reviewer #1:
+Remarks to the Author:
+There are currently several suggested gene sets the expression of which is proposed to correlate with senescence of the cell population under study. This paper proposes another such set designated "SenMayo" and compares this with 6 other published gene sets, suggesting its superiority and applying it several human and mouse tissues of different sources before and after treatment with senolytics. SenMayo was derived for screening 1,656 studies resulting in the identification of 125 genes from 15 studies after excluding duplicates, case reports, and non-human or non-murine genes. SenMayo intentionally excluded p16 and p21 so that these could be used independently to validate detection of senescent cells. The SenMayo gene set was then tested in several different scenarios, concluding that its expression was higher in samples from older humans and mice across different tissues and decreased after senolytic treatment, and that it could be used on data from bulk and scRNA-seq analyses to identify cells expressing high levels of senescence/SASP genes. The strength of the work lies in the several different conditions investigated but it could be made a little clearer and easier on the reader to decipher what the cohorts are. The M&M lists “young (n=15, 30.9±4.0 years and n=19, 30.3±5.4 years) and postmenopausal females (n=15, 68.7±4.8 years and n=19, 73.1±6.6 years)”. Please state here the difference between the two groups of young and older, and clarify their relationships with cohort A and B without requiring the reader to search intensively. I think it is also a far stretch to refer to the differences in gene expression between younger and older subjects in these cohorts as being informative or not for the “aging process”. These differences reflect the presence of SASP+ cells in different proportions in cross-sectional comparisons and in tissues as diverse as brain, bone and hematopoietic cells, but do not explicitly reflect an aging process. Thus, I think it is something of a tautology to say SenMayo is associated “not only with aging but also specifically with cellular senescence” – in fact, only the latter is shown, and it is taken that that reflects the “aging process”.
+
+The paper begins with a single gene analysis of CDKN1A/p21Cip1, CCL2, IL6, NFKB1, RELA, and STAT3, yielding expected results in that samples from older women displayed an upregulation of these genes (but not CDKN2A/p16Ink4a). However, of these, only IL 6 is included in SenMayo. Please discuss why the others are not and whether IL 6 alone could really not substitute for all? The authors made the point that p21 and p16 were purposefully excluded. Was that the case with all these others as well, and if so, why? Other “canonical” markers are all included in SenMayo, eg. CCL24, SEMA3F, FGF2, and IGFBP7.
+
+The authors argue for the superiority of SenMayo over other gene clusters and provide an example using Cohort A and reporting 2 of the 50 genes in R-HSA-2559582 that were significantly enriched in biopsies from older women, whereas 13 of the 120 SenMayo genes were, i.e. 4%-vs-10.8%, not such a big difference. What were the two R-HAS genes, were they contained in SenMayo, and is the expression pattern the same in different tissues and species?
+In the M&M, there is no description of the phase I pilot study in which the senolytic combination Dasatinib plus Quercetin was used to treat patients with diabetic kidney disease. Although this is published elsewhere, to assist the reader, please describe in the M&M here.
+
+Nonetheless, this is an impressive paper, especially the monitoring of gene expression in adipose tissue samples from people treated with Dasatinib plus Quercetin, as well as the broad range of consistent data in mouse and human, and the cross-talk experiments delineating infoammaging pathways. These data could have meaningful clinical consequences.
+
+Reviewer #2:
+Remarks to the Author:
+In the manuscript entitled” A New Gene Set Identifies Senescent Cells and Predicts Senescence-Associated Pathways Across Tissues” the authors developed a new senescence gene set ("SenMayo") and validated GSEA analysis of SenMayo from humans, mice, and changes in this gene set following the clearance of senescent cells. Furthermore, the utility of SenMayo was demonstrated at the single cell level.
+
+The technical quality of the work is high and supports the conclusions of the manuscript. The authors provide compelling and carefully controlled data from distinct model systems: human and mice; aging and senescent cell clearance. For improving this paper more, several points and suggestions are listed below.
+
+Specific comments:
+
+1. In methods - Single-cell RNA-seq (scRNA-seq) analysis and page 29, the authors define that "Plasmacytoid dendric cells", "Conventional dendric cells" were summarized as "B cells" combined with "CD10+ B cells", "CD20+ B cells", "Plasma cells". Why so? Authors should provide explanations.
+
+2. For Fig. 4E & Fig.5D, there is a lack of fair comparison and evaluation of the gene expression about members of MIF and PECAM1 signaling pathway among SASP cells and other cell types.
+
+3. The authors performed pseudotime analysis to demonstrate that the SASP cluster, in both bone marrow hematopoietic cells and bone/bone marrow mesenchymal cells, was in the final phases of cellular differentiation. Although, in Fig. 5E, authors coincidence the result with prior knowledge (the increased expression of Cdkn1a/p21Cip1 and Trp53), monocle cannot be used to determine the base state of the trajectory. Authors should use an unbiased trajectory method to confirm this.
+
+4. The authors validated the changes of Mif mRNA levels in the bone of mouse model. However, the authors also provided an interesting conclusion showing that the MIF pathway has been important in both hematopoietic and mesenchymal cells to participate in cellular interactions. Authors should provide validation of this interesting interaction analysis.
+
+Minor comments:
+
+1. In methods - Single-cell RNA-seq (scRNA-seq) analysis and page 29, there exists a minor error. “For Fig. 2C,” and “For Fig. 3C” should be “for Fig. 4C,” and “For Fig. 5C”, respectively.
+
+2. For Fig. S2 B-C & Fig. S3E, the color legend needs to show the cell-type names, to avoid confusion about the interpretation of the data.
+
+Reviewer #3:
+Remarks to the Author:
+This manuscript by Dominik Saul et al. generated a novel gene set (Sen Mayo) including previously reported genes that were enriched in senescent and/or SASP-secreting cells. For RNA-seq, transcriptome-wide gene expression data was obtained from 2 different cohorts and further employed these data to identify the senescent cell in vivo. Meanwhile, the author also validate their hypothesis in single-cell resolution, and combined with trajectory inference methods to explore senescence-associated pathways. Overall, this study provided comprehensive correlative data in a clearly written way, however, there are several concerns addressed as follows:
+
+Major comments:
+1. To determine whether senescence-and SASP-associated pathways were enriched with aging, the authors selected to analyze transcriptional regulatory relationships (Figure 1B). It would be very
+interesting, if the author can discuss what happens if these transcription factors and regulate signaling molecules are perturbed? This might straightforwardly leverage some public databases and tools, including PMID: 32051003, 28991892, and 25058159. Meanwhile, please provide further explanation regarding how SenMayo encodes a dense network of different protein classes in a strong interaction network (Figure 1F). Tables of cluster analysis results can be additionally included as part of the supplementary section.
+2. Since the senolytic drug combination, Dasatinib plus Quercetin (D+Q) in the context of diabetic kidney disease was used to validate the ability of SenMayo on predicting senescent cell clearance (Figure 3), please describe the concept for choosing diabetic kidney disease model to validate the data.
+3. In the previous analysis, principal component analysis (PCA) was performed to estimate/evaluate the variance displayed in Figure 3C. What about UMAP variance estimation/evaluation? Further explanations are required to clarify the theories (Figure 4A).
+4. How the cell types from single-cell transcriptomic data presented in Figures 4A and 5A were identified? Please explain in detail the methods for cell-type identification from single-cell transcriptomic data. Similar interpretation of scRNA-seq cell type annotation protocol presented in figures 4C and 5C. Since cell type annotation obtained from a previous study (PMID: 30518681) which is lack of canonical genes references for each cluster, should the new cluster referred as "SASP cells" generated by selecting top 10% highest expression of senescence/SASP-associated genes technically be aligned together in the whole UMAP representation? Besides that, please describe in more detail regarding the interaction values between SASP and the other particular cell types. The two aging signatures CellAge and GenAge and its significant correlation to SASP also need to be interpreted more clearly.
+5. Please present the reconstruction and basis of pseudo-time analysis in a more detailed manner, along with the procedure/protocol of trajectory analysis on the monocle package. The three main origins for the SASP cluster, namely Lepr+ MSCs, OLC 1, and OLC 2, were depicted in pseudo time by applying trajectory inference. Why only canonical markers of senescence were reported in Figure 5B other than the result of TGFB1 in a terminal developmental branch?
+6. To further test SenMayo in single-cell datasets and potentially contrast bone marrow hematopoietic cells to bone/bone marrow mesenchymal cells, a published murine dataset containing scRNA-seq data from bone and bone marrow mesenchymal cells was leveraged. Why the authors did not select the human bone marrow mesenchymal cells related dataset to avoid biological heterogeneity? Regarding the selection of canonical SASP markers or SASP/senescence markers, verification of existing references may also improve the reproducibility of the current study.
+7. The author used Seurat algorithm to analyze 500 unique molecular identifiers (UMIs) and data were obtained based on the following thresholds: log10 genes per UMI >0.8, >250 genes per cell, a mitochondrial ratio of less than 20%. Since results from Sequencing Data Alignment often undergo considerable fluctuations due to modification in specific parameters and tuning. Therefore, without detailed description of how the algorithms were applied, it may seem very difficult to reproduce these results. For example, how did the algorithms result in the number of subgroups and objects in each analysis and how was it concluded that these subgroups are statistically robust? To avoid being cluttered with unnecessary details, the authors may provide a summarized list in either the Supplementary or Code Availability section.
+
+Minor comments:
+1. All images are presented in a high-resolution and professional manner, however, to be more intelligible without reference, figure legends should provide sufficient details (such as the meaning of including solid line, dashed line, dash-dotted line, dotted line...) corresponding to each component part.
+2. In Figure S4D, it is unclear how GO/KEGG pathway enrichment is analyses. Please also make sure the color codes clarify in these figures and tables. Meanwhile, this would make sense to state as an advantage if the study had indeed identified a novel pathway or any interaction not previously known, either via bulk or single-cell seq data.
+Reviewer 1
+
+There are currently several suggested gene sets the expression of which is proposed to correlate with senescence of the cell population under study. This paper proposes another such set designated "SenMayo" and compares this with 6 other published gene sets, suggesting its superiority and applying it several human and mouse tissues of different sources before and after treatment with senolytics. SenMayo was derived for screening 1,656 studies resulting in the identification of 125 genes from 15 studies after excluding duplicates, case reports, and non-human or non-murine genes. SenMayo intentionally excluded p16 and p21 so that these could be used independently to validate detection of senescent cells. The SenMayo gene set was then tested in several different scenarios, concluding that its expression was higher in samples from older humans and mice across different tissues and decreased after senolytic treatment, and that it could be used on data from bulk and scRNA-seq analyses to identify cells expressing high levels of senescence/SASP genes. The strength of the work lies in the several different conditions investigated but it could be made a little clearer and easier on the reader to decipher what the cohorts are.
+
+1. The M&M lists “young (n=15, 30.9±4.0 years and n=19, 30.3±5.4 years) and postmenopausal females (n=15, 68.7±4.8 years and n=19, 73.1±6.6 years)”. Please state here the difference between the two groups of young and older, and clarify their relationships with cohort A and B without requiring the reader to search intensively.
+Response: We have clarified this point in the Methods (page 18). As now stated, both were independent cohorts of healthy young and older postmenopausal women we have previously studied. We have also clarified which groups corresponded to cohort A versus cohort B.
+
+2. I think it is also a far stretch to refer to the differences in gene expression between younger and older subjects in these cohorts as being informative or not for the “aging process”. These differences reflect the presence of SASP+ cells in different proportions in cross-sectional comparisons and in tissues as diverse as brain, bone and hematopoietic cells, but do not explicitly reflect an aging process. Thus, I think it is something of a tautology to say SenMayo is associated “not only with aging but also specifically with cellular senescence” – in fact, only the latter is shown, and it is taken that that reflects the “aging process”.
+Response: We acknowledge this point and have gone through the manuscript to dissociate, as much as possible, senescence from aging per se, as the Reviewer suggests.
+
+3. The paper begins with a single gene analysis of CDKN1A/p21Cip1, CCL2, IL6, NFKB1, RELA, and STAT3, yielding expected results in that samples from older women displayed an upregulation of these genes (but not CDKN2A/p16Ink4a). However, of these, only IL 6 is included in SenMayo. Please discuss why the others are not and whether IL6 alone could really not substitute for all? The authors made the point that p21 and p16 were purposefully excluded. Was that the case with all these others as well, and if so, why? Other “canonical” markers are all included in SenMayo, eg. CCL24, SEMA3F, FGF2, and IGFBP7.
+Response: We thank the reviewer for this comment. From the initial analysis, CDKN2A and CDKN1A were purposely excluded, while CCL2 and IL6 are members of the SenMayo. The transcription factor NF-κB family with RELA and NFKB1 are known regulators of the SASP, as is STAT3 ¹. Although some SASP members are indeed transcription factors, we aimed to exclude the higher-level regulators from the panel in order to not bias the subsequent analyses into one particular direction. Indeed, the findings in Fig. 1B drove us to further elucidate which SASP members would be affected. To clarify these insights for the reader, we have added “Likewise, and to not bias the subsequent analyses towards NF-κB-dependent SASP members, we excluded key regulatory factors like RELA and NF-κB1” to the Methods (page 18). Also, a summary of the
+transcription factors that are important for SenMayo, and how they affect the RNA-seq as single cell RNA-seq data (making use of iRegulon and SCENIC), is now included in the new Supplementary Figures 1 and 8.
+
+4. The authors argue for the superiority of SenMayo over other gene clusters and provide an example using Cohort A and reporting 2 of the 50 genes in R-HSA-2559582 that were significantly enriched in biopsies from older women, whereas 13 of the 120 SenMayo genes were, i.e. 4%-vs-10.8%, not such a big difference. What were the two R-HSA genes, were they contained in SenMayo, and is the expression pattern the same in different tissues and species?
+Response: We thank the reviewer for the opportunity to clarify this. The two genes in R-HSA-2559582 were CDKN1A (padj<0.001) and IGFBP7 (padj=0.036). While the former was intentionally excluded from SenMayo, the latter is part of it. We agree that a 2/50 vs. 13/120 "hit rate" is not impressive, but want to point out the real strength of SenMayo, which results in a NES of 1.51 (p=0.0023) compared to R-HSA-2559582 with a NES of 1.11 (p=0.2826) for this cohort (Fig. 1 D and G). Also, as pointed out on page 6, the GSEA analysis includes not only genes that differ significantly between groups, but also evaluates overall trends for differences in gene expression between groups and hence provides considerably greater power than examining individual genes.
+
+Regarding the expression pattern of CDKN1A and IGFBP7 across tissues and species we analyzed both of our single cell datasets for CDKN1A/IGFBP7 and Cdkn1a/lgfbp7 expression (Reviewer only. Fig. 1), demonstrating the high expression of both in the SASP population.
+
+![Expression of CDKN1A/IGFBP7 in our human and Cdkn1a/lgfbp7 in our murine dataset. Four panels showing expression levels for CDKN1A, IGFBP7, Cdkn1a, and lgfbp7 across various tissues and species.](page_184_670_1207_496.png)
+
+Reviewer only. Figure 1. Expression of CDKN1A/IGFBP7 in our human and Cdkn1a/lgfbp7 in our murine dataset. (A) CDKN1A shows a high expression in the SASP cells of our human bone marrow dataset, as does (B) IGFBP7. In the murine dataset, (C) Cdkn1a is highly expressed in
+the SASP cells and EC, Fibroblast, Lepr+ MSCs and Pericytes, while (D) Igfbp7 shows a similar pattern.
+
+5. In the M&M, there is no description of the phase I pilot study in which the senolytic combination Dasatinib plus Quercetin was used to treat patients with diabetic kidney disease. Although this is published elsewhere, to assist the reader, please describe in the M&M here.
+Response: We now provide additional details regarding this study, in addition to referring the reader to the original reference.
+
+Nonetheless, this is an impressive paper, especially the monitoring of gene expression in adipose tissue samples from people treated with Dasatinib plus Quercetin, as well as the broad range of consistent data in mouse and human, and the cross-talk experiments delineating inflammaging pathways. These data could have meaningful clinical consequences.
+
+Reviewer 2
+
+In the manuscript entitled" A New Gene Set Identifies Senescent Cells and Predicts Senescence-Associated Pathways Across Tissues" the authors developed a new senescence gene set ("SenMayo") and validated GSEA analysis of SenMayo from humans, mice, and changes in this gene set following the clearance of senescent cells. Furthermore, the utility of SenMayo was demonstrated at the single cell level. The technical quality of the work is high and supports the conclusions of the manuscript. The authors provide compelling and carefully controlled data from distinct model systems: human and mice; aging and senescent cell clearance. For improving this paper more, several points and suggestions are listed below.
+
+1. In methods - Single-cell RNA-seq (scRNA-seq) analysis and page 29, the authors define that "Plasmacytoid dendric cells", "Conventional dendric cells" were summarized as “B cells” combined with "CD10+ B cells", "CD20+ B cells", "Plasma cells". Why so? Authors should provide explanations.
+Response: We thank the reviewer for the opportunity to clarify this. When performing a thorough analysis with all cell types and their communication patterns, we concluded that the overall message of CellChat was not conveyed as clearly as it would be if we combined the cell clusters into functional subunits (please see Reviewer only. Fig. 2), as the authors of CellChat suggest (2 and https://github.com/sqjin/CellChat). This way, the message conveyed is more obvious and the importance of SASP cells more directly conveyed, especially when it comes to the SASP-cell/T-cell axis. We have now added “we aimed to summarize functional cell types in order to highlight the functional importance of SASP cells and their communicational patterns. Subsequently, we combined [...]” to the Methods (page 21) to point that out more clearly.
+Reviewer only. Figure 2. Full depiction of cell types and their interaction strength in CellChat. The full cellular interaction with each cell type demonstrates the prominent interaction of SASP cells with CD8+ effector T cells and CD8+ naïve T cells.
+
+2. For Fig. 4E & Fig.5D, there is a lack of fair comparison and evaluation of the gene expression about members of MIF and PECAM1 signaling pathway among SASP cells and other cell types.
+Response: We agree with the reviewer and are thankful for the opportunity to show the complete MIF and PECAM1 signaling pathways. We added these two to the Fig. 4 associated Supplementary Figure 4 as A and B:
+
+![Full depiction of cell types and their interaction strength in CellChat](page_186_120_670_495.png)
+Supplementary Figure 4. MIF and PECAM pathways in human hematopoietic bone marrow cell types. (a) The MIF pathway and its key members show a highly heterogeneous expression pattern among all cell clusters. While CD10+ B cells show a high expression of *MIF*, *CD74* and *CXCR4*, the expression of *CD44* is low. An overall high expression of all MIF members is evident in CD8+ effector T cells and conventional dendritic cells and SASP cells. (b) The PECAM pathway shows an expression of PECAM1 in CD16+ monocytes, plasma cells and SASP cells.
+
+3. “The authors performed pseudotime analysis to demonstrate that the SASP cluster, in both bone marrow hematopoietic cells and bone/bone marrow mesenchymal cells, was in the final phases of cellular differentiation. Although, in Fig. 5E, authors coincidence the result with prior knowledge (the increased expression of Cdkn1a/p21Cip1 and Trp53), monocle cannot be used to determine the base state of the trajectory. Authors should use an unbiased trajectory method to confirm this.”
+Response: We thank the reviewer for this reasoned thought. Indeed, we used monocle to determine the trajectory state, giving us just two options of trajectory interference (rev=TRUE or rev=FALSE). By taking into account *Cdkn1a* and *Trp53* we tried to reduce this bias as much as possible, and since the original raw fastqs were not provided by the authors, we did not make use of other (unbiased) methods of trajectory interference.
+
+An unbiased way for cellular dynamic analysis, as beautifully demonstrated by La Manno et al. is RNA velocity, which needs raw fastqs to recreate spliced and unspliced mRNA matrices3. Since the bam files were provided, we were able to recreate the fastqs for our single cell dataset from there, using the cellranger pipeline. After that, we made use of bustools and velocity to create the spliced and unspliced matrices of each of the eight samples, finally merging them and
+calculating velocity to receive an unbiased trajectory interference. The results are demonstrated in the new Supplementary Fig. S9a-b. As predicted, we found that SASP cells are mostly derived from OLC1, OLC2 and Lepr+ MSCs (UMAP on the top). When focusing on these four cell types (UMAP on the bottom), it was seen mostly consistent that SASP cells were at the developmental end, originating from Lepr+ MSCs and OLC1 (upper-left continent) and Lepr+ MSCs as OLC2 (bottom-right continent). These results confirm our trajectory interference with monocle.
+
+![Trajectory interference using velocity plots showing cell types and clusters](page_347_384_1057_670.png)
+
+Supplementary Figure 9. Trajectory interference using velocity (La Manno et al. 2018). (a) The overall trajectory interference shows that SASP cells are mostly developing from OLC1, OLC2 and Lepr+ MSCs. (b) A focus on these four cell types reveals the OLC1 and Lepr+ MSCs as main origin of the upper-left continent, and the OLC2 and Lepr+ MSCs as the origin of a different SASP cell population in the bottom-right continent.
+
+4. *The authors validated the changes of Mif mRNA levels in the bone of mouse model. However, the authors also provided an interesting conclusion showing that the MIF pathway has been important in both hematopoietic and mesenchymal cells to participate in cellular interactions. Authors should provide validation of this interesting interaction analysis.*
+Response: We agree with the Reviewer that MIF signaling may be of particular interest in the context of cellular senescence. In this paper, we primarily used this pathway to validate our *in silico* predictions using experimental genetic clearance of senescent cells. Further dissection of this pathway and its possible role in immune evasion by senescent cells is, however, beyond the
+scope of the present work and is the subject of future studies in our laboratory. We do address this issue in the Discussion on page 16 where we note that further studies are needed to address this issue.
+
+Minor comments:
+
+1. In methods - Single-cell RNA-seq (scRNA-seq) analysis and page 29, there exists a minor error. “For Fig. 2C,” and “For Fig. 3C” should be “for Fig. 4C,” and “For Fig. 5C”, respectively.
+Response: We thank the reviewer for pointing this out and corrected the two mistakes.
+
+2. For Fig. S2 B-C & Fig. S3E, the color legend needs to show the cell-type names, to avoid confusion about the interpretation of the data.
+Response: We thank the reviewer for pointing out the missing clarity. To verify that the analyzed cells on the right side in B and in C are SASP cells, we color-coded the font, consistent with the previous figures, and surrounded the whole figure C with a rectangle using the same color (previously Fig. S2B-C, now Supplementary Fig. 3e-f).
+
+![Supplementary Fig. 3e-f](page_370_682_1047_377.png)
+
+Supplementary Fig. 3e-f
+
+For Supplementary Fig. 5e (previously S3e), this color-coding functionality was not provided by Cellchat, so we colored the cluster manually and hope that this way, the cell types are distinct at first glance:
+Supplementary Fig. 5e
+For consistency, we corrected Supplementary Fig. 7c-d and g in the same manner.
+
+Reviewer 3
+
+This manuscript by Dominik Saul et al. generated a novel gene set (Sen Mayo) including previously reported genes that were enriched in senescent and/or SASP-secreting cells. For RNA-seq, transcriptome-wide gene expression data was obtained from 2 different cohorts and further employed these data to identify the senescent cell in vivo. Meanwhile, the author also validate their hypothesis in single-cell resolution, and combined with trajectory inference methods to explore senescence-associated pathways. Overall, this study provided comprehensive correlative data in a clearly written way, however, there are several concerns addressed as follows:
+
+1. To determine whether senescence-and SASP-associated pathways were enriched with aging, the authors selected to analyze transcriptional regulatory relationships (Figure 1B). It would be very interesting, if the author can discuss what happens if these transcription factors and regulate signaling molecules are perturbed? This might straightforwardly leverage some public databases and tools, including PMID: 32051003, 28991892, and 25058159. Meanwhile, please provide further explanation regarding how SenMayo encodes a dense network of different protein classes in a strong interaction network (Figure 1F). Tables of cluster analysis results can be additionally included as part of the supplementary section.
+Response: We thank the reviewer for these challenging yet valuable suggestions. The regulatory elements of the SenMayo in total are indeed of major interest and we decided to add both of the revierer’s suggestions, iRegulon and SCENIC, combine them, and leverage these tools for our datasets. This led to the new Supplementary Fig. 1 and 8. Indeed, the major motif controlling the SASP members was Factorbook-NFKB1 (Supplementary Fig. 1), which is in accordance with our Fig. 1B (RELA and NFkB1 are both both NF-kB subunits). Further exploring the associated transcription factors (TF) with iRegulon, BCL3, RXRA and NFIC were the highest enriched (Supplementary Fig. 1b), with the transcription co-activator BCL3 furthermore controlling BCL3, NFKB1, NFKB2, RELA and IKZF1 (Supplementary Fig. 1c). The three main TFs (BCL3, RXRA and NFIC) controlled a major proportion of the SenMayo genes (Supplementary Fig. 1d). To verify
+these regulators as substantial, we used SCENIC to first create a tSNE visualization along 50 PCs and 50 perplexity according to the AUCell determined major regulons (Supplementary Fig. 8a). Interestingly, most of the SASP cells can be found within the upper central continent (Fig. Supplementary Fig. 8b).
+
+An overlay with two of the key regulons (BCL3 and RXRA, a third one would get too confusing with the two red colors just distinguishable) upon the new tSNE revealed the iRegulon-predicted importance of both BCL3 and RXRA for the SASP cells (Fig. Fig. S5F).
+
+We thank the reviewer for these very helpful suggestions and have now added “The key regulatory elements of the SenMayo genes according to iRegulon 4 feature the Factorbook-NFkB1 motif (Suppl. Fig. S5A), and BCL3 (Suppl. Fig. S5B-C) represents the leading transcription factor for a majority of SASP genes (Suppl. Fig. S5D).” and “Interestingly, and as predicted from the human RNA-seq data (Fig. 1B), the SASP cells were mainly controlled by the transcription factor BCL3 (and RXRA, Suppl. Fig. S5E-F).” to the main text (page 6).
+
+In addition, we report the characteristics of the two networks (Fig. 1E-F) and Suppl. Fig. 1 like average number of neighbors, characteristic path length, network heterogeneity and network centralization in the new Suppl. Table. 1.
+
+![Motif diagram, table of TFs and targets, and network diagram showing transcription factors and their targets](page_120_670_1342_496.png)
+
+Supplementary Figure 1. iRegulon (Janky et al. 2014) predicts the key regulons for the SASP cells. (a) The motif with the highest enrichment for the SASP genes, according to iRegulon, was Factorbook-NFkB1. (b) The most important transcription factors with 92, 28 and 34 targets within SenMayo were BCL3, RXRA and NFIC, respectively. The first transcription factor controlled (c) BCL3, NFkB1 and -2, RELA and IKZF1, thus confirming the RNA-Seq predictions in the young and old dataset (Fig. 1B). (d) The three transcription factors control a majority (95/125) of SenMayo genes.
+Supplementary Figure 8. SCENIC (Aibar et al. 2017) predicts the key regulons for the SASP cells within the human single cell dataset. (a) A regulon-based tSNE is constructed, where the SASP cells contribute substantially to the upper-middle continent (purple). (b) The predicted regulons, BCL3 and RXRA, indeed control the SASP cells containing continent.
+
+2. Since the senolytic drug combination, Dasatinib plus Quercetin (D+Q) in the context of diabetic kidney disease was used to validate the ability of SenMayo on predicting senescent cell clearance (Figure 3), please describe the concept for choosing diabetic kidney disease model to validate the data.
+Response: As now noted on page 18, the original trial examined patients with diabetic kidney disease because both obesity (associated with type 2 diabetes mellitus) and chronic kidney disease are linked to an increase in senescent cell burden.
+
+3. In the previous analysis, principal component analysis (PCA) was performed to estimate/evaluate the variance displayed in Figure 3C. What about UMAP variance estimation/evaluation? Further explanations are required to clarify the theories (Figure 4A).
+Response: We thank the reviewer for this suggestion. We thought that the genes of interest would be best described in the easiest graphical depiction possible for bulk RNA-seq data, especially since we just looked at the dimension “treatment” with three characteristics (young vs old_veh vs old_ap). But indeed, a umap-representation is used afterwards, so we performed a normalization of the DESeq data, followed by a transformation needed for the umap-package (0.2.7.0) and plotted the treatment groups as UMAP, unfortunately not resulting in a better visual representation compared to the PCA-plot, but still a good distinction of young vs. both old groups (Reviewer only. Fig. 3):
+Rev. only. Figure 3. UMAP depiction of mouse INK-ATTAC RNA-Seq dataset from Fig. 3C. While the young group can be distinguished from the old_veh and the old_ap group, a distinction between ap-treatment and vehicle-treatment remains more difficult than in the PCA-plot in Fig. 3C.
+
+To continue these thoughts and give more insights into the UMAP representation of the human single cell RNA-seq data from Fig. 4A, we aimed to combine the more gene-focused visual representation of a PCA-plot, with the UMAP from Fig. 4A, leading to a Similarity Weighted Nonnegative Embedding (SWNE) representation of the (before SenMayo-enriched) representation. The leading genes for this SWNE plot are the SenMayo genes:
+
+![UMAP depiction of mouse INK-ATTAC RNA-Seq dataset from Fig. 3C](page_186_256_1097_670.png)
+Reviewer only Figure 4. (A) SWNE depiction of the UMAP from Fig. 4A. All SenMayo genes are embedded within the SWNE and represent the places with the “highest” expression of a specific gene. (B) Examples of expression of CD9 (right part, coloured in red) and (C) CCL4 (bottom-left part, coloured in red) in the SWNE representation.
+
+These analyses give an interesting idea on the importance of different genes for the individual clusters. However, we feel that for the reader, this would be more confusing than the original Fig. 4A, in which the general enrichment is shown. Also, a strength of the SenMayo is that all SASP genes are enriched simultaneously, and not one single gene is of higher importance than others.
+
+4. How the cell types from single-cell transcriptomic data presented in Figures 4A and 5A were identified? Please explain in detail the methods for cell-type identification from single-cell transcriptomic data. Similar interpretation of scRNA-seq cell type annotation protocol presented in figures 4C and 5C. Since cell type annotation obtained from a previous study (PMID: 30518681) which is lack of canonical genes references for each cluster, should the new cluster referred as “SASP cells” generated by selecting top 10% highest expression of senescence/SASP-associated genes technically be aligned together in the whole UMAP representation? Besides that, please describe in more detail regarding the interaction values between SASP and the other particular cell types. The two aging signatures CellAge and GenAge and its significant correlation to SASP also need to be interpreted more clearly.
+Response: The clustering for the human dataset 5 was obtained as follows, and in now added to the methods (page 21): “After quality control and integration, we performed a modularity optimized Louvain clustering with the resolution “1.4”, leading to 40 distinct clusters in the human dataset. Subsequently, we performed the labelling for these 40 clusters manually with established key marker genes (Suppl. Fig. 3a).” We also added to the methods section:
+“For the murine dataset, we chose the same order of analysis, and picked the resolution “1.4”, leading to 40 distinct clusters, which were manually assigned according to established marker genes (Suppl. Fig. 6a).”
+
+However, as the reviewer pointed out, there were no canonical reference genes in this paper. In order to enable the reader to reproduce these results, we added a dotplot highlighting the canonical genes for each cluster, along with the underlying references:
+
+![Dotplot depicting the canonical genes per cluster.](page_232_579_1107_482.png)
+
+Reviewer only. Figure 5. Dotplot depicting the canonical genes per cluster. They key genes per cluster are demonstrated in both the (A) human dataset along with the reference for each marker and cell type and in the (B) murine dataset along with references for each marker and cell type.
+
+We have added the human dotplot as Suppl. Fig. 3a, and the murine dotplot as Suppl. Fig. 6a. To assure that the reader can reproduce the clustering for both the human and murine dataset, we also added a notebook for the Seurat-file acquisition until the clustering (“notebook_human_murine_seurat_acquisition.Rmd”, accessible via https://datadryad.org/stash/share/YdD6C2ZFDqSizXehPR0qqPy4io7oRQJMGRIrPuij9WU).
+
+Since the SASP cells are generated by enriching for SenMayo genes, we do not necessarily expect the same cell type to enrich for these genes. Subsequently, some clusters with the capability of secreting a SASP phenotype, like monocytic cells would be more expected to enrich in SenMayo, while others like erythroid progenitors would be less expected to enrich for SenMayo. Thus, the highest enrichment in certain parts of the continents is expected, but an occasionally occurring enrichment in others is also not unexpected.
+For the interaction values in Fig. 4C and Fig. 5C, we added “the numbers represent the relative interaction strength as sum of interaction weights. Edge weights are proportional to interaction strength, and a thicker line refers to a stronger signal”2.
+
+We agree that the interaction between genAge and SenMayo as CellAge and SenMayo with plotted three variables may not be as clear as intended at first sight. We subsequently chose to plot them separately with a spearman correlation: For SenMayo and genAge, we found a significant correlation with an R of 0.43, while for SenMayo and CellAge, this was R=0.35 in the human dataset. In the murine dataset, the R was 0.61 for SenMayo and genAge and R=0.67 for SenMayo and CellAge, respectively (Reviewer only. Fig. 6, and added to Supplementary Fig. 3c,d and Supplementary Fig. 6b,c).
+
+![Bivariate correlation plots for the human (A, B) and murine (C, D) dataset.](page_384_629_1092_496.png)
+
+Reviewer only. Figure 6. Bivariate correlation plots for the human (A, B) and murine (C, D) dataset. Both SenMayo and genAge show reliable correlations (A: R=0.43, C: R=0.61) as do SenMayo and CellAge (B: R=0.35, D: R=0.67).
+
+5. Please present the reconstruction and basis of pseudo-time analysis in a more detailed manner, along with the procedure/protocol of trajectory analysis on the monocle package. The three main origins for the SASP cluster, namely Lepr+ MSCs, OLC 1, and OLC 2, were depicted in pseudo time by applying trajectory inference. Why only canonical markers of senescence were reported in Figure 5B other than the result of TGFB1 in a terminal developmental branch?
+Response:
+Please see Rev. 2 – point 3
+
+We thank the reviewer for this reasoned thought. Indeed, we used monocle to determine the trajectory state, giving us just two options of trajectory interference (rev=TRUE or rev=FALSE). By taking into account Cdkn1a and Trp53 we tried to reduce this bias as much as possible, and since the original raw fastqs were not provided by the authors, we did not make use of other (unbiased) methods of trajectory interference.
+
+An unbiased way for cellular dynamic analysis, as beautifully demonstrated by La Manno et al. is RNA velocity, which needs raw fastqs to recreate spliced and unspliced mRNA matrices3. Since the bam files were provided, we were able to recreate the fastqs for our single cell dataset from there, using the cellranger pipeline. After that, we made use of bustools and velocity to create the spliced and unspliced matrices of every of the eight samples, finally merging them and
+calculating velocity to receive an unbiased trajectory interference. The results are demonstrated in the new Supplementary Fig. S7A-B. As predicted, we found that SASP cells are mostly derived from OLC1, OLC2 and Lepr+ MSCs (UMAP on the top). When focusing on these four cell types (UMAP on the bottom), it was seen mostly consistent that SASP cells were at the developmental end, originating from Lepr+ MSCs and OLC1 (upper-left continent) and Lepr+ MSCs as OLC2 (bottom-right continent). These results confirm our trajectory interference with monocle.
+
+![Trajectory interference using velocity plots showing UMAP projections and cell type annotations](page_349_355_1087_670.png)
+
+Supplementary Figure 9. Trajectory interference using velocity (La Manno et al. 2018). (a) The overall trajectory interference shows that SASP cells are mostly developing from OLC1, OLC2 and Lepr+ MSCs. (b) A focus on these four cell types reveals the OLC1 and Lepr+ MSCs as main origin of the upper-left continent, and the OLC2 and Lepr+ MSCs as the origin of a different SASP cell population in the bottom-right continent.
+
+We provide the underlying R code for the velocity calculations in the notebook “R_notebook_Fig4_5_sup2to10.Rmd” (accessible via https://datadryad.org/stash/share/YdD6C2ZFDgSizXehPR0qqPy4io7oRQJMGRlrPuij9WU).
+
+Since the expression of Tgfbl along pseudotime was explicitly requested, we plot it here (Reviewer only. Fig. 8):
+Reviewer only. Figure 8. *Tgfb1* expression along pseudotime. The inlay on the top-left shows the general pseudotime development (originating in the bottom-right and ending in both bottom-left and middle-top). The *Tgfb1* expression is enriched in the end of the pseudotemporal development.
+
+In addition, we provide the R code for the pseudotime calculations in the notebook “R_notebook_Fig4_5_sup2to10.Rmd” accessible via https://datadryad.org/stash/share/YdD6C2ZFDgSizXehPR0qqPy4io7oRQJMGRIrPuij9WU.
+
+6. To further test SenMayo in single-cell datasets and potentially contrast bone marrow hematopoietic cells to bone/bone marrow mesenchymal cells, a published murine dataset containing scRNA-seq data from bone and bone marrow mesenchymal cells was leveraged. Why the authors did not select the human bone marrow mesenchymal cells related dataset to avoid biological heterogeneity? Regarding the selection of canonical SASP markers or SASP/senescence markers, verification of existing references may also improve the reproducibility of the current study.
+Response: We thank the reviewer for the opportunity to clarify this. Indeed, we think that the applicability of SenMayo in both human and murine datasets is a strength of SenMayo. In our own mouse studies, we frequently faced the obstacle of not having a reliable, yet multifaceted tool to reveal cells with a SASP-like transcriptome in RNA- and single cell RNA-seq datasets. We aimed to establish a panel that can be used in bulk RNA-seq and single cell RNA-seq datasets to uncover SASP-like cells and monitor a treatment effect in a reliable manner.
+To further verify an existing reference to improve the reproducibility of the current study within the bone marrow, we leveraged the Tabula Muris Senis single cell dataset \( ^6 \) and combined one month and three old month mice as “young” and 24 month and 30 month old mice as “old”. We saw an increase of SenMayo in the old mice’s bone marrow (***, Reviewer only. Fig. 9).
+Reviewer only. Figure 9. Comparison of bone marrow from young (1+3m) and old (24 and 30m) mice from the tabula muris senis⁶. Enriching for SenMayo, the old mice showed an overall higher enrichment score compared to the young mice (Wilcoxon rank-sum test, p<0.001).
+
+7. The author used Seurat algorithm to analyze 500 unique molecular identifiers (UMIs) and data were obtained based on the following thresholds: log10 genes per UMI >0.8, >250 genes per cell, a mitochondrial ratio of less than 20%. Since results from Sequencing Data Alignment often undergo considerable fluctuations due to modification in specific parameters and tuning. Therefore, without detailed description of how the algorithms were applied, it may seem very difficult to reproduce these results. For example, how did the algorithms result in the number of subgroups and objects in each analysis and how was it concluded that these subgroups are statistically robust? To avoid being cluttered with unnecessary details, the authors may provide a summarized list in either the Supplementary or Code Availability section.
+Response: We thank the reviewer for these helpful suggestions. For both the human and murine single cell datasets, we now provide a notebook with with both of these Seurat objects can be acquired and generated the way we did for the manuscript ("notebook_human__murine_seurat_acquisition.nb.html"). Likewise, we provide a notebook for the RNA-Seq (GSE72815_YOE_Notebook) and for the creation of Fig. 4-5 as well as Suppl. 2-10 (R_notebook_Fig4_5_sup2to10, accessible via https://datadryad.org/stash/share/YdD6C2ZFDqSizXehPR0qqPv4io7oRQJMGRIrPuij9WU).
+
+Minor comments:
+
+1. All images are presented in a high-resolution and professional manner, however, to be more intelligible without reference, figure legends should provide sufficient details (such as the meaning of including solid line, dashed line, dash-dotted line, dotted line...) corresponding to each component part.
+Response: We thank the reviewer for the opportunity to clarify and improve our figure legends. Specifically, we added “arrows point the direction of these interactions” to Fig. 1E and “grey lines represent interactions” to Fig. 1F and “The highlighted genes represent variables, and the arrows
+drawn from the origin indicate their “weight” in different directions, according to the theories of Gabriel (https://doi.org/10.2307/2334381)” to Fig. 3C, as “the numbers represent the relative interaction strength as sum of interaction weights. Edge weights are proportional to interaction strength, and a thicker line refers to a stronger signal”2 to Fig. 4C, and “the numbers represent the relative interaction strength as sum of interaction weights. Edge weights are proportional to interaction strength, and a thicker line refers to a stronger signal”2 to Fig. 5C and “the solid line represents the expression values as a function of pseudotime-progress” to Fig. 5E.
+
+2. In Figure S4D, it is unclear how GO/KEGG pathway enrichment is analyses. Please also make sure the color codes clarify in these figures and tables. Meanwhile, this would make sense to state as an advantage if the study had indeed identified a novel pathway or any interaction not previously known, either via bulk or single-cell seq data.
+Response: We added “The gene ontology and KEGG analyses (Supplementary Fig. 3f, Supplementary Fig. 7d) with gprofiler2 were done for homo sapiens (hsapiens) and mus musculus (mmusculus) after the positively regulated genes were selected with the “FindMarkers” function (used test=”MAST”, logfc.threshold = 0.25). For the gost function, we used an user threshold of 0.05 and fdr correction method.” to the methods section to clarify the GO/KEGG analyses.
+
+We color-coded the Fig S4C, D and G (now Supplementary Fig. 3e,f and Supplementary Fig. 7c-d) with the color for the SASP cells to be consistent and verify which cells were analyzed. Since we carved out a new cellular component, “SASP cells” from single cell data, their interactions with other cell types (as expected from cells that secrete potentially detrimental cytokines) are novel. However, we regret that in neither bulk nor single cell seq-data, we discovered new pathways. Nonetheless, we analyzed which genes – apart from the already selected 125 SenMayo genes – would be upregulated in our SASP cell cluster (Reviewer only. Fig. 10).
+
+![Bar chart showing top genes in the SASP cells cluster, sorted along their fold average-fold change compared to all other clusters.](page_109_670_495_377.png)
+
+Reviewer only. Figure 10. Top genes in the SASP cells cluster, that were not included in the SenMayo, sorted along their fold average-fold change compared to all other clusters.
+
+The highest fold-change was detected for the genes S100A9, CST3 and TYROBP. To further characterize the importance of these genes, and characterize the SASP cells in more detail, as elucidate their secretory phenotype in more detail, is part of ongoing studies in our lab.
+
+We are submitting our extensively revised manuscript for further consideration and hope it is now acceptable for publication in Nature Communications.
+Sincerely,
+
+Dominik Saul
+Sundeep Khosla
+References
+1. Lopes-Paciencia, S. et al. The senescence-associated secretory phenotype and its regulation. Cytokine **117**, 15–22; 10.1016/j.cyto.2019.01.013 (2019).
+2. Jin, S. et al. Inference and analysis of cell-cell communication using CellChat. *Nature communications* **12**, 1088; 10.1038/s41467-021-21246-9 (2021).
+3. La Manno, G. et al. RNA velocity of single cells. *Nature* **560**, 494–498; 10.1038/s41586-018-0414-6 (2018).
+4. Janky, R. et al. iRegulon: from a gene list to a gene regulatory network using large motif and track collections. *PLoS computational biology* **10**, e1003731; 10.1371/journal.pcbi.1003731 (2014).
+5. Oetjen, K. A. et al. Human bone marrow assessment by single-cell RNA sequencing, mass cytometry, and flow cytometry. *JCI insight* **3**; 10.1172/jci.insight.124928 (2018).
+6. The Tabula Muris Consortium. A single-cell transcriptomic atlas characterizes ageing tissues in the mouse. *Nature* **583**, 590–595; 10.1038/s41586-020-2496-1 (2020).
+Reviewers’ Comments:
+
+Reviewer #1:
+Remarks to the Author:
+Thank you for revising. I find that you have responded satisfactorily to my comments.
+
+Reviewer #2:
+Remarks to the Author:
+The authors have suitably addressed my concerns. I agree that it can set a new reference on identifying senescent cells.
+
+Reviewer #3:
+Remarks to the Author:
+The authors addressed most of the reviewers' concerns; now they are more readable and make sense. Especially the addition of the iRegulon/ SCENIC and data generated with this single-cell technology is a great improvement of the manuscript. Meanwhile, the author also provided the R code in the notebook for further development to enhance throughput, therefore, I recommend acceptance of the manuscript for publication.

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+Peer Review File
+
+Mating harassment may boost the effectiveness of the sterile insect technique for Aedes mosquitoes
+Reviewers' Comments:
+
+Reviewer #1:
+Remarks to the Author:
+The study titled “Mating harassment may boost the effectiveness of the sterile insect technique for Aedes mosquitoes” by Zhang et al. presents relevant results about the effect of sexual harassment on the longevity of the Aedes aegypti and Aedes albopictus females, as well as the biting rates on humans. The results presented are of broad interest to the scientific community working on controlling vectors of human diseases, especially those using the Sterile Insect Technique (SIT) for mosquitoes control.
+
+The document is well-written. The methods are explained in detail and in an understandable way. The conclusions are drawn based on the results presented, and their impact is well discussed.
+
+The manuscript has some minor typos and redundant phrases. For example, line 166 should say “at” instead of and. In Supplementary Information, pg. 45, line 4, the word some is repeated twice.
+
+I would like to point out that the term “native” (line 50) is wrongly used in this context. The SIT is not only used in the control of native insect species but also in the control of exotic ones. For example, SIT is used in different countries of the Americas to control the Mediterranean fruit fly, an exotic species. I suggest changing “native” to “wild” females.
+
+Another imprecise term is “virgin” (line 50). Even though the main objective of the SIT is that sterile males mate with virgin wild females, it is also desirable that released males can mate with already mated females. For this reason, I also suggest removing the word “virgin”.
+By using “virgin native” females, the authors wrongly constrain the SIT’s extent.
+
+Reviewer #2:
+Remarks to the Author:
+This paper explores whether inundative releases of sterile male Aedes aegypti and Aedes albopictus result in harassment of female mosquitoes, and suggests that this harassment can interfere with female feeding success, reducing their lifespan, host contact, and thereby pathogen transmission potential. The authors have explored this in a number of different lab and semi-field settings, as well as (for Ae. albopictus) in a field setting. This mechanism could explain why SIT and related control methods are potentially more effective than they would be based only on predictions regarding sterile mating. The main conclusions drawn from this work are presented as hypotheses regarding high male:female sex ratios reducing female feeding success, and that this may occur in a wider range of control methods that rely on distorting sex ratios. I think this is valuable and interesting, I do have the following comments regarding the study, which make it – to me – a bit challenging to clearly interpret the results as being due to harassment and reduced feeding success per se:
+
+One of the concerns I have regarding the experimental design, is that although the sex ratio is changed among treatments, at the same time overall mosquito density is changed as well (e.g., page 27, line 125 – m:f numbers of 1980:20 and 20:20 were contrasted – this isn’t completely clear everywhere, but it suggests that density was not kept at a constant level). From the methods, it is not clear why this decision was made, rather than varying sex ratio while keeping the overall density constant (presumably because it would be too cumbersome to perform the experiment otherwise).
+This potentially confounds the interpretation, as some of the results may then not have so much to do with male harassment per se, but could just be a consequence of density. This might explain for instance why in Ae. albopictus male mortality also increases with more biased sex ratios (although not in Ae. aegypti).
+How the semi-field human landing catch was used to determine m:f ratios, or female feeding success is a bit unclear. Particularly, it is stated that a volunteer would kill mosquitoes as they land, but not described what this consists of or how this was performed. Particularly, I’d be concerned that with that many males flying around, it would become quite a difficult task to spot females as they’re landing? In other words, how can you be sure females were less likely to approach or feed, rather than volunteers struggling to spot or kill them due to large number of males flying around their legs? At least a clearer description of the way these catches were performed would be helpful.
+
+It’s not clear how or whether the field trial can separate out effects related to feeding inhibition and harassment and an overall reduction in female numbers due to a reduction in population size. There is the more skewed sex ratio found in human landing catches compared to that found in BG traps, but it strikes me that it could be more helpful to compare differences in the proportion of eggs that hatched vs differences in abundance of eggs that hatched, since then you could potentially separate out differences in suppression due to sterility, versus suppression due to other effects on females. Was data on percent hatch rate in the different areas collected?
+
+I do think the evidence for feeding inhibition from the lab is very interesting and raises the question whether and how this plays out in the field, and how that depends on the mating system of the species in question. For instance, could this suggest that SIT is actually potentially more effective against certain Aedes species than it is for Anopheles or Culex, due to the host-based mating system and possible disruption of feeding? What about species like Ae. polynesiensis, that appear to have swarms instead or in addition to host-based mating? Some discussion along these lines to put the current results and impact on SIT in the context of different mating habits of mosquitoes would be helpful.
+
+The introduction is clear, and gives a good overview of the sterile insect technique and its potential for use to control Aedes spp. mosquitoes. There are a few citations that could potentially be added that have also touched on the issue of mating harassment in mosquitoes. For instance, Dao et al 2010 (Journal of Medical Entomology, 47(5), pp.769-777.) provides some evidence that also is suggestive of a cost of harassment, namely exposure to males, rather than consequences of mating, on female longevity. And Stone 2013 (PLoS One 8 (9), e76228) considers a number of aspects of male life history and mating behavior, including harassment of females, and explores their impact on SIT effectiveness using simple models.
+
+Line 145 – “In nature, ..." This is speculative, and better kept for the discussion. One could also argue that in nature harassment might be much less important as females are more likely to be able to evade males, disperse to areas with fewer males, or possibly even shift their feeding behavior to hosts where males are less likely to aggregate?
+
+In Fig 2, and the part of the results section that describes these results, please specify here (in addition to the methods) which species these results are based on. In general, the rationale for using both species for some, but only a single species, and not always the same, for other aspects of the study is not particularly clear. Replicating these studies among different locations and with different strains certainly is a strong point of the study, but at the same time, not everything is replicated everywhere, and being clear about the rationale behind these choices would strengthen the paper. For instance, why was the field trial performed with Ae. albopictus, rather than with Ae. aegypti?
+
+Why are data not presented for the buffer zone? From fig 3 you had traps placed there as well, and this could tell you something about (possibly) whether females are avoiding / dispersing away from the release zone, or potentially whether your released males were having some impact in a surrounding area.
+Line 249-254: This statement ("females that were exposed to males at a 1:3 or 99:1 ratio...did not show any increase in mortality") is unclear – from ext. data fig 5 it seems that both these treatments have a mortality cost associated with them, i.e., a lower survival than the virgin females of the same age. Doesn’t that suggest the opposite, that it was the act of mating leading to this difference, rather than the act of harassment and possible energetic costs, which surely would have been much more intense at 99:1?
+
+Reviewer #3:
+Remarks to the Author:
+Zhang et al study focused on the sterile insect technique (SIT) is a method of controlling insect pest populations that involves releasing large numbers of sterile males into the wild. The sterile males mate with wild females, but no offspring are produced, which helps to reduce the overall population of the pest species. However, recent research has shown that the release of sterile males in high ratios to females may also have unintended consequences.
+
+Under laboratory conditions, they showed that female Aedes mosquitoes had reduced feeding success and shorter lifespans when exposed to male to female ratios above 50 to 1. Semi-field experiments also showed reduced blood uptake from artificial hosts and lower biting rates on humans. In a field trial conducted in China, the release of sterile males led to a reduction in female mosquito density and biting rates, but also resulted in increased female mortality due to mating harassment.
+
+These findings suggest that while the SIT can effectively suppress mosquito populations and reduce disease transmission, it is important to carefully consider the ratio of sterile males to females in order to minimize unintended consequences such as increased female mortality and reduced feeding success.
+
+Major comments:
+
+1. The number of mosquitoes needed to be released continuously to achieve a certain level of reduction in the population would depend on several factors, such as the size of the target population, the release ratio of sterile males to wild females, and the frequency of releases. It would require a comprehensive analysis of the specific situation to determine the appropriate release strategy and the number of mosquitoes needed. How did these variables accounted in this study?
+
+2. The manuscript does not provide information on the population of wild males or the size of natural swarms. The study mainly focuses on the impact of different ratios of sterile males to wild females on the target female population. How big was the swarm? Did they mark the swarming sites?
+
+3. The manuscript does not provide information on the yearly biting rate and surveillance in the area before the release of sterile males. Could you please add more the details of the surveillance in that area before and after treatment?
+
+4. Reaching the ratio of success would require careful planning and execution of the release strategy, taking into account factors such as the size of the area, the target population density, and the frequency of releases. It is possible that the SIT mosquitoes and natural mosquitoes could generate two different swarms, but this would depend on several factors, including the release strategy and the behaviour of the mosquitoes.
+
+5. The graphs could be presented in a clearer manner with statistical significance accurately reported. This would help readers to better understand the level of accuracy of the data.
+
+6. It is possible that the change in the location of the natural swarm may have contributed to the
+sharp rise in the suppression observed in Figure 4a. However, further analysis would be required to confirm this.
+
+7. The manuscript does not provide detailed information on the traps used or the reasons behind their selection. However, it is possible that alternative methods of capture could be explored to increase the number of mosquitoes captured and improve the statistical significance of the data.
+
+8. The ethics are not clearly addressed. There is no information for ethics and protocol numbers, etc.
+
+Minor comments:
+
+The format of writing, whether US or British English, should be chosen and consistently applied throughout the manuscript. The entire manuscript should be revised accordingly to ensure adherence to the chosen format.
+
+The lines that require revision for writing errors:
+1. Page 2, lines 37-38
+2. Page 30, line 200, "ad libitum" should be italicized
+2. Page 45, line 4
+REVIEWER COMMENTS
+
+Reviewer #1 (Remarks to the Author):
+
+The study titled “Mating harassment may boost the effectiveness of the sterile insect technique for Aedes mosquitoes” by Zhang et al. presents relevant results about the effect of sexual harassment on the longevity of the Aedes aegypti and Aedes albopictus females, as well as the biting rates on humans. The results presented are of broad interest to the scientific community working on controlling vectors of human diseases, especially those using the Sterile Insect Technique (SIT) for mosquitoes control.
+
+The document is well-written. The methods are explained in detail and in an understandable way. The conclusions are drawn based on the results presented, and their impact is well discussed.
+
+Many thanks for your positive comments.
+
+The manuscript has some minor typos and redundant phrases. For example, line 166 should say “at” instead of and. In Supplementary Information, pg. 45, line 4, the word some is repeated twice.
+
+OK, corrected
+
+I would like to point out that the term “native” (line 50) is wrongly used in this context. The SIT is not only used in the control of native insect species but also in the control of exotic ones. For example, SIT is used in different countries of the Americas to control the Mediterranean fruit fly, an exotic species. I suggest changing “native” to “wild” females.
+
+Agreed and corrected accordingly.
+
+Another imprecise term is “virgin” (line 50). Even though the main objective of the SIT is that sterile males mate with virgin wild females, it is also desirable that released males can mate with already mated females. For this reason, I also suggest removing the word “virgin”. By using “virgin native” females, the authors wrongly constrain the SIT’s extent.
+
+Agreed and corrected accordingly.
+
+Reviewer #2 (Remarks to the Author):
+
+This paper explores whether inundative releases of sterile male Aedes aegypti and Aedes albopictus result in harassment of female mosquitoes, and suggests that this harassment can interfere with female feeding success, reducing their lifespan, host contact, and thereby pathogen transmission potential. The authors have explored this in a number of different lab and semi-field settings, as well as (for Ae. albopictus) in a field setting. This mechanism could explain why SIT and related control methods are potentially more effective than they would be based only on predictions regarding sterile mating. The main conclusions drawn from this work are presented as hypotheses regarding high male:female sex ratios reducing female feeding success, and that this may occur in a wider range of control methods that rely on distorting sex ratios. I think this is valuable and interesting. I do have the following comments regarding the study, which make it – to me – a bit challenging to clearly interpret the results as being due to harassment and reduced feeding success per se:
+One of the concerns I have regarding the experimental design, is that although the sex ratio is changed among treatments, at the same time overall mosquito density is changed as well (e.g., page 27, line 125 – m:f numbers of 1980:20 and 20:20 were contrasted – this isn’t completely clear everywhere, but it suggests that density was not kept at a constant level). From the methods, it is not clear why this decision was made, rather than varying sex ratio while keeping the overall density constant (presumably because it would be too cumbersome to perform the experiment otherwise). This potentially confounds the interpretation, as some of the results may then not have so much to do with male harassment per se, but could just be a consequence of density. This might explain for instance why in Ae. albopictus male mortality also increases with more biased sex ratios (although not in Ae. aegypti).
+
+There is a misunderstanding here: in all lab trials aiming at measuring the impact of the ratio on the mortality, the overall density of mosquitoes was kept constant to avoid this confounding factor. We totally agree with the reviewer that otherwise, it would have impacted the mortality. It was already clearly stated in the Methods section (L46-50): “To study the sexual harassment of males on Aedes mosquito females without allowing potential density-dependent mortality, batches of 3,000 Ae. aegypti mosquitoes aged 0 to 1 day were placed in the Bugdorm cages (30 × 30 × 30 cm) at six male to female sex ratios (SR): SR= 3:7, SR = 1:3 (control, used in the colony maintained in mass-rearing conditions), SR = 10:1, SR = 23:2, SR = 49:1 and SR = 99:1.”. So there were always 3000 individuals per cage, and only the sax-ratio varied. To make it easier to understand by readers, we now have made it very clear in the main text, at the beginning of the section “Survival of mosquitoes caged at different sex ratios” by adding this sentence: “All experiments aiming to measure survival were done at a constant density of mosquitoes per cage, only varying the sex ratio, in order to control density-dependent mortality.”
+
+Now in the semi-field trial, we wanted to mimic what is happening in field conditions, where the release of large numbers of sterile males lead them to aggregate around human hosts, actually increasing the overall density of mosquitoes around hosts (swarms of males are visible and can even represent a nuisance). This time, we did not measure any mortality and we kept the vector (females) to host ratio constant to see how males can interfere with the vector-host contact measured by the engorgement rate for the artificial host, and the human landing catch (like in the field experiment) for the human host. We believe this was the right protocol to explore feeding interference? We added this sentence at the beginning of the corresponding section to guide the reader “In this experiment, we varied the male to female ratio while keeping the vector (female) to host ratio constant, in order to study the impact of mating harassment on host-vector contact.”
+
+How the semi-field human landing catch was used to determine m:f ratios, or female feeding success is a bit unclear. Particularly, it is stated that a volunteer would kill mosquitoes as they land, but not described what this consists of or how this was performed. Particularly, I’d be concerned that with that many males flying around, it would become quite a difficult task to spot females as they’re landing? In other words, how can you be sure females were less likely to approach or feed, rather than volunteers struggling to spot or kill them due to large number of males flying around their legs? At least a clearer description of the way these catches were performed would be helpful.
+
+We totally understand the concerns of the reviewers. It was indeed a challenging experiment and the volunteers were actually fully protected and killed all potentially successful females while not killing the males or unsuccessful females. We also checked at the end that there was no engorged females in the cages by collecting all of them. We now have included much more details in the Methods section as follows:
+"We conducted a second experiment based on Human Landing Catch in China to assess whether male harassment can prevent blood feeding on humans in semi-field conditions. Wild type virgin Ae. albopictus (GUA strain) females were inseminated at 5-6 days old. They were starved for 24 hours before the experiment start. Irradiated HC males were virgin and 5-6 days old. Irradiated HC males were released into semi-field cages (1.80 × 1.80 × 1.80 m, containing two sugar water containers). GUA females were released 24 hours later into the semi-field cages. Male and female release numbers were 1980 versus 20 for the 99:1 ratio and 20 versus 20 for the 1:1 ratio. The mosquitoes were immobilized by placing them in a chilling room with a temperature of 8 ± 2°C. Subsequently, we conducted a precise count of the required number of mosquitoes. Ten minutes after releasing the females, an adult volunteer wearing long-sleeved shirt, long pants, gloves, and mosquito-proof hat entered and sat on a chair in the middle of each cage. The collector exposed one of his legs from foot to knee and killed mosquitoes as soon as they landed on the exposed leg before they started feeding. Since there were female mosquitoes attempting to feed on the volunteers but failed due to mating harassment from males, only the females that successfully landed on exposed skin were classified as potential "successful bloodsuckers". To avoid the collection of male mosquitoes and "unsuccessful bloodsuckers", we opted to eliminate the landed females by swatting and killing them rather than using an aspirator. This approach was necessary due to the large number of male mosquitoes forming a swarm around the volunteer and the presence of female mosquitoes facing harassment while attempting to feed. This method prevented the collection of non-target mosquitoes. Mosquito collection was conducted for 15 min for each cage and ratio. All collected females were removed and counted. After 15 min of collection, remaining mosquitoes were collected with an aspirator and females individually checked for blood feeding or not. Three repeats were conducted with three different collectors managing one 99:1 and one 1:1 cage each. Collectors received appropriate information and gave their informed consent prior to participating in this study."
+
+We hope that the reviewer will be happy with these details.
+
+It’s not clear how or whether the field trial can separate out effects related to feeding inhibition and harassment and an overall reduction in female numbers due to a reduction in population size. There is the more skewed sex ratio found in human landing catches compared to that found in BG traps, but it strikes me that it could be more helpful to compare differences in the proportion of eggs that hatched vs differences in abundance of eggs that hatched, since then you could potentially separate out differences in suppression due to sterility, versus suppression due to other effects on females. Was data on percent hatch rate in the different areas collected?
+
+We agree that the egg hatch rate can be potentially used to separate the difference. However, in this field trial we initially did not use the hatch rate because we encountered a problem with the methodology: the ovitraps were collected after 7 days of setting in the field and were left for another 7 days for incubation in the lab, but some of early laid eggs hatched in between and hatched larvae ate some of the eggs, which resulted in more larvae than eggs for some time/trap points (see raw data). We tried to conduct an analysis following your request, considering a hatching rate of 1 in all traps where the number of larvae exceeded the number of eggs (the number of larvae was considered equal to the number of eggs). We analysed the impact of the releases on the hatching rate using mixed binomial models with the time after the beginning of the releases, the treatment (release, buffer, control) and their first order interaction as fixed effects, and traps id and dates as random effect.
+The graphs below present the dynamics of the hatch rate (and standard error) (the month is presented as a number and the releases started on 16th August):
+
+![Dynamics of the hatch rate per month (option 1)](page_246_357_1017_489.png)
+
+We did not observe any significant effect of the treatment, meaning that all the observed suppression effect on both adults and eggs is probably due to mating harassment that can reduce female longevity and feeding success, as demonstrated in the other experiments, which will in turn result in reduced fecundity. We believe that the release area (1.17 ha) was too small and non isolated from the control area to make it possible to observe the effect of induced sterility, because fertile females could migrate from the control and buffer areas into the release area. However, such a small size with huge numbers of males was perfect to measure the effect of mating harassment, because sterile males do not move much. We made a similar observation during a MRR in Albania recently (Velo et al. 2022), where all males stayed <100m from the release site whereas we did not observe any spatial trend in induced sterility within 250m from the release point, suggesting stronger dispersal of egg-laying females than males.
+
+We added this part to the results section:
+
+“After the beginning of the releases, we did not observe any significant impact of the hatch rate of eggs between the release (0.43, min to max: 0.32-0.52) and the control (0.44, min to max: 0.36-0.52) areas (z = 1.684, p = 0.092), showing that induced sterility did not contribute to population suppression.”
+
+We also acknowledged in the discussion that the hatching methodology is problematic and that we should not consider the absolute values. Removing all data points with more larvae than eggs also led to the same result:
+![Dynamics of the hatch rate per month](page_184_120_1080_670.png)
+
+Finally, we analysed all hatching data from 2022 and 2023 during this revision process and found similar results than in 2021 despite the correction of the hatching protocol, with no significant induced sterility in 2022, and a limited induced sterility of ~10% in 2023, unable to explain the observed suppression rates. Thanks for this remark that allowed to greatly improve the evidence of a strong impact of mating harassment on females.
+
+I do think the evidence for feeding inhibition from the lab is very interesting and raises the question whether and how this plays out in the field, and how that depends on the mating system of the species in question. For instance, could this suggest that SIT is actually potentially more effective against certain Aedes species than it is for Anopheles or Culex, due to the host-based mating system and possible disruption of feeding? What about species like Ae. polynesiensis, that appear to have swarms instead or in addition to host-based mating? Some discussion along these lines to put the current results and impact on SIT in the context of different mating habits of mosquitoes would be helpful.
+
+We totally agree with this remark and added this paragraph to the discussion:
+“In both species studied here, feeding inhibition was demonstrated in the lab, together with an impact on female suppression in the field in the case of Ae. albopictus. However, such an impact will strongly depend on the mating system of the target species (Lees et al. 2014) and it would be important to study this phenomenon in Anopheles or Culex species, or even Ae. polynesiensis that may use swarms triggered by visual cues instead or in addition to host-based mating.”
+
+The introduction is clear, and gives a good overview of the sterile insect technique and its potential for use to control Aedes spp. mosquitoes. There are a few citations that could potentially be added that have also touched on the issue of mating harassment in mosquitoes. For instance, Dao et al 2010 (Journal of Medical Entomology, 47(5), pp.769-777.) provides some evidence that also is suggestive of a cost of harassment, namely exposure to males, rather than consequences of mating, on female longevity. And Stone 2013 (PLoS One 8 (9), e76228) considers a number of aspects of male
+life history and mating behavior, including harassment of females, and explores their impact on SIT effectiveness using simple models.
+
+Many thanks for these references, which are indeed totally in line with our work! We added that of Dao et al. to the intro and that of Stone in the discussion.
+
+Line 145 – “In nature, ...” This is speculative, and better kept for the discussion. One could also argue that in nature harassment might be much less important as females are more likely to be able to evade males, disperse to areas with fewer males, or possibly even shift their feeding behavior to hosts where males are less likely to aggregate?
+
+OK, it was moved to the discussion section.
+
+In Fig 2, and the part of the results section that describes these results, please specify here (in addition to the methods) which species these results are based on. In general, the rationale for using both species for some, but only a single species, and not always the same, for other aspects of the study is not particularly clear. Replicating these studies among different locations and with different strains certainly is a strong point of the study, but at the same time, not everything is replicated everywhere, and being clear about the rationale behind these choices would strengthen the paper. For instance, why was the field trial performed with Ae. albopictus, rather than with Ae. aegypti?
+
+OK, we have now explained the rational for species, strains and site selection in the relevant sections of the Methods. To be honest, the choice of the field trial was quite opportunistic to test our theory against at least one of the species because we took the opportunity of a preliminary SIT trial organized in China offering perfect settings to investigate the impact of male mating harassment in the absence of a strong induced sterility component, particularly a small and non-isolated release area. It is now specified in the Methods section.
+
+Why are data not presented for the buffer zone? From fig 3 you had traps placed there as well, and this could tell you something about (possibly) whether females are avoiding / dispering away from the release zone, or potentially whether your released males were having some impact in a surrounding area.
+
+Thanks for this suggestion. We now included data from the buffer area in the results section of the manuscript. When we analysed the data on the number of females and the male/female ratio captured via BG and HLC in the buffer site, and compared to both release and control sites, we observed that the number of females captured showed no difference between the buffer and control sites, despite higher male/female ratios in the buffer than in the control area, but much lower than in the release site. This indicates that few sterile males dispersed to the buffer area and that the male to female ratio was insufficient to have impacts on the population density.
+
+The following table summarizes the results for the period 3-6th Nov that we included in the paper:
+
+<table>
+  <tr>
+    <th rowspan="2">Dates</th>
+    <th colspan="3">No. of female capture via BG</th>
+    <th colspan="3">Male/female ratio via BG</th>
+  </tr>
+  <tr>
+    <th>Release site</th>
+    <th>Buffer site</th>
+    <th>Control site</th>
+    <th>Release site</th>
+    <th>Buffer site</th>
+    <th>Control site</th>
+  </tr>
+  <tr>
+    <td>11.3-11.4</td>
+    <td>2.5 ± 1.3</td>
+    <td>3.40 ± 1.4</td>
+    <td>4.33 ± 0.9</td>
+    <td>12.5 ± 5.5</td>
+    <td>1.45 ± 0.7</td>
+    <td>0.44 ± 0.2</td>
+  </tr>
+  <tr>
+    <td></td>
+    <td>No. of females</td>
+    <td>Male/female ratio via HLC</td>
+    <td></td>
+    <td></td>
+    <td></td>
+    <td></td>
+  </tr>
+</table>
+<table>
+  <tr>
+    <th rowspan="2">captured via HLC</th>
+    <th colspan="3">Release site</th>
+    <th colspan="3">Buffer site</th>
+    <th colspan="3">Control site</th>
+  </tr>
+  <tr>
+    <th>Release site</th>
+    <th>Buffer site</th>
+    <th>Control site</th>
+    <th>Release site</th>
+    <th>Buffer site</th>
+    <th>Control site</th>
+  </tr>
+  <tr>
+    <td>11.3, 11.4 and 11.6</td>
+    <td>0.5 ± 0</td>
+    <td>3.33 ± 0.6</td>
+    <td>2.72 ± 0.2</td>
+    <td>101.3 ± 35.8</td>
+    <td>4.21 ± 1.1</td>
+    <td>0.96 ± 0.3</td>
+  </tr>
+</table>
+
+To better understand the threshold for feeding inhibition, we performed a new experiment to observe the effects of male/female ratio on the feeding rate as shown in the below table. We did not observe negative impact on the feeding rate when the male/female ratio was 10:1, as compared to 1:1. However, when the ratio of male/female reached 30:1, we observed a significant reduced feeding rate in a lab cage (30*30*30cm) with a mouse as a host. The average feeding rate was 16.7% in comparison to 56.7% in 1:1 ratio. This confirmed that a strong male to female ratio is necessary to observe feeding inhibition and we now included these results in the result section and fig. 2.
+
+Line 249-254: This statement ("females that were exposed to males at a 1:3 or 99:1 ratio...did not show any increase in mortality") is unclear – from ext. data fig 5 it seems that both these treatments have a mortality cost associated with them, i.e., a lower survival than the virgin females of the same age. Doesn’t that suggest the opposite, that it was the act of mating leading to this difference, rather than the act of harassment and possible energetic costs, which surely would have been much more intense at 99:1?
+We agree with your interpretation and our sentence was unclear: we rephrased it.
+
+Reviewer #3 (Remarks to the Author):
+
+Zhang et al study focused on the sterile insect technique (SIT) is a method of controlling insect pest populations that involves releasing large numbers of sterile males into the wild. The sterile males mate with wild females, but no offspring are produced, which helps to reduce the overall population of the pest species. However, recent research has shown that the release of sterile males in high ratios to females may also have unintended consequences.
+
+Under laboratory conditions, they showed that female Aedes mosquitoes had reduced feeding success and shorter lifespans when exposed to male to female ratios above 50 to 1. Semi-field experiments also showed reduced blood uptake from artificial hosts and lower biting rates on humans. In a field trial conducted in China, the release of sterile males led to a reduction in female mosquito density and biting rates, but also resulted in increased female mortality due to mating harassment.
+
+These findings suggest that while the SIT can effectively suppress mosquito populations and reduce disease transmission, it is important to carefully consider the ratio of sterile males to females in order to minimize unintended consequences such as increased female mortality and reduced feeding success.
+Thanks for this summary. There is however a misunderstanding in the last sentence: it is actually desirable to have increased female mortality and reduced feeding success because this will reduce disease transmission risk, even if it is an unintended effect.
+
+Major comments:
+
+1. The number of mosquitoes needed to be released continuously to achieve a certain level of reduction in the population would depend on several factors, such as the size of the target population, the release ratio of sterile males to wild females, and the frequency of releases. It would require a comprehensive analysis of the specific situation to determine the appropriate release strategy and the number of mosquitoes needed. How did these variables accounted in this study?
+We totally agree with this remark and we even published a paper with such a recommendation (Bouyer et al. 2020). However, this study was a preliminary trial to set up procedures and measure the quality of the sterile males in order to prepare a suppression trial at a larger scale.
+
+2. The manuscript does not provide information on the population of wild males or the size of natural swarms. The study mainly focuses on the impact of different ratios of sterile males to wild females on the target female population. How big was the swarm? Did they mark the swarming sites?
+
+We indeed performed two mark-release-recapture (MRR) experiments to estimate wild mosquito population before release but we did not provide this information in the previous version of the manuscript. We now added one sentence in the maintext: “The density of the wild Ae. albopictus males was estimated to range from 6553 to 10076 males/ha and from 2875 to 5292 males/ha via two independent performed mark-release-recapture experiments performed just before the beginning of this trial (data not shown).”
+
+Regarding to the swarm and swarm sites, we have to clarify that we did not observe “big swarms” observed in Aedes albopictus, but rather small diffused swarms upon hosts and visual markers. We thus did not mark swarming sites.
+
+3. The manuscript does not provide information on the yearly biting rate and surveillance in the area before the release of sterile males. Could you please add more the details of the surveillance in that area before and after treatment?
+
+Even though we did not continuously monitor the biting rate yearly, there were 4 independent human landing captures (HLCs) performed respectively in May, June, July and August before release (please see Extended Dada Fig. 6b). For the surveillance of mosquito population, we used ovitraps placed in the natural breeding sites from 8th March to 17th August before release (please see extended data Fig. 6a). Similar mosquito density in the release and un-release area based the number of the hatched eggs per ovitrap and the captured females (equal to biting index). The above-mentioned information has been shown in our Extended data Fig.6.
+
+We now provided more detailed information on how we did the surveillance using the ovitraps. We added this paragraph in the Methods section:
+
+“Briefly, the ovitrap constituted of transparent bottles with a black lid with three holes, allowing engorged females entering the trap for laying eggs. The ovitraps were cylindrical plastic containers of 70-75 mm diameter and 100 mm height. Before using, a piece of filter
+paper (70 mm width and 45 mm height) was inserted along the ovitrap wall. A 50 mL bamboo leaf solution was added in the ovitrap to increase the trapping efficiency. Ovitraps were placed close to the natural breeding sites of Ae. albopictus for 7 days. The positive ovitraps were collected and incubated for another 7 days at room temperature before counting the number of eggs and the hatched larvae. Positive traps where eggs or larvae were observed were selected for further evaluation. The filter paper with eggs were removed from the ovitrap and the egg hatch rate was determined under a stereomicroscope. Boiling water was used to kill the remaining larvae and the number of larvae was counted. Unfortunately, we observed that some of early laid eggs hatched before initiating the hatching procedure and that larvae ate some of the floating eggs, which resulted in more larvae than eggs for some time-point data (see raw data). We thus considered a hatch rate of 1 for all these data points in the analysis."
+
+4. Reaching the ratio of success would require careful planning and execution of the release strategy, taking into account factors such as the size of the area, the target population density, and the frequency of releases. It is possible that the SIT mosquitoes and natural mosquitoes could generate two different swarms, but this would depend on several factors, including the release strategy and the behaviour of the mosquitoes.
+
+As already presented in the manuscript based on both HLC and BG data, we indeed reached very high male to female ratios in our study (70.5:1 vs 16.6:1 respectively, Fig. 4d). As stated upon, there is no big swarms in Aedes albopictus, and the HLC collections do collect the males swarming upon human hosts where we saw that the mosquitoes were clearly mixed wild and sterile males using PCR.
+
+5. The graphs could be presented in a clearer manner with statistical significance accurately reported. This would help readers to better understand the level of accuracy of the data.
+
+OK, this was done as requested.
+
+6. It is possible that the change in the location of the natural swarm may have contributed to the sharp rise in the suppression observed in Figure 4a. However, further analysis would be required to confirm this.
+
+Again, there is not a single swarm in this species and we demonstrated that sterile and wild males were swarming together upon hosts.
+
+7. The manuscript does not provide detailed information on the traps used or the reasons behind their selection. However, it is possible that alternative methods of capture could be explored to increase the number of mosquitoes captured and improve the statistical significance of the data. We used BG-Sentinel traps for collecting Aedes albopictus in this study since they are widely used for trapping Aedes mosquitoes (see studies Zheng X et al. Nature, 2019, 572(7767):56-61; Le Goff G et al. Parasit Vectors, 2019, 12(1):81; Le Goff G et al. Parasit Vectors, 2016, 9(1):514; Velo E et al. Front Bioeng Biotechnol, 2022, 10:833698.). To assess the biting index via human landing capture (HLC), fan trap is used to collect the surrounded mosquitoes which are attracted by the volunteers (as we did in a previous study, see (Zheng et al. 2019)). The description on how to use the fan trap is shown in the maintext in lines 241-243. Finally,
+ovitraps were used to monitor the larval index. More detail information on the ovitrap has been added in the Method sections (see upon).
+
+We fully agree with the Reviewer that different trapping methods will result in varied trapping efficiency. In our study, we used three important indicators via ovitrap, BG traps and HLC in both the release and control areas to ensure robust data. We believe that the three methods used in parallel were appropriate to give a good monitoring of the impact of the sterile male releases on the wild population.
+
+8. The ethics are not clearly addressed. There is no information for ethics and protocol numbers, etc.
+
+OK, this has been addressed.
+
+Minor comments:
+
+The format of writing, whether US or British English, should be chosen and consistently applied throughout the manuscript. The entire manuscript should be revised accordingly to ensure adherence to the chosen format.
+
+OK, we applied English(UK) throughout our manuscript.
+
+The lines that require revision for writing errors:
+1. Page 2, lines 37-38
+2. Page 30, line 200, “ad libitum” should be italicized
+2. Page 45, line 4
+
+OK, these typos have been corrected, thanks
+
+References cited
+
+Bouyer, J., H. Yamada, R. Pereira, K. Bourtzis, and M. J. B. Vreysen. 2020. Phased Conditional Approach for Mosquito Management using the Sterile Insect Technique. Trends Parasitol. 36: 325-336.
+Lees, R. S., B. G. J. Knols, R. Bellini, M. Q. Benedict, A. Bheecarry, H. Bossin, D. D. Chadee, J. P. Charlwood, R. K. Dabire, and L. Djogbenou. 2014. Improving our knowledge of male mosquito biology in relation to genetic control programmes. Acta Trop. 132: S2-S11.
+Velo, E., F. Balestrino, P. Kadriaj, D. Carvalho, A. H. Dicko, R. Bellini, A. Puggioli, D. Petric, A. Michaelakis, F. Schaffner, D. Almenar, I. Pajovic, A. Beqirliari, M. Ali, G. Sino, E. Rogozi, V. Jani, A. Nikolla, T. Porja, T. Goga, E. Falcuta, M. Kavran, D. Pudar, O. Mikov, N. Ivanova-Aleksandrova, A. Cvetkovicj, M. M. Akiner, R. Mikovic, L. Tafaj, S. Bino, J. Bouyer, and W. Mamai. 2022. A Mark-Release-Recapture study to estimate field performance of imported radio-sterilized male Aedes albopictus in Albania. Frontiers in Bioengineering and Biotechnology 10: 833698.
+Zheng, X., D. Zhang, Y. Li, C. Yang, Y. Wu, X. Liang, Z. Yan, L. Hu, Q. Sun, Y. Liang, J. Zhuang, X. Wang, Y. Wei, J. Zhu, W. Qian, A. G. Parker, J. R. L. Gilles, K. Bourtzis, J. Bouyer, M. Tang, J. Liu, Z. Hu, J.-T. Gong, X.-Y. Hong, Z. Zhang, L. Lin, Q. Liu, Z. Hu, Z. Wu, L. A. Baton, A. A. Hoffmann, and Z. Xi. 2019. Incompatible and sterile insect techniques combined eliminate mosquitoes. Nature 572: 56-61.
+Reviewers' Comments:
+
+Reviewer #2:
+Remarks to the Author:
+The authors have thoroughly and clearly addressed all my concerns and I now recommend this paper be accepted.
+
+Reviewer #3:
+Remarks to the Author:
+Thank you! I am happy with the responses.

0a660decf706a7bae16eaad20f5cee68c5f0e65b8e6c8aae0702e8860aab4ec1/preprint/preprint.md

@@ -0,0 +1,741 @@
+Mating harassment may boost the effectiveness of the sterile insect technique for Aedes mosquitoes
+
+Jérémy Bouyer
+bouyer@cirad.fr
+
+Insect Pest Control Sub-Programme, Joint FAO/IAEA Centre of Nuclear Techniques in Food and Agriculture, International Atomic Energy Agency (IAEA)  https://orcid.org/0000-0002-1913-416X
+
+Dongjing Zhang
+Sun Yat-sen University - Michigan State University Joint Center of Vector Control for Tropical Diseases, Sun Yat-Sen University
+
+Hamidou Maiga
+IAEA
+
+Yongjun Li
+Guangzhou University
+
+Mame Thiemo Bakhoum
+IAEA  https://orcid.org/0000-0001-6794-4426
+
+Gang Wang
+Sun Yat-sen University
+
+Yan Sun
+Sun Yat-sen University
+
+David Damiens
+Institut de Recherche pour le Développement
+
+Wadaka Mamai
+IAEA
+
+Nanwintoum Somda
+IAEA
+
+Thomas Wallner
+IAEA
+
+Odet Bueno Masso
+IAEA
+
+Claudia Martina
+IAEA
+
+Simran Kotla
+IAEA
+
+Hanano Yamada
+IAEA
+Lu Deng
+Environmental Health Institute, National Environment Agency
+Cheong Huat Tan
+Environmental Health Institute   https://orcid.org/0000-0001-6263-9721
+Jiatian Guo
+Sun Yat-sen University
+Qingdeng Feng
+Sun Yat-sen University
+Junyan Zhang
+Sun Yat-sen University
+Xufei Zhao
+Sun Yat-sen University
+Dilinuer Paerhande
+Sun Yat-sen University
+Wenjie Pan
+SYSU Nuclear and Insect Biotechnology Co.,
+Yu Wu
+Sun Yat-sen University
+Xiaoying Zheng
+Sun Yat-sen University
+Zhongdao Wu
+Zhongshan School of Medicine, Sun Yat-sen University, Guangzhou, 510080, China
+Zhiyong Xi
+Michigan State University   https://orcid.org/0000-0001-7786-012X
+Marc Vreysen
+IAEA
+
+Biological Sciences - Article
+
+Keywords:
+
+Posted Date: August 11th, 2023
+
+DOI: https://doi.org/10.21203/rs.3.rs-3128571/v1
+
+License: © (c) This work is licensed under a Creative Commons Attribution 4.0 International License.
+Read Full License
+
+Additional Declarations: There is NO Competing Interest.
+Version of Record: A version of this preprint was published at Nature Communications on March 4th, 2024. See the published version at https://doi.org/10.1038/s41467-024-46268-x.
+Mating harassment may boost the effectiveness of the sterile insect technique for Aedes mosquitoes
+
+Dongjing Zhang1*, Hamidou Maiga2*, Yongjun Li3,4*, Mame Thierno Bakhoum2,5*, Gang Wang1*, Yan Sun1, David Damiens6, Wadaka Mamai2, Nanwintoum Séverin Bimbilé Somda2,7, Thomas Wallner2, Odet Bueno Masso2, Claudia Martina2, Simran Singh Kotla2, Hanano Yamada2, Deng Lu8, Cheong Huat Tan8, Jiatian Guo1, Qingdeng Feng1, Junyan Zhang1, Xufei Zhao1, Dilinuer Paerhandel1, Wenjie Pan9, Yu Wu1, Xiaoying Zheng1, Zhongdao Wu1, Zhiyong Xi4,10, Marc J.B. Vreysen2, Jérémy Bouyer2,11*#
+
+1Chinese Atomic Energy Agency Center of Excellence on Nuclear Technology Applications for Insect Control, Key Laboratory of Tropical Disease Control of the Ministry of Education, Sun Yat-sen University, Guangzhou, China
+
+2Insect Pest Control Laboratory, Joint FAO/IAEA Centre of Nuclear Techniques in Food and Agriculture, IAEA, Vienna, Austria
+
+3Department of Pathogen Biology, School of Medicine, Jinan University, Guangzhou, China
+
+4Guangzhou Wolbaki Biotech Co., Ltd, Guangzhou, China
+
+5Institut Sénégalais de Recherches Agricoles, Laboratoire National de l’Elevage et de Recherches Vétérinaires, BP 2057 Dakar, Sénégal
+
+6 Institut de Recherche pour le Développement (IRD), UMR MIVEGEC (CNRS/IRD/Université de Montpellier), IRD Réunion/GIP CYROI (Recherche Santé Bio-innovation), Sainte Clotilde, Reunion Island- France
+
+7Unité de Formation et de Recherche en Science et Technologie (UFR/ST), Université
+Norbert ZONGO (UNZ), BP 376 Koudougou, Burkina Faso
+
+8 National Environment Agency, Singapore
+
+9SYSU Nuclear and Insect Biotechnology Co., Ltd., Dongguan, China
+
+10Department of Microbiology and Molecular Genetics, Michigan State University, East Lansing, MI, USA
+
+11UMR ASTRE, CIRAD, F-34398 Montpellier, France
+
+*These authors contributed equally to this work
+
+#corresponding author: j.bouyer@iaea.org
+
+The sterile insect technique (SIT) is based on the overflooding of a target population with released sterile males inducing sterility in the wild female population. The SIT has proven to be effective against several insect pest species of agricultural and veterinary importance and is under development for Aedes mosquitoes. Here, we show that the release of sterile males in high sterile male to wild female ratios may also impact the target female population through mating harassment. Under laboratory conditions, male to female ratios above 50 to 1 reduced the longevity of female Aedes mosquitoes by reducing their feeding success. Under semi-field conditions, blood uptake of females from an artificial host and biting rates on humans were also strongly reduced. Finally, in a field SIT trial conducted in a 1.17 ha area in China, the female biting rate was reduced by 80%, concurrent to a reduction of female mosquito density of 40% due to the swarming of males around humans attempting to mate with the female mosquitoes. This suggests that the SIT does not only suppress mosquito vector populations through the induction
+of sterility, but might also reduce disease transmission due to increased female mortality and lower host contact.
+
+The SIT is based on the sequential release of sterile male insects over the target area where they will mate with the virgin native female insects¹, resulting in the induction of sterility in the wild female population proportionally to the ratio of sterile to wild insects. This impairs the reproduction rate of the female population and as a result, fewer insects will be available in subsequent generations, reducing the density of the target population over time. The SIT has been successfully used to manage populations of various insect pests of agricultural, animal, or human health importance², and more recently, there has been a renewed interest to develop and implement the SIT against mosquitoes³. Aedes mosquitoes are major vectors of viruses such as dengue, chikungunya, Zika and yellow fever that are severely impacting human health. Traditional vector control strategies such as the use of broad-spectrum insecticides have serious environmental drawbacks and sanitation through reduction or removal of mosquito breeding sites requires the collaboration of the resident human population and has limited impact⁴,⁵. In 2023, 42 SIT pilot projects were being implemented worldwide against mosquitoes⁶. Released males are attracted by hosts, including humans⁷, and can swarm around them in the search of mates, a behaviour that is exploited to monitor their density through the Human Landing Catch method⁸. Alternatively, they can be trapped using CO₂-baited adult traps⁹. Continuous, inundative releases of sterile males, like those requited for SIT, can lead to high sterile to wild male and male to female ratios, sometimes over 100 to 1, particularly when the target population is suppressed. Could such high sex ratios have some influence on the fitness of females?
+
+Mating is an essential component of adult life for all species with sexual reproduction. In most insects, a single or a moderate number of matings are sufficient for females to
+maximize their reproductive success^{10-12}. Therefore, females generally prefer a lower mating rate than males^{13} and are often resistant or reluctant to re-mate^{14}. This apparent divergence leads males from a wide range of animal species to compel females to mate by coercion or harassment^{15}. As a consequence, a ratio of 10 sterile male *Aedes aegypti* to 1 female resulted in increased mortality of the females but did not impact the fitness of the surviving ones^{12}. Mating harassment is a form of sexual conflict where repeated attempts to copulate by the male can be costly for the female^{15}. These costs can be direct (effects on harassed females) or indirect (effects on descendants of harassed females)^{12}. Harassment behaviours are even more frequent when individuals are confined to closed environments, like a rearing cage in the laboratory. Under mass-rearing conditions for example, a reduced 1:3 male to female ratio is recommended to reduce mating harassment and maximize production in both *Ae. albopictus*^{16,17} and *Ae. aegypti*^{18}. The same applies to other insects like tsetse flies where a 1:4 male to female ratio increases female fecundity in *Glossina fuscipes fuscipes* and *G. pallidipes*^{19}. However, the effects of large sex ratios such as those observed during an SIT programme are largely unknown.
+
+Here we explored the impact of mating harassment by sterile male mosquitoes on the survival and feeding success of *Ae. albopictus* and *Ae. aegypti* females under laboratory, semi-field and field conditions. We show that both parameters are strongly reduced by mating harassment.
+
+Survival of mosquitoes caged at different sex ratios
+
+We first observed the effect of high fertile male to female ratios in *Ae. aegypti* and *Ae. albopictus* in confined laboratory cages. In both species, increased male to female ratios were associated with higher mortality of the females and also of male *Ae. albopictus* (Extended Data Figs. 1, 2, 3). Even with a male to female ratio of 3:7, which is only slightly higher than the
+control at 1:3, mortality of female Ae. aegypti significantly increased (Extended Data Fig. 2, Extended Data Table S1, \( P = 0.021 \)). Female mortality reached 14.5% \( \pm \) 3.9% after 8 days under a male to female ratio of 99:1 as compared with 2.8% \( \pm \) 1.2% in the control group (male to female ratio of 1:3). The impact of harassment on the survival of female Ae. albopictus was even more pronounced than in Ae. aegypti. A male to female ratio of 50:1 was enough to increase mortality of females significantly after 8 days (Extended Data Fig. 1, Extended Data Table 1, \( P = 1.47e^{-08} \)), i.e., 38.9% \( \pm \) 1.9%, similarly to under a male to female ratio of 100:1, whereas in the control group mortality remained at 1.5%.
+
+Fertile male Ae. aegypti did not experience increased mortality with increased sex ratios (Extended Data Figs. 1, 2, Extended Data Table 1, \( P > 0.05 \)). On the contrary, the mortality of male Ae. albopictus also increased with a male to female ratio of 50:1 after 8 days (Extended Data Fig. 1, Extended Data Table 1, \( P = 8.42e-08 \)), i.e. 19.0% \( \pm \) 4.2%, similarly to the batch with a male to female ratio of 100:1, whereas in the control group mortality remained at 2.9%. This may be related to more male Ae. albopictus being more aggressive, but this will warrant further research.
+
+A practical application is that the increase in female mortality could be used as an additional process to separate the sterile males from the females by keeping them for some days in the insectary following mechanical separation that results in 1% or more female contamination of the sterile male batches\(^{20}\) (see Supplementary Information). We thus repeated the same experiments with irradiated mosquitoes to assess whether similar results would be obtained. In general, irradiation exacerbated the negative impact of mating harassment (Fig. 1). Caging of sterile males and females under laboratory conditions at a sex ratio of 100:1 decreased the female contamination of the sterile male batches to ~0.6% and 0.7% due mortality for female Ae. aegypti and Ae. albopictus, respectively, within the first eight days. When a predetermined threshold is agreed with the public health authorities, e.g., 1%\(^{20}\), this
+might be an effective way of eliminating females instead of removing residual females manually or discarding the full batch of sterile males. Nevertheless, this would probably be cost-prohibitive in an operational programme (see Supplementary Information).
+Fig. 1. Cumulative mortality rate of irradiated Aedes mosquitoes exposed to three sex ratio (SR) (Males/Females) treatments (1:3 = control, 49:1 and 99:1 for Ae. aegypti; and 50:1 and
+100:1 for Ae. albopictus) over 8 days. Probabilities that the observed differences are significant from the control group are presented on the top of each panel, the colour indicating the sex to which it refers (3 repeats). a) Cumulative mortality rate of Ae. aegypti females increased with sex ratio and was \(26.7\% \pm 14.0\%\) at 8 days for a ratio of 99:1 as compared to \(3.9\% \pm 2.4\%\) in the control group. b) In Ae. albopictus, the tendency was even stronger and the cumulative mortality reached \(40.0\% \pm \text{SD} = 8.8\%\) at 8 days for a ratio of 100:1 as compared to 3.8% in the control group. In Fig (a) and (b), *ns* represents not significant; ** represents \(P < 0.01\); *** represents \(P < 0.001\).
+
+What causes mortality in high male to female ratios?
+
+To better understand the mechanisms leading to increased mortality, we filmed sexual interactions of the mosquitoes at a high resolution (1080P). Females were strongly harassed when sex ratios were biased towards males (see Suppl. Movie S1). At the highest male to female ratio of 99:1, females were completely prevented from feeding and were lying immobile at the bottom of the cage to escape further mating attempts from males who were aggregated around the females by groups of three to five individuals. Any attempt of females to escape attracted more males, probably induced by their wing beat. To verify this hypothesis, some females were glued on their back to a pin (see Suppl. Movie S2), and those females accepted two or three mates, but refused to re-mate thereafter. However, each time they were trying to escape and fly off, new males were attracted and were aggregating around them. In nature, such aggregates may drop to the ground, where they attract immediately predators, and again increase female mortality.
+
+From these mosquito recordings, it was clear that feeding inhibition was the main factor increasing mortality in females. Although described here for the first time intra-specifically, this finding is consistent with the previous study\(^{21}\) showing feeding inhibition of female *Ae.*
+aegypti by male Ae. albopictus. Interspecific mating of male Ae. albopictus with female Ae. aegypti actually occurs and is named satyrization\(^{22,23}\).
+
+Mating harassment and feeding success in semi-field cages
+
+We first explored the impact of a high irradiated males to non-irradiated female ratio on the feeding success of females on an artificial host (Hemotek). A male to female ratio of 99:1, reduced blood feeding success to \(1\% \pm 1\%\)) as compared with \(16\% \pm 4\%\) at a male to female ratio of 1:1 (odds ratio 16.50, SE = 9.98, \(P < 10^{-4}\)) (Fig. 2a). Male mosquitoes were observed forming swarms around the artificial hosts waiting to mate with a female attempting to take a blood meal thus reducing their feeding success (see Suppl. Movie S3).
+
+A similar experiment was set up but now using a human host. When a collector exposed one of his legs from foot to knee (human bait) in a semi-field cage, and killed the female mosquitoes after landing on the exposed leg but before feeding began, the rate of caught females was reduced to 38% (SE = 6%) at a male to female ratio of 99 to 1 as compared to 77% (SE = 6%) with a male to female ratio of 1:1 (odds ratio 5.30, SE = 2.15, \(P < 10^{-4}\)) (Fig. 2b).
+Fig. 2. Impact of mating harassment on feeding success in semi-field cages. a. Impact of the male to female ratio on the engorgement rate of females on an artificial host (Hemotek). Fewer females were engorged in the male: female treatment ratio 99:1 as compared to the control ratio 1:1 (\( n = 4 \), odds ratio 16.50, SE = 9.98, \( P < 10^{-4} \)). b. Impact of the male to female ratio on the engorgement on the catch rate of females by a volunteer collector. Fewer females were collected when attempting to bite a human collector in the male: female treatment ratio of 99:1 as compared to the control ratio 1:1 (\( n = 3 \), odds ratio 5.30, SE = 2.15, \( P < 10^{-4} \)).
+
+In both semi-field trials, mating harassment thus resulted in feeding inhibition. Aggregation of sterile males around human hosts during mosquito SIT programmes is well-known\(^{7,24}\).
+
+Mating harassment and human landing catches under field conditions
+The data from an Ae. albopictus field trial conducted in the centre of Guangzhou, China, were used to investigate the existence of feeding inhibition in real settings (Fig. 3). Before the release of sterile males, ovitraps were deployed bi-weekly in both the release and the untreated site to collect baseline data from March to August 2021 (Extended Data Fig. 6a). In addition, the density of the adult female populations was estimated with Human Landing Catch (HLC) (Extended Data Fig. 6b). Before the beginning of the release, no significant difference was observed in the number of hatched eggs per ovitrap and number of females caught with HLC in the untreated and release areas (Extended Data Fig. 6a, 6b).
+
+![Satellite maps and spatial distribution of monitoring tools/methods](page_374_563_1002_482.png)
+
+Fig. 3. Study site and climatic conditions. a, Satellite maps of field site in Guangzhou city (map data: Google, DigitalGlobal). Release area outlined with green while control and buffer areas are outlined with blue and orange in the satellite image respectively. b, Spatial distribution of the monitoring tools/methods. Grey points represent ovitraps, blue points represent BG traps, and the purple points represent the positions to perform Human Landing Catch. c, d, Daily average temperature (c) and precipitation (d) in the study area from March to November 2021.
+On 13th August 2021, the release of sterile male mosquitoes was initiated at a frequency of twice per week. During a period of 15 weeks, a total of 3 million male mosquitoes were released (Extended Data Fig. 6c). Aedes albopictus populations were monitored weekly with ovitraps, adult-collecting BG traps and irregular HLC. During the release period, the mosquito population was reduced in the release area by 47.56% and 35.96% as measured in the ovitraps and the BG traps, respectively, in comparison with the untreated area (Figs. 4a, 4b). From 6th September to 8th November, the efficiency of suppression was maintained at an average rate of 60.53% (min to max: 39.03%-86.07%) in the ovitrap catches. However, the suppression efficiency showed large variations after 8 November, and this might be attributed to the low ambient temperatures (12-22 °C) (Fig. 3b) or to possible immigration of fertile females in the release area in view of its small size (1.17 ha). The temporal fluctuations of adult females were similar to the larval samples, i.e., an average suppression of 47.2% (min to max: 34.62%-92.5%) for the period 15 September to 2 December (excluding the data collected on 29 to 30 September) (Fig. 4b).
+
+We compared the sex ratio obtained by BG traps and HLC from 3rd to 6th November (11 weeks after the first release of sterile males), and a higher sex ratio was found in HLC than in the BG traps (70.5:1 vs 16.6:1, Fig. 4d). Quantitative polymerase chain reaction (qPCR) targeting Wolbachia wsp gene indicated that over 95% of caught males with BG traps or HLC were the released sterile males (Fig. 4e). In HLC, the sex ratio was close to the experimental set-up in our lab and semi-field studies presented above. An average of 0.5 adult females were collected in the release area versus 2.8 females in the untreated area using HLC. This indicated a suppression of > 82.0% of adult females, a much higher suppression rate than what was observed with BG traps during the same period (42.3% during 3rd-4th November, Fig. 4d). The higher suppression rate obtained with the HLC might possibly be due to the high
+overflooding rate of males surrounding the catchers, which could have prevented the approach of female mosquitoes by the sterile males, as was observed in the semi-field trial. In Aedes species, males are known to swarm around the hosts using pheromonal and acoustic cues, presumably to intercept females attempting to feed^{25-27}. Male Ae. albopictus are particularly attracted to humans^{7} and our results show that they aggregated in higher numbers around humans than BG traps.
+
+![Graphs showing dynamics of larval suppression and adult female suppression, number of female adults captured via HLC, suppression efficiency vs male/female ratio, and proportion of sterile males captured](page_312_684_1127_496.png)
+
+Fig. 4. Suppression efficiency of mosquito populations after sterile male releases. a, Dynamics of larval suppression. Larval reduction is observed in the release area as compared to the control area (\( n = 14, P = 0.0023 \), Two-tailed Wilcoxon matched-pairs signed rank test). b, Dynamics of adult female suppression. A total of 4 BG traps in the release area and 6 in the control area. Female reduction is observed in the release area (\( n = 16, P = 0.0107 \), Two-tailed Wilcoxon matched-pairs signed rank test). The red dotted lines indicate the suppression efficiency in both (a) and (b). c, Number of female adults captured via Human Landing Catch (HLC) in the release and control areas after 11 weeks of release. Two positions were selected to perform HLC in
+the release area and 6 positions in the control area. Three replicates were performed. An average of 0.5 females were collected in the release area while 2.8 females were collected in the control area. d, Relation between the suppression efficiency and ratio of males to females. An average of 82.86% suppression of adult female was achieved via HLC on 3rd and 4th November with a 70.5 ratio of males to females, while 42.31% reduction of adult females was observed via BG trapping on 3-4 November (indicated by black arrow in (b)) with a 16.6 ratio of males to females. e, Proportion of sterile males in the collected males via HLC and BG trapping. In both collecting methods, over 95% of collected males (HLC: 39/40; BG: 88/92) are sterile males, which were identified through qPCR based on the wsp gene of Wolbachia. The Wolbachia-negative samples were considered as the released sterile males.
+
+In various insect species, mating harassment is associated with costs that negatively affect the physical condition and hence, longevity of females, either through physical damage\(^{28,29}\) or toxic effects from the accessory gland secretions\(^{30,31}\). In this study, however, females that were exposed to males at a 1:3 or 99:1 ratio and that were separated from the males immediately after the mating (Extended Data Fig. 5), did not show any increase in mortality. This would indicate that depletion of energy reserves and reduced feeding success were the main factors that reduced their longevity, as observed in other studies where reduced fertility was also documented\(^{11,32}\). Similar results were observed in other species when sex ratios were strongly biased toward males, although to a lesser extent, like in the tsetse fly G. morsitans morsitans\(^{33}\), in the dung fly Sepsis cynipsea\(^{34}\), and the field cricket Gryllus bimaculatus\(^{35}\). Prevention of copulation by blocking or damaging the external genitalia of male tsetse flies resulted in reduced longevity of females caged with them, suggesting that the reduced female survival resulted from the physical aspects of male harassment rather than by components of the ejaculate\(^{33}\). In addition, male tsetse flies have a shorter lifespan due to being engaged in
+mating harassment of the females, as was likewise observed in our study in Ae. aegypti. Like in tsetse, Ae. aegypti female mortality was increased equally by caging them with males that had modified claspers to prevent mating or unmodified males\(^{12}\). These authors even suggest potential benefits (higher fitness) obtained from ejaculate components, a common phenomenon in insects that is considered as part of nuptial feeding\(^{36}\).
+
+The SIT is generally combined with other methods in an integrated pest management approach to first suppress the target population to a level low enough that sufficient sterile to wild male ratios can be obtained to induce enough sterility in the female wild population, e.g. in Aedes mosquitoes\(^{6}\) or tsetse\(^{37}\). Hence, high sex ratios are not uncommon in SIT field trials. In operational tsetse fly SIT programmes, sterile to wild male ratios up to 100 were observed in some cases\(^{37,38}\). The sterile to wild male ratio peaked at 50 to 1 in another successful suppression program against Ae. albopictus in China\(^{39}\). One of the main benefits of the SIT is its inverse density-dependent properties\(^{40}\) or in other words, the sterile to wild male ratio increases with each generation and with the rate of suppression and this can drive an insect population to extinction\(^{38}\). Our data show that feeding inhibition of the females might act synergistically to the induction of sterility in the female population.
+
+Conclusion
+
+Overall, our results allow us to propose two new additional mechanisms contributing to the efficiency of the SIT against mosquito-borne diseases. First, we hypothesize that high male to female ratio increases female mortality through feeding inhibition thus directly reducing female lifespan. Second, at high male to female ratios, males reduce female feeding success and biting rate (and hence transmission rate). The SIT may thus directly reduce disease transmission at high male to female ratios through an impact on two critical components of vectorial capacity, namely female longevity and host contact\(^{41}\). This may as well occur in all
+genetic control methods based on inundative release of males, like the incompatible insect technique\(^{39,42}\) or RIDL\(^{43}\) or even those driving maleness into wild populations\(^{44}\). These hypotheses warrant more field research to assess the impact of these mechanisms on disease transmission.
+
+Authors contributions
+
+J. Bouyer, D.Z., and Z.X. developed the concept and methodology; H. Maiga, M.T.B., D.D., W. M., N.S.B.S., T.W., O.B.M., C.M. and S.S.K performed the lab experiments; Y. Li, H.M., W.M., N.S.B.S. and H.Y. performed the semi-field experiments ; D. Zhang, G.W., Y.S., J.G., Q.F., J.Z., X. Zhao, D.P., W.P., Y.W., X. Zheng, and Z.W. performed the field trial, D. Lu, C.H.T. and J.B. performed the movies; J. Bouyer, D.Z., C.H.T., Y.W., Z.X. and M.J.B.V. performed coordination for the project; D. Zhang obtained regulatory approvals for mosquito releases; Z. Xi obtained the ethical permit for the semi-field trial involving human bait; J. Bouyer provided oversight of the project and contributed to all experimental designs, data analysis and data interpretation; J. Bouyer, D.Z., Y.L., D.D., C.M., D.L., Z.X. and M.J.B.V. wrote the manuscript. All authors participated in manuscript editing and final approval.
+
+Supplementary Information is available for this paper.
+
+Correspondence and requests for materials should be addressed to JB. Reprints and permissions information is available at www.nature.com/reprints.
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+Methods
+
+1. Laboratory trials
+
+All experiments on Ae. aegypti were carried out at the Insect Pest Control Laboratory (ICPL), IAEA, Vienna, Austria whereas experiments on Ae. albopictus were conducted independently at IRD, Saint-Denis, La Reunion Island, except one preliminary experiment on Ae. albopictus also conducted at IPCL (Extended Data Fig. 4).
+
+1.1 Mosquito colonies and mass-rearing
+
+Three established mosquito colonies of Ae. aegypti and Ae. albopictus were used to perform these experiments.
+
+At the IPCL, the strain of Ae. aegypti and Ae. albopictus originated respectively from Juazeiro, Brazil in 2012 (provided by Biofabrica Moscamed, IAEA Collaborative Center) and Rimini, Italy in 2018 (provided by Centro Agricoltura Ambiente, IAEA Collaborative Center). These two strains were maintained at the IPCL in a 264 m^2 container-based laboratory under controlled environmental conditions: the larval rearing room was maintained at 28 ± 2°C, 80 ± 10% RH and the adult rearing room at 26 ± 2°C, 60 ± 10% RH, with a 14:10 hour light: dark (L:D) photoperiod with 1-hour periods of simulated dawn and dusk in both rooms. Aedes mosquito eggs older than 2 weeks were obtained from mass-rearing procedures developed at the IPCL^{42,43}. Based on the egg hatch rate calculated from sub-samples of 100 eggs, batches of eggs corresponding to approximately 18,000 first instar larval (L1) were estimated following the method described by Zheng, et al. ^{44}, weighed and then hatched separately in glass jam jars filled with 700 mL of boiled and cooled reverse osmosis water with the addition of 10 mL of larval FAO/IAEA diet^{42,45}. The larvae were reared into mass-rearing trays following the mass-rearing procedures developed by the IPCL^{42}. Larvae were reared with larval diet (4% w/v)
+composed of a combination of powdered tuna meal (50%), black soldier fly (35%) and brewer's yeast (15%).
+
+At IRD, Saint-Denis, Reunion Island, the strain of Aedes albopictus used in the experiments originated from Saint-Benoit, Reunion Island and was reared as adults in a climate-controlled room maintained at a temperature of 27± 2°C and 75± 1% relative humidity; the light regime was LD 12:12 h photoperiod. For larval production, batches of four thousand first instar larvae were counted on day 0 into rearing trays (52x32x6 cm) containing 2 L of tap water. Larvae were reared at a room temperature of 31°C and a photoperiod of 12:12 (L:D) and fed with 10,20,25,25 and 20 ml per tray of a solution at 7.5% (w:v) slurry of diet (50% ground rabbit-food and 50% ground fish-food Tetramin, Tetra, Germany) on days 0,1,2,3 and 4, respectively. Pupae appeared from the fifth to the seventh day.
+
+1.2 Experimental design
+
+At the IPCL, Ae. aegypti pupae were sexed mechanically using a Fay-Morlan glass plate separator\(^{46}\) as redesigned by Focks (John W. Hock Co., Gainesville, FL)\(^{47}\). With this method, the female contamination in males collected on the first tilting is generally \(1.11 \pm 0.27\%\), on the first day of tilting\(^{48}\).
+
+Additionally, samples of sorted male pupae were checked under a binocular microscope to measure the desired ratio. Batches of 3,000 male and female pupae were counted and left to emerge inside separate Bugdorm cages (\(30 \times 30 \times 30\) cm). Throughout emergence, the cages were monitored to remove females from the male batches and males from the female batches to achieve complete male and female separation. Adults were maintained with 10% sucrose solution supplied *ad libitum* in a 150 mL plastic cup containing a sponge.
+
+To study the sexual harassment of males on *Aedes* mosquito females without allowing potential density-dependent mortality, batches of 3,000 *Ae. aegypti* mosquitoes aged 0 to 1 day were placed in the Bugdorm cages (\(30 \times 30 \times 30\) cm) at six male to female sex ratios (SR): SR= 3:7,
+SR = 1:3 (control, used in the colony maintained in mass-rearing conditions), SR = 10:1, SR = 23:2, SR = 49:1 and SR = 99:1. Every day at 10 am, these cages were monitored and mortality was recorded during 8 days (13 days in the preliminary trials on non-irradiated males). During preliminary trials, the cumulative mortality rate of females increased for batches with SR of 10:1; 23:2; 49:1; and 99:1 after eight days. It was thus decided to focus on SR of 99:1 and 49:1 to study the effects of sexual harassment in sterilized Aedes mosquitoes. Batches of sterile mosquitoes with a SR of 1:3 were again used as controls. Furthermore, one trial was organized for the Ae. albopictus Rimini strain using a SR of 99:1 and a SR of 1:3 as control (Extended Data Fig. 4). The batches of Ae. aegypti (both sexes) were irradiated at the adult stage at 60 Gy while the batches of Ae. albopictus at the pupal stage at 40 Gy.
+
+To assess the longevity of harassed females after separation from the males, 20 irradiated females from batches at the SR of 99:1, 20 irradiated females from batches at the SR of 1:3 and 20 irradiated virgin females of the same age were placed into cages (15 × 15 × 15 cm, Bugdorm.com, Taiwan) at the IPCL. Mortality checks were carried out daily over 14 days.
+
+At IRD, Saint-Denis, Reunion Island, Ae. albopictus pupae were sexed mechanically using standard metal sieves with a square-opening mesh through which males swim upward49. With this method, the female contamination in males collected is 0.5 ± 0.7% (unpublished data).
+
+After sex separation, male pupae were allowed to emerge into Bugdorm cages (30 x 30 x 30 cm) with constant access to a 5% sucrose solution [w/v]. Female pupae were first isolated in tubes (5 per tube) to check the accuracy of the sexing at the emergence and then transferred into cages already containing males. Two treatments were repeated three times, a ratio of 100 : 1 (male :female) and a ratio of 50 :1 with 3000 males and 30 females and 3000 males and 60 females respectively, in Bugdorm cages (30 x 30 x 30 cm) with constant access to a 5% sucrose solution. Control cages consisted of regular rearing cages with a ratio of 1 :3 (male :female).
+Each treatment has been done with non-irradiated and irradiated males. Mortality checks were carried out daily and recorded over 8 days.
+
+To produce irradiated males, male and female pupae of more than 30-h-old were irradiated at 35 Gy during 5 minutes with an X-ray irradiator (Blood X-RAD 13-19, Cegelec, France) at the Blood bank coordinated by Etablissement Français du Sang (EFS) located at the Bellepierre hospital, St Denis de La Réunion. The irradiated pupae were brought back to the lab and treated as described above.
+
+2. Mosquito recordings
+
+The strain of Ae. aegypti used for filming originated from Singapore and reared at the National Environment Agency–Environmental Health Institute (NEA-EHI) Singapore, mosquito production facility. The larvae were reared at a High Density Mosquito Rearing System (Orinno Technology, Singapore) at larvae density of 12,000 per tray containing 6 litres of water and maintained at an air temperature of 29 ± 1 °C and 85 ± 5% RH with a photoperiod of 12:12h L:D cycle. Aedes aegypti pupae were sexed mechanically using an Auto-Pupae Separation System (Orinno Technology, Singapore). Male and female pupae were placed into two separated Bugdorm cages (30 × 30 × 30 cm) to allow emergence. Adults were supplied with 10% sucrose solution ad libitum. Adult mosquitoes with age of 5-6 days post emergence were selected for filming via mouth aspirator.
+
+All footages were recorded by DJI OSMO pocket and Nikon D750 DSLR camera with Sigma 70mm F2.8 Macro lens. Two Yongnuo YN900 LED panel lights were used as light source. For Movie S1, two female Ae. aegypti adults were introduced into a Bugdorm cage (30 × 30 × 30 cm) with 200 males. Footage was captured by manual tracking at 60 Frame Per Second (FPS) and down speed to 30FPS in the post editing. For Movie S2, a single female was knocked down by exposure to ethyl acetate and carefully sticking it to the head of pin with latex glue. The
+immobilized female was then placed into a Bugdorm cage (30 × 30 × 30 cm) with an additional 100 males for filming. Footage was captured at frame rate of 30 FPS.
+
+3. Semi-field trials
+
+3.1 Artificial bait (Austria)
+
+Mosquito strains, rearing, and irradiation
+
+Two mosquito laboratory strains of Ae. aegypti (FAO/IAEA, 2017, 2020) were used for these experiments. The strains were maintained following FAO-IAEA guidelines \(^{50}\). Aedes aegypti strains originating from Brazil (Juazeiro) and Senegal (Dakar) were transferred to the IPCL from the insectary of Biofabrica Moscamed, Juazeiro, Brazil, and from the ISRA-LNERV, Dakar-Hann, Senegal in 2012 and 2021, respectively.
+
+The larval rearing period had controlled conditions of temperature of 28 ± 2 °C, 80 ± 10% RH, and lighting of 14:10 h L:D, including 1 h of dawn lighting and 1 h of dusk lighting for larval stages. Adults were separately maintained under 26 ± 2 °C, 60 ± 10% RH, and 14:10 h light: dark, including 1 h dawn and 1 h dusk. To perform the experiments, mosquitoes were reared following modified mass-rearing procedures developed at the IPCL\(^{51}\). Pupae were collected and mechanically sex-separated using a semi-automatic pupal sex sorter (Wolbaki, China).
+
+Pupae were counted manually and placed in 30 × 30 × 30 cm and 15 × 15 × 15 cm Bugdorm cages for male and female mosquitoes, respectively. Pupae were aliquoted into 600 mL plastic cups, each holding 2,100 male pupae and into 100 mL plastic cups (Medi-Inn, United Kingdom) each holding 25 female pupae. Adults were maintained with *ad libitum* access to a 10% (w/v) sucrose solution until the day of the irradiation. Mortality was assessed daily until the day of releases.
+Two-to-three–day-old male adults were exposed to 45 Gy using an X-ray blood irradiator (Raycell MK2)52. Male adult mosquitoes were held in a cold room at 4°C for ten min in compacted batches of 100/cm³ (about 1,000 males /cell) to simulate mass-transport conditions prior to irradiation. Irradiated male mosquitoes were placed back into the cages with ad libitum access to a 10% (w/v) sucrose solution until testing day (Ecosphere, suppl. mov. 3). Approximatively 24h prior to the releases, female mosquitoes were starved by removing the sugar solution from all cages. Two ratios of males to virgin females of 99:1 (1980: 20) and the control ratio 1:1 (20:20) were used with three cages each (technical repeats).
+
+Sexual harassment assay in large cages
+
+Experiments were conducted in six large cages (1.80 × 1.80 × 1.80 m, Live Monarch, Boca Raton, USA) at the FAO/IAEA IPCL climate-controlled Ecosphere in Seibersdorf (Austria) under natural light, average temperatures of 28 ± 2 °C and 70±10% RH (suppl. mov. 3). One tray (30 × 40 × 8 cm) containing 1 L tap water was provided in each cage with two 100mL plastic cups of 10% sugar solution. A stand made of wood was placed inside each cage to hold an Hemotek (Ltd Unit 5 Union Court Great Harwood Business Zone Blackburn BB6 7FD, United Kingdom) blood feeding plate53 as artificial bait. One bleeding plate was filled up with 100 mL fresh pig blood and was hung upside down. The Hemotek heating system was turned on for 30 min. The plate was placed half-way of the wooden stand at one meter above the floor and allowed females to feed easily.
+
+Five-to-six-day-old, irradiated males and virgin non-treated female mosquitoes were briefly knocked down for five to ten minutes at 4 °C prior to release. Mosquitoes were then transferred into 100mL plastic containers. Each container was labelled according to treatment or control groups. All the containers were then transferred to the Ecosphere and males were released into large cages. Females were released 30 min later where they were allowed to blood feed for two hours starting from 10 am.
+After 2h-exposure time, all females were recaptured separately from the treatment and the control cages using mechanical aspirator device54. The operator wore coverall protective suit and gloves preventing any biting from the females during collection. The number of recaptured females was recorded per cage. To assess the blood-feeding status of females, each recaptured female mosquito was crushed between two pieces of white paper and the visual presence/absence of blood was observed based on the blood stain. The number of blood-fed females was recorded per cage. In total, three technical replicates (cage) were prepared for the control sex ratio (males: virgin females) of 1:1 (20:20) and the treatment sex ratio of 99:1 (1980: 20).
+
+The full experiment was repeated four times.
+
+3.2 Human bait (China)
+
+Mosquito strains, rearing, and irradiation
+
+The female mosquito GUA line was collected from more than 10 field localities of Guangzhou City, China, and has been reared in the laboratory for less than one year (< 12 generations). The rearing conditions for GUA were described previously 55. Briefly, about 300 first-instar larvae were reared in a plastic tray (36 cm × 25 cm × 5 cm) with 1.5 L dH2O and bovine liver powder was supplied as larvae food. The establishment, mass-raring, sex-separation and irradiation of HC mosquitoes were described previously56.
+
+Human Landing Catch in large cages
+
+We conducted a second experiment based on Human Landing Catch in China to assess whether male harassment can prevent blood feeding on humans in semi-field conditions. Wild type virgin Ae. albopictus (GUA strain) females were inseminated and 5-6 days old. They were
+starved for 24 hours before the experiment start. Irradiated HC males were virgin and 5-6 days old. Irradiated HC males were released into semi-field cages (1.80 × 1.80 × 1.80 m, containing two sugar water containers). GUA females were released 24 hours later into the semi-field cages. Male and female release numbers were 1980 versus 20 for the 99:1 ratio and 20 versus 20 for the 1:1 ratio. Ten minutes after releasing the females, an adult volunteer entered and sat on a chair in the middle of each cage. The collector exposed one of his legs from foot to knee and killed mosquitoes as soon as they landed on the exposed leg before they started feeding. Mosquito collection was conducted for 15 min for each cage and ratio. All collected females were removed and counted. After 15 min of collection, remaining mosquitoes were collected with an aspirator and females checked to see whether some females had blood meals. Three repeats were conducted with three different collectors managing one 99:1 and one 1:1 cage each. Collectors received appropriate information and gave their informed consent prior to participating in this study.
+
+4. Field trial
+
+4.1 Maintenance of mosquitoes
+
+We used the Ae. albopictus GT line (without Wolbachia infection) that can be distinguished from the wild Ae. albopictus (wAlbA and wAlbB double infections) via PCR/qPCR assays based on Wolbachia wsp gene. The GT line was maintained as previously described\(^{57}\). For routine colony maintenance, female mosquitoes were blood-fed on mice according to protocols approved by the Ethics Committee on Laboratory Animal Care of the Zhongshan School of Medicine, Sun Yat-sen University (No. 2017-041).
+
+4.2 Mass-production and irradiation of GT males
+
+Mass-production of GT males included adult and larval rearing according to protocols described previously with slight modifications\(^{58,59}\). Approximately 15,000 female pupae and 5,000 male
+pupae (3:1 ratio of female to male) were placed into an adult cage (90 × 90 × 30 cm). Adults were provided with a 10% sugar solution ad libitum. Sheep blood mixed with ATP was provided to females twice per rearing cycle. Oviposition cup was provided to the engorged females for laying eggs 48 h after each blood meal. Eggs were collected for 72 h and then matured for at least one week before hatching. After hatching, 4,000-5,000 larvae were added to each tray (51.5 × 36.0 × 5.5 cm) and fed daily with larval food. At day 8, pupae mixed with larvae were collected and then separated by an automatic sex separator (Orinno Technology, Singapore). After sexing, 16,000 male pupae were transferred to a cage (90 × 90 × 30 cm) for emergence. The temperature was set at 27-28 °C. Cotton soaked in 10% sugar solution was placed on top of the cage for mosquitoes to feed ad libitum. The average female contamination rate was 0.05% (\( n = 30, \ SE = 0.02\% \)) in the sterile male release batches (Fig. S6c). Male mosquitoes at 2-3-day old were immobilized and then packed in plastic dishes (diameter 10 cm × height 1.2 cm) in a cooling room set at 10 °C. Each plastic dish contained 5,000 male mosquitoes and was then placed in a PMMB canister. Each irradiated canister contained 3 dishes and two canisters were irradiated each time. The exposure was done in an X-ray irradiator (XL1606HD, NUCTECH, China) at a dose of 60 Gy with dose rates of 3.74 Gy/min or 7.33 Gy/min. The irradiator was configured with a cooling system to maintain the chamber temperature at 10 °C, which ensured the immobilization of male mosquitoes during exposure without impacting their quality\(^{60-62}\). The irradiated male mosquitoes were recorded as IGT\(_{60\text{Gy}}\) males. Exposing adult male mosquitoes to 60 Gy resulted in an average of 99.0% sterility (\( n = 30, \ SE = 0.22\%, \) Fig. S6c).
+
+**4.3 Quality control**
+
+One of the key quality control parameters for release of sterile males was the female contamination rate (FCR), which was monitored at the adult stage. Each batch of male adults was checked by randomly selecting 800-1,000 of the mosquitoes for sex identification based
+on morphology. In addition, male sterility was monitored for each batch through egg hatch rate assessment. In details, 100 IGT_{60Gy} males were allowed to mate with 100 virgin GT females. Blood feedings and egg collections were the same as mentioned above. Eggs from each blood meal were hatched and egg hatch rate was assessed as previously described^{57}. Egg hatch rate from crosses between 100 GT males and 100 virgin GT females was considered as fertile control. Male sterility was calculated as: Induced Sterility (IS%) = 100% - ((Hs/Hn) * 100%), where Hs was the egg hatch rate from the sterile control, and Hn was the egg hatch rate from the fertile control.
+
+4.4 Study area description
+
+The study site is located at the North Campus of Sun Yat-Sen University in Yuexiu District, Guangzhou, China (Latitude: 23°7'39.74"N, Longitude: 113°17'22.07"E), covering an area of about 20.9 ha (Fig. 1a). The campus has a population of 4,750 people (mainly students and faculty) and is located in a bustling metropolitan area with parks, hospitals, and residential areas nearby. The west and south areas of the campus were selected as the control area (6.55 ha), the northeast was the release area (1.17 ha), and a buffer zone (4.87 ha) was set between the release and the control area (Fig. 1b). The average temperature in the study area was 24.6°C in 2021 (Fig. 1c) and the annual precipitation was 1,511.4 mm with a rainy season between May and October (Fig. 1d).
+
+4.5 Pre-release monitoring of release and control areas
+
+Before release, Ae. albopictus populations were monitored using ovitraps every two weeks from 8^{th} March to 17^{th} August 2021. The number of ovitraps was 17 in the release area, 40 in the control area and 33 in the buffer area, respectively (Fig. 3b). The methods to place and collect ovitraps as well as hatch eggs were the same as described in^{56}. We also performed Human Landing Catch (HLC) to estimate the mosquito adult populations. There were two positions in
+the release area and 6 positions in the control area (Fig. 3b). The HLC was performed 4 times pre-release of sterile males. Briefly, well-protected volunteers stand in the selected position and used a locally manufactured hand-held electric aspirator to collect the adult mosquitoes fly around the performers for 15 mins. The collected mosquitoes were identified and counted by morphological characteristics.
+
+4.6 Field release of IGT_{60Gy} males
+
+IGT_{60Gy} males were maintained in a mobile-refrigerator set at 10 °C and transported from the mass-rearing factory to the study site by a van two times per week. The distance between the factory and the study site was about 100 km. The release was performed at 13:00-14:00 pm. During release, dishes were opened, and mosquitoes were allowed to fly away freely. Over 95% of mosquitoes could recover after transportation under chilling conditions. On average, 200,000 mosquitoes were released weekly, and a total of about 3-million mosquitoes were released from mid-August to end of November 2021.
+
+4.7 Monitoring population suppression.
+
+Throughout the period of IGT_{60Gy} male release, Ae. albopictus populations were monitored weekly by using ovitraps and BG-Sentinel traps (Biogents, Germany). The number of BG traps was 4 in the release area, 6 in the control area and 5 in the buffer area (Fig. 3b). The methods to place and run BG traps as well as count the number of mosquitoes were the same as described in^{56}. The average number of hatched eggs per ovitrap, in both release and control areas, was determined and used to measure population suppression efficiency at the larval stage. In addition, the average number of females in both release and control areas per BG trap was determined each week, and used to measure population suppression at the adult stage. Moreover, HLC was repeated three times to estimate the suppression efficiency at 11 weeks’ post release of IGT_{60Gy} males.
+4.8 qPCR assays of Wolbachia infection
+
+Each captured adult mosquito was stored separately in a 1.5 mL tube and maintained at -20 °C before Wolbachia detection. DNA was extracted according to the protocols of Fast Pure Cell/Tissue DNA Isolation Mini Kit (Vazyme, China). A 20 μL qPCR reaction consisted of 1 μl DNA template, 10 μL qPCR 2X mix (Vazyme, China), 8 μL nucleic-free water, 0.5 μL primer-F, and 0.5 μL primer-R. The specific-primers used for the assay were designed for Wolbachia wsp gene and consisted of wAlbB-F: ACGTTGGTGGTGCAACATTTTG; wAlbB-R: TAACGAGCACCCAGCATAAAGC. The qPCR procedures (LightCycler 96, Roche) comprised 10 s at 95 °C, followed by 40 cycles of 10 s at 95 °C, 10 s at 50 °C, 10 s at 72 °C, and finally 10 s at 95 °C, 60 s at 65 °C, 1 s at 97 °C, 30 s in 37 °C to generate the melting curve for confirmation that the fluorescence detected was for the specific PCR product. The Wolbachia negative samples were considered as IGT_{60Gy} mosquitoes.
+
+5. Statistical analysis
+
+All statistical analyses were performed using R version 4.2.1 (https://cran.r-project.org) using RStudio 2022.07.1 (RStudio, Inc. Boston, MA, United States, 2016). Shapiro and Bartlett's tests were performed respectively to test the normality and to determine whether the variance in cumulative mortalities was the same for various sex ratios. The relationships between cumulative mortalities and the different sex ratios during the study period were analysed for each Aedes species. For this purpose, binomial linear mixed effect models were used with the assigned sex ratios as response variables and cumulative mortality rates as explanatory variable using the lme4 package^{63}. The various sex ratios were then used as fixed effects and the repetitions as random effects. The generalized linear mixed models were fitted by maximum likelihood. For each species, the cumulative mortality curves were plotted by sex ratios using the ggpubr package. The longevity of harassed, non-harassed and virgin Ae. aegypti females was analyzed using Kaplan-Meier survival analyses. The log-rank test (Mantel-Cox)
+was used to compare the level of survival between the different treatments (status of females) using the survival and survminer packages\(^{64}\). Two-tailed Wilcoxon matched-pairs signed rank test was used to compare the hatched eggs and the captured female adults via BG or HLC before and after the release of sterile males, between the released and control areas. The feeding rates and recapture rates of females in semi-field trials were analysed using binomial generalized linear mixed models fit by maximum likelihood (Laplace approximation) with the SR as fix factor and the repeats as random factors\(^{65}\). The odds ratio were computed using the emmeans function (in package emmeans)\(^{66}\).
+
+Ethical statement
+
+The study involving Human Landing Catch in large cages received the approval to the Institutional Ethics Committee from Guangzhou University. The field trial on applying SIT for *Aedes albopictus* control has been reported to and approved by Zhongshan School of Medicine (ZSSM), SYSU before the release of sterile males in 2021.
+
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+Extended Data Fig. 1. Cumulative mortality rate of non-irradiated Aedes mosquitoes exposed to three sex ratio (SR) (Males/Females) treatments (1:3=control, 49:1 and 99:1 for Aedes aegypti; and 1:3=control, 50:1 and 100:1 for Aedes albopictus) over 8 days. Probabilities that the observed differences are significant from the control group are presented on the top of each panel, the colour indicating the sex to which it refers (ns = not significant ie p>0.5).
+Extended Data Fig. 2. Cumulative mortality rate of non-irradiated Aedes aegypti exposed to six sex ratios (SR) (Males/Females) treatments (3:7, 1:3, 10:1, 23:2, 49:1, and 99:1) over 8 days during preliminary trials. Probabilities that the observed differences are significant from the control group are presented on the top of each panel, the colour indicating the sex to which it refers (ns = not significant ie p>0.5). Mortality rate of female reached 14.5% (SD=3.9%) after 8 days in the 99:1 batch in comparison to 2.8% (SD=1.2%) in the 1:3 control group.
+Extended Data Fig. 3. Cumulative mortality rate of non-irradiated Aedes aegypti exposed to three sex ratio (SR) (Males/Females) treatments (1:3=control, 49:1 and 99:1) over 13 days. Probabilities that the observed differences are significant from the control group are presented on the top of each panel, the colour indicating the sex to which it refers (ns = not significant ie p>0.5).
+Extended Data Fig. 4. Cumulative mortality rate of irradiated Aedes albopictus exposed to two sex ratio (SR) (Males/Females) treatments (1:3=control and 99:1) over 8 days (experiment conducted at ICPL). Probabilities that the observed differences are significant from the control group are presented on the top of each panel, the colour indicating the sex to which it refers (ns = not significant ie p>0.5). Mortality of females reached 90% (SD=6.1) at 8 days for a ratio of 99:1 as compared to 17.3% (SD=4.1) in the control group.
+
+![Cumulative mortality rate of irradiated Aedes albopictus exposed to two sex ratio treatments over 8 days](page_222_180_1002_670.png)
+Extended Data Fig. 5. Survival of female Aedes aegypti exposed to three treatments (harassed female, unharassed female and virgin female) over 14 days. Any difference was observed of survival between females previously exposed to males at a 1:3 or 99:1 ratio after their separation from the males
+Extended Data Fig. 6. Mosquito population and the release of sterile males. a, Weekly number of hatched eggs per ovitrap in the release (green dashed lines) and control area (blue dashed lines) before release. A total of 17 ovitraps were used for monitoring in the release area and 40 in the control area. No significant difference was observed in the number of hatched eggs between release and control area (n=10, P=0.1055, Two-tailed Wilcoxon matched-pairs signed rank test). b, Number of female adults captured via HLC in the release (green histogram) and control area (blue histogram) before release. Two positions were selected to perform HLC in the release area and 6 positions in the control area. Four independent HLCs were performed. No significant difference was observed in the captured female adults via HLC (n=4, P>0.9999, Two-tailed Wilcoxon matched-pairs signed rank test). c, Sterile male mosquitoes were released twice per week for a total of about 3 million males. The average female contamination rate (red
+dashed lines) was 0.053% (n=30, 95%CI: 0.019%-0.086%) and the male sterility (purple dashed lines) 99.03% (n=30, 95%CI: 98.59%-99.47%) with 30 batches assessed in total.
+
+Extended Data Table 1. Effects of various sex-ratios on the cumulative mortality rates of non-irradiated Aedes mosquitoes based on the generalized linear mixed model fit by maximum likelihood using Binomial linear mixed effect models.
+
+<table>
+  <tr>
+    <th>Aedes species</th>
+    <th>Sex</th>
+    <th>Estimate</th>
+    <th>Std. Error</th>
+    <th>z value</th>
+    <th>Pr(>|z|)</th>
+  </tr>
+  <tr>
+    <td rowspan="6">Aedes aegypti</td>
+    <td rowspan="5">Female</td>
+    <td>(Intercept)</td>
+    <td>4.62</td>
+    <td>0.24</td>
+    <td>19.54</td>
+    <td>< 2e-16 ***</td>
+  </tr>
+  <tr>
+    <td>Sex Ratio = 3:7</td>
+    <td>-0.59</td>
+    <td>0.26</td>
+    <td>-2.31</td>
+    <td>0.0211 *</td>
+  </tr>
+  <tr>
+    <td>Sex Ratio = 10:1</td>
+    <td>-0.95</td>
+    <td>0.24</td>
+    <td>-3.91</td>
+    <td>9.25e-05 ***</td>
+  </tr>
+  <tr>
+    <td>Sex Ratio = 23:2</td>
+    <td>-1.25</td>
+    <td>0.23</td>
+    <td>-5.36</td>
+    <td>8.28e-08 ***</td>
+  </tr>
+  <tr>
+    <td>Sex Ratio = 49:1</td>
+    <td>-1.13</td>
+    <td>0.24</td>
+    <td>-4.78</td>
+    <td>1.74e-06 ***</td>
+  </tr>
+  <tr>
+    <td></td>
+    <td>Sex Ratio = 99:1</td>
+    <td>-1.79</td>
+    <td>0.22</td>
+    <td>-8.03</td>
+    <td>9.92e-16 ***</td>
+  </tr>
+  <tr>
+    <td rowspan="5">Male</td>
+    <td>(Intercept)</td>
+    <td>4.30</td>
+    <td>0.18</td>
+    <td>24.19</td>
+    <td><2e-16 ***</td>
+  </tr>
+  <tr>
+    <td>Sex Ratio = 3:7</td>
+    <td>0.38</td>
+    <td>0.28</td>
+    <td>1.36</td>
+    <td>0.17</td>
+  </tr>
+  <tr>
+    <td>Sex Ratio = 10:1</td>
+    <td>0.53</td>
+    <td>0.29</td>
+    <td>1.81</td>
+    <td>0.07</td>
+  </tr>
+  <tr>
+    <td>Sex Ratio = 23:2</td>
+    <td>0.17</td>
+    <td>0.26</td>
+    <td>0.65</td>
+    <td>0.51</td>
+  </tr>
+  <tr>
+    <td>Sex Ratio = 49:1</td>
+    <td>0.58</td>
+    <td>0.30</td>
+    <td>1.96</td>
+    <td>0.05</td>
+  </tr>
+  <tr>
+    <td></td>
+    <td>Sex Ratio = 99:1</td>
+    <td>0.43</td>
+    <td>0.28</td>
+    <td>1.51</td>
+    <td>0.13</td>
+  </tr>
+  <tr>
+    <td rowspan="4">Aedes albopictus</td>
+    <td rowspan="2">Female</td>
+    <td>(Intercept)</td>
+    <td>4.85</td>
+    <td>0.47</td>
+    <td>10.39</td>
+    <td>< 2e-16 ***</td>
+  </tr>
+  <tr>
+    <td>Sex Ratio = 50:1</td>
+    <td>-2.62</td>
+    <td>0.46</td>
+    <td>-5.67</td>
+    <td>1.47e-08 ***</td>
+  </tr>
+  <tr>
+    <td></td>
+    <td>Sex Ratio = 100:1</td>
+    <td>-2.91</td>
+    <td>0.46</td>
+    <td>-6.34</td>
+    <td>2.32e-10 ***</td>
+  </tr>
+  <tr>
+    <td rowspan="2">Male</td>
+    <td>(Intercept)</td>
+    <td>4.89</td>
+    <td>0.41</td>
+    <td>11.92</td>
+    <td>< 2e-16 ***</td>
+  </tr>
+  <tr>
+    <td></td>
+    <td>Sex Ratio = 50:1</td>
+    <td>-2.26</td>
+    <td>0.42</td>
+    <td>-5.36</td>
+    <td>8.42e-08 ***</td>
+  </tr>
+  <tr>
+    <td></td>
+    <td>Sex Ratio = 100:1</td>
+    <td>-2.16</td>
+    <td>0.42</td>
+    <td>-5.17</td>
+    <td>2.36e-07 ***</td>
+  </tr>
+</table>
+
+Values were compared to the Sex Ratio = 1:3 [Control], *p-value < 0.05; ***p-value < 0.001,
+
+Std. Error= standard error
+Extended Data Table 2. Effects of various sex-ratios on the cumulative mortality rates of irradiated Aedes mosquitoes based on the generalized linear mixed model fit by maximum likelihood using Binomial linear mixed effect models.
+
+<table>
+  <tr>
+    <th rowspan="2">Aedes species</th>
+    <th rowspan="2">Sex</th>
+    <th colspan="1">Estimate</th>
+    <th>Std. Error</th>
+    <th>z value</th>
+    <th>Pr(&gt;|z|)</th>
+  </tr>
+  <tr></tr>
+  <tr>
+    <td rowspan="5"><i>Aedes aegypti</i></td>
+    <td>Female (Intercept)</td>
+    <td>4.09</td>
+    <td>0.18</td>
+    <td>22.93</td>
+    <td>&lt; 2e-16 ***</td>
+  </tr>
+  <tr>
+    <td>Female Sex Ratio = 49:1</td>
+    <td>-0.61</td>
+    <td>0.19</td>
+    <td>-3.29</td>
+    <td>0.001 **</td>
+  </tr>
+  <tr>
+    <td>Female Sex Ratio = 99:1</td>
+    <td>-1.96</td>
+    <td>0.15</td>
+    <td>-13.13</td>
+    <td>&lt; 2e-16 ***</td>
+  </tr>
+  <tr>
+    <td>Male (Intercept)</td>
+    <td>3.88</td>
+    <td>0.15</td>
+    <td>26.33</td>
+    <td>&lt; 2e-16 ***</td>
+  </tr>
+  <tr>
+    <td>Male Sex Ratio = 49:1</td>
+    <td>1.01</td>
+    <td>0.27</td>
+    <td>3.77</td>
+    <td>0.00016 ***</td>
+  </tr>
+  <tr>
+    <td>Male Sex Ratio = 99:1</td>
+    <td>0.27</td>
+    <td>0.17</td>
+    <td>1.58</td>
+    <td>0.115</td>
+  </tr>
+  <tr>
+    <td rowspan="5"><i>Aedes albopictus</i></td>
+    <td>Female (Intercept)</td>
+    <td>4.83</td>
+    <td>0.47</td>
+    <td>10.30</td>
+    <td>&lt; 2e-16 ***</td>
+  </tr>
+  <tr>
+    <td>Female Sex Ratio = 50:1</td>
+    <td>-2.24</td>
+    <td>0.46</td>
+    <td>-4.83</td>
+    <td>1.40e-06 ***</td>
+  </tr>
+  <tr>
+    <td>Female Sex Ratio = 100:1</td>
+    <td>-2.69</td>
+    <td>0.46</td>
+    <td>-5.83</td>
+    <td>5.47e-09 ***</td>
+  </tr>
+  <tr>
+    <td>Male (Intercept)</td>
+    <td>4.86</td>
+    <td>0.42</td>
+    <td>11.67</td>
+    <td>&lt; 2e-16 ***</td>
+  </tr>
+  <tr>
+    <td>Male Sex Ratio = 50:1</td>
+    <td>-2.37</td>
+    <td>0.42</td>
+    <td>-5.62</td>
+    <td>1.91e-08 ***</td>
+  </tr>
+  <tr>
+    <td>Male Sex Ratio = 100:1</td>
+    <td>-2.50</td>
+    <td>0.42</td>
+    <td>-5.96</td>
+    <td>2.51e-09 ***</td>
+  </tr>
+</table>
+
+Values were compared to the Sex Ratio = 1:3 [Control], **p-value &lt; 0.01; ***p-value &lt; 0.001, Std. Error= standard error
+Supplementary Information (SI)
+
+1. Mating harassment increases female mortality
+
+1. Supplementary Results
+
+At the beginning of the experiment, we monitored some of some non irradiated groups up to 13 days and mortality of females reached 43.3% (SD=4.7%) in the 99:1 batch in comparison to 4.1% (SD=1.7%) in the 1:3 control group (Extended Data Fig. 2, p-value < \(10^{-3}\)).
+
+In irradiated mosquitoes, the cumulative mortality rate of female *Ae. aegypti* increased with sex ratio and was 26.7% (SD = 14.0%) after 8 days for a male to female ratio of 99:1 as compared with a mortality rate of 3.9% (SD = 2.4%) in the control group (Fig. 1 and Extended Data Table 2, \(P < 10^{-3}\)). Male *Ae. aegypti* mortality after 8 days did not increase with a male to female ratio of 99:1 (Extended Data Table 2, \(P = 0.115\)) and was even lower than in the control group for a ratio of 49:1.
+
+The cumulative mortality of *Ae. albopictus* (Reunion strain) females was even higher as compared with *Ae. aegypti* and reached 40.0% (SD = 8.8%) after 8 days with a male to female ratio of 100:1 as compared with 3.8% in the control group (Fig. 1 and Extended Data Table 2, \(P < 10^{-3}\)). Again, the cumulative mortality of males significantly increased with increasing sex ratio in this species, reaching 24.8% (SD = 0.61%) and 25.3% (SD = 4.1%) after 8 days with male to female ratios of 50:1 and 100:1, respectively, as compared with 2.9% in the control group. Comparable results were obtained in a similar trial with another strain of *Ae. albopictus* (Rimini), except that the mortality of females reached 90% (SD = 6.1%) after 8 days with a female to male ratio of 99:1 as compared with 17.3% (SD = 4.1%) in the control group (Extended Data Fig. 4, p <\(10^{-3}\)).
+2. Supplementary Discussion
+
+Female mosquitoes are compulsory blood feeders and hence, the pathogen-transmitting sex. Even when irradiated, female mosquitoes require regular blood meals after release and may therefore still contribute to the transmission of diseases despite being sterile¹. This can only be avoided if accurate sex-separating systems that remove all female mosquitoes from the release batches are available². Different sexing techniques based on biological, genetic and transgenic approaches have been proposed for some mosquito species considered for SIT³⁴. While most contemporary SIT programmes use mechanical devices to sex pupae, female contamination rates close to 1%, a threshold considered as the maximum acceptable contamination rate for release, are common⁵⁶. The sex separation of Aedes mosquitoes is then carried out at the pupal stage, i.e., by using standard metal sieves with a square-opening mesh through which male Aedes swim upward, or by using the glass plate sex separation system. Given the substantial number of mosquitoes required for SIT, such methods are time-costly and require dedicated personnel to manually operate the sorting devices⁴. More recently, a sex-sorting pipeline including a mechanical pupal sieve, real-time adult visual inspection, a cloud-based machine learning classifier, and non-expert review has been described, but its cost-effectiveness remains uncertain⁷⁸.
+
+When a predetermined threshold is agreed with the public health authorities, e.g., 1%⁵, keeping the sterile males for 8 days might be an effective way of eliminating females instead of removing residual females manually or discarding the full batch of sterile males. Nevertheless, this would probably be cost-prohibitive in an operational programme. The feasibility of such action would require for instance, evaluating how long sterile males can be kept in the rearing facility without reducing their competitiveness. On La Réunion island, the competitiveness index of sterile male Ae. albopictus in semi-field conditions increased with the
+age of sterile males, from 0.14 one day after emergence to 0.53 after 5 days\textsuperscript{9}. A similar result was observed in Mauritius\textsuperscript{10} but this would require field validation.
+
+2. Potential impact of mating harassment on female survival after release
+
+1. Supplementary results
+To assess the potential impact of mating harassment on female survival after release, we monitored female survival after separation from the sterile males in *Aedes aegypti*. Mating harassment did not reduce the survival of females in the 99:1 group in comparison to the control group (p > 0.05). However, mated females had a much lower survival rate than virgin females (Extended Data Fig. 4, p-value = 0.014).
+
+References
+
+1 Guissou, E. *et al.* Effect of irradiation on the survival and susceptibility of female *Anopheles arabiensis* to natural isolates of *Plasmodium falciparum*. *bioRxiv preprint* (2020).
+2 Lutrat, C. *et al.* Sex sorting for pest control: it’s raining men! *Trends Parasitol.* **35**, 649-662 (2019).
+3 Papathanos, P. A. *et al.* Sex separation strategies: past experience and new approaches. *Malar J.* **8**(Suppl 2):S5, doi:10.1186/1475-2875-8-S2-S5 (2009).
+4 Lutrat, C. *et al.* Combining two Genetic Sexing Strains allows sorting of non-transgenic males for *Aedes* genetic control. *Communications Biology* **6**, 646, doi:10.1038/s42003-023-05030-7 (2023).
+5 WHO & IAEA. Guidance Framework for Testing the Sterile Insect Technique as a Vector Control Tool against Aedes-Borne Diseases, Geneva & Vienna. (2020).
+Bouyer, J., Yamada, H., Pereira, R., Bourtzis, K. & Vreysen, M. J. B. Phased Conditional Approach for Mosquito Management using the Sterile Insect Technique. Trends Parasitol. 36, 325-336 (2020).
+
+Crawford, J. E. et al. Efficient production of male Wolbachia-infected Aedes aegypti mosquitoes enables large-scale suppression of wild populations. Nat. Biotechnol. in press: 1-11. (2020).
+
+Bouyer, J., Maiga, H. & Vreysen, M. J. B. Assessing the efficiency of Verily’s automated process for production and release of male Wolbachia-infected mosquitoes. Nat. Biotechnol., 1-2 (2022).
+
+Oliva, C. F., Jacquet , M., Gilles, J., Lemperiere, G. & Maquart, P.-O., et al. The Sterile Insect Technique for Controlling Populations of Aedes albopictus (Diptera: Culicidae) on Reunion Island: Mating Vigour of Sterilized Males. PLoS ONE 7(11): e49414. doi:10.1371/journal.pone.0049414, doi:10.1371/journal.pone.0049414 (2012).
+
+Iyaloo, D. P., Oliva, C., Facknath, S. & Bheecarry, A. A field cage study of the optimal age for release of radio-sterilized Aedes albopictus mosquitoes in a sterile insect technique program. Entomol. Exp. Appl. in press (2019).
+Supplementary Files
+
+This is a list of supplementary files associated with this preprint. Click to download.
+
+• MovieS1voiceovercut1.wmv
+• MovieS2voiceovercut1.wmv
+• MovieS3voiceovercut1.wmv

0a7d3b5c38049654725a92dddc6647507a06a31feb5a95590bc5e681ea7206ac/preprint/preprint.md

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+Thunder-DDA-PASEF enables high-coverage immunopeptidomics and identifies HLA class-I presented SarsCov-2 spike protein epitopes
+
+David Gomez-Zepeda
+davidgz.science@gmail.com
+
+Helmholtz-Institute for Translational Oncology Mainz (HI-TRON) https://orcid.org/0000-0002-9467-1213
+Danielle Arnold-Schild
+University Medical Center of the Johannes Gutenberg University Mainz
+Julian Beyrle
+Helmholtz-Institute for Translational Oncology Mainz (HI-TRON)
+Elena Kumm
+University Medical Center of the Johannes-Gutenberg-University Mainz
+Ute Distler
+University Medical Center of the Johannes Gutenberg University Mainz https://orcid.org/0000-0002-8031-6384
+Hansjörg Schild
+Johannes Gutenberg-University Medical Center
+Stefan Tenzer
+University Medical Center of the Johannes-Gutenberg-University Mainz https://orcid.org/0000-0003-3034-0017
+
+Article
+
+Keywords:
+
+Posted Date: March 9th, 2023
+
+DOI: https://doi.org/10.21203/rs.3.rs-2625909/v1
+
+License: This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License
+
+Additional Declarations: There is NO Competing Interest.
+Version of Record: A version of this preprint was published at Nature Communications on March 13th, 2024. See the published version at https://doi.org/10.1038/s41467-024-46380-y.
+Thunder-DDA-PASEF enables high-coverage immunopeptidomics and identifies HLA class-I presented SarsCov-2 spike protein epitopes
+
+David Gomez-Zepeda1,2,*, Danielle Arnold-Schild1, Julian Beyrle1,2, Elena Kumm1, Ute Distler1,3, Hansjörg Schild1,2,3, Stefan Tenzer1,2,3,*
+1Institute for Immunology, University Medical Center of the Johannes-Gutenberg University, Mainz, 55131, Germany.
+2Helmholtz-Institute for Translational Oncology Mainz (HI-TRON), Mainz, 55131, Germany.
+3Research Center for Immunotherapy (FZI), University Medical Center of the Johannes-Gutenberg University, Mainz, 55131, Germany.
+
+*To whom correspondence should be addressed:
+David Gomez-Zepeda, email: david.gomez-zepeda@dkfz-heidelberg.de;
+Stefan Tenzer, email: tenzer@uni-mainz.de
+
+23/02/2022
+
+Abstract
+Human leukocyte antigen (HLA) class I peptide ligands (HLAIps) are key targets for developing vaccines and immunotherapies against infectious pathogens or cancer cells. Identifying HLAIps is challenging due to their high diversity, low abundance, and patient-specific profiles. Here, we developed a highly sensitive method for identifying HLAIps using liquid chromatography-ion mobility-tandem mass spectrometry (LC-IMS-MS/MS). The optimized method, Thunder-DDA-PASEF, semi-selectively fragments HLAIps based on their IMS and m/z, thus increasing the coverage of immunopeptidomics analyses. Thunder-DDA-PASEF includes singly-charged peptides, which contributes to more than 35% of the HLAIp identifications. Combined with MS2Rescore, Thunder-DDA-PASEF improved ligandome coverage by 150% compared to the original-DDA-PASEF method, and enabled in-depth profiling of HLAIps from two human cell lines, JY and Raji, transfected to express the SARS-CoV-2 spike protein. We identified seventeen spike protein HLAIps, thirteen of which had been reported to elicit immune responses in human patients.
+1 Introduction
+
+Identifying ligands of the major histocompatibility complex (MHC) or human leukocyte antigen (HLA), also called immunopeptides, is key for developing vaccines and immunotherapies (extensively reviewed in [1] [2] [3]). Human HLA class-I complexes bind peptides (HLAIps) of typically 9 to 12 amino acids generated by a multi-step process called antigen processing, which involves multiple proteolytic events by the proteasome and aminopeptidases [4] [5] [6] [7] [8]. Loaded HLA complexes are then displayed on the cell surface, where CD8+ T-cells scrutinize them. Detection of a "non-self" antigen, e.g., HLAIps derived from viral proteins or mutated cancer-related proteins, leads to the efficient elimination of the presenting cell by cytotoxic T lymphocytes. Thus, non-self HLAIps constitute key targets for developing peptide or mRNA vaccines in the context of personalized immunotherapies, or diagnostic tools. Various *in silico* tools have been developed to predict HLA-binding peptides from genomic, transcriptomic, or riboSeq data. Still, most predictors are primarily based on HLA binding affinity, thus not fully considering the antigen processing and presentation mechanisms, resulting in discrepancies between predicted and presented HLAIps [9] [10]. Therefore, liquid chromatography mass spectrometry (LC-MS)-based immunopeptidomics is essential for directly identifying HLA class I presented peptides from cells, tissues, and biofluids [9] [11].
+
+LC-MS immunopeptidomics faces different challenges than bottom-up proteomics, where proteins are usually digested using trypsin (reviewed in [3] [12]). HLAIps are generated by a complex multi-step process, including various proteolytic events [13] [14]. This results in peptides with restricted size and sequence patterns imprinted by the specificities of TAP transport and HLA binding. While these motifs differ between individual HLA alleles, they restrict the sequence space presented by a single allele. Thus, immunopeptidomics samples are more likely to contain isobaric peptides, potentially co-eluting from the LC, than enzyme-digested samples [2]. Since tryptic peptides are usually multi-charged, typical bottom-up proteomics workflows often omit the fragmentation and identification of singly-charged ions, which are more challenging to identify. In addition, singly-charged peptides are often masked by chemical noise, and their fragmentation generates many uncharged segments not detected by the MS [2]. Moreover, individual HLAIps are low abundant, and the sample preparation recovery yields are low (around 0.5-3% [15]). These factors demand tailored and high-sensitivity LC-MS methods and have major implications in database searches. The unspecific cleavage of HLAIps increases the search space by up to 2 orders of magnitude compared to tryptic digests. This impairs the discrimination of false positive from true positive peptide-spectrum matches (PSMs), negatively impacting peptide identification yield and confidence [16].
+
+Coupling ion mobility separation (IMS) to LC-MS provides an extra dimension of separation, resolving ions in the gas phase by their size and shape. This enhances the signal-to-noise ratio and resolves isobaric ions, thus increasing the number and confidence of peptide identifications. In the timsTOF Pro instruments, a dual trapped ion mobility spectrometry (TIMS) analyzer is employed to perform a parallel accumulation–serial fragmentation (PASEF) of ions, resulting in a high sequencing speed without compromising sensitivity for data-dependent
+acquisition (DDA-PASEF) [17,18], which has already been proven to perform well for immunopeptidomics [19].
+
+During the ongoing Covid-19 pandemic, there have been significant efforts to identify SARS-CoV-2 HLAIPs, mainly focusing on characterizing the immunogenicity in vitro or in vivo of large libraries of synthetic peptides or in silico predicted HLA-binders (25 studies reviewed in [20]). This has provided important insights into possible immunodominant regions in the viral proteome, HLA allele-dependent responses to SARS-CoV-2, and the protection capabilities of vaccines (reviewed in [20][21][22]). More than 2,000 possible HLA-binding peptides have been predicted from the SARS-CoV-2 genome [23]. However, only a few SARS-CoV-2 immunopeptides have been detected by LC-MS until now [21][25][26], including less than ten HLAIPs for the spike glycoprotein [21][26], the main target of vaccines and diagnostic tests. This emphasizes the challenges of LC-MS immunopeptidomics and the need for more sensitive and robust methods.
+
+Here, we present Thunder-DDA-PASEF, an optimized LC-IMS-MS method for immunopeptidomics and its application in the discovery of SARS-CoV-2 spike protein derived HLAIPs. The optimized method uses an extended TIMS separation time (300 ms) to improve IMS resolution, and sensitivity [17,27]. To include singly charged peptides while efficiently using instrument cycle time, precursors are selected by using a tailored isolation polygon for semi-selectively fragmenting potential HLAIPs. Compared to the standard method (100 ms TIMS, bottom-up proteomics-optimized isolation polygon), Thunder-DDA-PASEF increased the HLAIPs identifications from JY cells by 2.3-fold, including more than 35% of identifications derived form singly-charged. Moreover, MS^2Rescore-based rescoring [16] further boosted the identification to 3.5-fold relative to the non-rescored standard DDA-PASEF. Subsequently, we employed Thunder-DDA-PASEF to study the HLAIP ligandome repertoire of two cell lines recombinantly expressing the canonical spike protein of SARS-CoV-2. This resulted in deep coverage of 14,313 and 17,806 peptides from JY and Raji cells, respectively, including seventeen HLAIPs derived from the SARS-COV-2 spike protein. Notably, thirteen of these peptides have been previously reported to elicit immune responses in human patients, confirming the potential of our improved method for efficient epitope discovery. In conclusion, optimized Thunder-DDA-PASEF achieved deep and reproducible profiling of the HLA class I ligandome.
+
+2 Results
+
+2.1 General workflow for LC-IMS-MS immunopeptidomics
+
+For our immunopeptidomics experiments, we followed the general procedure shown in Fig. 1 and described in Material and Methods. The settings used for the LC-MS methods and data processing are fully detailed in Supplementary Material S2a and the ready-to-use MS method for timsTOF Pro instruments is included in Supplementary Material S2b. Briefly, we enriched HLAIPs from JY cells by immunoprecipitation (W6/32 antibody), and analyzed them by nanoLC-IMS-MS on a nanoElute coupled to timsTOF-Pro-2 in DDA-PASEF mode, using PEAKS XPro for subsequent peptide identification. We performed several iterations to optimize
+2.2 An HLAIp-tailored DDA-PASEF fragmentation scheme including singly-charged ions efficiently identified possible HLAIps
+
+Contrarily to tryptic peptides, HLAIps originate from a large diversity of antigen processing events [13, 14] and do not necessarily contain basic amino acid residues [2]. Thus, many HLAIps can only be detected as singly-charged ions in LC-MS since only their N-ter residue can carry a positive charge (H^+). Although this varies depending on the HLA alleles, up to 40% of singly-charged ions have been reported for peptides bearing hydrophobic anchor residues such as HLA-B07:02 [28, 29]. In addition, HLAIps have a restricted size of typically 9 to 12 amino acids (AAs) [2], but between 8 to 13 in some instances [30, 31]. For this reason, HLAIp-immunopeptidomics workflows have recently incorporated the fragmentation of singly-charged ions (with 2^+ and 3^+) within the m/z range of possible HLAIps [2, 19, 29, 28, 32, 33, 34, 35, 36]. We hypothesized that the IMS separation and sensitivity of the timsTOF Pro-2 could provide high-quality MS2 spectra to identify singly-charged peptides confidently.
+
+First, we tested the original-DDA-PASEF method for proteomics [17] to analyze JY HLAIps samples (Fig. 2a, d, g). DDA-PASEF takes advantage of the charge-state-dependent mobility separation to selectively fragment ions detected within an isolation polygon on the inverse reduced ion mobility (1/K_0) vs. m/z space. Since it was designed for tryptic peptides, the standard isolation polygon covers the multiply-charged ion cloud, clearly separated from the singly-charged ones (Fig. 2a). This resulted in almost 5,000 unique peptides from three injection replicates of JY HLAIps (Fig. 2b), mainly comprising doubly-charged ions (89%, Fig. 2b) and almost 77% of 8-13-mers (Fig. 2g, j). As expected, most singly-charged ions were excluded from fragmentation, and only a few were identified due to IMS peak tailing into the isolation polygon.
+
+Our next step was to remove the isolation polygon (Fig. 2b). Omitting the isolation polygon enabled the fragmentation of singly-charged peptides, representing more than half (54.5%) of all the peptides identified and 59.6% of the 8-13-mers (Fig. 2f, h). Furthermore, the proportion of peptides with 8 to 13 AAs was 12.4% higher than in the standard-polygon (Fig. 2h, j), corresponding to 72% more 8-13-mers identified on average (\( p \leq 0.0001 \), Fig. 2n). However, without an isolation polygon, many low m/z singly-charged ions and high mass multiply-charged ions were fragmented (Fig. 2b).
+
+Therefore, we designed fragmentation isolation polygons covering the singly-charged and multiply-charged 8-13-mer peptides[2; h] (Table 1). This HLAIp-tailored scheme efficiently identified peptides within the isolation polygon (Fig. 2c, f, i), roughly maintaining the charge distribution of peptides identified, with 56.4% of all the ions and 59.7% of the 8-13-mers being singly-charged. The proportion of 8-13 mers was almost 92%, which is 15% and 2.6% higher than the standard- and no-polygon, respectively (Fig. 2j, k, respectively). As a result, the HLAIp-tailored polygon increased the identification of 8-13-mers by 75% relative to the standard (\( p \leq 0.0001, [2n] \)). Compared to no polygon, the HLAIp-tailored polygon resulted in 24% fewer MS2 scans
+(p \leq 0.001, [2]), but a similar yield of 8-13-mers identified (Fig. 2m). This 18% increase in the identification rate shows that the HLAIp-tailored polygon used the cycle time more efficiently to fragment 8-13-mers. In contrast, without an isolation polygon, a large proportion of the cycle time was used inefficiently to fragment ions that are not of interest for HLAIp profiling. These may include non-peptidic small ions or larger peptides (Fig. 2b, Supplementary Fig. S1a, b) originating from the degradation of HLA proteins, the antibody, or other co-enriched proteins (Supplementary Fig. S1c). Once having established the capabilities of DDA-PASEF with the HLAIp-tailored isolation scheme for immunopeptidomics, we optimized several other parameters of the MS method (detailed in Supplementary Material S2).
+
+2.3 Optimized Thunder-DDA-PASEF enhanced the identification of 8-13-mers by 2.2-fold
+
+In PASEF methods, each analysis cycle comprises several frames where the trapping TIMS tunnel accumulates a package of ions. Simultaneously, the second TIMS resolves the previous package of ions by ramping down the elution voltage. Increasing TIMS times enhances IMS resolution and accommodates more fragmentation events per MS2 frame while preserving the sensitivity [17]. Raising the TIMS time from 100 to 300 ms resulted in an 80% increase in peptide identification, while no substantial increase was observed between 400 ms and 300 (< 5% increase) (Supplementary Fig. S2a, b, c, d). However, the longer cycle times resulted in five-fold fewer MS1 frames and doubled the median coefficient of variation (CV) at 400 ms compared to 100 ms. Since the peak area reproducibility is essential for quantitative comparisons between samples (e.g., diseased vs. control), we compensated for this effect by decreasing the number of MS2 frames/cycle from 10 to 3, and the MS2 cycle overlap from 4 to 1 (Fig. S2e, f, g, h). This resulted in a cycle time of 1.2 s and reduced the median peak area CV from 19.3% to 10.3% (Fig. S2d,h). In addition, activating the high-sensitivity mode of the timsTOF Pro-2, which uses detector voltages optimized for low sample amounts, further increased the number of HLAIps identified by 30% (Supplementary Fig. S3).
+
+In summary, the optimized method resolves ions using a 300 ms TIMS ramp, fragmenting mainly ions with 1^+, 2^+, and 3^+ charges in 3 MS2 frames per MS1 frame within a 1.2 s cycle time and takes advantage of the high-sensitivity mode. Since the HLAIp-tailored isolation polygon resembles a lighting or thunder icon, we termed the fully optimized method Thunder-DDA-PASEF. In contrast, the original-DDA-PASEF designed for proteomics samples uses 100 ms ramps and selectively fragments multiply-charged ions in 10 MS2 frames per MS1 frame within a 1.2 s cycle time.
+
+We compared Thunder-DDA-PASEF to the original-DDA-PASEF method by analyzing triplicate injections of JY HLAIps (equivalent to approximately 50 million cells/injection, Supplementary Material S3). Thunder-DDA-PASEF identified 2.2-fold the number of 8-13-mers than the original method (\( p < 0.0001 \), Fig. 3h). This was partly due to the inclusion of singly-charged peptides in Thunder-DDA-PASEF, constituting 48% of the 8-13-mers in this data set (Fig. 3b). Thunder-DDA-PASEF improved the dynamic range for identification
+by almost half an order of magnitude towards the low abundant species (Fig. 3c). The number of peptides identified across all three replicates was 8.4% higher in Thunder-DDA-PASEF than in the original-DDA-PASEF, indicating a slight improvement in the data completeness (Fig. 3d). Although 8.7% of the peptides were only identified in the original method (Fig. 3e), this could be due to the sampling stochasticity of DDA. Then, we used NetMHCpan-4.1 [37] via MhcVizPipe [38] to predict peptide HLA-binding, which provides a ranking classifying the peptides into strong-binders (SB, \( rank \leq 0.5\% \)), weak-binders (WB, \( 0.5\% < rank \leq 2\% \)) or non-binders (NB, \( rank > 2\% \)). When focusing on the peptides predicted to bind JY HLA alleles, the 8-13-mers identified comprised 88.2% SB and 7.8% WB in the original method and 85.4% SB and 9.1% WB in Thunder-DDA-PASEF (Fig. 3, Supplementary Material S4). Altogether, these results proved a 2.2-fold increase in the coverage of the immunopeptidome using Thunder-DDA-PASEF compared to the original-DDA-PASEF (9,524 and 4,334 HLAIPs, respectively).
+
+2.4 Machine learning-based rescoring via MS^2Rescore enhanced the identification of HLAIPs and data completeness by more than 15%
+
+Several post-processing tools have shown improvements in immunopeptide identification by rescoring peptide spectrum matches (PSMs) based on characteristics disregarded in the initial search [16,34,39,40]. For instance, MS^2rescore (MS2R) [16] integrates the machine learning prediction of retention and fragmentation peak intensity using DeepLC [41] and MS^2PIP [42][43][44], respectively, with the semi-supervised machine learning-based FDR calculation of Percolator [45]. Since this strategy has shown the potential to boost immunopeptide identification [16], we decided to implement it in our workflow.
+
+Rescoring the results of Thunder-DDA-PASEF from JY IP-enriched HLAIPs (Supplementary Material S3) significantly increased the average number of 8-13-mer peptides identified per injection by 29.1% (\( p < 0.0001 \), Fig. 3a). The proportion of singly-charged peptides decreased (Fig. 3b) not due to a drop in their numbers but because most newly identified peptides were doubly charged (74.5%). Probably, the performance of MS^2Rescore for singly-charged ions was lower due to the fewer singly-charged ions in the MS^2PIP immunopeptidomics model training set. Thus, training a predictor model with orthogonal Thunder-DDA-PASEF data could improve its performance.
+
+Novel identifications were obtained across the whole dynamic range indicating that rescoring performed well even for low-intensity ions (Fig. 3c). Despite applying a stringent confidence filter independently for each file (PSM \( FDR \leq 0.01 \)), 77.1% of the peptides were consistently identified across all three replicates in the rescored results, meaning a 16.7% increase in data completeness (Fig. 3d). In addition, only a few peptide identifications were dropped by MS^2Rescore (< 1.5%, Fig. 3e), and it also recovered 263 peptides identified in the non-rescored original-DDA-PASEF but not in Thunder. The proportion of SB and WB was not affected by rescoring, indicating that no bias was introduced. The benefits of rescoring Thunder-DDA-PASEF identifications are summarized in a 14.7% increase in the number of predicted HLAIPs identified, yielding a total
+of 10,931 (Fig. 3f). Collectively, the Thunder-DDA-PASEF + MS2R strategy resulted in a 2.5-fold coverage of HLAIs compared to the non-rescored original-DDA-PASEF data for JY HLAIp IP-enriched peptides (Fig. 3f; Supplementary Material S4), with an average of 9,821 HLAIs per injection.
+
+In summary, combining the optimized Thunder-DDA-PASEF with MS^2Rescore resulted in a highly sensitive and reproducible workflow. This level of coverage could enable deep profiling of immunopeptides in patient samples and the comparability between healthy and pathological tissue for the discovery of disease-specific antigens.
+
+2.5 Thunder-DDA-PASEF enabled in-depth characterization of the HLA class I ligandome of JY and Raji cells
+
+We tested our optimized workflow to characterize the HLA class-I immunopeptidome of JY and Raji cells transfected to express a segment of the SARS-CoV-2 spike protein (Supplementary Material S5). Thunder-DDA-PASEF + MS2R identified in total 23,147 peptides from JY and 29,397 peptides from Raji, comprising 78% of 8-13-mers, with a median length of 9 AAs (Fig. 4h), as expected for HLAIs. The reproducibility between biological replicates ranged between 35.8% and 62.7% 8-13-mers identified in all the samples of the same genotype, and 67.7% to 81.3% regarding the proteins covered (Supplementary Fig. S4). Based on the HLA-binding prediction (NetMHCpan-4.1 [37] via MhcVizPipe [38], Supplementary Material S6), the 8-13-mers included 78.9% binders for JY (70% SB, 8.9% WB) and 77.6% for Raji (67.2% SB, 10.4% WB) (Fig. 4p), showing the respective peptide sequence motifs, as indicated by supervised clustering (GibbsCluster-2.0 [46], Fig. 4g, h). A lower proportion of HLAIs was detected as singly-charged ions in Raji, compared to JY (30.1% vs. 42.9%). This was due to the presence of basic amino acids at the anchor positions for Raji HLA alleles (Fig. 4g), including lysine or arginine at the C-ter (HLA-A03:01) or histidine at the second position (HLA-B15:10, HLA-C04:01). In contrast, the anchor residues binding JY HLA alleles were dominated by apolar amino acids (Fig. 4h).
+
+Thunder-DDA-PASEF achieved an extensive coverage of protein-HLAIp representation. A total of 14,074 and 17,469 HLAIs were detected in JY and Raji, respectively, summing up to 30,948 peptides (Fig. 4l, top). These peptides corresponded to 5,660 protein groups in JY, 6,170 in Raji, and 8,214 in total (Fig. 4l, bottom). Each protein group was represented by a median of 2 HLAIs per protein group and 75% of them with one to three peptides for both cell lines (Fig. 4k). As a comparison, the DIA analysis of JY HLAIs provided a median of one HLAIp per protein [32] despite a deep coverage of 7,627 peptides. This further shows the potential of our workflow to provide an in-depth characterization of the immunopeptidome, which may unravel novel antigen processing and presentation mechanisms.
+
+Although only 1.8% of all HLAIs were detected in both JY and Raji, 44% of all the protein groups were covered by the ligandomes of the two cell lines (Fig. 4l, top and bottom, respectively). A gene ontology (GO) enrichment analysis using GOrilla [47] indicated a significant over-representation (\( FDR \leq 0.001 \)) of proteins
+involved in essential processes, such as the metabolism of nucleic acids (GO:0090304), macromolecule biosynthesis (GO:0034645), macromolecule localization (GO:0033036), and regulation of the cell cycle (GO:0022402) (Supplementary Material S7 and S8). Thus, the cell lines presented complementary peptides for these same crucial proteins due to their different HLA alleles and probably also due to differences in the antigen processing pathway. Because of the large number of HLAIPs covered (30,984 binders) (Fig. 4b, d), including more than 11,000 singly-charged peptides (Supplementary Material S3), this combined immunopeptidome of JY and Raji cells constitutes an essential resource for future exploitation.
+
+2.6 Thunder-DDA-PASEF identified seventeen spike HLAIPs in JY and Raji spike-transfected cells
+
+To explore the potential of Thunder-DDA-PASEF on a clinically relevant subject, we focused on the transfected SARS-CoV-2 spike protein, and the GFP reporter included in the construct. Importantly, peptides from these proteins were only detected in the transfected cells and not in the wild-type cells. Three GFP-derived HLAIPs were identified in JY and six in Raji cells (Fig. 5 b), serving as a control for successful antigen processing of the transfected constructs. Five spike HLAIPs were identified in JY and thirteen in Raji (Fig. 5c) across a large dynamic range corresponding to four orders of magnitude (Fig. 5c). While the Raji spike HLAIPs were distributed across the whole dynamic range, they were mainly in JY’s middle to low range. The sequence and characteristics of the spike HLAIPs are shown in Fig. 5d and detailed in the Supplementary material S9. Nomenclature in Fig. 5c and d denotes identified spike HLAIPs (e.g., SIIAYTMSL*0691-0699) both by peptide sequence and position (N- to C-ter) in the full-length spike protein. Notably, six of the thirteen spike HLAIPs were singly charged, showing the advantage of the Thunder HLAIP-tailored isolation polygon for identifying potential clinically relevant immunopeptides.
+
+In addition to the 1% FDR threshold applied, the spike HLAIPs were assessed based on the number of identifications across biological and technical replicates (n BR, n TR; Fig. 5d, yellow to green scales) and by the similarity of their fragmentation spectra against synthetic peptides or in silico predictions, based on the Pearson correlation coefficient (PCC) [8] (Fig. 5d, blue scale with letters, S = synthetic, P = predicted). The mirrored spectra comparisons are shown in Supplementary Material S10. At the same time, SIIAYTMSL*0691-0699 and TLKSFTVEK*0302-0310 are shown in Fig. 6 as examples of the confident identification of peptides with high and low abundance, respectively. Around 82% of the reported spike HLAIPs were identified in two biological replicates with a PCC >= 0.85, indicating both robust sample preparation and high-confidence identifications. The synthetic peptides analyzed independently with the same method were eluted at similar indexed retention times (iRT) as the corresponding endogenous peptides (ratio iRT endogenous/synthetic >= 0.99). Even though peptides GVLTESNKK*0550-0558 from Raji and RLQSLQTYV*1000-1008 from JY were identified in only one injection replicate in one of the biological replicates, their PCC were 0.94 and 0.96, respectively (\( FDR < 0.005 \)). Peptide AIHVSGTNGTK*0067-0077 showed a low PCC (0.47) against the predicted spectra but was detected in
+five injection replicates across both biological replicates with an \( FDR < 0.0005 \), thus validating its detection.
+
+While a large proportion of the HLAIPs were predicted to be strong binders (Fig. 5I), there was a deficient number of HLAIPs for both the HLA-C alleles in Raji (HLA-C04:01) and JY (HLA-C07:02 ). This could be due to the low expression of this gene in JY cells, whose effect on its immunopeptidome has been previously reported [49]. Interestingly, some spike HLAIPs were predicted to bind to the HLA alleles of both cell lines, but only SIIAYTMSI_{s0691-0699} was identified in both cell lines. Once more, this highlights the need for direct validation of *in silico*-predicted HLA class I binders. However, the challenge of LC-MS immunopeptidomics is exemplified here since only one of the seventeen spike HLAIPs had been previously reported by MS (SIIAYTMSI_{s0691-0699}) [40]. Moreover, four represent completely novel identifications (AIHVSGTNGTK^{s0067-0077}, YGVSPTKL^{s0380-0387}, RVYSTGSNVFQTR^{s0634-0646}, NRALTGIAV^{s0764-0772}). The remaining thirteen spike HLAIPs have been reported to exhibit positive results in T-cell or MHC ligand assays according to the IEDB [60] (December 18, 2022) (Fig. 5I, dot range plot). This shows the capabilities of Thunder-DDA-PASEF for identifying potential HLA class I-restricted immunogenic targets which could be employed for vaccine development.
+
+In summary, we report seventeen spike peptides identified with high stringency and confidence, which are predicted to bind HLA class I in two cell lines expressing different HLA alleles. Accordingly, this set of peptides constitutes a key resource, comprising novel spike HLAIPs, and confirms many previously reported peptides capable of eliciting a T-cell response.
+
+3 Discussion
+
+Here, we present Thunder-DDA-PASEF, an LC-IMS-MS method tailored and optimized for identifying HLA class I peptide ligands (HLAIPs). We showed that the HLAIP-tailored isolation polygon enabled the identification of singly-charged peptides, expanding the universe of identifiable MHC peptide ligands. Thunder-DDA-PASEF uses a thunder-shaped isolation polygon (Fig. 2), optimized detector voltages (high sensitivity mode), enhanced IMS resolution (300 ms TIMS), and fewer MS2 frames (3 MS2 frames/cycle, 1 cycle overlap), resulting a cycle time of 1.2 s, compatible with nanoLC peak width (Supplementary Fig. S2h, Supplementary Material S2a and S2b). Altogether, this resulted in more than a 2.2-fold higher number of 8-13-mers identified from JY cells, compared to the standard DDA-PASEF optimized for proteomics samples (excluding singly-charged ions, 100 ms TIMS ramp, 10 MS2 frames/cycle, 4 overlap) (Fig. 3I). MS^2Rescore further boosted the identifications up to 2.5-fold compared to the standard, unrescored DDA-PASEF. In addition, Thunder + MS^2Rescore improved the identification data completeness, reliably and constantly identifying 77.1% of the peptides across three technical replicates (Fig. 3A).
+
+Field asymmetric waveform ion mobility spectrometry (FAIMS) has been combined with LC-MS to identify singly-charged HLAIPs [29]. However, FAIMS acts as a gas-phase fractionation device, filtering ions in function of their mobility in the electric field. Since only a population of ions can be analyzed simultaneously, identifying
+multiply and singly-charged HLAIPs requires dividing the cycle time within an LC-MS run between or performing multiple injections per sample [29]. In contrast, TIMS-MS profiles ions across a \(1/K_0\) range. In addition, PASEF maximizes the duty cycle by trapping a package of ions while the previous is being separated and synchronizing ion fragmentation with TIMS elution. We adapted this concept for HLAIPs by taking advantage of their size- and charge-dependent separation forming two distinct ion clouds for the singly and multiply-charged 8-13-mer peptides. Thus, PASEF-MS2 frames are efficiently used to fragment singly-charged ions during the first half of the TIMS ramp and multiply-charged during the second half.
+
+Additional adaptations could further improve the identification of immunopeptides. For instance, the Thunder isolation polygons could be more restrictive towards 9 to 12-mers to improve fragmentation selectivity for more challenging samples. For example, soluble HLAPs enriched from plasma samples tend to include larger peptides resulting from the degradation of proteins adhering non-specifically to the beads, such as blood clotting and other plasma proteins [51]. Here, we decided to employ broad limits to account for variability between HLA alleles and to accommodate slight variations in the instrument (e.g., IMS variations between days). In addition, disease-associated HLAIPs can be composed of larger sequences [30] [52] [53] or include modifications that are key for their immunogenicity [1] [54] [55].
+
+Sensitivity and reproducibility could be further improved by using a data-independent acquisition (DIA) method including singly-charged ions. Although DIA requires spectral libraries for peptide identification, recent publications have shown its value for immunopeptidomics [32] [40]. For instance, using Orbitrap instruments, more than 97% of the combined identifications from 3 DDA runs used to create the library were identified in each single DIA injection of HLAIP-enriched peptides from cell lines. Using this strategy, Pak et al. [32] identified 7,627 HLAIPs per injection of JY cell W6/32 IP-enriched peptides. However, sample fractionation by SPE or in the gas phase, or at least multiple DDA injections, is required to obtain the spectral libraries. In contrast, Thunder-DDA-PASEF can achieve higher HLAIPs identification coverage in a single run (10,000 on average). Considering this, we propose a future strategy where a spectral library is acquired using Thunder-DDA-PASEF and then used to identify the peptides for quantitative DIA analysis.
+
+Thunder-DDA-PASEF enabled the deep profiling of the HLA class I ligandomes from two cell lines with distinct HLA alleles. We detected 14,074 predicted HLAIPs from JY and 17,469 from Raji, with a median coverage of two HLAIPs per protein, surpassing the number of HLAIPs identified for a single cell line in previous publications [32] [40] [49]. In total, 30,984 HLAIPs were identified (Fig. [1b], d), including more than 11,000 singly-charged peptides (Supplementary Material S3). Thus, this combined data set constitutes an important resource for future exploitation (data available via ProteomeXchange, identifier: PXD040385). For instance, using the identifications for training DeepLC and MS2PIP prediction models could further improve the performance of MS\(^2\)Rescore on timsTOF immunopeptidomics data [16], and other prediction algorithms could be explored ([34] [40] [56]). In addition, different strategies for data analysis remain to be evaluated (Fragpipe, MSmill). Besides, a deeper PTM search could be performed using the PTM algorithm from PEAKS [57], or PROMISE
+The onset of the ongoing SARS-CoV-2 pandemic has fueled the discovery of antigen candidates for vaccination, employing *in silico* prediction algorithms, genetic screens, or peptide library T-cell response assays. Even though immunogenicity testing of hypothesized vaccine candidates yielded some positive outcomes (reviewed in [20][21][22]), direct evidence of MHC peptide ligand antigens relies mainly on direct identification by LC-MS. The 17 SARS-CoV-2 spike HLAIPs (Fig. 5I) identified included thirteen peptides with proven immunogenicity (IEDB) and four possibly novel antigens that could be explored as targets for therapy development. Notably, six of the seventeen spike peptides were only identified as singly charged ions, and only the peptide identified in both cell lines (SIIAYTMSL^s0691-0699^) was reported by MS before ([40]). Altogether these results show that Thunder-DDA-PASEF substantially expands the MS-detectable immunopeptidome providing the means for reproducible antigen discovery and direct validation of immunopeptides hypothesized by non-MS methods.
+
+In summary, Thunder-DDA-PASEF enables an in-depth coverage of HLAIPs in a highly reproducible manner. This opens new opportunities to dig deeper into the immunopeptidome in our search to discover novel and specific antigens to target infectious diseases and cancer.
+
+4 Methods
+
+4.1 Cell culture
+
+The human B lymphoblastoid cell line JY expressing HLA-A02:01, B07:02, C07:02 was purchased from ATCC and the human Burkitt lymphoma cell line Raji expressing HLA-A03:01, B15:10, C03:04, 04:01 was obtained by the DSMZ-German Collection of Microorganisms and Cell Cultures. Both cell lines were maintained in RPMI1640 medium supplemented with 10 % FCS (Gibco), 2 mM glutamine, 1 mM sodium pyruvate, 100 units/ml penicillin and 100 pg/ml streptomycin. Cells were harvested at 220 x g for 10 min and washed three times with 1x PBS prior counting and freezing at -80°C until further use.
+
+4.2 Cell transfection
+
+The pcDNA3.1-SARS2-spike vector containing the full-length cDNA encoding for the SARS-CoV2 spike protein was obtained from Fang Li (Addgene plasmid #145032 : https://www.addgene.org/145032). The spike S cDNA was split into S1 (2016 bp) and S2 (1761 bp) subunits for cloning by PCR into the NheI and XhoI restriction sites from the multiple cloning site of the pcDNA3.1+P2AeGFP vector (Genscript). The following oligonucleotides (all purchased by Sigma) were used : GCAT GCT AGC ATG TCT CAG TGC GTG AAC CTG ACT ACT AGA ACC and GCAT CTC GAG ACG GCG AGC CCT CCT TGG GGA GTT GGT CTG GGT CTG for the S1 cDNA and GCAT GCT AGC ATG AGC GTG GCC AGC CAG TCC ATC ATC GCC TAC and GCAT CTC GAG AGC GGG AGC GAC CTG GGA TGT CTC GGT GGA G for the S2 cDNA cloning. To generate stable JY and Raji transfectants expressing either the S1 or the S2 protein fragments
+(Supplementary Material S1, Material and Methods), 2 million cells were exposed to 230 V and 500 μF in the presence of 10 μg plasmid DNA using the Bio-Rad Gene Pulser II. After electroporation, cells were cultured 24 h before starting G418 (Gibco) selection at a concentration of 400 μg/ml for JY cells and 800 μg/ml for Raji cells. G418-resistant and eGFP-expressing cells were selected by three rounds of screening using a FACS Aria (BD Biosciences) at the Core Facility of the Research Center for Immunotherapy (University Medical Center, Johannes Gutenberg University Mainz).
+
+4.3 Immuno-affinity purification of HLA peptide ligands
+
+HLA class I ligands were enriched by immunoprecipitation as described by [59] with modifications [60]. Briefly, 500 million cells were washed three times with PBS, harvested, flash-frozen, and stored at -80°C until further preparation. The cell pellets were thawed and lysed in a non-denaturant buffer (1% CHAPS in PBS (m/v)) aided by sonication. Immunoprecipitation was performed using an anti-panHLA Class I antibody (W6/32, anti-HLA-A, -B, -C), immobilized on CNBr-activated beads. After overnight incubation, the beads were washed once with PBS and once with water before peptide ligands were eluted under acidic conditions (0.2% TFA (v/v)). Next, peptides were ultrafiltered (10 kDa cutoff) and then desalted by SPE on a Hydrophilic-Lipophilic-Balanced sorbent (HLB, Waters Corp.), applying 35% ACN (v/v) + 0.1% TFA (v/v) for elution. Finally, dried peptides were dissolved in 15 μL of water with 0.1% FA (v/v) for subsequent LC-MS/MS analyses.
+
+4.4 LC-MS/MS
+
+NanoLC-MS analysis was performed using a nanoElute coupled to a timsTOF-Pro-2 mass spectrometer. The desalted peptides were directly injected in a C18 Reversed-phase (RP) analytical column (Aurora 25 cm x 75 μm ID, 120Å pore size, 1.7 μm particle size, IonOpticks, Australia) and separated using either a 47 min or 110 min gradient (Supplementary Material S2a) increasing the proportion of phase B (ACN + 0.1% FA (v/v)) to phase A (water + 0.1% FA (v/v)), as detailed in Supplementary Material S2. A Captive Spray source was used for ionization, with a capillary voltage of 1600 V, dry gas at 3.0 L/min, dry temperature at 180 °C, and TIMS-in pressure of 2.7 mBar. MS data were acquired in DDA-PASEF mode. Different MS parameters were evaluated during method development, as detailed in Supplementary Material S2a. The JY and Raji spike-transfected data set was acquired using the optimized conditions described in the following lines. HLAIp IP-enriched, ultrafiltered, and desalted peptides were analyzed in three injection replicates each, using a volume of 1.5 μL/injection, equivalent to 50 million cells from the original sample. Peptides were separated in a 110 min. gradient from 2 % to 37 % of ACN +0.1% FA (v/v). The MS was configured with the optimized Thunder-DDA-PASEF method, employing an HLAIp-tailored isolation polygon (Fig. 2), a 300 ms TIMS ramp, three MS2 frames/cycle, one cycle overlap, using the high-sensitivity mode (optimized detector voltages). The settings used for LC-MS are detailed in Supplementary Material S2a and the timsTOF Pro method is included as Supplementary Material S2b.
+4.5 Peptidomics database search
+
+Data analysis was performed in PEAKS XPro (v10.6, build 20201221). Raw LC-MS files were loaded with the configuration for timsTOF DDA-PASEF data with CID fragmentation. The option timstof_feature_min_charge (in file PEAKSSstudioXpro\algorithmmpara\feature_detection_para.properties) was set to 1 to allow the identification of singly-charged features. The protein database was composed of the UniProtKB (Swiss-Prot) reference proteomes of Homo sapiens (Taxon ID 9606, downloaded 02/Feb/2020), Epstein-Barr virus (strain GD1, Taxon ID 10376, downloaded 06/Feb./2022), GFP from Aequorea victoria (P42212), and SARS-CoV-2 (Taxon ID 2697049, downloaded 10/March/2021), as well as the SiORF1 reported by [61] [62], supplemented with a list of 172 possible contaminants. For database searches, protein *in silico* digestion was configured to unspecific cleavage and no enzyme. Methionine oxidation, cysteine cysteinylated, and Protein N-terminal acetylation were set as variable modifications. Peptides were identified with mass accuracy thresholds of 15 ppm for MS1 and 0.03 Da for MS2. Results were filtered at *FDR* \( \leq 0.01 \) for peptides and \( -10lgP \geq 20 \) for proteins. For rescoring, spectra were exported in MGF format and identifications in mzIdentML format, including decoys and without any score filter (\( -10lgP \geq 0 \) for peptides and proteins). Identifications were then rescored using MS\(^2\)Rescore [16] using the Immuno-HCD MS2PIP model and an MS2 mass accuracy tolerance of 0.03 Da. The settings used for data processing are also detailed in Supplementary Material S2a.
+
+4.6 Experiment design
+
+For method development, pooled samples of IP-enriched HLAIPs from JY WT cells were used. For the final JY and Raji data set, the IP protocol was used to enrich the HLAIPs from three cultures of each WT cell line (JY_WT, and Raji_WT) and two different cultures of each transfected cell line (JY_S1, JY_S2, Raji_S1, and Raji_S2). In every experiment, each sample was analyzed in three LC-MS injection replicates.
+
+4.7 Data analysis and statistics
+
+MHC-binding was predicted using NetMHCpan 4.1 [37] and GibbsCluster 2.0 [46] through MhcVizPipe (v0.7.9) [38]. R scripts [63] were used for data analysis, including merging the MS\(^2\)Rescore [16] output with PEAKS peptide results, as well as with MhcVizPipe output. The main R packages used were as follows; the statistical difference was assessed by two-sided t-test using *ggpubr* (v. 0.4.0) [64]; plots were generated using *ggplot2* (v. 3.4.0) [65]; Venn plots with *ggvenn* (v. 0.1.9) [66]; and upset plots with *ggupset* (v. 0.3.0) [67].
+
+We employed the Universal Spectrum Viewer (USE) [48] to compare the spectra acquired from the cells against spectra obtained from synthetic peptides (n=7) or predicted *in silico* (n=10), based on the similarity Pearson correlation coefficient (PCC). Prosit [54] [66] was used for *in silico* prediction since it’s an orthogonal model to MS\(^2\)Rescore [16] used for rescoring.
+4.8 Data availability
+
+The mass spectrometry immunopeptidomics data have been deposited to the ProteomeXchange Consortium (http://proteomecentral.proteomexchange.org) via the jPOSTrepo partner repository with the dataset identifiers PXD040385 for ProteomeXchange and JPST002044 for jPOSTrepo.
+
+5 Acknowledgements
+
+We would like to acknowledge Lucas Kleinort (HI-TRON, Mainz) for his technical assistance and contributions to sample preparation, Kristina Marx (Bruker) for the fruitful scientific discussions, Arthur Declercq for his help on adapting MS^2Rescore for PEAKS XPro output, and Kevin Kovalchik for his help with MhcVizPipe. We acknowledge the support of the flow cytometry core facility, the mass spectrometry core facility and the sequencing core facility of the Research Center for Immunotherapy (FZI) at the University Medical Center Mainz. The graphical abstract and Figure 1 were designed in part using images from Servier Medical Art (SMART, smart.servier.com). This work was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) SFB1292 TP13 (H.S.) and TPQ01 (S.T.), the Helmholtz-Institute for Translational Oncology Mainz (HI-TRON Mainz) – a Helmholtz institute by DKFZ, Mainz, Germany.
+
+6 Author contributions
+
+Conceptualization: DGZ, DAS, UD, HS, ST. Methodology: DGZ, DAS, HS, ST. Software: DGZ. Validation: DGZ, DAS, JB. Formal analysis: DGZ, DAS, JB. Investigation: DGZ, DAS, JB, EK. Resources: DAS, HS, ST. Data Curation: DGZ, DAS, JB, UD. Writing - Original Draft: DGZ, DAS, JB. Writing - Review & Editing: DGZ, DAS, JB, EK, UD, HS, ST. Visualization: DGZ, JB. Supervision: DGZ, DAS, HS, ST. Project administration: DGZ, DAS, UD, HS, ST. Funding acquisition: HS, ST.
+
+7 Competing interests
+
+The authors have no conflicts of interest to declare.
+
+8 Materials & Correspondence
+
+Correspondance should be addressed to:
+David Gomez-Zepeda, email: david.gomez-zepeda@dkfz-heidelberg.de
+Stefan Tenzer, email: tenzer@uni-mainz.de
+References
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+9 Figures
+
+Graphical abstract
+
+Raji ± spike
+JY ± spike
+HLA class ligands
+spike
+total
+Thunder DDA-PASEF
+Mhcvizpipe NetMHCpan GibbsCluster
+PEAKS X PRO
+MS*Rescore
+Figure 1: Immunopeptidomics workflow using Thunder-DDA-PASEF. (a) Sample preparation: 500 million cells of the human JY or Raji cell lines were harvested, then lysed by sonication in 1% CHAPS in PBS buffer (m/v). (b) MHC-ligand peptide enrichment: was performed by immunoaffinity using the W6/32 anti-human-MHC-A, B, C antibody coupled to CNBr-activated agarose beads; after overnight incubation and several washes, peptides were eluted with 0.2% trifluoro-acetic acid, ultrafiltered on molecular weight cutoff filters (MWCO, 10 kDa cutoff) and desalted in HLB plates (Waters Corp.). (c) NanoLC-MS: analysis was performed using a nanoElute coupled to timsTOF-Pro-2 in DDA-PASEF [17] with different parameters to optimize the MS acquisition. (d) Data analysis: Database search was performed in PEAKS XPro using unspecific cleavage. Data analysis was performed in R and predicted MHC-binding affinity was evaluated using NetMHCpan 4.1 [37] and GibbsCluster 2.0 [46] through MhcVizPipe (v0.7.9) [38].
+Figure 2: Evaluation of the different fragmentation isolation filters: "standard", "None" and "HLAIP-tailored". (a, b, c): Exemplary heatmaps of ion intensities (gray-scale) across the inversed ion mobility (1/K_0) vs m/z dimensions showing fragmentation events (red rhombus). (d - i): Correspondent peptides identified across the 1/K_0 vs m/z dimensions colored by charge state, including all peptides (d, e, f) or only those with 8 to 13 amino acids (AAs) (g, h, i). (j, l,m): Length distribution and percentage of peptides (pie-charts) with 8 to 13 AAs or other lengths; cut-off at 20 AAs dropping 5.4%, 1.6% and 0.26% of peptides identified for standard, None and HLAIP-tailored, respectively. (m) Average number of unique peptides identified per injection in each method (3 injection replicates, mean ± sd). (n) Average number of MS2 scans triggered per injection in each method (3 injection replicates, mean ± sd). Two-sided t-test, ns: \( p > 0.05 \), *: \( p \leq 0.05 \), **: \( p \leq 0.01 \), ***: \( p \leq 0.001 \), ****: \( p \leq 0.0001 \).
+Figure 3: Evaluation of the original-DDA-PASEF method (original) compared to the optimized Thunder-DDA-PASEF (Thunder) profiling of JY immunopeptides, and the effect of identification rescoring using MS²Rescore (Thunder + MS2R), considering only peptides of 8 to 13 amino acids long. (a) Average number of unique peptides identified per injection in each method (3 injection replicates, mean ± sd; two-sided t-test, ****: \( p \leq 0.0001 \)). (b) Proportion of peptides (considering modifications) identified in function of their charge state. (c) Dynamic range plot showing the peptides identified (considering modifications), ranked in descending order (x-axis) in function of the average peak area across three replicates (y-axis); the dashed gray line indicates the lowest limit of identification for the original method. (d) Identification data completeness, measured as the proportion of peptides identified across three, two, or only one replicate. (e) Upset plot showing the number (barplot) and percentage (text) of 8-13-mers identified identified uniquely in each method or their combinations; the intersection matrix at the bottom indicates that the same peptides shown above (columns) were detected in the methods (rows) highlighted with a blue dot. (f) Total number of peptides identified in each workflow and the proportion predicted as strong-binders (SB, \( rank \leq 0.5\% \)), weak-binders (WB, \( 0.5\% < rank \leq 2\% \)) or non-binders (NB, \( rank > 2\% \)) by NetMHCpan 4.0 [37].
+Figure 4: HLA class I ligandome of JY and Raji cells employing Thunder-DDA-PASEF, combining wild type and spike-transfected cells. (a) Size distribution of total peptides identified from JY and Raji cells. (b) Number of 8-13-mer peptides identified in each workflow and the proportion predicted as strong-binders (SB, \( rank \leq 0.5\% \)), weak-binders (WB, \( 0.5\% < rank \leq 2\% \)) or non-binders (NB, \( rank > 2\% \)) by NetMHCpan 4.0 [7] against the matched HLA alleles expressed by each cell line (JY = HLA-A02:01, B07:02, C07:02; Raji: HLA-A03:01, B15:10, C03:04, C04:01) (c) Charge distribution for the predicted HLA class I binders (HLAIPs, SB & WB). (d) Total number of predicted HLAIPs (SB & WB) identified (top) and protein groups covered (bottom) for JY, Raji, and in total. (e) Distribution of the number of HLAIPs per protein group represented as boxplots (center line, median; box limits, upper and lower quartiles; whiskers, 1.5x interquartile range) (top) and histogram (bottom); y-axis cut-off at 12 for simplicity, excluding 0.7% of JY HLAIPs (13 to 34 Binders/Protein) and 1.4% of Raji HLAIPs (13 to 53 Binders/Protein). (f) Overlap of HLA ligand peptides (top) and protein groups (bottom) between JY and Raji. (g, h) Supervised clustering (GibbsCluster-2.0 via MhcVizPipe) showing the peptide sequence motifs corresponding to the specific allele motifs for JY and Raji HLAIPs, respectively.
+Figure 5: Spike HLA class I binder peptides (HLAIps) identified in JY and Raji transfected cells.
+(a, b) Count of protein-specific HLAIps predicted strong-binders (SB, \( rank \leq 0.5\% \)) and weak-binders (WB, \( 0.5\% < rank \leq 2\% \)) using NetMHCpan 4.0 [37] for spike (a) and the reporter GFP (b).
+(c) Peptide peak area distribution of the spike peptides (black dots) and all the HLAIps identified in JY (orange) and Raji (purple).
+(d) Characteristics of spike HLAIps identified in JY (top) and Raji (bottom) transfected cells. From left to right: sequence code name indicating their position within the protein sequence (s[N-ter]-[C-ter], e.g., s0691-0699 for SHAYTMSL); sequence, with common peptides highlighted in gray; charge state (number of H+); the number of biological replicates (BR) and technical replicates (TR) where the peptide was identified; Log2 of the peptide peak area; Pearson’s correlation coefficient (PCC) comparing the fragmentation spectrum of the endogenous peptide against synthetic peptides (S) or Prosit-predicted (P) [56, 34] calculated employing the Universal Spectrum Explorer (USE) [48]; indexed retention times (iRT) ratio (endogenous/synthetic); Immune Epitope Database and Analysis Resource (IEDB) [50] immune response frequency (RF) = proportion of subjects with positive immune response in B-cell or T-cell assays (dots = RF, lines = 95% confidence interval (CI) range, color scale = lower 95% CI, empty = not reported), relative to the total number of subjects tested for the corresponding peptide; binding affinity to JY and Raji HLA alleles predicted by NetMHCpan 4.0 [37], with labels indicating SBs and WBs.
+Figure 6: Mirrored fragmentation spectra showing the spectrum from endogenous peptides at the top and synthetic or predicted spectra for two spike peptides. (a) SIAYTMSL^0691-0699 (bottom = synthetic), and (b) TLKSFTVEK^80302-80310 (bottom = Prosit predicted); obtained by USE [SN]; PCC = Pearson’s correlation coefficient, SA = spectral (contrast) angle.
+Supplementary Files
+
+This is a list of supplementary files associated with this preprint. Click to download.
+
+• S1ThunderDDAPASEFSpike20230224.pdf
+• S2Extendedmethodssettings.xlsx
+• S2bThunderDDAPASEF1600V300ms3rampsLSA.m.zip
+• S3pepall06131.zip
+• S4mhcpredall06131.zip
+• S5pepall06133.zip
+• S6mhcpredall06133.zip
+• S7gorillajyrajipepbinder.xlsx
+• S8GOJYRajiHLAlpsprotsfromHLAlps.pdf
+• S9spike06133.xlsx
+• S10spectraspikeUSEmirror.pdf
+• nreditorialpolicychecklistthunder.pdf
+• nrreportingsummarythunder.pdf
+• RSNCOMMS2308309.pdf

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+Peer Review File
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+Bayesian log-normal deconvolution for enhanced in silico microdissection of bulk gene expression data
+
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+Reviewers’ Comments:
+
+Reviewer #1:
+Remarks to the Author:
+In this paper, the authors present a new and promising deconvolution method for gene expression data. BLADE achieves accurate deconvolution results and also allows to estimate the gene expression profile per cell type. An important shortcoming in current deconvolution algorithms is the difficulty to handle gene expression variability without log-transformation. The log-normal convolution model of BLADE accounts for variability in gene expression, resulting in a method that can handle larger number of cell types in comparison to most other methods. In the manuscript, it is shown that BLADE outperforms CIBERSORTx (and NNLS) in deconvolution and gene expression profile estimation of each cell type.
+
+Results, last section: A major concern on this manuscript is that only a mix of 2 scRNA-seq PBMC datasets was used to evaluate the performance of BLADE by making simulated bulk datasets. Applying the method and comparing the performance on other types of data (not PBMC) (e.g. from tissues) would improve the performance evaluation of this method. In addition, at least 1 real bulk dataset (with known cell type composition) should be included in the manuscript for method evaluation, e.g. published paired bulk and single-cell datasets.
+
+Results, last section: It is not clear from the manuscript whether the expression data from the cells that were used as prior knowledge for deconvolution (reference dataset) were completely independent from the cells used to generate simulated bulk datasets. In other words: were cells split clearly into training and test-set. Did the authors not consider to use scRNA-seq PBMC dataset 1 as reference and PBMC dataset 2 for simulation of bulk dataset (or vice versa)? This last suggestion should be considered.
+
+Results, last section: It would be of interest to see how the performance of BLADE compares for high abundant versus low abundant cell types in the 20 simulated datasets. What is the rationale to only generate 20 simulated bulk datasets?
+
+Only one measure for performance analysis, i.e. Pearson correlation was used. Do other measures (e.g. mean squared error) give similar results/conclusions?
+
+Results, section 2: It is not clear why EPIC is used as deconvolution method to compare the probabilistic assumptions.
+
+Figure legend 2: b and c are switched.
+
+Reviewer #2:
+Remarks to the Author:
+Review of “BLADE: Bayesian Log-normAl Deconvolution for enhanced in silico microdissection of bulk gene expression data” by arbosa et al
+
+This paper develops a Bayesian deconvolution procedure for bulk gene expression data utilizing single-cell RNA-seq as prior knowledge. In contrast to existing deconvolution approaches, the proposed approach models the inherently variable nature of gene expression under the probabilistic framework and estimates both cellular make-up and gene expression profiles of each cell type in each sample. Computationally, an efficient variational inference has been proposed so data with a large number of cell types can be analyzed. Given these features, I believe BLADE will be a useful addition to the deconvolution tools, in particular for unraveling heterogeneous cellular activity in complex biological systems. However, given these good properties, I do have some serious concerns on the
+paper, which I include below:
+
+1. I’m really troubled by using maximal log-likelihood, or equivalently AIC/BIC (given the same # of parameters) as a way to compare across models from different distributions, since the underlying formulas are different and may not be comparable. The log-normal model consistently gives the highest maximal log-likelihood (Fig 2a) but this may not guarantee that it’s the best candidate distribution for the data.
+2. Practically, I’m not sure if deconvoluting bulk expression data up to >20 cell types is a good idea. Given a large number of cell types, some cell types are likely to be very similar in their gene expression which can lead to the so called collinearity issue, and thus unreliable cell composition estimates. Fig 5a shows that as the # of cell types increases, BLADE can have a very wide performance range. The authors need to further investigate and propose some practical guidelines on when and how to merge similar cell types, for examples. By the way, Figure 5 is very crowded and some sub-figures need to be deleted, such as Fig5 d-e. The same is true for Figure 6.
+3. MuSiC does weight genes based on their expression variabilities, and should be included as a comparison approach.
+4. Can the authors confirm if sigma (line 1 page 19) is set the same for all genes or gene dependent? Real data often suggests the second situation.
+5. Fig 5b, why there is a systematic dip at the variability of 0.2?
+6. Setting the # of cell to 100 (line 17 page 19) might be too low.
+7. It is mentioned that “Among the 15 cell types, plasmablasts and classical/nonclassical monocytes were the best predicted by all three methods, whereas the methods commonly failed to predict the composition of regulatory T-cells (Tregs), naive CD8+ T-cells (NaiveCD8T), and plasmacytoid dendritic cells (pDC). These poorly predicted cell types were low abundant (less than 2%; Supplementary Fig. S7), indicating the difficulty in deconvolution of rare cell populations. However, some of the low abundant cell types were well-predicted, such as plasmablasts, and thus the abundance is not the sole determinant of performance.” It would be interesting to investigate in addition to the cell abundance, what factors affect the deconvolution performance.
+
+Some example gramma errors etc:
+1. Line 4 from the bottom of page 9, “data The” please add . between the two words.
+2. Lines 3-4 of the 2nd paragraph on page 17, “for which we chose one value across the different t s since we do not have prior information on cellular composition”, please remove the space between t and s or change “t s” to “t values”
+3. Page 25, line 6, change “differentially expressed genes (red) and non-differentially expressed genes (DEG; blue)” to “differentially expressed genes (DEG; red) and non-differentially expressed genes (blue)”.
+
+Reviewer #3:
+Remarks to the Author:
+In this study, Barbosa et al. introduce a new computational method to deconvolve bulk gene expression using single cell RNA-Seq datasets – BLADE. BLADE is able to estimate cell type proportions and gene expression. The novelty of BLADE, over other methods, is that it uses a Bayesian framework and assuming log-normal distribution instead of normal to better capture the variance in gene expression. In addition, BLADE is able to handle over 20 cell types. Overall, BLADE outperforms existing methods both in estimating cell type proportions and expression profiles (outputting more genes and more accurately). I have concerns regarding the biological novelty that can be achieved using BLADE which the authors can demonstrate better and some minor concerns regarding the flow of the manuscript.
+
+Major comments:
+• Previous studies have shown that gene expression follows Poisson distribution (for example: Grun, Kester, and Oudenaarden 2014; Klein et al. 2015), especially scRNA-Seq. I suggest that the authors include this distribution in their analysis as well and compare it to the other distributions examined in the manuscript.
+
+• Figure 2c – this analysis can be generalized for all genes? Seeing only two genes is nice because you can understand the point the authors are trying to make, but I am afraid it might not represent all genes. For example, is there any dependency to the expression level of the gene?
+
+• The simulated data is done very nicely but I think it would be also interesting to use real bulk RNA-Seq PBMC data that we know the true fractions of each cell type using an independent method such as FACS measurements (for example the validation cohort of bulk RNA-Seq generated in the cibersortX paper - GEO: GSE127813 or any other that is available). Also, why only 100 cells were used to create the mixtures? Seems like it’s a small number of cells that does not represent real bulk data that usually has many more cells.
+
+• What happens if you one of the cell-types in the bulk dataset is missing from the single cell data? The authors discuss this a bit in the discussion ("Furthermore, BLADE may be beneficial in handling cell types without a precise prior knowledge". "For instance, BLADE can be applied to estimate gene expression profiles of each cell type that makes up the tumor microenvironment (TME).") but I think this point can be tested further. Sometimes, the dissociation to single cells done prior to scRNA-Seq can lead to depletion of some of the cells, for example, adipocytes, and therefore can lead to differences between bulk and single-cell RNA-Seq.
+
+• One of the things that is missing from the manuscript is a demonstration of what kind of biological novelty can be achieved with this method. In the discussion you mention TME in PDAC, can this be investigated more? Another option, can this method be used to now identify new subtypes of tumor types?
+
+Minor comments:
+• Figures management - there are several issues with the figures that interrupt the flow of the manuscript:
+o Captions font should be bigger and better defined. Some examples: ‘Ngene’ is not a phrase that will be clear for all readers, titles of panel in figure 1a have typos, legends in figure 1 are very small, figure 3 axis labels are not clear and should describe better what is shown, figure S6 (right instead of fright) and the caption is not finished, the titles and captions of figure 2 and 4 include additional text that should be in the main text, figure 1d x-axis tick labels are mixed up (there is twice 0.5). There are more typos and in general, the figures need work.
+o Merging figure: Figure 3 can be merged with another figure or in the supplementary material. Figure 4 and 5 can be merged.
+o Figure S4 quality is bad and should be enhanced.
+o Figure 5 has a lot panels and is very busy which makes it really hard to read. For example, panel b: maybe it will be better to show one condition for group mode purification and one for high-resolution purification. That way, the graphs can be bigger, and the reader will be able to see the differences. The rest of the panels can be shown in the supplementary. In addition, panels d and e – the colorbar direction is confusing and maybe can be inverse. Also, can we see the same analysis for BLADE?
+
+• Methods - PBMC single-cell RNA-seq data – what is the criteria for DE genes? What was the FDR? fold change? Or any other metric that was used.
+
+• Pearson correlation should state coefficient.
+We like to thank all the reviewers for their constructive comments. We further build on our manuscript based on these comments. In particular, on the following aspects:
+
+● We evaluated the log-normal distribution based on RMSE, in addition to the log-likelihood as in the previous manuscript. As described below, we think the maximum-likelihood approach is fair since the same number of parameters are used in a log-normal, normal, and negative binomial distribution. And we observed a similar outcome with the RMSE, where log-normal performs slightly better than the negative binomial. The negative binomial also performs comparably well, but we chose the log-normal over negative binomial since the log-normal assumption is more tractable in the Bayesian framework.
+
+● We found a small error in the derivation of the BLADE algorithm. We updated the algorithm accordingly and performed experiments using the new algorithm. The correction in the algorithm resolved one of the issues reviewers mentioned, the slight dip in the performance of algorithms. The latest version of python package is also available.
+
+● One extra method (MuSiC), a variant of NNLS that accounts for inter-subject variability, was introduced for the comparison as suggested. Note that since MuSiC explicitly requires single-cell data, we could not run MuSiC on simulation data that lacks single-cell data.
+
+● For the PBMC experiment, we introduced a simpler classification of immune cells to diversify the difficulty of deconvolution (4 different levels). It allows us to study the influence of the number of cell types in the deconvolution performance. We confirmed that all algorithms performed well with a smaller number of cell types (e.g., with four cell types, all algorithms reached > 0.5 Pearson correlation for estimating cell type fractions; Figure 5). We also noted that BLADE could achieve high performance with 15 cell types; however, not for all cell types. We found that the cell types with low performance are less abundant and have fewer differentially expressed genes. These experiments will help readers to choose the number of cell types for deconvolution.
+
+● We performed extra experiments using 36 scRNA-seq data from PDAC samples. For this experiment, no sampling was done to simulate bulk gene expression data but instead we pulled all cells per sample. Furthermore, we split auxiliary (7 samples) and main data sets (29 samples) in which only auxiliary data sets were used to derive signatures. This experiment is the most realistic data for evaluation, in which we confirmed the novelty and performance of BLADE.
+
+We will reply to the reviewer comments one by one.
+
+Reviewer #1 (Expertise: Deconvolution of Bulk RNASeq data):
+In this paper, the authors present a new and promising deconvolution method for gene expression data. BLADE achieves accurate deconvolution results and also allows to estimate the gene expression profile per cell type. An important shortcoming in current deconvolution algorithms is the difficulty to handle gene expression variability without log-transformation. The log-normal convolution model of BLADE accounts for variability in gene expression, resulting in a method that can handle larger number of cell types in comparison to most other methods. In the manuscript, it is shown that BLADE outperforms CIBERSORTx (and NNLS) in deconvolution and gene expression profile estimation of each cell type.
+
+Results, last section: A major concern on this manuscript is that only a mix of 2 scRNA-seq PBMC datasets was used to evaluate the performance of BLADE by making simulated bulk datasets. Applying the method and comparing the performance on other types of data (not PBMC) (e.g. from tissues) would improve the performance evaluation of this method. In addition, at least 1 real bulk dataset (with known cell type composition) should be included in the manuscript for method evaluation, e.g. published paired bulk and single-cell datasets.
+
+- Thanks for the suggestion. In the revised manuscript, we expanded our analysis further by including single-cell RNA-seq data from 36 pancreatic tissue samples. For this experiment, we split the training (7 samples) and test data set (29 samples) so that we can make the performance evaluation in a fair manner. Furthermore, no sampling was involved but instead obtained a cumulative count per gene and per sample (see Figure 6).
+
+Relevant part in the revised manuscript:
+- subsection Evaluation of BLADE for deconvolution of tumor RNA-seq data of Result section.
+
+Results, last section: It is not clear from the manuscript whether the expression data from the cells that were used as prior knowledge for deconvolution (reference dataset) were completely independent from the cells used to generate simulated bulk datasets. In other words: were cells split clearly into training and test-set. Did the authors not consider to use scRNA-seq PBMC dataset 1 as reference and PBMC dataset 2 for simulation of bulk dataset (or vice versa)? This last suggestion should be considered.
+
+- The training and test were not split in PBMC cases. This is not done since we intended to evaluate the algorithms when prior knowledge of cell-type specific gene expression profiles is perfect. Note that though the evaluation is still fair since the same prior knowledge (or signatures) were given to all the algorithms evaluated in the manuscript. In the revised manuscript, we kept the PBMC data as is, and revised in the text to make it clear that all cells were used to create the prior knowledge. In addition, we introduced PDAC datasets for the further evaluation, where samples were split into training and test data. We like to
+emphasize that the same prior knowledge was used for all the algorithms used in the study.
+
+Relevant part in the revised manuscript:
+- In Construction of PBMC simulation data of Methods section:
+"To construct realistic simulation data, 20 bulk gene expression data sets were generated by randomly sampling and merging a subset of 9,439 cells from the two PBMC scRNA-seq datasets."
+
+- In the subsection Evaluation of BLADE for deconvolution of tumor RNA-seq data in Results section.:
+“For a fair evaluation of deconvolution algorithms, the 36 samples and their cells were split into reference (nine samples, of which five are tumors) and main samples (27 samples, of which 20 are tumors; Supplementary Fig. S22).”
+
+- In the subsection Application of BLADE to in silico mixture of PBMC scRNA-seq data in Results section:
+“Using the bulk PBMC data generated above, we evaluated BLADE taking CIBERSORTx, NNLS, and also MuSiC as the baseline. We used the same list of genes and signatures for the baseline methods for a fair comparison.”
+
+Results, last section: It would be of interest to see how the performance of BLADE compares for high abundant versus low abundant cell types in the 20 simulated datasets. What is the rationale to only generate 20 simulated bulk datasets?
+
+- We compared the performance between the cell type abundance and the number of unique DEGs with deconvolution performance (Figure 5d, 6d, and Supplementary Figs. S17). There is a trend where a subset of low-abundant cells with a small number of unique DEGs achieved low performance. Furthermore, from the simulation experiment (Figure 4, Supplementary Fig. S6), we could observe, in general, lower performance for the simulation data set with many cell types. This trend is consistent between the four methods used in the study. We think this can help readers to decide the number of cell types for deconvolution.
+- We chose to generate 20 bulk datasets for PBMC as this could give us rather accurate estimation of the performance (e.g., 95% Confidence interval of 0.7 Pearson correlation is 0.37 and 0.87). Furthermore, we have multiple cell types to robustly estimate the performance. In the simulation data with varying sample size (n=5 to 100), we did not observe significant difference in the estimated performance between the datasets (Supplementary Fig. S8-9).
+
+Relevant part in the revised manuscript:
+- In Application of BLADE to in silico mixture of PBMC scRNA-seq data of Results section:
+“Among the 15 cell types, plasmablasts, classical monocytes, NK cells were the best
+predicted by all four methods, which commonly failed to predict the composition of regulatory T cells (Tregs), naive CD8+ T cells (NaiveCD8T), and central memory CD4+ T cells (CMCD4T). These cell types are commonly low abundant (fraction of <7% on average), and only a few unique DEGs were identified for each cell type (< 50 unique DEGs; **Fig. 5d**; see *Supplementary Fig. S17* for other levels)."
+
+- In *Evaluation of BLADE for deconvolution of tumor RNA-seq data* of Results section: "Most cell types achieved high performance (>0.5 of Pearson correlation coefficient) in all methods, except for B cells (in MuSiC and CIBERSORTx), T cells (in CIBERSORTx and NNLS), and Stellate cells (in NNLS). These cell types are often less dominant (less than <5%) and with a small number of DEGs (less than 40 unique DEGs; **Fig. 6d**)."
+
+Only one measure for performance analysis, i.e. Pearson correlation was used. Do other measures (e.g. mean squared error) give similar results/conclusions?
+
+- As by your suggestion, we now measure RMSE to complement the Pearson correlation coefficient. However, RMSE is very focused on the estimation of the abundant cell types, as the small fractions contribute very little. In fact, we noticed that when increasing the number of cell types (which practically leads to a decrease of abundances), the RMSE always improved. See Supplementary Figures S8 and S16 for the trend. This is quite misleading as the increasing number of cell types should make the problem more complicated. We included RMSE outcome (Supplementary Figs. S8, S16, and S23), but the discussion is still focused on the Pearson correlation coefficient, and we also placed a note in the legends that RMSE is not meant to be compared between datasets. We acknowledge that an additional performance metric is useful, so we also added Spearman’s rank correlation coefficients (Supplementary Figs. S7, S16, S23), which is mostly consistent with the Pearson correlation coefficients.
+
+Relevant part in the revised manuscript:
+- Supplementary Figures S7-8, S16, and S23.
+
+- In the legend of Supplementary Fig. S7 and S8:
+"Note that RMSE is not meant to be compared between data set with the different number of cell types, as it depends a lot on the abundance of cell types. (according to RMSE, the performance gets better with the higher number of cell types, which is misleading)."
+
+Results, section 2: It is not clear why EPIC is used as deconvolution method to compare the probabilistic assumptions.
+
+- The point of this part of the manuscript is to evaluate which statistical models can account for variability of gene expression pattern per cell type. For this, we need to provide cell type fractions, unlike Figure 2 a-c where the evaluation was done for bulk transcriptome. We chose EPIC for this since it was
+previously reported for deconvolution of TCGA data and is not part of the baseline methods. We revised the text to make this point clear.
+
+Relevant part in the revised manuscript:
+In Modeling gene-expression variability by probabilistic distribution of Results section: “First, we obtained TCGA RNA-seq data of mesothelioma (TCGA-MESO; n=84) and sarcoma (TCGA-SARC; n=256), from which we estimated the fraction of eight cell types using EPIC17, a deconvolution method previously applied to the TCGA.”
+
+Figure legend 2: b and c are switched.
+- Thank you so much for detecting the error. We corrected the legends as such.
+
+Reviewer #2 (Expertise: Deconvolution of Bulk RNASeq data):
+
+Review of “BLADE: Bayesian Log-normAl Deconvolution for enhanced in silico microdissection of bulk gene expression data” by arbosa et al
+
+This paper develops a Bayesian deconvolution procedure for bulk gene expression data utilizing single-cell RNA-seq as prior knowledge. In contrast to existing deconvolution approaches, the proposed approach models the inherently variable nature of gene expression under the probabilistic framework and estimates both cellular make-up and gene expression profiles of each cell type in each sample. Computationally, an efficient variational inference has been proposed so data with a large number of cell types can be analyzed. Given these features, I believe BLADE will be a useful addition to the deconvolution tools, in particular for unraveling heterogeneous cellular activity in complex biological systems. However, given these good properties, I do have some serious concerns on the paper, which I include below:
+
+1. I’m really troubled by using maximal log-likelihood, or equivalently AIC/BIC (given the same # of parameters) as a way to compare across models from different distributions, since the underlying formulas are different and may not be comparable. The log-normal model consistently gives the highest maximal log-likelihood (Fig 2a) but this may not guarantee that it’s the best candidate distribution for the data.
+
+- In principle, it is widely believed that, unlike the likelihood ratio-test, AIC can be used to compare non-nested models (as in our case). In fact, Akaike himself phrased this in his seminal AIC-paper [1]: "One important observation about AIC is that it is defined without specific reference to the true model [ f(x|kθ) ]. Thus, for any finite number of parametric models, we may always consider an extended model that will play the role of [ f(x|kθ̂) ] This suggests that AIC can be useful, at least in principle, for the comparison of models which are nonnested, i.e., the situation where the conventional log likelihood-ratio test is not applicable."
+In our case, comparisons AICs of the two models is equivalent to comparing the log-likelihoods, as the models have the same number of parameters. Nevertheless, we do agree it may be good to consider an alternative metric as well. By your suggestions, we have therefore also compared the two models in terms of root Mean Squared Error (with data and predictions on log-scale). We found that these also largely agree for the two models (see Supplementary Fig. S4).
+
+[1] Akaike, H. "Prediction and entropy." Selected Papers of Hirotugu Akaike. Springer, New York, NY, 1985. 387-410.
+
+Relevant part in the revised manuscript:
+In Modeling gene-expression variability by probabilistic distribution of Results section: “In terms of log-likelihood measured per gene, log-normal and negative binomial deconvolutions performed equally well for most of the genes, except for a few genes with a more favorable performance with log-normal (Fig. 2d and Supplementary Fig. S4).”
+
+2. Practically, I’m not sure if deconvoluting bulk expression data up to >20 cell types is a good idea. Given a large number of cell types, some cell types are likely to be very similar in their gene expression which can lead to the so called collinearity issue, and thus unreliable cell composition estimates. Fig 5a shows that as the # of cell types increases, BLADE can have a very wide performance range. The authors need to further investigate and propose some practical guidelines on when and how to merge similar cell types, for examples.
+
+- We appreciate this comment from the reviewer. We performed extra experiments with the PBMC dataset with a coarse classification of immune cells to reduce the number of cell types. In total, we introduced four different levels of immune cell classification. As the reviewer pointed out, we could see that the performance gets worse as the number of cell types gets higher, particularly for the lowly abundant cell types and those with small numbers of differentially expressed genes. This information can provide an insight to the reader on how to select the number of cell types.
+
+Relevant part in the revised manuscript:
+- In Application of BLADE to in silico mixture of PBMC scRNA-seq data of Results section: “We also generated three extra data sets with a coarse classification of the 15 cell types by four (level 1; 441 genes selected), eight (level 2; 604 genes), and 12 cell types (level 3; 880 genes) in the same manner to diversify the difficulty levels for deconvolution (see Supplementary Table. 1 for the details of classifications).”
+
+- In Application of BLADE to in silico mixture of PBMC scRNA-seq data of Results section: “Among the 15 cell types, plasmablasts, classical monocytes, NK cells were the best predicted by all four methods, which commonly failed to predict the composition of regulatory T cells (Tregs), naive CD8* T cells (NaiveCD8T), and central memory CD4* T cells
+(CMCD4T). These cell types are commonly low abundant (fraction of <7% on average), and only a few unique DEGs were identified for each cell type (< 50 unique DEGs; Fig. 5d; see Supplementary Fig. S18 for other levels)."
+
+- In Evaluation of BLADE for deconvolution of tumor RNA-seq data of Results section: "Most cell types achieved high performance (>0.5 of Pearson correlation coefficient) in all methods, except for B cells (in MuSiC and CIBERSORTx), T cells (in CIBERSORTx and NNLS), and Stellate cells (in NNLS). These cell types are often less dominant (less than <5%) and with a small number of DEGs (less than 40 unique DEGs; Fig. 6d)."
+
+By the way, Figure 5 is very crowded and some sub-figures need to be deleted, such as Fig5 d-e. The same is true for Figure 6.
+
+- We simplified the Figures 5 (Figure 4 in the revised manuscript) in the main by showing the result from a subset of the simulation data set while retaining them in the supplementary information. Also, we replace the radar plot in Figure 6 (Figure 5 in the revised manuscript) with a simpler visualization (boxplot). A consistent visualization was done across the Figures so that readers can follow easily.
+
+3. MuSiC does weight genes based on their expression variabilities, and should be included as a comparison approach.
+
+We really appreciate this comment. MuSiC does take into account gene expression variabilities, which practically weigh genes on their importance for deconvolution. As suggested, we included MuSiC in our evaluation using PBMCs and PDAC data. Note we do not have MuSiC for simulation data experiments as they explicitly require raw counts from the single-cell data. In our evaluation (Figures 5-6), MuSiC performed well, slightly better than BLADE in several data sets, including the PDAC data set. In particular, we noted a high correlation between MuSiC and BLADE, likely due to the gene expression variability commonly accounted for. Taken together with CIBERSORTx, it is clear that linear regression-based deconvolution can perform significantly better by focusing on a subset of genes, at least for fraction estimation. CIBERSORTx selects the genes that are difficult to reconstruct (support vector regression) while MuSiC weighs genes based on their known variability. However, this strategy reduces the completeness in purification, and in fact, a significant proportion of genes were left out by CIBERSORTx, which performs the purification using a linear regression method. Note that MuSiC does not perform purification at all. Furthermore, the Bayesian framework of BLADE naturally estimates the uncertainty in the prediction outcome, which is not possible with MuSiC. We think the novelty of BLADE is more apparent thanks to this experiment. We revised the discussion session to make this point clear.
+Relevant part in the revised manuscript:
+- In Application of BLADE to in silico mixture of PBMC scRNA-seq data of Results section:
+"Using the bulk PBMC data generated above, we evaluated BLADE taking CIBERSORTx, NNLS, and also MuSiC as the baseline"
+"MuSiC is an exception where the performance gets higher from level 1 to 3. At level 4, BLADE outperformed CIBERSORTx (P-value of 0.0087; a one-tailed paired t-test) and NNLS (P-value of 0.021; a one-tailed paired t-test) and performed comparably to MuSiC (P-value of 0.46; one-tailed paired t-test)."
+
+- In Evaluation of BLADE for deconvolution of tumor RNA-seq data of Results section:
+“For predicting the fraction of 10 cell types, MuSiC performed the best, followed by BLADE and CIBERSORTx (Fig. 6b; see Spearman correlation coefficients in Supplementary Fig. S23). Interestingly, the performance of BLADE correlates the most with MuSiC (Pearson correlation coefficient of 0.62; P-value of 0.056), whereas it is less so with CIBERSORTx (Pearson correlation coefficient of 0.39; P-value of 0.27) and NNLS (Pearson correlation coefficient of -0.18; P-value of 0.62; Fig. 6c).”
+
+- In Discussion section:
+"CIBERSORTx and MuSiC are also linear-regression approaches that partially alleviate the issue by prioritizing genes for deconvolution. Support vector regression, the core algorithm of CIBERSORTx, depends on a subset of genes with high reconstruction errors. On the contrary, MuSiC explicitly learns gene weights from the single-cell RNA-seq data and prioritizes genes with low variability, which likely reduces skewness and hence improves accuracy of the normal distribution."
+“MuSiC outperformed BLADE in several cases, indicating normal distribution-based deconvolution can also be accurate if genes are prioritized based on the gene expression variability. However, the strategy of prioritizing genes reduces the completeness of the purification results (Figs. 4d, 5f, 6g).”
+“This similarity led to a highly correlated performance between BLADE and MuSiC (Figs. 5c and 6c), while BLADE also performs the purification. Furthermore, the Bayesian framework of BLADE allows estimation of the uncertainty in the prediction, which may be valuable to evaluate the quality of the results.”
+
+4. Can the authors confirm if sigma (line 1 page 19) is set the same for all genes or gene dependent? Real data often suggests the second situation.
+
+- Thanks for the interesting point. For PBMC and PDAC data indeed have a different variability per gene. In simulation data, sigma is one of the parameters we set per data set (i.e., fixed for all genes). We chose to set this because we wanted to evaluate the impact of gene expression variability in deconvolution performance. By having smaller sigma values for a subset of genes, a deconvolution algorithm may still perform well based on the small subset. We think this way, it is clearer to understand how gene expression variability can impact the deconvolution performance. Besides, we have several extra evaluation data sets (PBMC and PDAC dataset) that are more realistic than the simulation data.
+Relevant part in the revised manuscript:
+- In Construction of the simulation data with a controlled noise level of Methods section:
+"Then, we sample gene expression levels per sample and per cell type, \( x^{t}_{ij} \) from a log-normal distribution with mean \( \mu^{t}_{j} \) and standard deviation of \( \sigma \) (\( x^{t}_{ij} \sim LN(\mu^{t}_{j}, \sigma) \)), where \( \sigma \) is the parameter to control the variability in gene expression per cell type of each simulation data set."
+
+5. Fig 5b, why there is a systematic dip at the variability of 0.2?
+- We also noticed that BLADE sometimes performs less well on the data set with low variability. This was due to the error in the derivation, which impacts more when the variability is low. In the revised manuscript where corrected BLADE was used, the systematic dip does not appear anymore (see Supplementary Figures S8-9).
+
+6. Setting the # of cell to 100 (line 17 page 19) might be too low.
+- We agree with the reviewer that 100 cells per bulk data may seem low. We also initially sampled more cells to simulate the bulk gene expression data. However, when we sample more cells per sample, there are more cells commonly sampled in 20 simulated bulk samples, which resulted in low variability in cell-type-specific gene expression profiles between these samples. We decided to keep it low to maintain the variability also in the revised manuscript (see Supplementary Fig. S12). Instead, the newly introduced pancreatic data set in the revised manuscript used all cells per sample to obtain bulk profiles, so this should serve as the most realistic evaluation data set.
+
+Relevant part in the revised manuscript:
+- In Application of BLADE to in silico mixture of PBMC scRNA-seq data of Results section:
+“We chose to use 100 cells as we sample more, more cells get commonly selected in multiple samples, making the simulated bulk gene expression data lose variability between the samples.”
+“The resulting simulation data recapitulate the gene expression variability of 15 cell types (Fig. 5a; Supplementary Fig. S13).”
+
+7. It is mentioned that “Among the 15 cell types, plasmablasts and classical/nonclassical monocytes were the best predicted by all three methods, whereas the methods commonly failed to predict the composition of regulatory T-cells (Tregs), naive CD8+ T-cells (NaiveCD8T), and plasmacytoid dendritic cells (pDC). These poorly predicted cell types were low abundant (less than 2%; Supplementary Fig. S7), indicating the difficulty in deconvolution of rare cell populations. However, some of the low abundant cell types were well-predicted, such as plasmablasts, and thus the abundance is not the sole determinant of performance.” It would be interesting to investigate in addition to the cell
+abundance, what factors affect the deconvolution performance.
+
+- As stated earlier, we performed an extra analysis with PBMC and pancreatic data sets and confirmed that cell abundance and the number of unique differentially expressed genes could influence the deconvolution performance. The results are now presented in Figure 5d, Figure 6d, and Supplementary Fig. S17.
+
+Relevant part in the revised manuscript:
+- In Application of BLADE to in silico mixture of PBMC scRNA-seq data of Results section: “Among the 15 cell types, plasmablasts, classical monocytes, NK cells were the best predicted by all four methods, which commonly failed to predict the composition of regulatory T cells (Tregs), naive CD8* T cells (NaiveCD8T), and central memory CD4+ T cells (CMCD4T). These cell types are commonly low abundant (fraction of <7% on average), and only a few unique DEGs were identified for each cell type (< 50 unique DEGs; Fig. 5d; see Supplementary Fig. S18 for other levels).”
+
+- In Evaluation of BLADE for deconvolution of tumor RNA-seq data of Results section: “Most cell types achieved high performance (>0.5 of Pearson correlation coefficient) in all methods, except for B cells (in MuSiC and CIBERSORTx), T cells (in CIBERSORTx and NNLS), and Stellate cells (in NNLS). These cell types are often less dominant (less than <5%) and with a small number of DEGs (less than 40 unique DEGs; Fig. 6d).”
+
+Some example gramma errors etc:
+1. Line 4 from the bottom of page 9, “data The” please add . between the two words.
+2. Lines 3-4 of the 2nd paragraph on page 17, “for which we chose one value across the different t s since we do not have prior information on cellular composition”, please remove the space between t and s or change “t s” to “t values”
+3. Page 25, line 6, change “differentially expressed genes (red) and non-differentially expressed genes (DEG; blue)” to “differentially expressed genes (DEG; red) and non-differentially expressed genes (blue)”.
+
+- All the grammars errors were corrected, thanks for detecting them.
+
+Reviewer #3 (Expertise: Deconvolution of Bulk RNASeq data):
+
+In this study, Barbosa et al. introduce a new computational method to deconvolve bulk gene expression using single cell RNA-Seq datasets – BLADE. BLADE is able to estimate cell type proportions and gene expression. The novelty of BLADE, over other methods, is that it uses a Bayesian framework and assuming log-normal distribution instead of normal to better capture the variance in gene expression. In addition, BLADE is able to handle over 20 cell types. Overall, BLADE outperforms existing methods both in estimating cell type proportions and expression profiles (outputting more genes and more accurately). I have concerns regarding the biological novelty that can be achieved
+using BLADE which the authors can demonstrate better and some minor concerns regarding the flow of the manuscript.
+
+Major comments:
+
+• Previous studies have shown that gene expression follows Poisson distribution (for example: Grun, Kester, and Oudenaarden 2014; Klein et al. 2015), especially scRNA-Seq. I suggest that the authors include this distribution in their analysis as well and compare it to the other distributions examined in the manuscript.
+
+- Indeed, researchers have shown that the Poisson distribution can adequately model technical variability for both RNAseq and scRNAseq. However, it does generally not suffice for modelling biological variability (e.g. between individuals), which is why the negative binomial (NB) is often used for analysing sequencing data as an important extension of the Poisson, allowing for more dispersion [see e.g. Anders et al. (2013)]. As the Poisson distribution is a member of the NB family it can not outperform the NB in terms of fit to the data (because the NB has one more extra parameter), so therefore we feel the comparison between NB and log-normal suffices. For the sake of clarity we mention now that the negative binomial includes the Poisson distribution.
+
+Anders, S., McCarthy, D. J., Chen, Y., Okoniewski, M., Smyth, G. K., Huber, W., & Robinson, M. D. (2013). Count-based differential expression analysis of RNA sequencing data using R and Bioconductor. Nature protocols, 8(9), 1765.
+
+Relevant part in the revised manuscript:
+In Modeling gene-expression variability by probabilistic distribution of Results section:
+“Note that Poisson distribution was also introduced for modeling count data\(^{23,24}\), but it is a special case of negative binomial.”
+
+• Figure 2c – this analysis can be generalized for all genes? Seeing only two genes is nice because you can understand the point the authors are trying to make, but I am afraid it might not represent all genes. For example, is there any dependency to the expression level of the gene?
+
+- We performed this analysis with all genes, but then in a quantitative manner by comparing maximum likelihood. The scatter plots in Figure 2c in the revised manuscript compares the maximum-likelihood between lognormal, normal, and normal distribution for all genes. In general, normal distribution tends to be lower in likelihood. The examples in Figure 2b are those with a lower likelihood for normal distribution than other distributions. We clarify this point in the revised manuscript.
+
+Relevant part in the revised manuscript:
+In Modeling gene-expression variability by probabilistic distribution of Results section:
+"The log-normal distribution, in general, shows the best performance in per-gene maximum likelihood, followed by the negative binomial and normal distributions (Figs. 2a-c). In particular, we noted a biased fit of the normal distribution towards outlier observations, in contrast to the log-normal and negative binomial distribution (see four genes with a lower maximum likelihood for normal distribution in Fig. 2b)."
+
+• The simulated data is done very nicely but I think it would be also interesting to use real bulk RNA-Seq PBMC data that we know the true fractions of each cell type using an independent method such as FACS measurements (for example the validation cohort of bulk RNA-Seq generated in the cibersortX paper - GEO: GSE127813 or any other that is available). Also, why only 100 cells were used to create the mixtures? Seems like it’s a small number of cells that does not represent real bulk data that usually has many more cells.
+
+- Taking multiple suggestions from the reviewers, we expanded our analysis by introducing multi-sample single-cell RNA-seq data from multiple subjects. We chose this data as the major novelty of BLADE is the purification, and for evaluation of the performance, we need single-cell RNAseq data. We also explored the datasets from the CIBERSORTx paper as the reviewer suggested, but we could not find a good data set that can be used to evaluate purification and fraction estimation. We did not sample cells for the pancreatic data set to simulate bulk data but then pull all cells per sample to retain real inter-sample variability. We think this is the best evaluation data set we could find to evaluate the purification performance.
+
+• What happens if you one of the cell-types in the bulk dataset is missing from the single cell data? The authors discuss this a bit in the discussion ("Furthermore, BLADE may be beneficial in handling cell types without a precise prior knowledge". “For instance, BLADE can be applied to estimate gene expression profiles of each cell type that makes up the tumor microenvironment (TME).”) but I think this point can be tested further. Sometimes, the dissociation to single cells done prior to scRNA-Seq can lead to depletion of some of the cells, for example, adipocytes, and therefore can lead to differences between bulk and single-cell RNA-Seq.
+
+- We completely agree with the reviewer that it would be important to acknowledge that some cell types may not be covered by single-cell RNA-seq data. Also, BLADE is capable of reconstructing cell-type-specific gene expression profiles and including cell types without good prior knowledge. However, to establish this, we need to design a separate study on how to provide non-informative prior information for missing cell types. Furthermore, none of the baseline methods allows for the handling of cell types without any prior knowledge. Thus, we consider it as a future project. Note that the phrases pointed out by the reviewer are now replaced with a more detailed comparison between BLADE and MuSiC/CIBERSORTx.
+• One of the things that is missing from the manuscript is a demonstration of what kind of biological novelty can be achieved with this method. In the discussion you mention TME in PDAC, can this be investigated more? Another option, can this method be used to now identify new subtypes of tumor types?
+
+- This is a great point and an obvious next step with BLADE. The novel biology we can learn by the application of BLADE is from the estimated cell-type-specific gene expression profiles. Given the cell-type-specific gene expression profiles, we can identify each cell type's subtype and characterize distinct pathway activities in each cell type. We could also characterize molecular subtypes defined by bulk gene expression profiles, for instance, transcriptome-based PDAC subtypes previously reported. We clarified these points in the last paragraph of the discussion section.
+
+Relevant part in the revised manuscript:
+In Discussion section:
+“Enhanced in silico microdissection by BLADE opens up the possibility to molecularly characterize individual cell types in tissue based on the standard RNA-seq data. For instance, we demonstrated that BLADE could be applied to estimate each cell type's gene expression profiles that make up the tumor microenvironment (TME). This allows us to characterize pathway activity in each immune cell type and possibly to recognize additional cell (sub-)types. Furthermore, BLADE can aid previously established gene expression subtypes (e.g., PDAC\(^{28,29}\)) by characterizing the subtypes with distinct TME profiles. Finally, the detailed profiling of the TME, particularly immune TME profiles, may lead to a clinically applicable biomarker strategy for immunotherapy based on the standard bulk gene expression profiling.”
+
+Minor comments:
+• Figures management - there are several issues with the figures that interrupt the flow of the manuscript:
+o Captions font should be bigger and better defined. Some examples: ‘Ngene’ is not a phrase that will be clear for all readers, titles of panel in figure 1a have typos, legends in figure 1 are very small, figure 3 axis labels are not clear and should describe better what is shown, figure S6 (right instead of fright) and the caption is not finished, the titles and captions of figure 2 and 4 include additional text that should be in the main text, figure 1d x-axis tick labels are mixed up (there is twice 0.5). There are more typos and in general, the figures need work.
+
+- All of above comments are addressed in the revised figures.
+
+o Merging figure: Figure 3 can be merged with another figure or in the supplementary material. Figure 4 and 5 can be merged.
+
+- Figure 3 is now merged with Figure 2. We kept Figures 4 and 5 (3 and 4 in the revised manuscript) separate, as they looked too crowded when merged.
+
+o Figure S4 quality is bad and should be enhanced.
+- The quality is enhance in the revised Figure.
+
+o Figure 5 has a lot panels and is very busy which makes it really hard to read. For example, panel b: maybe it will be better to show one condition for group mode purification and one for high-resolution purification. That way, the graphs can be bigger, and the reader will be able to see the differences. The rest of the panels can be shown in the supplementary. In addition, panels d and e – the colorbar direction is confusing and maybe can be inverse. Also, can we see the same analysis for BLADE?
+
+- We made a selection for Figure 5 and now present only a subset of panels as the reviewer suggested. All the information is still available in the Supplementary Information. The color bar direction has changed as suggested. Note that BLADE does not filter any gene for purification, so the missing value analysis is not necessary.
+
+• Methods - PBMC single-cell RNA-seq data – what is the criteria for DE genes? What was the FDR? fold change? Or any other metric that was used.
+
+- We selected the genes based on FDR cutoff of 0.2 (for PBMC) and 0.1 (for PDAC) and top 200 (for PBMC) or 100 genes (for PDAC) per cell type. In the revised manuscript, we made sure that the information is available.
+
+Relevant part in the revised manuscript:
+In Application of BLADE to in silico mixture of PBMC scRNA-seq data of Results section:
+“We constructed signature matrices that capture the true mean and the standard deviation of 1,007 DEGs measured using all of 9,439 cells (top 200 DEGs with FDR < 0.2 per cell type, combined).”
+
+In PBMC single-cell RNA-seq data of Methods section:
+“Top 200 differentially expressed genes per cell type were identified using a two-sided Wilcoxon Rank sum test by taking a contrast between one cell type versus the rest with an FDR cutoff of 0.2.”
+
+In Construction of PDAC evaluation data of Methods section
+“The signature genes were selected by the top 100 DEGs from each of the ten cell types (FDR<0.1; 818 DEGs in total), followed by obtaining mean and standard deviation from the reference data.”
+
+• Pearson correlation should state coefficient.
+
+- We changed it in the revised manuscript.
+Reviewers' Comments:
+
+Reviewer #1:
+Remarks to the Author:
+The authors have answered most of the questions appropriately, however they have not included a real bulk dataset (with cell proportions according to FACS/cytometry) in the validation section (for example the dataset in Finotello, F. et al. Molecular and pharmacological modulators of the tumor immune contexture revealed by deconvolution of RNA-seq data. Genome Med. 11, 34 (2019).) This would be an added value for the paper.
+
+The authors also have not mentioned in their rebuttal how the results of the experiments changed upon application of the new algorithm (after error correction).
+
+In the abstract, I would add 'simulated' to 'evaluation using >700 (simulated!) datasets', otherwise it might be misinterpreted by readers.
+
+In Fig 5C and 6C (per cell type performance comparison) it might be valuable to indicate (using different size or color-range of dots) how the (average) abundance of the cell type in the mixtures is.
+
+Reviewer #2:
+Remarks to the Author:
+The authors have addressed most of my concerns except one of the major concerns on the use of log-likelihood as an argument for the proposed log-normal transformation. I'm not against the log-normal transformation and I believe it is a reasonable transformation, in particular for computational efficiency. However, I'm still not convinced that log-likelihood is a good metrics for picking models. As a quick example, I simulated 100 data points from a standard normal distribution and shifted them to make all data points positive, which again are normally distributed. I then calculate the maximal log-likelihoods of the original normal data and the log-transformed data. The likelihood from the log-normal model is much larger than the one from the normal model. However, the normal model is the true model. It might be more reasonable to calculate MSE of the observed and predicted count data from each model and see which model gives the smallest MSE.
+
+Also some minor comments/questions:
+1. please be consistent in citing level #s. For example, page 9 line 229, "level 1" and "level4" are cited. Either don't allow the space in "level 1" or add a space in "level4". This happens at other places too.
+2. page 9 line 237, any explanation why "the performance of MuSiC gets higher from level 1 to 3". This seems counter-intuitive.
+3. For the real data analysis, what is the s value used? Do the results sensitive to the choice of s?
+4. page 21, line 520, why different FDR levels used for the two datasets? Any suggestions for the choose of FDR in practice?
+
+Reviewer #3:
+Remarks to the Author:
+My concerns have been addressed in the revision.
+We like to thank all the reviewers for their positive response and constructive comments. We further build on our manuscript based on these comments. Specifically,
+
+● We now included a real bulk dataset of PBMC immune cell mixtures (Finotello, F. et al.), following the suggestion. The PBMC scRNA-seq data used in our study reflect only two subjects, and it misses one of the cell types in the immune cell mixture, neutrophils. Therefore, we employed this data to evaluate BLADE for deconvolution when there is only an incomplete prior knowledge available. In this evaluation, we confirmed the superior performance of BLADE compared to other methods. Surprisingly, the other methods failed to detect many cells, particularly regulatory T cells missed in all methods other than BLADE. The robustness of BLADE is most likely thanks to the hierarchical approach of the Bayesian framework that makes it less dependent on prior knowledge.
+
+● We also introduced an alternative metric (accuracy in detecting the most probable gene expression level) to complement log-likelihood used to compare log-normal, normal, and negative-binomial distribution. The metric is similar to mean squared error but can compare two uni-modal distributions instead of evaluating point estimates. The normal distribution is clearly the least accurate in this metric due to the bias introduced especially when the empirical distribution is skewed.
+
+We will reply to the reviewer comments one by one.
+
+Reviewer #1 (Remarks to the Author):
+
+The authors have answered most of the questions appropriately, however they have not included a real bulk dataset (with cell proportions according to FACS/cytometry) in the validation section (for example the dataset in Finotello, F. et al. Molecular and pharmacological modulators of the tumor immune contexture revealed by deconvolution of RNA-seq data. Genome Med. 11, 34 (2019).) This would be an added value for the paper.
+
+We appreciate this comment. Following the suggestion, we obtained the raw gene expression data generated by Finotello, F. et al. We noted some cell types not covered by our PBMC data (neutrophils and also other cell types not quantified by flow cytometry). Therefore, we positioned this data to evaluate BLADE when there is only limited prior knowledge available for the cell types that contribute to the bulk RNA-seq data. Given the same signatures provided to BLADE and other baseline methods, we noted a superior performance of BLADE compared to the other methods. The robustness of BLADE is thanks to its hierarchical Bayesian approach for integrating prior information, which makes it relatively flexible from the given prior knowledge. Though, the common failure of predicting mDC fractions in all methods indicates that the quality of prior knowledge does matter. Overall, this is a valuable extra experiment that demonstrates the robustness of BLADE, as the reviewer anticipated.
+Relevant part in the revised manuscript:
+
+- a new subsection in the Result section: Application of BLADE to standard bulk RNA-seq data with incomplete prior knowledge, and new figure (Figure 6) associated with this part.
+
+- a new subsection in Method section: Standard bulk RNA-seq data for PBMC immune cell mixtures.
+
+The authors also have not mentioned in their rebuttal how the results of the experiments changed upon application of the new algorithm (after error correction).
+
+We want to apologize for not being clear enough about the changes due to the correction of the error in the code. We reproduced all the figures already based on the corrected code, but the difference was minor and thus not visible. The only difference was that the slight dip in performance with low number cell types got less apparent (see Supplementary Figure S9). The error concerns one of the parameters for modeling gene expression variability, so its influence is limited than major parameters which determine cell type fractions and cell-type-specific gene expression profiles. However, it is a very important fixation to be made for theoretical correctness, and we are happy that we were able to detect this before the final version gets published. The correction is reflected in the detailed derivation of BLADE in Supplementary Note 2.
+
+Relevant part in the revised manuscript:
+
+- Supplementary Note 2
+
+In the abstract, I would add 'simulated' to 'evaluation using >700 (simulated!) datasets', otherwise it might be misinterpreted by readers.
+
+Thanks to the above suggestion, we do have real data in the manuscript. To be completely clear that we use many simulation data in the manuscript, we revised the text to clarify that we used both simulation and real data sets.
+
+Relevant part in the revised manuscript:
+
+- In Abstract:
+“Throughout an intensive evaluation with >700 simulated and real datasets, BLADE demonstrated ...”
+
+In Fig 5C and 6C (per cell type performance comparison) it might be valuable to indicate (using different size or color-range of dots) how the (average) abundance of the cell type in the mixtures is.
+The information of cell type fractions is available in Fig. 5D and Fig. 6D. Still, we agree with the reviewer that it is easier for the readers to compare fractions and deconvolution performance if this is also shown in Fig. 5C and Fig. 6C. Therefore, we indicated the cell type fractions by the size of points in Fig. 5C and Fig. 6C (now Fig. 7C in the revised manuscript). We also did the same for the same type of plots in Supplementary Figures.
+
+Relevant part in the revised manuscript:
+
+- Figures 5C and 7C, and Supplementary Figures S16 and S18
+
+Reviewer #2 (Remarks to the Author):
+
+The authors have addressed most of my concerns except one of the major concerns on the use of log-likelihood as an argument for the proposed log-normal transformation. I'm not against the log-normal transformation and I believe it is a reasonable transformation, in particular for computational efficiency. However, I'm still not convinced that log-likelihood is a good metrics for picking models. As a quick example, I simulated 100 data points from a standard normal distribution and shifted them to make all data points positive, which again are normally distributed. I then calculate the maximal log-likelihoods of the original normal data and the log-transformed data. The likelihood from the log-normal model is much larger than the one from the normal model. However, the normal model is the true model. It might be more reasonable to calculate MSE of the observed and predicted count data from each model and see which model gives the smallest MSE.
+
+Thank you for the suggestion. MSE and log-likelihood evaluate different characteristics; the former is the accuracy of a point estimate, while the latter is the goodness of fit. In the previous round of revision, we agreed with the reviewer that these could be complementary. MSE is particularly valuable in a predictive setting (in our case, the full deconvolution model, which ‘predicts’ bulk RNAseq counts by the convolution over cell types). Therefore, we assessed MSE for flexible deconvolution context. We have now moved Supplementary Fig. S4 (comparing LN and NB distributions using MSE) to the main document (Fig. 2f) to give more balanced weight to the log-likelihood and MSE based evaluations.
+
+However, MSE is less suitable to evaluate distributions when there is no prediction per sample (i.e., no point estimates). Alternatively, we include a metric that evaluates a point estimate of the mode (i.e., the gene expression level with the highest probability) like the MSE. To this end, we identified the modes from the optimized negative binomial, normal, and log-normal distribution per gene and per cell type and then assessed the distance from the true mode as estimated from the empirical distribution. This comparison is fair since all of the distribution types considered in this study are unimodal. We confirmed that normal distribution indeed identified modes less accurately than the other two distributions (Fig. 2b), which is additionally illustrated by the four genes in Fig. 2d.
+Furthermore, we also noticed that there was not enough description in the Method section, so we included more details so that it can be reproduced
+
+Relevant part in the revised manuscript:
+
+- In Modeling gene-expression variability by probabilistic distribution of Result section
+
+“To evaluate the performance of these probability distributions on gene expression variability, we assessed 1) the maximum likelihood of fitting gene expression profiles and 2) the difference between estimated and empirical modes (i.e., the most probable gene expression level; Figs. 2a-c). The log-normal distribution, in general, shows the best performance in per-gene maximum likelihood, followed by the negative binomial and normal distributions (Figs. 2a,c). In particular, we noted a biased fit of the normal distribution towards outlier observations, which led to low accuracy in identifying modes (Fig. 2b; see four example genes with a biased fit with normal distribution in Fig. 2d). In terms of mode estimation log-normal and negative binomial appear to be fairly competitive with a somewhat worse median, but a better third quartile for the former (Fig. 2b).”
+
+- A new subsection in Method section: Comparison between Log-normal, Negative Binomial and Normal distribution in fitting raw gene expression counts
+
+- In Comparison of LN and NB based on the generic deconvolution technique of Methods section:
+
+“As an alternative metric, we also measured the accuracy in reconstructing bulk gene expression levels based on deconvolution. Taking actual and predicted bulk gene expression level in LN or NB deconvolution model, root mean-squared error (RMSE) was evaluated per gene and per model.”
+
+Also some minor comments/questions:
+
+1. please be consistent in citing level #s. For example, page 9 line 229, "level 1" and "level4" are cited. Either don’t allow the space in "level 1" or add a space in "level4". This happens at other places too.
+
+Thanks for pointing out the mistake, we made sure there is a space between after “level” in the revised manuscript.
+
+2. page 9 line 237, any explanation why "the performance of MuSiC gets higher from level 1 to 3. This seems counter-intuitive.
+
+It is quite an interesting outcome that we did not discuss enough in the text. When we carefully evaluate the performances, CIBERSORTx and BLADE also got better at level 3 than level 2. However, it is less obvious than MuSiC (e.g., improvement for BLADE is better visible with the Spearman correlation coefficient). One thing clear from the simulation experiment is that having more genes tends to be useful for deconvolution
+(see Fig.4 and Supplementary Fig. S5-S6). Since we identified more DEGs as the number of cell types increased, the advantage of having more genes had a more significant effect on the outcome than the extra complexity introduced by including more cell types. We extend the discussion a bit on this point.
+
+Relevant part in the revised manuscript:
+
+In Application of BLADE to in silico mixture of PBMC scRNA-seq data of Result section:
+
+“Interestingly, the performance was often higher in level 3 than level 2, especially for MuSiC, most likely since the advantage of having more genes overcomes the complexity due to the increased number of cell types (e.g., 880 genes in level 3, compared to 604 genes in level 2).”
+
+3. For the real data analysis, what is the s value used? Do the results sensitive to the choice of s?
+
+BLADE can indeed be sensitive to the choice of hyperparameters, including s. That is why we allow users to provide multiple possible hyperparameters and then find the best configuration using an empirical Bayes framework. Furthermore, the empirical Bayesian framework chooses the parameters without knowing true fractions and cell-type-specific gene expression levels. In this way, we can alleviate the difficulty in selecting parameters. As described in the Method section (subsection Selection of hyperparameters based on the empirical-Bayes framework), the final choice of s value is from {1, 0.3, 0.5}. Note that we kept it consistent across all the data sets used in the study.
+
+4. page 21, line 520, why different FDR levels used for the two datasets? Any suggestions for the choose of FDR in practice?
+
+We chose a less stringent cutoff for PBMC as there are fewer differentially expressed genes compared to the PDAC. The performance is best when there are more than 500 genes (see Supplementary Figures S5-7). Note that lowering the FDR may negatively influence performance, as there will be more genes with subtle differences in expression levels between cell types that may confuse deconvolution algorithms. We add this information in the Method section.
+
+Relevant part in the revised manuscript:
+
+In Construction of PDAC evaluation data of Methods section:
+“Note that we used more stringent criteria to select DEGs than for the PBMC data, because a sufficient number of DEGs (>500 DEGs) still satisfies these.”
+Reviewer #3 (Remarks to the Author):
+
+My concerns have been addressed in the revision.
+Reviewers’ Comments:
+
+Reviewer #1:
+Remarks to the Author:
+The authors have adequately adapted the manuscript based on my comments. I have no further comments.
+
+Reviewer #2:
+Remarks to the Author:
+The authors have addressed all my concerns and there are no further ones from me.

0b483a72e0c58a9950db9f28aced8eb28f2145605ee9fc9e2c0f9dd377ab37bd/preprint/preprint.md

@@ -0,0 +1,300 @@
+BLADE: Bayesian Log-normAl DEconvolution for enhanced in silico microdissection of bulk gene expression data
+
+Bárbara Andrade Barbosa
+Amsterdam UMC
+Saskia van Asten
+Amsterdam UMC   https://orcid.org/0000-0001-6498-1176
+Ji-won Oh
+Kyungpook National University
+Arantza Fariña-Sarasqueta
+Amsterdam University Medical Center
+Joanne Verheij
+Amsterdam University Medical Center
+Frederike Dijk
+Amsterdam UMC
+Hanneke van Laarhoven
+Department of Medical Oncology, Cancer Center Amsterdam, Amsterdam University Medical Center
+Bauke Ylstra
+Amsterdam UMC, Vrije Universiteit Amsterdam, Department of Pathology, Cancer Center Amsterdam, Amsterdam   https://orcid.org/0000-0001-9479-3010
+Juan Garcia-Vallejo
+Amsterdam UMC
+Mark van de Wiel
+Amsterdam UMC
+Yongsoo Kim ( yo.kim@amsterdamumc.nl )
+Amsterdam UMC, location VUmc   https://orcid.org/0000-0002-2995-2131
+
+Article
+
+Keywords: bulk gene expression, Bayesian Log-normAl Deconvolution
+
+Posted Date: December 15th, 2020
+
+DOI: https://doi.org/10.21203/rs.3.rs-123595/v1
+License: This work is licensed under a Creative Commons Attribution 4.0 International License.
+Read Full License
+
+Version of Record: A version of this preprint was published at Nature Communications on October 20th, 2021. See the published version at https://doi.org/10.1038/s41467-021-26328-2.
+BLADE: Bayesian Log-normAI DEconvolution for enhanced *in silico* microdissection of bulk gene expression data
+
+Bárbara Andrade Barbosa¹, Saskia D. van Asten¹,², Ji-won Oh³,⁴, Arantza Farina Sarasqueta⁵, Joanne Verheij⁶, Frederike Dijk⁵, Hanneke van Laarhoven⁶, Bauke Ylstra¹, Juan Garcia Vallejo², Mark van de Wiel⁷, Yongsoo Kim¹*
+
+¹Department of Pathology, Cancer-Center Amsterdam, Amsterdam UMC location VUmc, 1081 HV, Amsterdam, the Netherlands
+
+²Department of Molecular Cell Biology & Immunology, Amsterdam UMC location VUmc, Amsterdam Infection and immunity Institute, 1081 HZ, Amsterdam, the Netherlands
+
+³Department of Anatomy, School of Medicine, Kyungpook National University, 41940, Daegu, South Korea
+
+⁴Bio-Medical Research Institute, Kyungpook National University Hospital, 41944, Daegu, South Korea
+
+⁵Department of Pathology, Amsterdam UMC location AMC, 1105 AZ, Amsterdam, the Netherlands
+
+⁶Department of Medical Oncology, Cancer Center Amsterdam, Amsterdam UMC location AMC, 1105 AZ, Amsterdam, the Netherlands
+
+⁷Department of Epidemiology and Biostatistics, Amsterdam UMC location VUmc, 1081 HV, Amsterdam, the Netherlands
+
+* To whom correspondence should be addressed. Email: yo.kim@amsterdamumc.nl Email: mark.vdwiel@amsterdamumc.nl
+Abstract (145/150)
+
+High-resolution deconvolution of bulk gene expression profiles is pivotal to characterize the complex cellular make-up of tissues, such as tumor microenvironment. Single-cell RNA-seq provides reliable prior knowledge for deconvolution, however, a comprehensive statistical model is required for efficient utilization due to the inherently variable nature of gene expression. We introduce BLADE (Bayesian Log-normAl Deconvolution), a comprehensive probabilistic framework to estimate both cellular make-up and gene expression profiles of each cell type in each sample. Unlike previous comprehensive statistical approaches, BLADE can handle >20 cell types thanks to the efficient variational inference. Throughout an intensive evaluation using >700 datasets, BLADE showed enhanced robustness against gene expression variability and better completeness than conventional methods, in particular to reconstruct gene expression profiles of each cell type. All-in-all, BLADE is a powerful tool to unravel heterogeneous cellular activity in complex biological systems based on standard bulk gene expression data.
+
+Introduction
+Over the past decade, gene expression profiling has been applied to elucidate the complexity of transcriptional regulation in diverse biological contexts, such as cancer^{1,2}. Conventional gene expression profiling, based on either RNA sequencing (RNA-seq) or microarrays, captures cumulative gene expression levels of many cells combined. It is therefore often referred to as bulk gene expression profiling, in order to distinguish it from the recent single-cell gene expression profiling technologies^{3}. In oncology, single-cell RNA sequencing (scRNA-seq) is employed to study cellular heterogeneity within a tumor, composed of malignant (tumor) and non-malignant cells^{4-10}. However, scRNA-seq has serious limitations: apart from technical challenges such as drop-out, only a limited number
+of samples can be profiled due to the high cost and technical difficulties\(^{11,12}\) which altogether hinder its application to large series and translation to clinical applications.
+
+Several computational deconvolution methods have been developed to predict cellular composition from bulk RNA-seq by employing a signature of pre-determined cell type-specific gene expression profiles. Initially, these signatures were constructed by sorting each cell type followed by gene expression profiling\(^{13}\), whereas recent methods such as CIBERSORTx\(^{14}\) and MuSiC\(^{15}\) employed scRNA-seq data for this purpose. The majority of approaches perform linear regression to reconstruct the bulk gene expression profiles using the gene expression signatures, where the regression coefficients correspond to the cellular composition. However, the standard regression approach does not account for variability in gene expression within the same cell type, and may therefore render biased results.
+
+To the best of our knowledge, there is no deconvolution method that can adequately and also efficiently account for the variability of gene expression within the same cell type. Modelling gene expression variability is challenging specifically for deconvolution due to the incompatibility of the log-normalization\(^{16}\) which significantly stabilizes gene expression variability. Without the log-normalization (i.e., in linear-scale), gene expression data has a heavily skewed distribution, which is not properly accounted for by the standard linear regression approaches. Currently, there are few probabilistic deconvolution approaches that take skewed variability into account, but these methods handle only a restricted number of cell types due to difficulties in optimization (e.g. three cell types in DeClust\(^{17}\) and Demix/DemixT\(^{18}\)). Recently, CIBERSORTx introduced a two-step approach to address variable gene expression profiles across the samples: first estimate cellular fraction (deconvolution) and then reconstruct gene expression per cell type in each sample (purification). However, for some genes, the purification step of CIBERSORTx is an underdetermined optimization problem with infinite number of solutions, which leads to incomplete purification that excludes those genes.
+Here, we introduce BLADE (Bayesian Log-normAI DEconvolution), a novel Bayesian method that jointly performs deconvolution and purification in a single-step, taking into account prior knowledge of cell type specific gene expression profiles obtained from scRNA-seq data. BLADE takes a Bayesian framework that integrates two signatures of mean and variability of gene expression per-cell type using a log-normal probability model. The unified probabilistic model for both deconvolution and purification of BLADE can leverage the prior knowledge for purification as well, which may remedy the underdetermination issue. Furthermore, an efficient variational inference algorithm was developed for which we show that it can handle at least 20 cell types. Through a comprehensive evaluation based on more than 700 bulk gene expression data sets, we demonstrate a robust performance of BLADE regardless of gene expression variability. In particular, BLADE achieved high accuracy and completeness in gene expression purification, underpinning the power of the unified Bayesian framework for both tasks.
+
+Results
+
+Gene expression variability within a cell type
+We first assessed gene expression variability within a cell type using publicly available PBMC CITE-seq data from 10x Genomics. Based on the integration and clustering analysis followed by phenotyping of 10,403 cells, we identified fifteen immune cell types, among which nine are in common, with distinct cell-surface markers and gene expression profiles (Fig. 1a; see Methods and Supplementary Figs. S1-2). The size of cell populations ranges from 38 regulatory T cells (0.36%) to 2,518 classical monocytes (24%). We then identified differentially expressed genes (DEGs) for each cell type. Subsequently, the standard deviation of gene expression levels per gene and per cell type was measured to assess gene expression variability among the same cell types. We identified high gene expression variability among the same cell populations, especially for DEGs without log-transformation (i.e., linear-scale; Figs. 1b-c). The variability further increased when cells from the two scRNA-seq datasets were combined, indicating the presence of more variability between
+individuals (Fig. 1d; \( P<2.2\times10^{-16} \) from a paired t-test of within-sample and between-sample variability).
+
+Modeling gene-expression variability by probabilistic distribution
+To properly account for variation in gene expression, we examined multiple probability distributions. We evaluated normal distribution, negative binomial distribution, and log-normal distribution to fit the expression level of each gene per cell type without log-normalization. The normal distribution is the standard variability model in many deconvolution algorithms, including CIBERSORTx\(^{14}\), EPIC\(^{19}\), and ABIS\(^{20}\), while the negative binomial distribution is frequently used for handling RNA-seq data\(^{21}\). The log-normal distribution is identical to the normal distribution but includes an exponential function, assuming gene expression data is normally distributed on a log-scale but not on a linear-scale. In order to evaluate the performance of these probability distributions on gene expression variability, we assessed the maximum likelihood in fitting gene expression profiles per cell type from the scRNA-seq data. The log-normal distribution, in general, shows the best performance in per-gene maximum likelihood, followed by the negative binomial and normal distributions (Figs. 2a-b). In particular, we noted a biased fit of the normal distribution towards outlier observations, in contrast to the log-normal and negative binomial distribution (examples in Fig. 2c).
+
+We further evaluated the performance of the log-normal and negative binomial distributions in the context of deconvolution. To this end, we constructed a generic statistical deconvolution method that can model gene expression profiles with diverse probabilistic assumptions given known cellular fractions. The method approximates the convolution of random variables with an arbitrary distribution using a probabilistic generating function, for which both negative binomial and log-normal random variables can be accurately approximated (see Methods, Supplementary Note 1 and Supplementary Fig. S3). Based on this method, we evaluated the performance of negative binomial and log-normal distribution in fitting the gene expression profiles per cell type using RNA-seq data from
+TCGA. We obtained TCGA RNA-seq data of mesothelioma (TCGA-MESO; n=84) and sarcoma (TCGA-SARC; n=256), from which we estimated the fraction of eight cell types using EPIC\(^{19}\), a non-probabilistic deconvolution method. Then, we applied the flexible deconvolution method with two different probabilistic assumptions, log-normal and negative binomial, to estimate expression profiles per cell type of 200 random genes. In terms of log-likelihood measured per gene, log-normal and negative binomial deconvolutions performed equally well for most of the genes, except for a few genes with a more favorable performance with log-normal (**Fig. 3**). The lower performance of the negative binomial distribution might be due to the difficulty in finding maximum likelihood parameters. Cumulatively, we concluded that the log-normal distribution is an attractive probabilistic distribution to model gene expression variability of each cell type.
+
+**Overview of BLADE: Bayesian Log-normal Deconvolution**
+
+We constructed a Bayesian Log-normal Deconvolution model, BLADE, by emulating bulk gene expression profiles through convolution of gene expression profiles per cell type (**Fig. 4a**). The bulk gene expression level of each gene \( j \) in sample \( i \) was modeled by \( y_{ij} = \sum_t f_i^t x_{ij}^t + \epsilon_{ij} \). Here, the hidden variables \( f_i^t \) and \( x_{ij}^t \) denote the cell type \( t \) fraction for sample \( i \) and the purified cell type \( t \) gene \( j \) expression for sample \( i \). These hidden variables \( f_i^t \) and \( x_{ij}^t \) are respectively endowed with the Dirichlet distribution and the log-normal distribution. To incorporate prior knowledge from scRNA-seq data, we take a hierarchical approach to model \( x_{ij}^t \) by taking a conjugate prior of log-normal distribution with hyperparameters \( \mu_{0j}^t, \kappa_{0j}^t, \alpha_{0j}^t, \) and \( \beta_{0j}^t \) (**Fig. 4b**). The hyperparameters are chosen based on the mean and standard deviation of each gene per cell type from the scRNA-seq data by inferring the hidden variables, we can jointly estimate the fraction of cell types, captured by \( f_i^t \), and purified gene expression profiles of each cell type in each sample, captured by \( x_{ij}^t \). For inference, we employed a collapsed variational inference that maximize efficiency by integrates out a subset of hidden variables with a conjugate prior in
+advance. Furthermore, we employed the L-BFGS algorithm in conjunction with machine-code translated Python code for gradient and objective function calculations instead of native Python code. The compilation of native Python code by the Numba package\(^{22}\) significantly accelerates gradient and objective functions that are executed thousands of times during the L-BFGS optimization (**Supplementary Fig. S4**). See **Methods** and **Supplementary Note 2** for the further details of the framework. As a result, BLADE can handle many cell types (>20 cell types) and samples (>20 samples); unlike the previous log-normal based deconvolution that can account for a maximum of three cell types\(^{18}\).
+
+**Robustness of BLADE deconvolution against gene expression variability.**
+We assessed the robustness of BLADE, CIBERSORTx, and non-negative least squares (NNLS) against gene expression variability by applying them to model-based simulation data. The simulation data was created to have diverse but controlled variability levels of gene expression profiles (standard deviation of 0.1-1.5) as well as different numbers of cell types (5-20 cell types), marker genes (100-1000 genes), and samples (5-100 samples; in total 700 training data sets). Note that NNLS is a regularized linear regression, a type of constrained linear regression used in many deconvolution methods, including EPIC\(^{19}\), TIMER\(^{23}\), ABIS\(^{20}\), and also in the purification step of CIBERSORTx\(^{14}\). The variability levels of the simulation data were selected in order to recapitulate the range of the observed in the scRNA-seq data (up to standard deviation of 1.5 in log scale; **Fig. 1b-c**). In general, all three methods could accurately estimate cellular fractions in case of a high number of genes, a low number of cell types and a low variability level. In contrast, the performance decreased when a smaller number of genes are presented, and the number of cell types is increased (**Fig. 5a**). However, BLADE was more robust against gene expression variability. In particular, in the range of observed expression variability of differentially expressed genes in the PBMC scRNA-seq data (on average >0.5; **Fig. 1b**), BLADE significantly outperformed CIBERSORTx and NNLS.
+We then compared the performance of BLADE and CIBERSORTx in estimating gene expression profiles per cell type. In this comparison, NNLS is not included because of redundancy, since the purification step of CIBERSORTx is based on NNLS. There are two modes of purification in CIBERSORTx, both of which were compared with BLADE: 1) estimating average profile per cell type across the samples (group-mode purification), and 2) estimating the profile per cell type for each sample (high-resolution-mode purification). For the data set with low variability levels, both BLADE and CIBERSORTx accurately reconstructed gene expression profiles per cell type (**Fig. 5b-c**). However, unlike BLADE, the performance of CIBERSORTx decreased rapidly as the RNA expression variability within a cell type increased. Furthermore, CIBERSORTx often excludes genes for purification, especially in high-resolution mode, when: 1) the number of cell types is larger than the number of samples, and 2) the variability in gene expression is high (**Fig. 5d-e**). BLADE could accurately estimate the gene expression profiles of each cell type in both group-mode and high-resolution mode, regardless of the number of cell types and samples without any filtering (**Fig. 5b-c**).
+
+**Application of BLADE to *in silico* mixture of PBMC scRNA-seq data**
+
+We further evaluated our method based on actual scRNA-seq data from PBMC samples that were mixed *in silico* in various known proportions to generate bulk gene expression data without any model assumption. We generated 20 bulk gene expression data sets by random sampling, followed by mixing 100 cells among the 10,403 cells from the two PBMC scRNA-seq data sets. In order to make the simulation data as realistic as possible, a cumulative sum of raw counts of 100 cells was obtained, followed by a standard normalization of the count data The resulting simulation data recapitulate the gene expression variability of 15 cell types (**Fig. 6a; Supplementary Fig. S5**). We constructed signature matrices for the mean and the standard deviation of 1,007 genes selected by merging the top 200
+differentially expressed genes with FDR < 0.2 of each of the 15 cell types. We used the same mean signature matrix for the baseline methods, CIBERSORTx and NNLS, for a fair comparison.
+
+BLADE outperformed CIBERSORTx and NNLS to predict the fractions for most of the 15 cell types (P-values of paired T-tests < 0.05; Fig. 6b; Supplementary Fig. S6). The three methods performed similarly for most cell types (Pearson correlation > 0.7), except for a few cell types with a contradictory outcome. Taking a Pearson correlation of 0.25 as a threshold, BLADE had a good predictive performance in more cell types (11 cell types) than the baseline methods, CIBERSORTx and NNLS (7 cell types). Among the 15 cell types, plasmablasts and classical/non-classical monocytes were the best predicted by all three methods, whereas the methods commonly failed to predict the composition of regulatory T-cells (Tregs), naive CD8+ T-cells (NaiveCD8T), and plasmacytoid dendritic cells (pDC). These poorly predicted cell types were low abundant (less than 2%; Supplementary Fig. S7), indicating the difficulty in deconvolution of rare cell populations. However, some of the low abundant cell types were well-predicted, such as plasmablasts, and thus the abundance is not the sole determinant of performance.
+
+BLADE significantly outperformed CIBERSORTx in the estimation of gene expression profiles per cell type in both group-mode and high-resolution mode (Fig. 6c-e). For group-mode purification, CIBERSORTx reconstructed expression profiles per cell type with reasonable accuracy (>0.5 Pearson correlation except for pDC). The highest performance was achieved for classical monocytes. Here, performance of BLADE was near-perfect (Fig. 6c). In high-resolution mode, CIBERSORTx did not estimate expression levels of most genes, and essentially no genes were in silico purified for 11 cell types (Fig. 6d). Furthermore, even after filtering, the estimated gene expression profiles per cell type and per sample by CIBERSORTx are less accurate than those by BLADE (Fig. 6e). The performance of BLADE in high-resolution mode purification is consistently accurate (>0.7 Pearson correlation) across all 15 cell types. Cumulatively, Bayesian simultaneous
+deconvolution and in silico purification by BLADE significantly outperformed CIBERSORTx in both estimating cellular fraction and especially in reconstructing gene expression profiles per cell type.
+
+Discussion
+One of the major challenges in deconvolution of bulk RNAseq data is adequate and yet efficient handling of gene expression variability without log-normalization. This difficulty causes either of the two critical shortcomings in most of the available deconvolution algorithms: 1) only a small number of cell types can be handled; and 2) the inadequate variability model (usually normal distribution) implicitly or explicitly assumed in the core algorithm, such as support vector regression and non-negative least-squares, implies inferior results. We showed that, the normal distribution often renders a biased fit (Fig. 2b-c). The inadequate noise model leads to suboptimal performance of deconvolution algorithms when there is a realistic level of gene expression variability (Fig. 5). Furthermore, purification of gene expression involves more variables to be estimated, for which an incorrect variability model can have substantial impact on the performance (Figs. 5 and 6b-d). Statistical inference of log-normal convolution models, which were shown to appropriately capture variability, however, is very challenging, as demonstrated by previous log-normal deconvolution methods that handle three cell types maximally\(^{18}\).
+
+BLADE solves this by using a novel hierarchical Bayesian model that simultaneously performs deconvolution and estimation of gene expression profiles per cell type. The log-normal convolution model efficiently accounts for variability in gene expression (Fig. 3) and also for prior knowledge of gene expression profiles per cell type derived from scRNA-seq data (Fig. 4). Notably, thanks to the unified probabilistic model used in BLADE, the prior knowledge contributes to both deconvolution and gene expression purification. This prior knowledge significantly reduces the search space of solutions for both tasks, which leads to enhanced accuracy and coverage, especially for gene expression purification. The efficient
+variational inference of BLADE allowed to handle a large number of cell types (> 20 cell types) which was not possible by previous statistical approaches \(^{17,18}\). Furthermore, BLADE may be beneficial in handling cell types without a precise prior knowledge, for instance, cancer cells with highly variable gene expression profiles across the subject, unlike the non-malignant cells \(^{24}\). By integrating both signatures of mean and standard deviation, BLADE balances the contribution of genes with varying precision for deconvolution by prioritizing the genes with low variability (i.e., high precision) when estimating cell type fractions.
+
+Enhanced *in silico* microdissection by BLADE opens up the possibility to molecularly characterize individual cell types in tissue based on the standard RNA-seq data. For instance, BLADE can be applied to estimate gene expression profiles of each cell type that makes up the tumor microenvironment (TME). This allows us to characterize pathway activity in each immune cell type, and possibly to recognize additional cell (sub-)types. Furthermore, BLADE can aid previously-established gene expression subtypes (e.g., PDAC \(^{25,26}\)) by characterizing the subtypes with distinct TME profiles. The detailed profiling of the TME, in particular, immune TME profiles may lead to a clinically applicable biomarker strategy for immunotherapy based on the standard bulk gene expression profiling. In conclusion, BLADE is a novel tool that can significantly contribute to unravel cellular heterogeneity in complex biological systems.
+
+Methods
+
+**PBMC single-cell RNA-seq data**
+Two public Peripheral Blood Mononuclear Cell (PBMC) CITE-seq (Cellular Indexing of Transcriptomes and Epitopes by Sequencing) datasets of healthy donors were downloaded from 10x Genomics (https://support.10xgenomics.com/single-cell-gene-expression/datasets/3.0.2/5k_pbmc_protein_v3, https://support.10xgenomics.com/single-cell-gene-expression/datasets/3.0.0/pbmc_10k_protein_v3). Genes and cells were filtered based on the following criterions: percentage of mitochondrial genes < 10% and number of
+genes per cell between 200 and 4000. After the filtering, raw count data was normalized and scaled, using SCTransform, which performs normalization and variance stabilization using regularized negative binomial regression. Dimensionality reduction was done using principal component analysis (PCA) and t-distributed stochastic neighbor embedding (t-sne). Following that, k-nearest neighbors (knn) of each cell using 25 dimensions of PCA were determined. This knn graph was used to construct the Shared Nearest Neighbor (SNN) graph by calculating the neighborhood overlap (Jaccard index) between every cell and its 20 nearest neighbors. Cluster determination was done by SNN graph modularity optimization based on the Louvain algorithm with the resolution of 1. Cells were phenotyped separately in both datasets, using primarily cell surface markers and then gene expression levels in case of lack of usable cell surface markers (Supplementary Fig. S1-2). The two datasets were batch-corrected and integrated as described by Stuart T, et al\(^{27}\). Differentially expressed genes per cell type were identified using a Wilcoxon Rank sum test by taking a contrast between one cell type versus the rest.
+
+A generic deconvolution method with known cellular composition
+For a fair comparison of log-normal and negative binomial distribution for deconvolution, we developed a simple, generic maximum-likelihood based convolution model. Formally it is assumed that there are \( i = 1, \ldots, I \) samples in which \( t = 1, \ldots, T \) cell types jointly contribute to expression profiles of \( j = 1, \ldots, J \) genes. For each sample \( i \) and gene \( j \), a bulk expression level is given, indicated by \( y_{ij} \). As in other deconvolution methods, two hidden variables were introduced that jointly makeup \( y_{ij} \): 1) expression level of the gene per cell type, \( x^{t}_{ij} \); and 2) cellular composition for each cell type \( t \), \( f^{t}_{i} \), where \( \forall f^{t}_{i} \geq 0 \) and \( \sum_{t} f^{t}_{i} = 1 \). An important strength of our method here is that it applies to any underlying parametric distribution for \( x^{t}_{ij} \). \( y_{ij} \) is a (weighted) convolution:
+\[
+y_{ij} = \sum_{t=1}^T f_i^{t} X_{ij}^{t}
+\]
+(1)
+
+which implies, with \( \tilde{X}_{ij}^{t} = f_i^{t} X_{ij}^{t} \),
+
+\[
+g_{y_{ij}}(y) = \int_{u_1=0}^y \cdots \int_{u_T=0}^{y-\sum_{t=1}^{T-1} u_t} g_{\tilde{X}_{ij}^{1}}(u_1) \cdots g_{\tilde{X}_{ij}^{T-1}}(u_{T-1}) g_{\tilde{X}_{ij}^{T}}(y - \sum_{t=1}^{T-1} u_t) du_1 \cdots du_T.
+\]
+(2)
+
+By assuming \( X_{ij}^{t} \) follows log-normal distribution (i.e., \( X_{ij}^{t} \sim LN(\mu_j^t, (\sigma_j^t)^2) \)) and thus \( \tilde{X}_{ij}^{t} \sim LN(\mu_j^t + \log f_i^{t}, (\sigma_j^t)^2) \), \( y_{ij} \) is a convolution of \( T \) log-normal random variables.
+
+The interest lies in estimating parameters \( \theta_j = (\mu_j^t, \sigma_j^t) \) by maximum likelihood.
+
+While numerical evaluation of (2) may still be efficient for \( T = 2^{28} \), however, the extension to \( T > 2 \) is not straightforward to a \( T-1 \) dimensional integral. To this end, the log-normal density \( g_t = g_{\tilde{X}_{ij}^{t}} \) is approximated by a probability generating function (PGF). See Supplementary Note 1 for the details of PGF approximation. The PGF-based approximation of \( g_t \) showed higher accuracy than an alternative approximation method, Fenton-Wilkinson (FW) approximation\(^{29}\), which was also included as a benchmark (See Supplementary Methods and Supplementary Fig. S3).
+
+Comparison of MLE for LN and NB based on the generic deconvolution technique
+The aforementioned generic deconvolution was used to evaluate LN and NB for deconvolution. For this, two RNA-seq data sets are retrieved from The Cancer Genome Atlas (https://tcga-data.nci.nih.gov/tcga/) using TCGAbiolinks\(^{30}\). We considered all complete samples from the following tumor types: Mesothelioma (MESO\(^{31}\), n = 84; and Sarcoma (SARC\(^{32}\), n = 256. Data was preprocessed as described previously in Rauschenberger et al.\(^{33}\). The comparison procedure for LN and NB distributions is:
+
+1. Apply a non-statistical method, EPIC\(^{19}\), to estimate cell type fractions for bulk RNA-seq data using cell type specific reference signatures. It has shown that EPIC provides an
+reliable estimate of cellular fractions of \( T = 8 \) cell types\(^{34}\), and it provides absolute fractions that add up to 1.
+
+2. Fix the cellular fractions and fit generic deconvolution models with \( T = 8 \) LN or NB components using maximum likelihood.
+
+3. Compare the maximum likelihood values of the LN and NB models for \( J \) genes.
+
+The above procedure was done for 200 randomly selected genes with mean count per million larger or equal to 5 to exclude lowly expressed genes. Note that the comparison of the maximum likelihood values is fair, because the number of parameters used in the LN and NB components is the same, \( 2T = 16 \) per gene.
+
+Hierarchical Bayesian model for convolution of log-normal variables (BLADE)
+A novel Bayesian Log-normal Deconvolution model, BLADE, is introduced to efficiently perform log-normal convolution, while accounting for the prior knowledge of per cell-type gene expression profiles (see Overview at **Fig. 4a**). Formally, we assume \( y_{ij} = \sum_t f^t_i x^{t}_{ij} + e_{ij} \), where \( e_{ij} \) is a log-normal error with mean parameter 0 and variance parameter \( \gamma_j \). Then, \( x^{t}_{ij} \) follows a log-normal distribution: \( x^{t}_{ij} \sim LN(\mu^{t}_j, \frac{1}{\lambda^{t}_j}) \), where \( \mu^{t}_j \) and \( \lambda^{t}_j \) are expected value and precision in log-scale. Note that the parameters \( \mu^{t}_j \) and \( \lambda^{t}_j \) are shared across the samples. To incorporate prior knowledge on gene expression profiles per cell type, a hierarchical Bayesian approach was taken: \( \mu^{t}_j \) and \( \lambda^{t}_j \) are endowed with normal-gamma priors with hyperparameters \( \mu^{t}_{0j}, \kappa^{t}_{0j}, \alpha^{t}_{0j}, \beta^{t}_{0j} \). Note that the normal-gamma distribution is a conjugate prior of log-normal distribution, based on which marginal distribution of \( x^{t}_{ij} \) given the hyperparameters \( \mu^{t}_{0j}, \kappa^{t}_{0j}, \alpha^{t}_{0j}, \beta^{t}_{0j} \) is analytically tractable. The other hidden variable, \( f^t_i \), was endowed with Dirichlet distribution: \( (f^t_1, \ldots, f^t_T) \sim D(\alpha^t_1, \ldots, \alpha^t_T) \).
+For the inference, a collapsed variational inference was employed to handle analytically intractable posterior distribution of hidden variables given observed variables\(^{35}\). In the framework, the random variables with conjugate prior distribution, which are \( \mu_{j}^{t} \) and \( \lambda_{j}^{t} \), were integrated out, which allows us to find a fully Bayesian estimation of \( x_{ij}^{t} \) instead of estimation of the single most probable \( \mu_{j}^{t} \) and \( \lambda_{j}^{t} \)^{35}. By defining the variational distribution for the hidden variables, \( x_{ij}^{t} \) and \( f_{i}^{t} \), the objective function is to minimize the dissimilarity between the variational distribution and probability distribution, measured by Kullback-Leibler divergence (see Supplementary Note 2 for the detailed derivation). The minimization was done by the Limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm available in SciPy Python library with the constraints of \( f_{i}^{t} \geq 0 \) and \( \sum_{t} f_{i}^{t} = 1 \). Numba-compiled objective function and gradients were used for the acceleration.
+
+Selection of hyperparameters based on the empirical-Bayes framework
+BLADE has multiple hyperparameters for the hidden variables \( x_{ij}^{t} \) and \( f_{i}^{t} \), and also for observed variable \( y_{ij} \). For \( f_{i}^{t} \), a hyperparameter \( \alpha_{i}^{t} \) for Dirichlet distribution is required, for which we chose one value across the different \( t \)s since we do not have prior information on cellular composition. For \( y_{ij} \), we need to specify a precision of each gene, \( \gamma_{j} \), which we chose \( \frac{s}{\operatorname{var}(\log y_{ij})} \), where \( s \) and \( \operatorname{var}(\log y_{ij}) \) are a user-defined scale factor and a variance in log-scale measured per gene, respectively. For hyperparameters of \( x_{ij}^{t} \), \( \mu_{0j}^{t} \), \( \kappa_{0j}^{t} \), \( \alpha_{0j}^{t} \), and \( \beta_{0j}^{t} \), we incorporated prior knowledge of gene expression profiles per cell type obtained from the scRNA-seq data. Given log-normal likelihood and normal-gamma priors, average expression level and standard deviation of \( x_{ij}^{t} \) are: \( E(\log x_{ij}^{t}) = \mu_{0j}^{t} \) and \( \operatorname{var}(\log x_{ij}^{t}) = \frac{\beta_{0j}^{t}}{\alpha_{0j}^{t}} \), respectively. To make use of the prior knowledge, we obtained the sample estimates of \( E(\log x_{ij}^{t}) \) and \( \operatorname{var}(\log x_{ij}^{t}) \) from the scRNA-seq data,
+denoted by \( \mu^t_j \) and \( (\sigma^t_j)^2 \). Then, we assigned \( \mu^{t}_{0j} = \mu^t_j \) whereas \( \alpha^{t}_{0j} \) is set by users followed by deriving: \( \beta^{t}_{0j} = \alpha^{t}_{0j} (\sigma^t_j)^2 \). Here, \( \alpha^{t}_{0j} \) allows to adapt to how much information the single cell data carries for the bulk RNA-seq data. The other hyperparameter \( \kappa^{t}_{0j} \) is also user-defined, which serve as a scale factor for variance of \( \mu^t_j \) (see also Supplementary Note 2).
+
+An empirical Bayes approach was employed to select the best set of user-defined parameters\(^{36}\). For each configuration of parameters, a maximum likelihood estimate of variational parameters is obtained using a subset of samples. Then, the hyperparameter configuration with the highest likelihood is selected, followed by performing deconvolution using the entire data set. Only a subset of samples is used in the empirical Bayes step, not only to gain computational efficiency but also to avoid overfitting. Throughout the manuscript, we considered a total of 90 different parameter configurations that cover all possible combinations of: \( \alpha^t_i \in \{1,10\} \), \( \alpha^{t}_{0j} \in \{0.1, 0.5, 1, 5, 10\} \), \( \kappa^{t}_{0j} \in \{1, 0.5, 0.1\} \), and \( s \in \{1, 0.3, 0.5\} \).
+
+**Construction of the simulation data with a controlled noise level**
+We constructed simulation data sets of bulk gene expression profiles with known cellular fraction, gene expression profiles per cell type, and a diverse number of cell types and samples. To this end, given a number of cell types and genes, we first randomly sample an expected gene expression level \( \mu^t_j \) for gene \( j \) and cell type \( t \) from a normal distribution with 0 mean and standard deviation of 1.5: \( \mu^t_j \sim N(0, 2) \). Then, we sample gene expression levels per sample and per cell type, \( x^{t}_{ij} \) from a log-normal distribution with mean \( \mu^t_j \) and standard deviation of \( \sigma \) (\( x^{t}_{ij} \sim LN(\mu^t_j, \sigma) \)), where \( \sigma \) is the parameter to control the variability in gene expression per cell type of each simulation data set. Fraction of cell types are sampled from a Dirichlet distribution with uninformative prior: \( f^{t}_i \sim D(\forall_i \alpha^t_i) \), where
+\( \alpha^{t_i} = 1 \). Then, the bulk gene expression profiles are generated by: \( y_{ij} = \sum_t f_i^t x_{ij}^t \). We constructed in total of 700 training data sets with the following settings: 1) number of samples = [5,10,20,50,100]; 2) number of genes = [100,200,500,1000]; 3) number of cell types = [2,3,5,10,20]; and 4) level of variability in gene expression profiles per cell type: \( \sigma = [0.1,0.2,0.5,0.75,1,1.25,1.5] \).
+
+**Construction of PBMC stimulation data**
+To construct realistic simulation data, 20 bulk gene expression data sets were generated by randomly sampling and merging a subset of 10,403 cells from the two PBMC scRNA-seq datasets. For each sample, the cellular fraction was first sampled from a Dirichlet distribution. The actual fractions of the 15 cell types were used as the parameter of the Dirichlet distribution so that the sampled fraction is similar to the total fraction. The fraction was then converted into the count of each cell type, with the following constraints: 1) the total number of cells is 100, and 2) the minimum number of cells per type is one. Then, the given number of cells were sampled with replacement, followed by obtaining the raw counts per cell type as the cumulative sum of raw counts of the sampled cells. Up to three distinct cells per type were allowed to be sampled since otherwise, gene expression variability was over-stabilized due to the averaging. Finally, the simulated bulk raw counts were obtained by taking the cumulative sum of the raw counts per cell type among 15 cell types. The bulk gene expression data was log-normalized using the Seurat package\(^{27}\).
+
+**Systematic evaluation of BLADE and comparison against baseline methods**
+The original docker image of CIBERSORTx and NNLS, were obtained from https://cibersortx.stanford.edu/ and from the SciPy Python library, respectively. For all three methods, the same signatures of average gene expression profiles per cell type were used, while BLADE also used standard deviations of each gene. For the simulation data sets with
+the controlled gene expression variability level, true mean \( \mu_j^t \) and level of variability per cell type of all genes were retrieved. For the PBMC bulk transcriptome data, average and standard deviations of the union of differentially expressed genes of 15 cell types (in total 1,007 genes) were obtained from the PBMC scRNAseq data. For evaluation of the deconvolution performance, the Pearson correlation was measured between the predicted and true abundance of each cell type across the samples. For evaluation of purification, the Pearson correlation was measured between true and estimated gene expression profiles per cell type for group mode. For the high-resolution mode, the Pearson correlation was measured per sample. The performance evaluation for purification was done only for CIBERSORTx and BLADE as NNLS only estimate cellular fractions.
+
+Code availability
+BLADE python software along with a user-friendly demo is available and maintained at https://github.com/lgac-vumc/BLADE
+
+Acknowledgments
+This project was supported by stichting Cancer Center Amsterdam (CCA2019-9-62).
+
+Author contributions
+Y.K. and M.W. conceived the ideas, and designed the algorithm. Y.K. and B.A.B. developed the python software. B.A.B. and S.D.A. analyzed PBMC Cite-seq data. B.A.B., S.D.A. and J.G.V. classified immune cell types in the CITE-seq data. Biological interpretation of the outcome is done by S.D.A., J.O., A.F.S., J.V., F.D., H.L. B.Y., and J.G.V. Evaluation of the algorithm performance is designed and performed by Y.K., and B.A.B. All authors discussed the results and contributed to the writing.
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+FIGURES LEGENDS
+
+Fig. 1. Overview of single-cell RNA-seq data from two PBMC samples. a. t-SNE plots show gene-expression variability of two single-cell PBMC RNA-seq data, on left and right, respectively. Each unique cell type is denoted by color. b-c. Comparison of gene expression variability (standard deviation per gene; y-axis of box plots) in log-scale (b) and linear-scale (c) of both datasets (x-axis). Variability is measured per gene and per cell type, and they are split by differentially expressed genes (red) and non-differentially expressed genes (DEG; blue). d. Comparison of within-sample (x-axis) and between-sample variability (y-axis) in gene expression levels per cell type. Standard deviation is measured for each gene and cell type first separately in two PBMC single-cell datasets followed by taking average (x-axis), then also in merged PBMC data set (y-axis). Only the 9 cell types commonly detected in two data sets were used in the analysis.
+
+Fig. 2. Comparison of normal, negative binomial, and log-normal distribution in fitting linear-scale gene expression data. For each gene and cell type, maximum-likelihood parameter estimation is done for each of the three distribution assumptions. a. A bar chart of average log-likelihood of the three types of distribution fitted to PBMC single-cell RNA-seq data. The genes are split by DEGs (red) and non-DEGs (blue). b. Density plots for raw-counts (red) and optimized log-normal (green), normal (blue), and negative binomial distribution (purple) for two example genes, HLA-DRA (top) and CD74 (bottom). c. Pairwise comparison of per-gene log-likelihood of log-normal distribution (top (y-axis) and middle (y-axis)) and that of normal (top (x-axis) and bottom (y-axis)) and negative binomial distribution (middle (x-axis) and bottom (x-axis)). The genes are split into non-DEGs (left) and DEGs (right).
+Fig. 3. Comparison of negative binomial and log-normal components in generic deconvolution of gene expression data from TCGA. Maximum log-likelihood values of each gene for log-normal (y-axis) and negative binomial (bottom) convolutions of T=8 cell types, applied to TCGA-MESO (left) and TCGA-SARC (right) data. Cellular fractions are pre-estimated by EPIC.
+
+Fig. 4. BLADE workflow. a. To construct a prior knowledge for BLADE, we used CITE-seq data that contains gene expression and cell surface marker profiles of each cell. Cells are then subject to phenotyping, clustering, and differential gene expression analysis. Then, for each cell type, we retrieved average expression profiles (red cross and top heat map) and standard deviation per gene as the variability (blue circle and bottom heatmap). This prior knowledge is then used in the hierarchical Bayesian model (bottom right) to deconvolute bulk transcriptome profile. b. A Bayesian network of BLADE represents random variables, observed and hidden variables respectively in blue and gray nodes, and their dependency associations (arrows). The hyperparameters (\( \mu_{0j}^t, \kappa_{0j}^t, \alpha_{0j}^t, \) and \( \beta_{0j}^t \) on the left) and bulk gene expression data (\( y_{ij} \) on the right) are observed, where the hidden variables in the middle (\( \mu_j^t, \lambda_j^t, f_i^t \) and \( x_{ij}^{t,i} \)) are inferred. Among the hidden variables, \( f_i^t \) and \( x_{ij}^{t,i} \) respectively represent the fraction of cell type \( t \) and purified gene expression level of gene \( j \) in sample \( i \).
+
+Fig. 5. Performance evaluation BLADE in simulation data with diverse settings. a. Performances (Pearson correlation; y-axis) of BLADE (orange), CIBERSORTx (blue), and NNLS (green) in predicting cellular fraction of simulation data with diverse variability level (standard deviation of 0.1-1.5; x-axis), number of cells (2-20 cell types; rows), and number of genes (100-1000 genes; columns). b-c. Performances (Pearson correlation; y-axis) of BLADE (orange) and CIBERSORTx (blue) in predicting gene expression profiles per cell type for all samples jointly (group-mode; b) and for each sample separately (high-resolution mode; c) using the same simulation data. d-e. Fractions of genes with the inferred gene
+expression profiles per cell type by CIBERSORTx in group-mode (d) and high-resolution mode (e). x- and y-axis represents the number of cell types and samples in the simulation data, respectively.
+
+Fig. 6. Performance evaluation of BLADE in simulated PBMC bulk RNA-seq data. a. t-SNE plot showing variability of the cell populations in the simulated bulk RNA-seq data. b-c. Radar charts represent performance in Pearson correlation of BLADE (orange), CIBERSORTx (blue), and NNLS (green) for estimation of cellular fractions (b) and for group-mode purification (c). d. Fraction of genes *in silico* purified in group-mode (blue) and high-resolution-mode (red) by CIBERSORTx. e. Performance (Pearson correlation; y-axis) of BLADE (orange) and CIBERSORTx (blue) in estimating gene expression profiles per cell type and per sample.
+Figures
+
+Figure 1
+
+Overview of single-cell RNA-seq data from two PBMC samples. a. t-SNE plots show gene-expression variability of two single-cell PBMC RNA-seq data, on left and right, respectively. Each unique cell type is denoted by color. b-c. Comparison of gene expression variability (standard deviation per gene; y-axis of box plots) in log-scale (b) and linear-scale (c) of both datasets (x-axis). Variability is measured per gene and per cell type, and they are split by differentially expressed genes (red) and non-differentially expressed genes (DEG; blue). d. Comparison of within-sample (x-axis) and between-sample variability (y-axis) in gene expression levels per cell type. Standard deviation is measured for each gene and cell type first separately in two PBMC single-cell datasets followed by taking average (x-axis), then also in merged PBMC data set (y-axis). Only the 9 cell types commonly detected in two data sets were used in the analysis.
+Figure 2
+
+Comparison of normal, negative binomial, and log-normal distribution in fitting linear-scale gene expression data. For each gene and cell type, maximum-likelihood parameter estimation is done for each of the three distribution assumptions. a. A bar chart of average log-likelihood of the three types of distribution fitted to PBMC single-cell RNA-seq data. The genes are split by DEGs (red) and non-DEGs (blue). b. Density plots for rawcounts (red) and optimized log-normal (green), normal (blue), and negative binomial distribution (purple) for two example genes, HLA-DRA (top) and CD74 (bottom). c. Pairwise comparison of per-gene log-likelihood of log-normal distribution (top (y-axis) and middle (yaxis)) and that of normal (top (x-axis) and bottom (y-axis)) and negative binomial distribution (middle (x-axis) and bottom (x-axis)). The genes are split into non-DEGs (left) and DEGs (right).
+Figure 3
+
+![Scatter plots comparing log-normal and negative binomial components for TCGA-MESO (n=84) and TCGA-SARC (n=256)](page_120_120_1347_670.png)
+
+Figure 3
+
+Comparison of negative binomial and log-normal components in generic deconvolution of gene expression data from TCGA. Maximum log-likelihood values of each gene for log-normal (y-axis) and negative binomial (bottom) convolutions of T=8 cell types, applied to TCGA-MESO (left) and TCGA-SARC (right) data. Cellular fractions are preestimated by EPIC.
+Figure 4
+
+a
+
+![Diagram showing the BLADE workflow, including single cell CITE-seq data, phenotyping clustering, DEG analysis, and bulk RNA-seq data, leading to a hierarchical Bayesian model.](page_120_180_1347_693.png)
+
+b
+
+![Bayesian network diagram showing observed and hidden variables, with nodes labeled by genes, cell types, and samples.](page_120_850_1347_495.png)
+
+observed variable
+hidden variable
+j: genes
+t: cell types
+i: samples
+
+Figure 4
+
+BLADE workflow. a. To construct a prior knowledge for BLADE, we used CITE-seq data that contains gene expression and cell surface marker profiles of each cell. Cells are then subject to phenotyping, clustering, and differential gene expression analysis. Then, for each cell type, we retrieved average expression profiles (red cross and top heat map) and standard deviation per gene as the variability (blue circle and bottom heatmap). This prior knowledge is then used in the hierarchical Bayesian model (bottom right) to
+deconvolute bulk transcriptome profile. b. A Bayesian network of BLADE represents random variables, observed and hidden variables respectively in blue and gray nodes, and their dependency associations (arrows). The hyperparameters ( \( \mu t0j, \kappa t0j, at0j, \) and \( \beta t0j \) on the left) and bulk gene expression data (yijon the right) are observed, where the hidden variables in the middle ( \( \mu t j, \lambda jt, fit, \) and \( xijt \) ) are inferred. Among the hidden variables, fti and xijt respectively represent the fraction of cell type t and purified gene expression level of gene j in sample i.
+
+Figure 5
+
+![Performance evaluation BLADE in simulation data with diverse settings. a. Performances (Pearson correlation; y-axis) of BLADE (orange), CIBERSORTx (blue), and NNLS (green) in predicting cellular fraction of simulation data with diverse variability level (standard deviation of 0.1-1.5; x-axis), number of cells (2-20 cell types; rows), and number of genes (100-1000 genes; columns). b-c. Performances (Pearson correlation; y-axis) of BLADE (orange) and CIBERSORTx (blue) in predicting gene expression profiles per cell type for all samples jointly (group-mode; b) and for each sample separately (high-resolution mode; c) using the same simulation data. d-e. Fractions of genes with the inferred gene expression profiles per cell type by CIBERSORTx in group-mode (d) and high-resolution mode (e). x- and y-axis represents the number of cell types and samples in the simulation data, respectively.](page_184_370_1207_693.png)
+
+Figure 5
+
+Performance evaluation BLADE in simulation data with diverse settings. a. Performances (Pearson correlation; y-axis) of BLADE (orange), CIBERSORTx (blue), and NNLS (green) in predicting cellular fraction of simulation data with diverse variability level (standard deviation of 0.1-1.5; x-axis), number of cells (2-20 cell types; rows), and number of genes (100-1000 genes; columns). b-c. Performances (Pearson correlation; y-axis) of BLADE (orange) and CIBERSORTx (blue) in predicting gene expression profiles per cell type for all samples jointly (group-mode; b) and for each sample separately (high-resolution mode; c) using the same simulation data. d-e. Fractions of genes with the inferred gene expression profiles per cell type by CIBERSORTx in group-mode (d) and high-resolution mode (e). x- and y-axis represents the number of cell types and samples in the simulation data, respectively.
+Figure 6
+
+Performance evaluation of BLADE in simulated PBMC bulk RNA-seq data. a. t-SNE plot showing variability of the cell populations in the simulated bulk RNA-seq data. b-c. Radar charts represent performance in Pearson correlation of BLADE (orange), CIBERSORTx (blue), and NNLS (green) for estimation of cellular fractions (b) and for groupmode purification (c). d. Fraction of genes in silico purified in group-mode (blue) and highresolution- mode (red) by CIBERSORTx. e. Performance (Pearson correlation; y-axis) of BLADE (orange) and CIBERSORTx (blue) in estimating gene expression profiles per cell type and per sample.
+
+Supplementary Files
+
+This is a list of supplementary files associated with this preprint. Click to download.
+
+• SupplementaryFigures.pdf
+• SupplementaryNotes.pdf

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+Peer Review File
+
+Dissecting extracellular and intracellular distribution of nanoparticles and their contribution to therapeutic response by monochromatic ratiometric imaging
+
+Open Access This file is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. In the cases where the authors are anonymous, such as is the case for the reports of anonymous peer reviewers, author attribution should be to 'Anonymous Referee' followed by a clear attribution to the source work. The images or other third party material in this file are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.
+REVIEWER COMMENTS
+
+Reviewer #1 (expertise: PDT and tumour microenvironment)- Remarks to the Author:
+
+Comments to the Authors:
+The authors submit an interesting and important study that leverages a nanoconstruct based formulation for quantifying tumor distribution of nanoparticles and exploiting it for photodynamically targeting both intracellular and extracellular targets for a better treatment outcome. Although the study is an interesting one, there are however several concerns that have to be addressed.
+
+• The authors throughout the manuscript mention “extracellular nanoparticles” for the ones that are activated through an external trigger i.e NIR irradiation at 808 nm. However, it appears that a fraction of nanoparticles is internalized, yet not activated in the lysosomes. The authors should provide a discussion on that as well. For example, in figure 3b all the three nanoparticle formulations RNP0%, MRIN and RNP100% show a diffused intracellular fluorescence, yet the authors mention it as intracellular and extracellular fluorescence. It will be appropriate to quantify intracellular fluorescence through flow cytometry with and without irradiation of a cell suspension treated with the RNP0%, MRIN and RNP100%.
+• In figure 3d the quantification of percentage extracellular and intracellular nanoparticle fluorescence is confusing. It appears to be the reverse of what is depicted in figure 3c.
+• For quantification of intra and extracellular of nanoparticles, the authors use a 24 h time-point. However, for PDT studies the authors prefer a 3 h drug-light interval which is surprising given the relatively lower intracellular nanoparticle content at this time point (Supplementary figure 10a and 10b).
+• For the in vivo PDT treatment study, the authors use a PDT scheme with two PDT treatments on day 1 and day 5. Why was this treatment strategy followed and what were the tumor characteristics (size and volume) on day 1.
+• The authors suggest that the reduction in ECM and integrin expression of tumor cells could be possible reasons for reduction in metastasis. While this may be the case, the authors should discuss the negative consequences of ECM degradation which has been previously reported to enhance tumor metastasis. (1). Stromal Elements Act to Restrain, Rather Than Support, Pancreatic Ductal Adenocarcinoma, Cancer Cell, Volume 25, Issue 6, 16 June 2014, Pages 735-747. (2). Depletion of Carcinoma-Associated Fibroblasts and Fibrosis Induces Immunosuppression and Accelerates Pancreas Cancer with Reduced Survival, Cancer Cell, Volume 25, Issue 6, 16 June 2014, Pages 719-734.
+• The authors refer to “mild extracellular PDT” as a cause of ECM disruption and integrin down regulation. The authors should include discussion on photodynamic priming which in general includes the effects of therapeutic and sub-therapeutic doses of PDT. (1). Impacting Pancreatic Cancer Therapy in Heterotypic in Vitro Organoids and in Vivo Tumors with Specificity-Tuned, NIR-Activatable Photoimmunonanoconjugates: Towards Conquering Desmoplasia?, Nano Lett. 2019, 19, 11, 7573–7587. (2). Subtherapeutic Photodynamic Treatment Facilitates Tumor Nanomedicine Delivery and Overcomes Desmoplasia, Nano Lett. 2021, 21, 1, 344–352. (3). Photodynamic therapy, priming and optical imaging: Potential co-conspirators in treatment design and optimization, Journal of Porphyrins and Phthalocyanines. Vol. 24, No. 11n12, pp. 1320-1360 (2020).
+• The manuscript needs editing for grammar. For example, “The Cy5 signals of tumors greatly increased along with the disappeared Cy7.5 fluorescence at each time point after irradiation.”, “The increased Cy5 signals at the tumor sites before and after irradiation were all originated from extracellular nanoparticles”, “The tumor slices were also performed for collagen, fibronectin, and H&E staining as well as TUNEL assay, respectively”, etc.
+
+Reviewer #2 (expertise: Ratiometric imaging)- Remarks to the Author:
+
+In this manuscript entitled “Dissecting extracellular and intracellular distribution of nanoparticles and their contribution to therapeutic response by monochromatic ratiometric imaging”, Prof. Wang and collaborators developed a pH/light dual-responsive monochromatic ratiometric imaging nanoprobe (MRIN) for accurately quantifying the extracellular and intracellular distribution of NPs
+in several tumor models. This study indeed offers a valuable tool to visualize and dissect the contribution of extracellularly distributed nanophotosensitizer to therapeutic efficacy and maximize the treatment outcome of PDT. Overall, this study has a high impact on drug delivery and tumor theranostics, the experiments were well designed and carefully conducted with proper controls and the hypothesis and claims were scientifically vigorous. Thus, I recommend its publication after addressing the following issues.
+
+1. The stability of micelles depends on the CMC of copolymers. The authors should make sure that the MRIN keep self-assembled nanostructure in vivo before internalization.
+
+2. To quantify the extracellular and intracellular distribution of MRIN in tumor, the imaging of mice was conducted for 48 h, which showed the highest fluorescence signals of intracellular and extracellular nanoprobes. A longer time monitoring should be conducted to investigate the profile of microdistribution in tumors.
+
+3. The cyanine dyes can also work as photosensitizers (Pharmaceutics 2021, 13, 818). A mild elevated SOSG signal was observed after 808 nm irradiation in Fig. 5a. The authors should rule out the effect of Cy7.5 on photodynamic therapy.
+
+4. The quantitative data of lung metastasis in Fig.6b should be provided for significant difference analysis.
+
+5. The photograph and TEM image of MRIN at pH 5.4 with 808 nm irradiation should be provided in Figure 2b for direct comparison.
+
+6. A scheme should be provided to describe the “turn-on” mechanism of MRIN nanoprobe regarding pH-induced dissociation and 808 nm laser irradiation, respectively.
+
+Reviewer #3 (expertise: pH sensitive fluorescent nanoparticles)- Remarks to the Author:
+
+This manuscript described an approach on dissecting extracellular and intracellular distribution of nanoparticles. The authors developed a pH/light dual-response monochromatic ratiometric-imaging nanoparticle (MRIN), which precisely quantified nanocarrier micro-distribution. Particularly, the MRIN exhibited a sharp pH response and high Cy5 signal activation ratio. The application demonstrated in the manuscript has relevance and potential high impact in the field of imaging and photodynamic therapy of tumors. Several revisions are suggested aiming to improve quality of the results and presentation.
+1. According to the experimental procedure, the MRIN was formed by self-assembly of components with a fixed proportion, how to control such uniform size as shown in Figure 2b, and the author should provide a TEM of with high resolution.
+2. The author chose RNP0%, RNP100% as positive controls. According to the design, RNP100% as an always-on probe has no quenching effect of Cy7.5 without pH responsive, why there are good targeted imaging results in Figure 3c.
+3. Does the principle total=intracellular + extracellular applicable to MRIN also apply to RNP0%, RNP100%? For RNP100%, There is no acid response-mediated fluorescence recovery, so it is not certain that exhibited fluorescence means intracellular, extracellular nanoparticles also exhibited fluorescence. Similarly, the RNP0% did not produce fluorescence, which does not mean that they were extracellular, the author needs to provide a reasonable explanation or correct the description in Figure 3b.
+4. Four kinds of particles, MRIN, RNP0%, RNP100%, and MRITN are used in the manuscript, and the self-assembly components include UPS, UPS-Cy5, UPS-Cy7.5, pH-insensitive polymer, pH-insensitive polymer-Cy5, pH-insensitive polymer-Cy7.5, UPS-Ce6. Although components and ratio were listed separately in the experimental steps, it is not very clearly stated in the text. The self-assembly composition and ratio of each particles may be listed in a table or in the corresponding figure.
+5. Why Cy7.5 also quenched Ce6? the author needs to provide FRET related explanation.
+6. Regarding why PDT with intracellular and extracellular is better, the author needs to provide a mechanism explanation or further pathway data to support Figure 5.
+Point-by-point response to reviewers
+
+We would like to thank the reviewers for the insightful and constructive comments! We have revised the manuscript according to their advices, which should significantly improve the clarity and quality of our work. Below is a list of the point-by-point responses to the reviewer comments shown in italics and the corresponding changes that we made highlighted in yellow.
+
+Reviewer #1 (Remarks to the Author):
+
+The authors submit an interesting and important study that leverages a nanoconstruct based formulation for quantifying tumor distribution of nanoparticles and exploiting it for photodynamically targeting both intracellular and extracellular targets for a better treatment outcome. Although the study is an interesting one, there are however several concerns that have to be addressed.
+
+We appreciate the reviewer’s encouraging comments on the novelty and impact of the MRIN nanotechnology. We have revised the manuscript according to your advices and other referee’s comments.
+
+1. The authors throughout the manuscript mention “extracellular nanoparticles” for the ones that are activated through an external trigger i.e NIR irradiation at 808 nm. However, it appears that a fraction of nanoparticles is internalized, yet not activated in the lysosomes. The authors should provide a discussion on that as well. For example, in figure 3b all the three nanoparticle formulations RNP0%, MRIN and RNP100% show a diffused intracellular fluorescence, yet the authors mention it as intracellular and extracellular fluorescence. It will be appropriate to quantify intracellular fluorescence through flow cytometry with and without irradiation of a cell suspension treated with the RNP0%, MRIN and RNP100%.
+
+Re: Thanks for the reviewer’s good suggestion. We have performed new experiments to quantify intracellular fluorescence by flow cytometry and added the result as Supplementary Figure 4. Luminal pH decline from neutral to mild acidic (e.g. pH 6.0 for early endosome, pH 5.0 for lysosome) is a hallmark of cellular internalization. In our previous study, we have succeeded to target specific endocytic organelles with different pH values by precisely tuning the pH transitions (pH_i) of the UPS fluorescent nanoprobe library (Wang et al, Adv Mater 2017, 29, 1603794). In this manuscript, we developed a pH/light dual-responsive monochromatic ratiometric imaging nanotechnology (MRIN) to dissect extracellular and intracellular distribution of nanoparticles in tumor tissues. The pH transition of MRIN is 6.3, which can be activated in early endosomes (pH~6.0) upon internalization (Wang et al, Nat Mater, 2014, 13, 204; Zhou et al, Angew Chem Int Ed Engl 2011, 50, 6109 -6114). Due to the ultra-pH-sensitivity of MRIN, it can quickly dissociate into unimers with exponential Cy5 signal amplification into early endosome after being endocytosed (~5 min). As shown in Supplementary Figure 4, negligible enhancement of intracellular Cy5 signal was observed after 808 nm laser irradiation, demonstrating that the internalized MRIN was almost completely activated in the endo-lysosomes.
+
+In order to demonstrate the quantitative imaging feasibility of MRIN, RNP0% (Cy5-labeled pH-insensitive micelle) and RNP100% (Always-ON micelle) were established to simulate the artificial states of 0% and 100% endocytosis in vitro and in vivo. However, it doesn’t mean that they are true 0% and 100% endocytosis. The Cy5 signal of RNP0% was completely ‘OFF’ whether cellular endocytosis or not due to its pH-insensitive nanostructure, so it could be used to simulate the artificial states of 0% endocytosis. The Cy5 signal of RNP100% was completely ‘ON’ due to the Always-ON design, so it could be used to simulate the artificial states of 100% endocytosis. The intracellular Cy5 signal of RNP0% was completely activated after 808 nm irradiation with over 40-fold signal amplification. In contrast, the intracellular Cy5 signal of RNP100% kept constant after 808 nm laser irradiation due to the Always-ON design.
+Line 104-106: For MRIN, the Cy5 signal of which endocytosed into the cells was fully activated (Supplementary Fig. 4a), ……
+
+Line 121-126: Furthermore, the intracellular fluorescence behavior of three nanoparticles was also studied by flow cytometry (Supplementary Fig. 4b). The intracellular Cy5 signal of RNP0% was completely activated after 808 nm irradiation with over 40-fold signal amplification. Whereas, the intracellular Cy5 signal of RNP100% kept constant after 808 nm laser irradiation due to the Always-ON design. For MRIN, negligible enhancement of intracellular Cy5 signal was observed after 808 nm laser irradiation, demonstrating that the internalized MRIN were completely activated in the endo-lysosomes.
+
+![Intracellular fluorescence images and flow cytometry results of three nanoparticles](page_370_370_1002_370.png)
+
+Supplementary Figure 4. The intracellular fluorescence behavior of three nanoparticles. (a) The intracellular Cy5 fluorescence images of MRIN in 4T1 cells treated with MRIN before and after 808 nm irradiation. (b) The intracellular fluorescence intensity of three nanoparticles in 4T1 cell suspension before and after 808 nm irradiation measured by flow cytometry.
+
+2. In figure 3d the quantification of percentage extracellular and intracellular nanoparticle fluorescence is confusing. It appears to be the reverse of what is depicted in figure 3c.
+
+Re: We appreciate the reviewer for pointing it out. We are very sorry for our mistake and have made correction in Figure 3d according to your comments.
+
+3. For quantification of intra and extracellular of nanoparticles, the authors use a 24 h time-point. However, for PDT studies the authors prefer a 3 h drug-light interval which is surprising given the relatively lower intracellular nanoparticle content at this time point (Supplementary figure 10a and 10b).
+
+Re: We appreciate the insightful questions by the reviewer. As the reviewer mentioned, the intracellular nanoparticle content at 3 h post-injection is relative lower than that at 24 h. However, we chose the drug-light interval (DLI) of 3 h to perform the anti-tumor PDT studies, because that we have discovered that the anti-tumor efficacy of intracellular PDT at DLI of 3 h is much better than that of 24 h. The detailed studies and corresponding mechanisms have been submitted and revised on Nature Nanotechnology.
+
+In addition, we added the anti-tumor results of MRITN at DLI of 24 h that performed before the first submission of the manuscript. The result was in consistence with that of DLI of 3 h. The anti-tumor efficacy of MRITN with or without 808 nm laser irradiation groups has no significant difference as compared with PBS group. The antitumor efficacy of MRITN combined with 660 nm laser group (intracellular PDT) and MRITN combined with 660 nm + 808 nm group was significantly enhanced as compared with MRITN plus 808 nm group. However, harnessing 808 nm irradiation before 660 nm (intracellular + extracellular PDT) resulted in the most efficient antitumor efficacy. We have added the related results as Supplementary Figure 16.
+
+Line 256-258: In addition, the antitumour study of MRITN with DLI of 24 h was also performed.
+Similarly, combined PDT achieved the most effective tumour inhibition as compared with other treatment groups (Supplementary Fig. 16).
+
+![Anti-tumor study of MRITN with drug-light interval of 24 h.](page_184_370_1080_370.png)
+
+Supplementary Figure 16. The anti-tumor study of MRITN with drug-light interval of 24 h.
+
+4. For the in vivo PDT treatment study, the authors use a PDT scheme with two PDT treatments on day 1 and day 5. Why was this treatment strategy followed and what were the tumor characteristics (size and volume) on day 1.
+
+Re: The reviewer raises a good point. Firstly, we performed anti-tumor study when the tumor volumes of mice reached approximately 50-100 mm^3, the first day of anti-tumor study was defined as day 1. Secondly, in this manuscript, we developed a nanoparticle (MRITN) which could realize combined intracellular and extracellular PDT, aiming to reduce PDT dose (including photosensitizer dose and laser power) and prolong administration intervals for improved compliance without compromising the therapeutic effect.
+
+Currently, a majority of activatable PDT rely on the intracellular exposure to exert lethal tumor damage, which requires high photosensitizer dose or short administration intervals to achieve the desired therapeutic effect. Many literatures for photodynamic therapy performed treatment every 2-3 days for at least three times (Gao A, et al, Nano Lett 2020, 20, 353-362; Su J, et al, Theranostics 2017, 7, 523-537; Duan X, et al, JACS 2016, 138, 16686-16695.). Enabled by MRITN, we achieved efficient antitumor efficacy by two PDT treatments with 4 days intervals using 6-fold lower photosensitizer dose than most reported studies for PDT therapy (Wang T, et al, ACS nano 2016, 10, 3496-3508; Fu Y, et al, J Control Release 2020, 327, 129-139).
+
+5. The authors suggest that the reduction in ECM and integrin expression of tumor cells could be possible reasons for reduction in metastasis. While this may be the case, the authors should discuss the negative consequences of ECM degradation which has been previously reported to enhance tumor metastasis. (1). Stromal Elements Act to Restrain, Rather Than Support, Pancreatic Ductal Adenocarcinoma, Cancer Cell, Volume 25, Issue 6, 16 June 2014, Pages 735-747. (2). Depletion of Carcinoma-Associated Fibroblasts and Fibrosis Induces Immunosuppression and Accelerates Pancreas Cancer with Reduced Survival, Cancer Cell, Volume 25, Issue 6, 16 June 2014, Pages 719-734.
+
+Re: Thanks for the reviewer’s good suggestion, we have discussed the negative consequences of ECM degradation in the Discussions and cited related literatures.
+
+Line 321-327: Based on our findings, we speculate that the potential mechanism for the anti-metastasis effect of combined PDT is the ECM destruction and the downregulation of adhesion integrin β1. However, the tumour metastasis is a very complicated process, and influenced by various physiological factors. Although previous investigations have reported that excessive reduction of extracellular matrix and stromal
+cells promotes tumour metastasis53, 54, our MRITN-mediated PDT achieved remarkable inhibition of lung metastasis probably due to the lethal damage to tumour cells. However, the comprehensive mechanism needs to be further investigated in the future.
+
+6. The authors refer to “mild extracellular PDT” as a cause of ECM disruption and integrin down regulation. The authors should include discussion on photodynamic priming which in general includes the effects of therapeutic and sub-therapeutic doses of PDT. (1). Impacting Pancreatic Cancer Therapy in Heterotypic in Vitro Organoids and in Vivo Tumors with Specificity-Tuned, NIR-Activable Photoimmunonanoconjugates: Towards Conquering Desmoplasia?, Nano Lett. 2019, 19, 11, 7573–7587. (2). Subtherapeutic Photodynamic Treatment Facilitates Tumor Nanomedicine Delivery and Overcomes Desmoplasia, Nano Lett. 2021, 21, 1, 344–352. (3). Photodynamic therapy, priming and optical imaging: Potential co-conspirators in treatment design and optimization, Journal of Porphyrins and Phthalocyanines. Vol. 24, No. 11n12, pp. 1320-1360 (2020).
+
+Re: Thanks for the reviewer’s suggestion, we have added a discussion on photodynamic priming in the Discussions and cited related literatures.
+
+Line 309-316: Currently, photodynamic therapy (PDT) has been widely exploited for the treatment of various malignant tumours due to its minimal invasion and fast healing. The responses to PDT rely largely on the light dose, photosensitizer concentration and location50. In addition to the vascular damage and direct cell killing effect at therapeutic dose level, photodynamic priming (PDP) using subtherapeutic dose has also been demonstrated to efficiently enhance the antitumour efficacy of subsequent therapies. Several researches have revealed that PDP can sensitize tumours to immuno- and chemo-therapy via the tumour microenvironment modulation, including the decrease of extracellular matrix content and the enhancement of tumour vascular leakiness51, 52.
+
+Line 317-320: Our results demonstrated that the extracellular NPs played an equal important role in cancer treatment via both cell membrane damage (direct cell killing) and ECM destruction (photodynamic priming), enabling the maximized therapeutic outcomes of combined PDT.
+
+7. The manuscript needs editing for grammar. For example, “The Cy5 signals of tumors greatly increased along with the disappeared Cy7.5 fluorescence at each time point after irradiation.”, “The increased Cy5 signals at the tumor sites before and after irradiation were all originated from extracellular nanoparticles”, “The tumor slices were also performed for collagen, fibronectin, and H&E staining as well as TUNEL assay, respectively”, etc.
+
+Re: Thank you very much for your kind advice. We have checked the grammar carefully and made some changes in the revised manuscript. These changes will not influence the content and framework of the paper. We appreciate for reviewer’s warm work earnestly, and hope that the correction will meet with approval.
+Reviewer #2 (Remarks to the Author):
+
+In this manuscript entitled “Dissecting extracellular and intracellular distribution of nanoparticles and their contribution to therapeutic response by monochromatic ratiometric imaging”, Prof. Wang and collaborators developed a pH/light dual-responsive monochromatic ratiometric imaging nanoprobe (MRIN) for accurately quantifying the extracellular and intracellular distribution of NPs in several tumor models. This study indeed offers a valuable tool to visualize and dissect the contribution of extracellularly distributed nanophotosensitizer to therapeutic efficacy and maximize the treatment outcome of PDT. Overall, this study has a high impact on drug delivery and tumor theranostics, the experiments were well designed and carefully conducted with proper controls and the hypothesis and claims were scientifically vigorous. Thus, I recommend its publication after addressing the following issues.
+
+We thank the reviewer’s positive comments. We provide a point-by-point response to the reviewer comments.
+
+1. The stability of micelles depends on the CMC of copolymers. The authors should make sure that the MRIN keep self-assembled nanostructure in vivo before internalization.
+
+Re: We acknowledge the reviewer’s concern. Our previous article (Wang et al, Nat Mater, 2014, 13, 204) has investigated the dilution of ultra-pH-sensitive micelle in blood after intravenous injection. The plasma concentration of micelle at 24 h after injection was approximately 100 \( \mu \)g mL\(^{-1}\) (calculated from the 10 mg kg\(^{-1}\) injection dose and micelle pharmacokinetics), which was exponentially higher than the CMC of copolymers (The CMC was ranging from 0.88-2.48 \( \mu \)g mL\(^{-1}\) for different ultra-pH-sensitive copolymers). We have also measured the CMC of our nanoparticle to be 1.97 \( \mu \)g mL\(^{-1}\) by a pyrene assay. According to the in vivo pharmacokinetics of our nanoparticle (Supplementary Figure 15c) and 60 mg kg\(^{-1}\) injection dose, the plasma concentration of our nanoparticle at 2 min and 24 h after intravenous injection were 600 \( \mu \)g mL\(^{-1}\) and 107.4 \( \mu \)g mL\(^{-1}\), respectively, which were dozens of times higher than the CMC. Therefore, MRIN can remain stability in the blood circulation and will not disassemble until they are internalized by tumor cells.
+
+2. To quantify the extracellular and intracellular distribution of MRIN in tumor, the imaging of mice was conducted for 48 h, which showed the highest fluorescence signals of intracellular and extracellular nanoprobes. A longer time monitoring should be conducted to investigate the profile of microdistribution in tumors.
+
+Re: Per the reviewer’s advice, we have carried out new experiment for long-term monitoring the extracellular and intracellular distribution of MRIN in vivo using 4T1 tumor-bearing mice. As shown in the new Figure 4a-c, intracellular, extracellular, and total nanoparticle exposure in tumors all increased gradually over 48 h, which implied nanoprobes in circulation extravasated unceasingly from leaky tumor vasculature and then were internalized into intratumoral cells. In the following 2 days, the intracellular nanoparticle exposure remained unchanged, while the extracellular and total nanoparticle exposure were gradually decreased, which probably due to the slow clearance of nanoparticles from mice. Accordingly, the extracellular nanoparticle exposure percentage and extracellular/intracellular exposure ratio reached a maximum at 48 h post-injection followed by a slight decrease in the subsequent monitoring period.
+
+Line 187-193: The quantitative results revealed that the exposure level of nanoparticles in intracellular and extracellular compartments of tumour tissues was continuously enhanced within 48 h post-injection. However, the intracellular nanoparticle exposure remained unchanged, while the extracellular nanoparticle exposure was gradually decreased in the following 2 days, which probably due to the slow clearance of nanoparticles from mice (Fig. 4b). Accordingly, the percentage of extracellular nanoparticle exposure and
+the ratio of extracellular versus intracellular exposure reached a maximum at 48 h post-injection followed by a slight decrease in the subsequent monitoring period.
+
+![Quantitative imaging of extracellular and intracellular distribution of nanoparticles in different tumors.](page_120_153_1247_627.png)
+
+Fig. 4 Quantitative imaging of extracellular and intracellular distribution of nanoparticles in different tumors.
+
+3. The cyanine dyes can also work as photosensitizers (Pharmaceutics 2021, 13, 818). A mild elevated SOSG signal was observed after 808 nm irradiation in Fig. 5a. The authors should rule out the effect of Cy7.5 on photodynamic therapy.
+
+Re: Thanks for the reviewer’s good suggestion, we have carried out new experiments to investigate the effect of Cy7.5 on photodynamic therapy and added the related results as Supplementary Figure 13. For MRITN, Cy7.5 served as a fluorescence quencher of Ce6 through FRET effect. At pH 7.4, MRITN is micelle state with Ce6 signal “OFF”, therefore, it generates little singlet oxygen under 660 nm irradiation. The Ce6 signals of MRITN can be fully activated through both pH-induced micelles dissociation and 808 nm irradiation-induced Cy7.5 photobleaching, resulting in about 270-fold higher SOG than Ce6 “OFF” state under 660 nm irradiation. However, the singlet oxygen generated by UPS-Cy7.5 with 808 nm irradiation was 20-fold lower than MRITN with 660 nm irradiation in activated Ce6 state. Therefore, the SOG of Cy7.5 was negligible for the photodynamic effect of MRITN. In addition, for the photodynamic effect at cellular level, MRITN was pre-irradiated with 808 nm laser before incubation with cells, aiming at ruling out the effect of Cy7.5 on photodynamic therapy. What’s more, for in vivo anti-tumor study, the mice treated with MRITN plus 808 nm irradiation was also included as a control group. The results showed that 808 nm irradiation alone had no significant difference as compared with PBS group on tumor inhibition, further confirming the insignificant photodynamic effect of Cy7.5.
+
+Line 220-223: Although Cy7.5 can also work as photosensitizers, its singlet oxygen generation under 808 nm irradiation was 20-fold lower than MRITN under 660 nm irradiation. Hence, compared with Ce6, the SOG of Cy7.5 was negligible for the photodynamic effect of MRITN (Supplementary Fig. 13).
+Supplementary Figure 13. The effect of Cy7.5 on photodynamic therapy.
+
+4. The quantitative data of lung metastasis in Fig.6b should be provided for significant difference analysis.
+
+Re: We acknowledge the reviewer’s kind suggestion. We have added the quantitative data of lung metastasis in Figure 6c, and performed significant difference analysis.
+
+Figure 6c. The quantitative result of ex vivo lung metastasis.
+
+5. The photograph and TEM image of MRIN at pH 5.4 with 808 nm irradiation should be provided in Figure 2b for direct comparison.
+
+Re: Per the reviewer’s advice, we have added the photograph and TEM image of MRIN at pH 5.4 with 808 nm irradiation in Figure 2b.
+
+Figure 2b. The photographic images and TEM images of MRIN.
+6. A scheme should be provided to describe the “turn-on” mechanism of MRIN nanoprobe regarding pH-induced dissociation and 808 nm laser irradiation, respectively.
+
+Re: We appreciate the reviewer’s suggestion. In the MRIN platform, Cy7.5 served as a fluorescence quencher of Cy5 through FRET effect. Tertiary amino groups are incorporated into polymers as ionizable groups to impart pH sensitivity. When pH > 6.3, the hydrophobic segments of PEG5k-b-P(DPA40-r-EPA40-r-Dye) polymer self-assemble into the micelle cores, leading to fluorescence quenching of Cy5 fluorophore by hetero-FRET. In micelle state, the Cy5 fluorescence signal can be recovered by photobleaching Cy7.5 with 808 nm irradiation. When pH < 6.3, protonation of the PEG5k-b-P(DPA40-r-EPA40-r-Dye) segments results in micelle dissociation, leading to abolishment of FRET effect due to the long distance between fluorophore and fluorophore quencher. Therefore, both pH-induced dissociation and 808 nm laser irradiation can effectively turn on MRIN nanoprobe. We have included the scheme in Supplementary Figure 3.
+
+Line 94-96: The ‘turn-on’ mechanisms of MRIN based on pH-induced dissociation and 808 nm laser irradiation are shown in Supplementary Fig. 3.
+
+![The 'turn-on' mechanism of MRIN based on pH-induced dissociation and 808 nm laser irradiation.](page_212_668_1022_496.png)
+
+Supplementary Figure 3. The ‘turn-on’ mechanism of MRIN based on pH-induced dissociation and 808 nm laser irradiation.
+Reviewer #3 (Remarks to the Author):
+
+This manuscript described an approach on dissecting extracellular and intracellular distribution of nanoparticles. The authors developed a pH/light dual-response monochromatic ratiometric-imaging nanoparticle (MRIN), which precisely quantified nanocarrier micro-distribution. Particularly, the MRIN exhibited a sharp pH response and high Cy5 signal activation ratio. The application demonstrated in the manuscript has relevance and potential high impact in the field of imaging and photodynamic therapy of tumors. Several revisions are suggested aiming to improve quality of the results and presentation.
+
+We appreciate the thorough and thoughtful comments by the reviewer. We provide a point-by-point response to the reviewer comments.
+
+1. According to the experimental procedure, the MRIN was formed by self-assembly of components with a fixed proportion, how to control such uniform size as shown in Figure 2b, and the author should provide a TEM of with high resolution.
+
+Re: Thanks for the reviewer’s positive comments on our nanoparticles. As the reviewer mentioned, the MRIN was a self-assembly of three components with a fixed proportion for PEG5k-b-P(DPA40-r-EPA40)-r-Cy5 (5%), PEG5k-b-P(DPA40-r-EPA40-r-Cy7.5) (45%), and PEG5k-b-P(DPA40-r-EPA40) (50%). The three components are from the same copolymer. Because of the high molecular weight (Mw) of ultra-pH-sensitive copolymer (~22.0 kDa), the conjugation of small molecules, such as Cy5 (Mw: 616) and Cy7.5 (Mw: 782) have negligible effect on the physicochemical properties of copolymer. Therefore, the MRIN can be prepared by a one-step self-assembly procedure. In addition, sonication dispersion method was applied to prepare MRIN, enabling the relatively uniform particle size. According to the reviewer’ advice, we have provided the TEM of MRIN with high resolution in Supplementary Figure 2e.
+
+![TEM images of MRIN at different pH conditions](page_393_1012_1002_312.png)
+
+Supplementary Figure 2e. The TEM images of MRIN with high resolution.
+
+2. The author chose RNP0%, RNP100% as positive controls. According to the design, RNP100% as an always-on probe has no quenching effect of Cy7.5 without pH responsive, why there are good targeted imaging
+results in Figure 3c.
+
+Re: We appreciate the insightful questions by the reviewer. The tumor targeting effect of RNP_{100\%} can be attribute to the Enhanced Permeability and Retention (EPR) effect of tumor. Because of the leaky tumor blood vessels and lack of lymphatic drainage, the nanoparticles accumulated at tumor sites can be higher than that in the adjacent normal tissues. As seen in Supplementary Figure 6a, the tumor accumulation of RNP_{100\%} increases along with the longer blood circulation time, leading to the enhanced imaging contrast with the surrounding normal tissues. However, because of the Always-ON design, the tumor-to-muscle ratio of RNP_{100\%} was significantly lower than MRIN that can achieve pH responsive Cy5 signal amplification (new Supplementary Figure 6c).
+
+Line 154-157: It's worth noting that although both RNP_{100\%} (Always-ON micelle) and MRIN exhibited good tumor targeting effect due to the enhanced permeability and retention (EPR) effect, MRIN achieved significantly higher tumor-to-normal tissue contrast due to the pH-responsive Cy5 signal amplification (Supplementary Fig. 6c).
+
+![In vivo fluorescence images of mice after treatment with different micelles.](page_232_682_1002_627.png)
+
+Supplementary Figure 6. In vivo fluorescence images of mice after treatment with different micelles. (a) In vivo fluorescence images of the bilateral 4T1 tumor-bearing mice with or without 808 nm irradiation on right tumors at 3, 6, 12, and 24 h post-injection of different micelles. (b) The quantified extracellular percentages of different micelles in vivo at 3, 6, 12, 24 h post injection from the results of Supplementary Fig. 6a (\( n = 4 \)). (c) The quantified Cy5 fluorescence ratio of tumor to adjacent normal tissues by the results of Supplementary Figure 6a (\( n = 4 \)).
+3. Does the principle total=intracellular + extracellular applicable to MRIN also apply to RNP_{0\%}, RNP_{100\%}? For RNP_{100\%}, There is no acid response-mediated fluorescence recovery, so it is not certain that exhibited fluorescence means intracellular; extracellular nanoparticles also exhibited fluorescence. Similarly, the RNP_{0\%} did not produce fluorescence, which does not mean that they were extracellular, the author needs to provide a reasonable explanation or correct the description in Figure 3b.
+
+Re: Thanks for the reviewer’s suggestion. We have added the related explanation in the revised manuscript. In our paper, we developed a pH/light dual-responsive monochromatic ratiometric imaging nanotechnology (MRIN) to dissect extracellular and intracellular distribution of nanoparticles in tumor tissues. In order to demonstrate the quantitative imaging feasibility of MRIN, RNP_{0\%} (Cy5-labeled pH-insensitive micelle) and RNP_{100\%} (Always-ON micelle) was established to simulate the artificial states of 0% and 100% endocytosis in vitro and in vivo. As the reviewer mentioned, it doesn’t mean they are true 0% and 100% endocytosis. Because that the Cy5 signal of RNP_{0\%} was completely ‘OFF’ whether cellular endocytosis or not due to its pH-insensitive nanostructure, so it could be used to simulate the artificial states of 0% endocytosis. And the Cy5 signal of RNP_{100\%} was completely ‘ON’ due to the Always-ON design, so it could be used to simulate the artificial states of 100% endocytosis.
+
+Line 114-116: These results demonstrated that RNP_{0\%} and RNP_{100\%} are suitable to simulate the artificial states of 0% and 100% endocytosis regardless of their real distribution in extracellular and intracellular compartments.
+
+The caption of Figure 3b: The images of RNP_{0\%} and RNP_{100\%} before 808 nm irradiation were served as the extrapolated states of 0% and 100% internalization of nanoparticles.
+
+4. Four kinds of particles, MRIN, RNP_{0\%}, RNP_{100\%}, and MRITN are used in the manuscript, and the self-assembly components include UPS, UPS-Cy5, UPS-Cy7.5, pH-insensitive polymer, pH-insensitive polymer-Cy5, pH-insensitive polymer-Cy7.5, UPS-Ce6. Although components and ratio were listed separately in the experimental steps, it is not very clearly stated in the text. The self-assembly composition and ratio of each particles may be listed in a table or in the corresponding figure.
+
+Re: Thanks for the reviewer’s good suggestion, we have listed the self-assembly composition and ratio of each particle in Supplementary table 1.
+
+Supplementary Table 1. The polymer composition and their ratios for each nanoparticle.
+
+<table>
+  <tr>
+    <th>Nanoparticle</th>
+    <th>Polymer 1</th>
+    <th>Polymer 2</th>
+    <th>Polymer 3</th>
+    <th>Ratio (%)</th>
+  </tr>
+  <tr>
+    <td>RNP_{0\%}</td>
+    <td>PEH-Cy5<sub>1</sub></td>
+    <td>PEH-Cy7.5<sub>3</sub></td>
+    <td>Blank PEH</td>
+    <td>5:45:50</td>
+  </tr>
+  <tr>
+    <td>MRIN</td>
+    <td>UPS-Cy5<sub>1</sub></td>
+    <td>UPS-Cy7.5<sub>3</sub></td>
+    <td>Blank UPS</td>
+    <td>5:45:50</td>
+  </tr>
+  <tr>
+    <td>RNP_{100\%}</td>
+    <td>UPS-Cy5<sub>1</sub></td>
+    <td>/</td>
+    <td>Blank UPS</td>
+    <td>5:95</td>
+  </tr>
+  <tr>
+    <td>MRITN</td>
+    <td>UPS-Ce6<sub>1</sub></td>
+    <td>UPS-Cy7.5<sub>3</sub></td>
+    <td>/</td>
+    <td>50:50</td>
+  </tr>
+</table>
+
+a UPS is the abbreviation of ultra-pH-sensitive PEG<sub>5k</sub>-b-P(DPA<sub>40</sub>-r-EPA<sub>40</sub>) copolymer.
+b PEH is the abbreviation of pH-insensitive PEG<sub>5k</sub>-b-PEH<sub>80</sub> copolymer.
+c The right subscript of the dye represents dye conjugated numbers.
+5. Why Cy7.5 also quenched Ce6? the author needs to provide FRET related explanation.
+
+Re: Thanks for the reviewer’s question. The overlap between the donor fluorescence emission spectra and the acceptor fluorescence excitation spectra is necessary for efficient FRET (Broussard JA, et al. Nat Protoc 2013, 8, 265-81). In our study, Ce6 is the donor fluorophore and Cy7.5 is applied as acceptor fluorophore. As seen in Supplementary Figure 11a, there is good overlap between the emission spectrum of Ce6 and the excitation spectrum of Cy7.5, enabling the FRET effect from Ce6 to Cy7.5. In addition, we also have verified the FRET signal of MRITN (UPS-Ce6/UPS-Cy7.5 hybrid micelle) and UPS-Cy7.5 micelles at 630 nm for Ce6 excitation (Supplementary Figure 11b). The result showed that UPS-Cy7.5 micelle had no emission peak at 825 nm with excitation at 630 nm, while MRITN has two emission peaks at 670 nm and 825 nm, respectively, indicating that Cy7.5 can absorb the energy of Ce6 emission to emit its own signal. Therefore, the above results proved that FRET effect can occur between Ce6 and Cy7.5. We included the results in Supplementary Figure 11.
+
+Line 218-219: Cy7.5 could quench the fluorescence and photosensitivity of Ce6 due to the FRET effect between them (Supplementary Fig. 11).
+
+![Two line graphs showing normalized fluorescence intensity versus wavelength for UPS-Cy7.5 and UPS-Ce6, and another graph comparing UPS-Cy7.5 and MRITN fluorescence.](page_420_670_600_300.png)
+
+Supplementary Figure 11. The FRET effect between Ce6 and Cy7.5.
+
+6. Regarding why PDT with intracellular and extracellular is better, the author needs to provide a mechanism explanation or further pathway data to support Figure 5.
+
+Re: Thanks for the reviewer’s suggestion. As seen in new Supplementary Figure 14, we found that MRITN bound to the cell membrane at physiological pH, and the cell binding ability of MRITN was significantly enhanced in a slightly acidic environment such as tumor microenvironment. Many studies have revealed that cell membrane-targeted PDT can lead to membrane dysfunction and disintegration only by a mild treatment (Liu L-H, et al, Adv Funct Mater 2017, 27, 1700220; Kim J, et al, J Control Release 2014, 191, 98-104). We also have proved that increased fluorescence of Ce6 and SOG was observed at cell membrane after photobleaching of Cy7.5 in Figure 5a. Therefore, the extracellular PDT relies on the damage to cell membrane for our in vitro cellular studies. While for the in vivo anti-tumor study, the extracellular PDT results from both the cell membrane-based PDT and destruction of extracellular matrix (ECM). What’s more, the PDT dose (including photosensitizer dose and laser power) is one of the determinants for the anti-tumor efficacy of PDT. Currently, most activatable PDT rely on the intracellular exposure to exert lethal tumor damage, while a majority of nanophotosensitizers distributed in the extracellular space of the tumor site are useless (Zhou S, et al, Angew Chem Int Ed Engl 2020, 59, 23198-23205; Lovell JF, et al, Chem Rev 2010, 110, 2839-2857). Based on MRITN technology, we can light up the extracellular nanophotosensitizer to specifically increase the efficient photosensitizer dose in tumor, leading to significantly better tumor inhibition than intracellular PDT.
+Line 228-231: Damage to the cell membranes plays an important contribution to the extracellular PDT. We found that MRITN could bind to the cell membrane at physiological pH, and the cell binding ability of MRITN was significantly enhanced in a slightly acidic environment such as tumour microenvironment (Supplementary Fig. 14)
+
+a
+
+![Fluorescence microscopy images showing cell membrane binding of MRITN at different pH values](page_256_320_1047_384.png)
+
+b
+
+![Bar graph showing fluorescence intensity (FI) at different pH values](page_256_768_496_384.png)
+
+Supplementary Figure 14. The cell membrane binding ability of MRITN at different pH values. The MRITN was activated by 808 nm irradiation before cell treatment.
+REVIEWERS' COMMENTS
+
+Reviewer #2 (Remarks to the Author):
+
+I suggest to accepting the revised manuscript.
+Point-by-point response to reviewers
+
+We would like to thank the reviewers for the insightful and constructive comments! Below is a list of the point-by-point responses to the reviewer comments.
+
+Reviewer #2 (Remarks to the Author):
+
+    I suggest to accepting the revised manuscript.
+
+Re: We thank the reviewer for the very supportive comments.

0b92679e0a33c91b3ee101070f503fa196a94bd7dd0248fd4430201cd91d30a9/peer_review/peer_review.md

@@ -0,0 +1,119 @@
+Peer Review File
+
+Machine learning-enabled constrained multi-objective design of architected materials
+
+Open Access This file is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. In the cases where the authors are anonymous, such as is the case for the reports of anonymous peer reviewers, author attribution should be to 'Anonymous Referee' followed by a clear attribution to the source work. The images or other third party material in this file are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.
+Editorial Note: This manuscript has been previously reviewed at another journal that is not operating a transparent peer review scheme. This document only contains reviewer comments and rebuttal letters for versions considered at Nature Communications.
+
+REVIEWER COMMENTS
+
+Reviewer #5 (Remarks to the Author):
+
+1. The paper reports an active machine learning (AML) approach to understand the mechanism of the arrangement and enables the fast design to meet the specific performance requirements, which is kind similar to the paper by Li et al. (https://arxiv.org/abs/2302.01078). It means the framework is not completely new to the reviewer. Multiobjective Bayesian optimization (one kind of active learning approach) has been widely used, for example, in mechanical property optimization through formulation (Erps, et al 2021). The reviewer believes the above arxiv paper is closely relevant and should be cited.
+2. The reviewer is not sure how are the 95 initial data points selected. Why 95?
+3. The authors mentioned that the gyroid structures are generated in Matlab, and converted in to stl format, and then drew the mesh through Hypermesh, and input it to Abaqus in inp format. This process sounds not very automated. Can you integrate these separate modules to make the pipeline automated?
+4. As the reviewer understands the paper wants to claim multi-objective design and optimization, however, Fig. 2C is more like a single-objective optimization. It might be better to show how multi-objective performance evolves with different iterations.
+5. The insets in Fig. 3B are not very clear, especially the curve.
+6. One question raised by reviewer #4 regarding ground truth is not completely addressed. As the FEM simulation couldn’t guarantee the experimental measurement, it would be necessary to validate the so-called ground truth (FEM simulation). If the simulation and experimental measurement do not match with each other, then, the authors might have a risk of missing excellent candidates. In reviewer’s opinion, using simulation as the ground truth should be very careful, especially when deal with 3D printing samples.
+
+References
+Erps, T., Foshey, M., Luković, M.K., Shou, W., Goetzke, H.H., Dietsch, H., Stoll, K., von Vacano, B. and Matusik, W., 2021. Accelerated discovery of 3D printing materials using data-driven multiobjective optimization. Science Advances, 7(42), p.eabf7435.
+Response to the Reviewers' Report
+
+We would like to express our sincere appreciation to the reviewers for the insightful suggestions and comments on our paper. Our response is structured in the following manner. The original comments from the reviewers or quotes from the original manuscript are copied below in black and italic font. Each comment is followed by a detailed response in blue font, and the corresponding manuscript modifications are indicated in red font. In the revised manuscript, the amended parts are highlighted in red font.
+
+Reviewer #5:
+
+1. The paper reports an active machine learning (AML) approach to understand the mechanism of the arrangement and enables the fast design to meet the specific performance requirements, which is kind similar to the paper by Li et al. (https://arxiv.org/abs/2302.01078). It means the framework is not completely new to the reviewer. Multiobjective Bayesian optimization (one kind of active learning approach) has been widely used, for example, in mechanical property optimization through formulation (Erps, et al 2021). The reviewer believes the above arxiv paper is closely relevant and should be cited.
+
+Response:
+
+We thank the reviewer for the comment. We wish to clarify that the paper by Li et al. was published in February 2023. However, the preprint of our study was, in fact, made available earlier on Research Square in 2022 (https://doi.org/10.21203/rs.3.rs-2082876/v1).
+
+The mentioned references have now been included in the manuscript. Furthermore, we have conducted exhaustive Bayesian optimization on this task. The related setup and results are available in the supplementary material. Bayesian optimization did not yield favorable results, likely due to the high dimensionality of the input. The authors believe that the novelty of this manuscript is not about understanding the mechanism of the arrangement and enabling the fast design to meet the specific performance requirements but mainly lies in the following points: Our GAD-MALL method showed excellent performance at solving high-dimensional multi-objective optimization problems, which is a subject full of challenges and innovations. We also showed that GAD-MALL outperforms other current state-of-the-art approaches by a large margin.
+Modification:
+
+Two references have been added to the manuscript:
+
+31. Li, B. et al. Computational Discovery of Microstructured Composites with Optimal Strength-Toughness Trade-Offs. arXiv preprint arXiv:2302.01078 (2023).
+32. Erps, T. et al. Accelerated discovery of 3D printing materials using data-driven multiobjective optimization. Sci Adv 7, eabf7435 (2021).
+
+2. The reviewer is not sure how are the 95 initial data points selected. Why 95?
+
+Response:
+
+We appreciate the reviewer's comment. To clarify, the initial dataset comprised a random selection of 100 data points. However, five of these points encountered some errors during the mesh generation process in Hypermesh or during the simulation stage. As a result, the initial round effectively consisted of 95 data points, while the model already showed good performance (\( R^2 \) ratio ~ 0.9 and mean absolute error=3.1 on the test set).
+
+Modification:
+
+We added the following lines to the manuscript at line 130:
+
+'since the predictive model based on this dataset already showed good performance on the testing dataset (\( R^2 \) ratio ~ 0.9).'
+
+3. The authors mentioned that the gyroid structures are generated in Matlab, and converted in to sil format, and then drew the mesh through Hypermesh, and input it to Abaqus in inp format. This process sounds not very automated. Can you integrate these separate modules to make the pipeline automated?
+
+Response:
+
+We appreciate the reviewer's comment. Since our initial submission of the manuscript, we have pursued our goal of automating the pipeline and have successfully achieved this. The associated code can be accessed at https://github.com/Bop2000/GAD-MALL.
+4. As the reviewer understands the paper wants to claim multi-objective design and optimization, however, Fig. 2C is more like a single-objective optimization. It might be better to show how multi-objective performance evolves with different iterations.
+
+Response:
+
+We thank the reviewer for the comment. The figure was now updated as suggested.
+
+![Baseline comparison of GAD-MALL with random search and Bayesian optimization. The red line represents the increase in yield strength, and the blue line represents the corresponding elastic modulus.](page_355_613_879_377.png)
+
+Fig. 2C. Baseline comparison of GAD-MALL with random search and Bayesian optimization. The red line represents the increase in yield strength, and the blue line represents the corresponding elastic modulus.
+
+Modification:
+
+Fig. 2C has been updated in the manuscript.
+
+5. The insets in Fig. 3B are not very clear, especially the curve.
+
+Response:
+
+We thank the reviewer for the comment. We redrew Fig. 3B with improved resolution and quality.
+Fig. 3B. The distribution of elastic modulus (E) and yield strength (Y) derived from the Finite Element Method (FEM) simulation results. The inset reflects the maximum yield strength value amongst the structures that fulfill the required elastic modulus criteria, drawn from the 20 selected structures in each iteration.
+
+Modification:
+
+Fig. 3B has been updated in the manuscript.
+
+6. One question raised by reviewer #4 regarding ground truth is not completely addressed. As the FEM simulation couldn't guarantee the experimental measurement, it would be necessary to validate the so-called ground truth (FEM simulation). If the simulation and experimental measurement do not match with each other, then, the authors might have a risk of missing excellent candidates. In reviewer's opinion, using simulation as the ground truth should be very careful, especially when deal with 3D printing samples
+
+Response:
+
+We appreciate the reviewer's comments. We definitely agree with you and reviewer #4's remarks on potential problems of using FEM simulation as the database. Indeed, it should be very careful to use simulation results as the ground truth, especially regarding 3D printed samples, since the repeatability and credibility may be in question.
+
+In response to these concerns, we have conducted comprehensive simulation and
+experimental studies. These can be found in the revised manuscript (lines 376 - 378 and Extended Data Fig. 5 C-G):
+
+'For the labeled dataset, the labels (the elastic modulus (E) and yield strength (Y) of the corresponding scaffolds are computed by the FEM, whose accuracy is verified through careful calibration with experimental data. The deviations between the experiment and simulation are confirmed to be less than 10%.'
+
+![Stress-strain curves for various scaffold geometries, comparing experimental and simulation results](page_246_393_1097_410.png)
+
+Extended Data Fig. 5 (C-H) simulation calibration. Extended Data Fig. 5. (C to H) The simulation calibration (from the manuscript). The FEM simulation agrees with experimental observations. Three replicates were tested to ensure reproducibility. The error of the E and Y between the FEM simulation and experimental results was less than 10%. (C to E) refer to 3 Ti scaffolds with random shapes, and (F to H) refer to 3 Zn scaffolds with random shapes. (C to H) All stress-strain curves are adjusted in the x-axis direction to make them overlap. ABAQUS/Explicit software was used for compression simulation.
+
+And lines 607 - 608:
+
+'Three replicates were printed and tested to ensure reproducibility. The error of the E and Y between the FEM simulation and experimental results was less than 10%. (Extended Data Fig. 5 C-G)'
+
+Modification:
+
+To make this important statement more visible to the audience, we added the following lines to the manuscript at line 83:
+'An important prerequisite is that the simulated properties agree with experimental observation within an acceptable error range. Therefore, several replicates (to ensure reproducibility) of candidate materials were manufactured and tested, by which the experimental measurements (E and Y) were used to calibrate the FEM parameters such that the error between the simulation and experimental results was less than 10% (see extended data Fig. 5 C-G).'
+REVIEWERS' COMMENTS
+
+Reviewer #5 (Remarks to the Author):
+
+The authors have carefully replied and addressed all the reviewers' concerns. It is believed that this manuscript can be considered for acceptance.
+Response to the Reviewers' Report
+
+Reviewer #5 (Remarks to the Author):
+
+The authors have carefully replied and addressed all the reviewers' concerns. It is believed that this manuscript can be considered for acceptance.
+
+Response:
+
+We would like to cordially thank the reviewer for the valuable suggestions and comments on our paper.

0b92679e0a33c91b3ee101070f503fa196a94bd7dd0248fd4430201cd91d30a9/preprint/preprint.md

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+Machine learning-enabled design of architected materials
+
+Bo Peng
+Tsinghua university    https://orcid.org/0000-0003-0416-9076
+Ye Wei (yeweiastronomer@gmail.com)
+Tsinghua university    https://orcid.org/0000-0003-1965-2298
+Yu Qin
+Peking University
+Jiabao Dai
+Tsinghua university
+Yue Li
+Max Planck Institute for Iron Research    https://orcid.org/0000-0003-3377-6676
+Aobo Liu
+Tsinghua university
+Yun Tian
+Peking University Third Hospital
+Liuliu Han
+Max Planck Institute for Iron Research
+Yufeng Zheng
+Peking University
+Peng Wen
+Tsinghua University
+
+Article
+
+Keywords:
+
+Posted Date: November 2nd, 2022
+
+DOI: https://doi.org/10.21203/rs.3.rs-2082876/v1
+
+License: This work is licensed under a Creative Commons Attribution 4.0 International License.
+Read Full License
+
+Additional Declarations: There is NO Competing Interest.
+Version of Record: A version of this preprint was published at Nature Communications on October 19th, 2023. See the published version at https://doi.org/10.1038/s41467-023-42415-y.
+Machine learning-enabled design of architected materials
+
+Bo Peng1,4,7, Ye Wei2,7*, Yu Qin6,7*, Jiabao Dai1,4, Yue Li3, Aobo Liu1,4, Yun Tian5, Liuliu Han3, Yufeng Zheng6, Peng Wen1,4*
+1State Key Laboratory of Tribology in Advanced Equipment, Tsinghua University, Beijing, China
+2Institute for Interdisciplinary Information Science, Tsinghua University, Beijing, China
+3Max-Planck-Institut für Eisenforschung, Düsseldorf, Germany
+4Department of Mechanical Engineering, Tsinghua University, Beijing, China
+5Department of Orthopaedics, Peking University Third Hospital, Beijing, China
+6Department of Materials Science and Engineering, Peking University, Beijing, China
+7These authors contributed equally
+*To whom correspondence should be addressed: E-mail: weiye@mail.tsinghua.edu.cn qinyu95@126.com, wenpeng@tsinghua.edu.cn
+
+Architected materials that consist of multiple subelements arranged in particular orders can demonstrate a much broader range of properties than their constituent materials. However, the rational design of these materials generally relies on experts’ prior knowledge and requires painstaking effort. Here, we present a data-efficient method for the multi-property optimization of 3D-printed architected materials utilizing a machine learning (ML) cycle consisting of 3D neural networks and the finite element method (FEM). Specifically, we applied our method to orthopedic implant design. Compared to expert designs, our experience-free method designed microscale heterogeneous architectures with biocompatible elastic modulus and higher strength. Furthermore, inspired by the knowledge learned by the neural networks, we devel-
+oped a machine-human synergy, adapting the ML-designed architecture to fix a macroscale, irregularly shaped animal bone defect. Such adaptation exhibits **20% higher experimental load-bearing capacity than the expert design**. Thus, our method opens a new paradigm for the fast and intelligent design of architected materials with tailored mechanical, physical, and chemical properties.
+
+**Introduction**
+
+Architected materials are one of the most widely adopted engineering materials. Due to their excellent mechanical performance and adaptable properties, architected materials are very popular in many fields, such as those of light-weight structures (*1–7*), acoustics (*8*), battery electrodes (*9*), electromagnetics (*10–12*), and tissue engineering (*13–17*). Moreover, recent progress in 3D printing has further enabled the customized and inexpensive fabrication of complex material geometries.
+
+Despite the broad applicability and immense potential of architected materials, designing them is particularly difficult. The traditional design method generally relies on numerical simulation, theoretical analysis, and topology optimization. These undertakings are usually exhausting and time-consuming, and the performance of resultant designs highly depends on the designer’s professional knowledge and their initial guesses (*18–21*). Recently, machine learning (ML) has merged as a promising technique to circumvent this problem and find the optimal solution without any prior knowledge requirements (*22–25*). However, the proposed ML methods require massive amounts of simulation data and mainly aim to solve 2D-structure-related problems. Efforts toward solving 3D real-world problems are often obfuscated by the lack of credible data sources, the enormity of design space and multidimensional complex patterns. Moreover, real-world design problems usually require multiobjective property optimization under possible external constraints, yet the current ML methods mostly attempt to solve
+unconstrained single-objective optimization problems. Therefore, we propose an ML approach for data-efficient, multiobjective architected material design. As demonstrated in Fig. 1(A to D), our approach consists of three main parts: 1) generative architecture design (GAD). In this step, GAD leverages the encoder-decoder neural network (autoencoder) to generate architecture sets with unknown properties. Until recently, experimental discovery of architected materials has relied on simple surrogate models and Bayesian optimization, which are limited to low-dimensional data, thus showing property improvements only after many iterations (26). Unlike the Bayesian methods, the autoencoder learns an effective representation of the high-dimensional data in an unsupervised manner, which converts the exploration in a high-dimensional design space into a lower one. This method has been proven to be a revolutionary technique in materials discovery (27, 28). However, to the best of our knowledge, this is the first time that a 3D convolutional autoencoder(3D-CAE) has been applied to 3D structure generation with high dimensionality (for details see Section S2). 2) Multi-objective Active Learning Loop (MALL). MALL evaluates the generated dataset and searches for high-performance architecture by recursively querying the finite element method (FEM). Active learning describes a specialized ML algorithm that interactively queries an information source such that the algorithm identifies high-value data with fewer labeled data than typical ML (29, 30). Such data efficiency is highly desirable since constructing a large dataset with known properties is very difficult both computationally and experimentally. 3) 3D printing and testing. Finally, we fabricate the ML-designed architected materials via a specialized 3D printing technique (laser powder bed fusion) and experimentally verify the corresponding mechanical properties. We call the overall method 'GAD-MALL'.
+Fig. 1. An overview of the proposed workflow (GAD-MALL). (A) The neural network proposes candidates with unknown properties. (B) The ML algorithm interactively queries the FEM to propose new designs. (C) The 3D printing technique fabricates the proposed architectural design. (D) GAD-MALL explores the design landscape of architected materials and discovers various high-performance architected materials.
+
+Results
+
+Multiobjective active learning algorithm
+
+We applied the GAD-MALL approach to a multiproperty optimization problem with clinical importance - bone grafting implants. Bone is a typical architected material primarily consisting of cortical and cancellous parts, with the elastic modulus (E) ranging from 0.03 to 30 GPa depending on the bone mineral density and varying according to age, sex, and race (31). Although bone can repair itself, a bone defect of a critical size necessitates a grafting implant to support the load and induce bone growth. Metals are the first choice for bone implant materials due to their excellent mechanical properties. However, the E of the existing metal bulk materials is much greater than that of the bones (i.e., titanium – 100 GPa; iron - 200 GPa, etc.), which results in the stress shielding effect and impedes the recovery of the bone (32). One effective solution is introducing a 3D-printed scaffold architecture to lower the E. The geometrical shape and mechanical properties of the scaffold should be comparable to those of the individual defective bone to provide reliable structural support and smooth stress conduction. Fig. 2(A)
+demonstrates a typical mechanical response of the scaffold. The slope of the linear section of the curve indicates E, which measures a material’s ability to resist external stress before being deformed permanently, and the yield point with 0.2% strain represents the yield strength (Y), which quantifies the maximum resistance before the onset of nonreversible deformation. Overall, the design tasks are multiobjective: First, the E of the replacement scaffold must match that of the bone. Second, The Y must be as high as possible to sustain bone movement. In addition, the overall weight of the scaffold should not go beyond a certain threshold since a minimum usage is always required considering long-term biosafety.
+
+A cubic scaffold and its 3D-printed experimental counterpart are shown in inlets of Fig. 2(A). To balance complexity and computing efficiency, we adopted the \(3 \times 3 \times 3\) cubic arrangement of the gyroid unit for the optimization task(see Methods for the structure generation). The gyroid geometry is categorized in the triply periodic minimal surfaces (TPMS) family - it is an ideal porous structure for bone scaffolds due to its high interconnectivity, smooth surface, and mathematically adjustable geometrical attributes (\(33, 34\)). Instead of a uniform-sized array of periodic subunits (the expert design), the ML design introduced heterogeneity: GAD-MALL adjusts the size of the gyroid unit (porosity) within the scaffold, resulting in a geometrical alteration that modulates the overall mechanical properties.
+
+Fig. 2(B) shows the models of the 3D convolutional neural network (3D-CNN) for the E and Y prediction. The 3D-CNN was designated for volumetric data representation learning (\(35, 36\)). It included three main components: input, convolution, and output layers. At the input layer, the scaffold structure was voxelized into \(60 * 60 * 60\) pixels. A pixel can be in either the solid (1) or void (0) phase in the scaffold. The convolution layers consisted of a series of 3D convolution kernels that extracted high-level information about the scaffold, and the output layer provided the final prediction. Finally, a training dataset was prepared using the protocol described in the Methods.
+Fig. 2. The workflow of multiobjective active learning. (A) The task was to design scaffolds with a better mechanical response - fixed E and maximized Y. (B) The 3D-CNN models for predicting E and Y. (C) The generative model for targeted scaffold generation. The encoder \( q_\phi \) (zlx) with parameters \( \phi \) took the scaffold porosity matrix as input and the decoder \( p_\theta \) (xlz) with parameters \( \theta \) could act as a generator for proposing new scaffolds based on the learned latent z representation. (D) The MALL for the high-performance scaffold discovery. First, the sampling algorithm sampled new data points from the latent z representation. Second, the decoder reconstructed the corresponding scaffolds so that the 3D-CNNs could infer their mechanical properties. Third, the most suitable candidates were selected based on the predicted E and Y. Finally, the strain-stress curves of the selected scaffolds were calculated by the FEM. New data were either fed back to the dataset or 3D-printed for further experiments.
+Fig. 2(C) illustrates the 3D-CAE with a typical two-neural network model, an encoder and a decoder. Notably, the original 60 * 60 * 60 scaffold structure was not used because the decoder could not reliably recover the original gyroid geometry due to the nonzero reconstruction error. However, thanks to the high mathematical controllability of gyroid geometry, we circumvented this problem by adopting the porosity matrix, a 3D matrix representation (3 * 3 * 3) that uniquely determines the overall geometry through Gyroid equations (see Methods). It measures the relative density (positive scalars) rather than the actual shape of the gyroid subunits, thereby allowing nonzero reconstruction errors. The encoder \( q_{\phi}(z|x) \) with parameters \( \phi \) compressed the porosity matrix into a hidden feature representation (8-dimension) using the neural encoder. Then the decoder \( q_{\varphi}(x|z) \) with parameters \( \varphi \) reconstructed the output from the 8-dimension hidden features. A lower-dimension (e.g., 4-dimension) latent space was shown to suffer from high reconstruction error, while a higher-dimension (e.g., 16-dimension) doubled the search space without a sufficient increase in reconstruction accuracy. Ultimately, 8-dimensional represented a balance between loss and efficiency (Supplementary Information S1).
+
+Fig. 2(D) shows the primary steps of the MALL workflow, which comprised three steps. First, the scaffold generation was formulated as a process of sampling and reconstruction from the latent representation \( z \). The sampling process required the latent representation to be modeled as a continuous probabilistic distribution (Supplementary Information S1). Secondly, the decoder \( q_{\phi}(x|z) \) reconstructed the porosity matrices from the sampled latent points, which were then converted to their original shapes in Cartesian space. The scaffold selection method was a variant of the epsilon-greedy search: in each sampling iteration, we sampled 2000 data points and selected those whose 3D-CNN-predicted E met the target and whose 3D-CNN-predicted Y exceeded the best data point in the current dataset, with a chance of epsilon (5%) chances that the lower ones were chosen. The selected data points would still be rejected if their weights were 15% higher than preset criteria. Such a search method generally had a higher success
+rate than the Edisonian approach, which hinged on a trial-and-error search (37). Last, the FEM calculated the E and Y of the queried scaffolds, and the results would augment the dataset, from which the 3D-CNNs were re-trained for the following active learning round. The workflow stopped when all the preset criteria were met.
+
+Applications to orthopedic implants
+
+The properties of the architected materials are determined by both the scaffold architecture and the constituent materials. For orthopedic implants, the orthopedic materials Ti6Al4V (Ti) and pure zinc (Zn) were used as the constituent materials. Ti alloy is bioinert in human bodies and has been the de facto choice for 3D-printed orthopedic implants, achieving successful clinical application to repairing bone defects. Biodegradable Zn provides an alternative option to bioinert materials and is regarded as promising for addressing the clinical concerns associated with permanent existence and secondary surgery (38). Such features are especially desirable for bone regeneration. As both materials are worthy of investigation, to demonstrate the effectiveness and general applicability of the GAD-MALL framework, we designed two optimization tasks for both constituent materials and applied the learned design principle to the real bone replacement architecture. Specifically, the Ti alloy scaffolds were assigned a high E while the pure Zn scaffolds had a low E, indicating different clinical needs based on the constituent materials. In addition, two tasks were given different initial data distributions to demonstrate that GAD-MALL can work under different initial conditions. Notably, all tasks were completed in one week with the current hardware setup, as tasks in the clinical scene are usually time-constrained. In the following section, we begin with the Ti cubic scaffolds.
+A data-efficient route toward high-performance structure
+
+To mimic the mechanical behavior of trabecular and compact bones, the task was to design high-Y scaffolds with E = 2500 MPa and 5000 MPa (E2500 and E5000). The expert-designed uniform scaffolds at E = 2500 MPa and 5000 MPa set the 'golden criteria' for the mechanical performance of the scaffolds. GAD-MALL stopped if the Y of the designed scaffolds significantly surpassed the golden criteria (termed the 'treasure' scaffold) or the learning process showed no further progress. The initially labeled dataset was composed of merely 75 data points (the simulation took ca. 7 days, hardware specified in Methods). Fig. 3B shows that the scaffolds had been precisely manufactured - the cross-sections of the microcomputed tomography (Micro-CT) of the scaffolds largely overlapped (92.2%) with that of the designs. Fig. 3(A and C) demonstrates the good performance of 3D-CNNs on the test dataset (uniformly sampled from the labeled dataset) in the 1st round and last round, in which both 3D-CNNs demonstrate high accuracy (\( R^2 \) ratio > 0.92). A more detailed performance evaluation can be found in Supplementary Information S1.
+
+Fig. 3(E) shows the overall data distribution in terms of E and Y with the treasure scaffolds indicated by blue stars. Each active learning iteration is characterized by colored eclipses. Fig. 3(D and F) demonstrates two distinct exploration paths for two different tasks. The E2500 exploration path shows a steady upward trend, and GAD-MALL quickly discovered the treasure scaffolds at the 3rd and 5th rounds with more than a 30% increase in Y. However, the E5000 task was more complicated - the learning process experienced a downhill before it recovered and found the treasure scaffolds. Specifically, the batches from 1st to 3rd round either fell out of the target E region or had inferior Y values. The 4th-round batch finally hit the target of E; albeit Y was not notably better than that of the expert designs. Finally, the treasure scaffolds were discovered on the 5 and 6th rounds. This oscillatory trend is likely due to the sparsity of data within this range (with only two initial data points available). The computed mechanical
+properties of the resultant designs are tabulated in Supplementary Information S4.
+
+The experiments confirmed the discovery - the ML-designed scaffolds (A1-A4) showed better performance than the expert-designed scaffolds (H1 and H2, Fig.3(G)). For example, the experimental strain-stress curves of the A1 and H1 scaffold are also displayed in the inset (full detail in Supplementary Information S4). To understand the ML design, we further analyzed the ML-designed scaffold by extracting the corresponding regression activation map (RAM) and performing FEM mechanical analysis. As an illustrative example, we applied the RAM to the Y-predicting 3D-CNN to reveal the driving mechanism behind the high Y of the A1 scaffold. RAM is a variant of a classification activation map, that extracts the last convolutional layer to visualize the discriminative regions used by a 3D-CNN to predict the output (39). In this case, the RAM highlights the scaffold’s spatial characteristics that correlate to its mechanical strength, identifying the regions that contribute to the enhancement of strength. Fig. 3(H) demonstrates the A1 scaffold geometrical structure, the corresponding porosity matrix and the RAM. The RAM implies that the ‘attention’ distribution extracted from the 3D-CNN resembled a heterogeneous ’face-centered’ lattice. Indeed, a closer look at the A1 scaffold revealed that the gyroid units at each face center of the scaffold show a minimal porosity (0.3). This observation indicates that instead of uniformity, a heterogeneous scaffold with more materials distributed at the face centers could significantly enhance the strength. Moreover, from a macroscopic point of view, the strength of a typical porous structure can be approximated by the Gibson-Ashby equation (40):
+
+\[
+Y = C(1 - p)^{\alpha} Y_0
+\]
+
+where \( Y_0 \) stands for the strength of the constituent material, \( C \) represents a geometry-related parameter, \( p \) is the porosity of the unit, and the exponent \( \alpha \) relates to the deformation behavior of the structure. According to the FEM calculated data in Table S4, we fitted the curve of strength Y as a function of \( p \) for ML and expert-designed scaffolds and found: \( a_{ML} = 2.11,\ a_{ED} = 1.86,\ )
+\( C_{ML} = 0.84 \) and \( C_{ED} = 0.64 \), in which ED stands for expert design. The ML-designed scaffold had a larger \( a \) and \( C \) than the expert design. Generally, increasing the mechanical anisotropy of a porous structure leads to an increase in the exponential factor \( a \); while an increase in parameter C can be found in the material distribution in favor of the load direction (41).
+
+Microscopically, FEM analysis confirmed the above observation. Fig. 3(I) shows the distribution of von Mises stress and hydrostatic pressure of the A1 and H1 scaffolds. Compared with the H1 scaffold, the A1 scaffold endures a much weaker effect of stress concentration; moreover, more struts of the A1 scaffolds are compressed rather than stretched. The ML model preferentially places more materials on the face center of the scaffolds, which optimizes the stress distribution and improves the structural strength with increasing limited mass. Hence, GAD-MALL was able to find the optimal architectures by efficiently learning from a few initial data points.
+Fig. 3. Data-efficient learning of high-performance scaffolds. (A and C) The regression plots (1st and last rounds of active learning) of the 3D-CNNs for E and Y. Both 3D-CNNs demonstrate excellent accuracy on the testing set, showing low mean absolute error (MAE) and high \( R^2 \) ratio. (B) Micro-CT shows that the designated scaffolds were accurately manufactured. (D to F) The overall data distribution in terms of the E-Y plot. The colored eclipses indicate the area covered by 6 rounds of active learning data, and the learning paths are marked by black arrows. (G) Comparison of the experimental E and Y between ML-designed (A1, A2 for E2500 and A3, A4 for E5000) and expert-designed (H1 for E2500, H2 for E5000) scaffolds. The Y of the ML-designed scaffolds was obviously higher than that of the expert designs. (H) The upper figures show the mathematical model of the A1 scaffold and its porosity matrix. The lower figures contain the 3D view and three cross-section views of the RAM. The RAM reveals a 'face-centered' lattice in the A1 scaffold, implying its prominent role in enhancing the Y. This face-centered lattice is displayed in the upper right part of the figure. (I) Numerical compression analysis. Here we show the y-z cross-sections of A1 and H1 scaffolds in terms of von Mises stress and hydrostatic pressure under 10% deformation.
+Learning without prior data at target range
+
+To demonstrate the robustness of the GAD-MALL approach, we designed a learning task by which GAD-MALL found the appropriate scaffolds ’from scratch’ - the initial Zn dataset did not contain any prior data points in the target range by design. The task of this section was to design high-Y scaffolds at E = 500 MPa and 1000 MPa (E500 and E1000) targeting to replacement of cancellous bone. Again, the expert-designed scaffolds at E = 500 MPa and 1000 MPa set the ’golden criteria’.
+
+Fig. 4(A to C) illustrate the E-Y distribution of the initial data (marked in gray) and the results from each active learning round characterized by colored eclipses. Fig. 4(B) demonstrates that the GAD-MALL exploration paths of the missing data were complicated, exhibiting back-and-forth trends. For the E500 task, the E distribution of the 1st round shows a significant standard deviation. It is noteworthy that some scaffolds from the 1st round had already reached the target E \( \approx 500 \) MPa. The 2nd round shows improvement - the overall standard deviation was significantly reduced (from 52 to 19 MPa). While all scaffolds’ E located at approximately 500 MPa, the Y values were still 30% less than the golden criteria. In the following rounds, the exploration path reached a plateau, and the selected candidates were slightly better than the golden criteria (14.8 MPa). The E500 task was terminated after the 5th round since no further progress was observed (see inset). The detailed results of each learning round are described in Supplementary Information S1.
+
+On the other hand, GAD-MALL excelled at the E1000 tasks, outperforming the golden criteria by a large margin. More specifically, the 1st round already showed promising results, in which all scaffolds exhibited the targeted E, although with slightly worse Y (\( \approx 10\% \)). The subsequent round witnessed a significant decrease in porosity (Supplementary Information S1), which in turn remarkably enhanced Y. However, the reduced porosity resulted in another problem - the E increased to 1200 ~ 1400 MPa. GAD-MALL incorporated this knowledge into the
+database in the subsequent learning process. Eventually, the average porosity increased, and the treasure scaffolds were discovered in the 3 and 4th rounds. The entire learning process took approximately 9 days, and the mechanical properties of the resultant designs are tabulated in Supplementary Information S4.
+
+Fig. 4(D) illustrates the model and micro-CT of an exemplary ML-designed scaffold (more ML designs see Supplementary Information S4). From the cross-section view, the model and manufactured sample were shown to agree with each other. The ML-designed scaffolds were manufactured, and their mechanical properties were measured experimentally (Fig. 4(E)). The ML design had a significant performance advantage over the expert design, whose Y (26.4 ± 0.7 MPa) exceeded the golden criteria (21.7 ± 1.8 MPa) by a large margin of 21.6%, with a slightly lower porosity (full detail in Supplementary Information S4). As the E and Y of the bulk Zn were less than those of the Ti alloy, the Zn scaffold still had a lower porosity even though the target E was only 1000 MPa. Similar to the Ti scaffold, the FEM analysis in Fig. 4(F) shows that the low-porosity face-centered units in the ML-designed scaffold had higher stress concentrations, leading to enhanced strength. Since the face-centered and the central unit of the Zn scaffold had reached the lower limit (porosity = 0.2) and the excess weight was allocated to the central and the ridge center unit of the cubic scaffold, the E of the scaffold did not hit the targeted E range (E = 1000 ± 100 MPa). Thus, the central and ridge-center units promoted E to the target range, without decreasing Y.
+
+In this task, we showcased that GAD-MALL was able to find the optimal architecture even when the initial data distribution and the constituent material are considerably different from the previous section. Such robustness is highly desirable since clinical situations can be variable-the patient data (target material and mechanical range) are often unknown beforehand and the initial data can have various distributions.
+Fig. 4. Learning without prior data at the target range. (A to C) The E-Y distribution. The colored eclipses indicate the area covered by 5 rounds of active learning data and black arrows specify the learning paths. (D) Micro-CT shows that the designated Zn scaffolds were manufactured with good precision. (E) The experimental strain-stress curves of the ML and expert-designed scaffolds. The ML design yielded a 20% increase in Y. (F) The porosity of the ML-designed scaffold reached the lower limit (0.2) at the face centers and the center of the scaffold. Similar to the ML-designed Ti scaffold, the compression analysis shows that the low-porosity units of the ML-designed Zn scaffold have higher stress concentrations.
+
+ML-inspired anatomic bone implants
+
+Most real-world bone implants require scaffolds in anatomical shapes that fit to the defective bone. Fig. 5(A and B) shows a large, irregular-shaped bone defect in a New Zealand rabbit model animal model - a defect of critical size (30 mm) occurred in the middle part of the tibia. Fig. 5(C) shows the 3D shape of the tibia, which was acquired through micro-CT scanning. It is difficult and time-consuming to find the optimal scaffold architecture to fit the shape, whether by experimental or by numerical trials, since there are many possible choices. Here, we demonstrate how a machine-learned design principle can be readily adapted to a clinical scene through
+a facile machine-human design workflow.
+
+Concretely, to use the ML-designed cubic scaffold for a larger implant for large, irregularly shaped bone defect fixation, our workflow constituted the following two steps: 1) Using the ML-designed cubic scaffold as the basic unit, we manually created a cuboid of \(3 * 3 * 9\) units with width, length, and height of 18 mm, 18 mm, and 54 mm respectively. 2) Subsequently, we caved out an irregularly shaped scaffold from the interior of the cuboid that matched the bone shape (shown in Fig. 5(D)). The detailed workflow is described in Supplementary Information S5. The resultant implant design and its 3D-printed counterpart are illustrated in the inset of Fig. 5(E). The mechanical behaviors at the macroscale could be characterized by the displacement-force curves in Fig. 5(E), which confirmed that the stiffness of expert-designed and ML-inspired implants were almost the same, while the ML-inspired implant’s load-bearing capacity (indicated by stars) was considerably higher (20%). The von Mises stress distribution, given in the inset of Fig. 5(E), showed that the overall stress (under 6% deformation) of ML-inspired design was considerably higher than that of the expert design. With the same bone shape and deformation, the higher inner stress of the ML-inspired design indicated stronger support of the bone implant. Therefore, the strengthening effect of ML-learned face-centered lattice was accumulative; a large structure made up of many individual strengthened cubes still demonstrated better load-bearing capacity than the expert design of the same scale.
+Fig. 5. Anatomic bone fixation with ML design. (A and B) A 30 mm bone defect in the middle part of the tibia in a New Zealand rabbit. (C) Micro-CT of the tibia. (D) Cross-sectional view of ML-inspired and expert design. (E) Experimental displacement-force curves of the ML-inspired design versus expert design. The inset shows the cross-sections of von Mises stress under 0.6 mm deformation for both designs.
+
+Conclusion
+
+This work demonstrates a multiobjective active learning approach for designing 3D-printed architected materials with generative models and 3D neural networks. With only 75 initial
+fine-tuned FEM simulation data points, our approach quickly discovered high-performance architected materials. Thus, by fusing high-precision simulation, ML, and 3D printing, our framework was developed into a powerful and robust tool that excels at complex multiobjective architecture optimization. It represents a data-efficient, intelligent method that requires no prior knowledge and can be readily adopted in wide-ranging architected materials applications. In this study, porosity is the only variable; in the future, our method can be extended to more advanced intelligent designs of geometrically complex metamaterials (42). For example, one can either set new optimization objectives with the same algorithm (e.g., weight reduction, etc.) or introduce more architectural degrees of freedom such as the geometries of subunits to design 3D-printed materials with exotic architectures and customized properties. Furthermore, our framework provides interpretable patterns that bring new insights into the design philosophy of multidimensional architected materials. As a proof of concept, we demonstrated that ML-obtained knowledge from a relatively simple problem setting can be readily adapted to a complex, real-world scenario. Here, we developed a synergistic machine-human design methodology that uses machine-learned small-scale, regular structures as subunits to create large-scale, irregularly shaped architecture. In principle, such synergy can be extended to other types of architected materials. Overall, we anticipate that our methodology can be used for designing novel 3-D architectures where optimal responses to various stimuli are desirable, including mechanical, thermal, and chemical conditions or application requirements.
+
+Methods
+
+TPMS structure generation
+
+Triply periodic minimal surfaces (TPMS) and related structures are widespread in natural biological systems (43–50). TPMS is considered to be the ideal geometric shape to describe the biological form of the human skeleton (51). Numerous studies have shown that the curved sur-
+faces of TPMS contribute to enhanced plasma membrane elongation during cell crawling and spreading (52–54). In this study, we adopted the Gyroid minimal surface structure, which is a member of the TMPS family. In addition to these above-mentioned advantages of TMPS, the unique helical surface structure of the Gyroid unit makes the force distribution more uniform, leading to its excellent mechanical properties. The equation of Gyroid surface is as follows (55):
+
+\[
+\phi_G \equiv \sin X \cos Y + \sin Y \cos Z + \sin Z \cos X = c
+\]
+
+The equation \( \phi(X, Y, Z) \) defines a surface evaluated at the isovalue (i.e., level-set constant) \( c \) and has a topology similar to that of a minimal surface. \( X = 2\alpha \pi x,\ Y = 2\beta \pi y,\ Z = 2\gamma \pi z,\ \alpha,\ \beta,\ \text{and}\ \gamma \) are constants related to the unit cell size in the \( x,\ y \) and \( z \) directions, respectively. In this work, we created the Gyroid lattice based on the minimal surface by considering one of the volumes divided by the surface as the solid domain and the other as the void domain. This was done by considering the volume bounded by the minimal surface such that \( \phi(X, Y, Z) > c \) to create a solid-network lattice. The porosity of Gyroid lattices can be graded by varying the value of the level-set constant \( c \) spatially in the Cartesian space depending on a certain function or tabulated data such that (56):
+
+\[
+\phi_G > c(x, y, z)
+\]
+
+To achieve a smooth transition between units on the edge, we describe the iso-value as a linear function along one of the Cartesian coordinates such that \( c = Ax + B \) where \( A \) and \( B \) are constants. This smooth transition is a prerequisite for representing the actual geometry shape using a porosity matrix (see Supplementary Information S2 for more detail).
+
+The scaffold contains 27 Gyroid sub-units in total, arranged as a 3*3*3 cubic. The geometry of the scaffold is controlled by the 3 * 3 * 3 porosity matrix. The porosity \( c \) of each sub-unit can take discrete values from 20 to 80 %, with an increment of 10 %.
+Dataset generation
+
+The unlabeled dataset consisted of 18000 data points and was generated for the training of the 3D-CAE. In principle, the porosity of a sub-unit can take any value from 0 to 1. Therefore, the possible arrangement is infinite. To simplify the problem, we allow the scaffold’s porosity takes discrete values from 10 to 80 % with an interval of 10% (more detail is described in Supplementary Information, TMPS structure generation). Nevertheless, there are still \(7^{27}\) possible combinations in the design space. Three thousand matrices of various porosities were generated at each interval. For each interval, there are three kinds of symmetry in the database: central, vertical, horizontal, and random arrangement. The porosity matrices also have three kinds: \(2 * 2 * 2\), \(3 * 3 * 3\) and \(4 * 4 * 4\), which then all expand to a \(12 * 12 * 12\) matrix. In such a way, our 3D-CAE can generate three different kinds of porosity matrices. This study chose the \(3 * 3 * 3\) arrangement to balance structural complexity and computational efficiency; nonetheless, our GAD-MALL can handle three different scaffold arrangements in principle.
+
+For the labeled dataset, the labels (the elastic modulus (E) and yield strength (Y) of the corresponding scaffolds) were computed by the finite element method (FEM), whose accuracy was verified through careful calibration with experimental data. It was confirmed that the deviations between the experiment and simulation were less than 10% (see Supplementary Information S2).
+
+3D printing and compression tests
+
+The performance of powder shows much influence on the formation quality of 3D-printed products. spherical Ti6Al4V (Ti) powders with few satellite particles were observed, suggesting good flowability. The powder sizes of D10, D50 and D90 in statistics were 23.9, 37.8 and 58.5 \(\mu\)m respectively. The Ti scaffolds with the size of \(6 \times 6 \times 6\) mm were additively manufactured by laser powder bed fusion (LPBF) process using an EOS M290 machine in this work. The pro-
+cessing chamber was filled with argon gas to avoid harmful reactions. The key LPBF parameters used were as follows: the laser power of 280 W, the laser scanning speed of 1200 mm/s, and the layer thickness of 30 μm. After heat treatment at a temperature of 800 °C for 2 hours and cooled in a furnace, the Ti scaffolds were surface treated by sandblasting. The Ti6Al4V sand with an average grain size of 106 μm was used in the sandblasting process. Uniformly blasted the outer surface of the Ti scaffolds to remove the adhered powder particles, with a pressure of 0.6 MPa at the outlet of the spray gun. The relative density of the composing struts in the Ti scaffolds was greater than 99.5%.
+
+The powder sizes of the pure zinc (Zn) of D10, D50 and D90 in statistics were 10.2, 19.6 and 39.4 μm respectively. The Zn scaffolds of \( 6 \times 6 \times 6 \) mm were processed using a BLT S210 machine. The processing chamber was filled with argon gas and a gas circulation system was employed to inhibit the negative effect of vaporization during the LPBF process. The Zn scaffolds were fabricated with a laser power of 40 W, a laser scanning speed of 500 mm/s, and a layer thickness of 0.03 mm. Chemical etching with 5% nitric acid and 5% hydrochloric acid (RT, 2 min) was applied to remove the adhered powder particles, and the relative density of the composing struts in Zn scaffolds reached 98.5%. More detail can be found in Supplementary Information S3.
+
+Compression tests were conducted using an Instron machine (10 kN load cell) at a crosshead speed of 1mm/min at room temperature. The compress direction was parallel with the building direction. Three replicas were manufactured in order to ensure reproducibility.
+
+Numerical simulation parameters
+
+We performed the compression simulation on a CPU (Intel Xeon Gold 6226R Processor) with 32-Core and 64-Thread using ABAQUS/Explicit software (57). The FEM was based on the same rigid-cylinder and deformable-implant-structure model. The material was homogeneous,
+and the Poisson’s ratio was 0.25. The E was set to 5 GPa and the Y to 120 MPa based on the compression experiments of the block pure Zn prepared by LPBF. Ductile damage was used to simulate the plastic deformation to the failure stage. Fracture strain was set as 0.03, and the effects of triaxiality deviation and strain rate were neglected. We extracted displacements and forces in post-processing and then converted them to strains and stresses, respectively.
+
+Machine learning algorithms
+
+The 3D-CAE consisted of an encoder and decoder. The encoder was composed of 3 3D convolutional layers (Conv3D). The input size was (12, 12, 12, 1). The first, second, third, and fourth layers contained 60, 30, and 15 filters. Three max-pooling layers between the convolutional layers were responsible for the down-sampling. For example, one max pooling layer reduced the size of Conv3D from (12, 12, 12) to (6, 6, 6), shrinking each (2, 2, 2) box down to (1, 1, 1), and taking the maximum as its value. The size of the final layer is (3, 3, 3, 15). Another max-pooling reduced it to the hidden representation (1, 1, 1, x), where x represents the dimension. The decoder is of the same Conv3D architecture, but with up-sampling, converting the hidden feature (1, 1, 1, x) back to (12, 12, 12, 1). Reconstruction loss was the mean square error (MSE) between input and output.
+
+The 3D-CNN model consisted of 3 convolutional layers. The first, second, and third layers contain 8, 4, and 2 filters, respectively; three max-pooling layers are located behind each convolutional layer. Finally, before reaching the output node, the last layer was flattened into 1048 neurons, followed by a series of fully connected layers (128, 64, 32). The activation function was the exponential linear unit. Moreover, the loss function was the mean square error. The program was written using Keras and Tensorflow (58). We trained the 3D-CAE and 3D-CNNs using a GPU (NVIDIA GeForce RTX 3080) with 10GB of memory. The training results and performance evaluation of both the 3D-CAE and 3D-CNNs can be found in Supplementary In-
+formation S1.
+
+Acknowledgements: This work was supported by the National Key R&D Program of China (grant number 2018YFE0104200) and the National Natural Science Foundation of China (grant number 52175274, 51875310); Ye Wei would like to acknowledge the financial support of the Shuimu fellowship of Tsinghua University.
+
+Author contributions: Y.W. and Y.Q. conceived the idea; P.W. planned the study; Y. W. designed the machine learning framework; Y.L. and B. P. wrote the relevant code; Y.Q. contributed to the digital design framework. J.D. and Y.Q. performed the FEM simulation and analysis; J.D., B. P., and A.B.L. performed the experiments; Y.W., B.P., J.D., and Y.Q. wrote the manuscript; B.P., Y.W. and Y.Q. designed and produced the figures; All authors participated in discussions and commented on the manuscript.
+
+Competing interests: Authors declare that they have no competing interests.
+
+Supplementary Information:
+Section S1 to S5
+Figure S1 to S23
+Table S1 to S5
+
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+Supplementary Files
+
+This is a list of supplementary files associated with this preprint. Click to download.
+
+• SI.pdf

0be9eeae9b556d120e798bfcebf02432e565fe87c2a307aed440d75c79f4497a/preprint/preprint.md

@@ -0,0 +1,722 @@
+scMINER: a mutual information-based framework for identifying hidden drivers from single-cell omics data
+
+Jiyang Yu
+Jiyang.Yu@st.jude.org
+
+St. Jude Children's Research Hospital https://orcid.org/0000-0003-3629-4330
+Liang Ding
+St. Jude Children's Research Hospital
+Hao Shi
+St. Jude Children's Research Hospital
+Chenxi Qian
+St. Jude Children's Research Hospital
+Chad Burdyshaw
+St. Jude Children's Research Hospital https://orcid.org/0000-0002-4730-1586
+Joao Veloso
+St. Jude Children's Research Hospital
+Alireza Khatamian
+St. Jude Children’s Research Hospital
+Qingfei Pan
+St. Jude Children's Research Hospital
+Yogesh Dhungana
+St. Jude Children's Research Hospital
+Zhen Xie
+St. Jude Children's Research Hospital
+Isabel Risch
+St. Jude Children’s Research Hospital https://orcid.org/0000-0003-3356-0349
+Xu Yang
+St. Jude Children's Research Hospital
+Xin Huang
+St. Jude Children’s Research Hospital
+Lei Yan
+St. Jude Children's Research Hospital
+Michael Rusch
+St. Jude Children's Research Hospital   https://orcid.org/0000-0002-5363-1848
+
+Michael Brewer
+St. Jude Children's Research Hospital
+
+Koon-Kiu Yan
+St. Jude Children's Research Hospital
+
+Hongbo Chi
+St. Jude Children's Research Hospital
+
+Article
+
+Keywords: mutual information, single-cell omics, clustering, gene network, hidden driver
+
+Posted Date: January 27th, 2023
+
+DOI: https://doi.org/10.21203/rs.3.rs-2476875/v1
+
+License: This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License
+
+Additional Declarations:
+Yes there is potential Competing Interest. L.D. is currently an employee at Spatial Genomics Inc. All the other authors declare no competing financial interests.
+
+Table 1 is not available with this version.
+
+Version of Record: A version of this preprint was published at Nature Communications on May 8th, 2025. See the published version at https://doi.org/10.1038/s41467-025-59620-6.
+scMINER: a mutual information-based framework for identifying hidden drivers from single-cell omics data
+
+Liang Ding1,6, Hao Shi1,2,6, Chenxi Qian1, Chad Burdyshaw3, Joao Pedro Veloso1, Alireza Khatamian1, Qingfei Pan1, Yogesh Dhungana1,4, Zhen Xie1,5, Isabel Risch1,2, Xu Yang1, Xin Huang1, Lei Yan1, Michael Rusch1, Michael Brewer3, Koon-Kiu Yan1, Hongbo Chi2, Jiyang Yu1,*
+
+1 Department of Computational Biology, St. Jude Children’s Research Hospital, Memphis, TN 38105, USA.
+2 Department of Immunology, St. Jude Children’s Research Hospital, Memphis, TN 38105, USA.
+3 Department of Information Services, St. Jude Children's Research Hospital, Memphis, TN 38105, USA.
+4 Graduate School of Biomedical Sciences, St. Jude Children’s Research Hospital, Memphis, TN 38105, USA.
+5 Department of Physiology, University of Tennessee Health Science Center, Memphis, TN 38163, USA.
+6 These authors contributed equally.
+
+* Correspondence should be addressed to
+Jiyang Yu, Ph.D.
+Associate Member
+Department of Computational Biology
+St. Jude Children’s Research Hospital
+262 Danny Thomas Place, MS1135
+Memphis, TN 38105-3678, USA
+Email: Jiyang.Yu@STJUDE.ORG
+Phone: +1 (901) 595-7311
+Fax: +1 (901) 595-0822
+
+Keywords: mutual information, single-cell omics, clustering, gene network, hidden driver
+Abstract
+
+The sparse nature of single-cell omics data makes it challenging to dissect the wiring and rewiring of the transcriptional and signaling drivers that regulate cellular states. Many of the drivers, referred to as "hidden drivers", are difficult to identify via conventional expression analysis due to low expression and inconsistency between RNA and protein activity caused by post-translational and other modifications. To address this issue, we developed scMINER, a mutual information (MI)-based computational framework for unsupervised clustering analysis and cell-type specific inference of intracellular networks, hidden drivers and network rewiring from single-cell RNA-seq data. We designed scMINER to capture nonlinear cell-cell and gene-gene relationships and infer driver activities. Systematic benchmarking showed that scMINER outperforms popular single-cell clustering algorithms, especially in distinguishing similar cell types. With respect to network inference, scMINER does not rely on the binding motifs which are available for a limited set of transcription factors, therefore scMINER can provide quantitative activity assessment for more than 6,000 transcription and signaling drivers from a scRNA-seq experiment. As demonstrations, we used scMINER to expose hidden transcription and signaling drivers and dissect their regulon rewiring in immune cell heterogeneity, lineage differentiation, and tissue specification. Overall, activity-based scMINER is a widely applicable, highly accurate, reproducible and scalable method for inferring cellular transcriptional and signaling networks in each cell state from scRNA-seq data.
+
+The scMINER software is publicly accessible via: https://github.com/jyyulab/scMINER.
+Main
+
+Cell fate determination and specification are governed by the wiring and rewiring of characteristic proteins including transcription factors (TFs) and upstream signaling factors (SIGs). Systematic identification of these cell-type specific drivers is crucial to understanding the cellular plasticity and dynamics, and providing therapeutic targets for diseases¹. Nevertheless, many drivers, especially SIG drivers, can undergo activity alteration at the posttranslational level without drastic changes in their gene expression level, making them “hidden drivers” and difficult to capture by differential expression analysis. Network-based systems biology algorithms such as NetBID² have been developed to uncover hidden drivers from bulk omics data. However, computational algorithms to infer cell-type specific hidden drivers and network rewiring from single-cell omics data are lacking.
+
+The use of single-cell RNA-sequencing (scRNA-seq) methods have revolutionized our ability to identify cell states with unprecedented resolution. The scRNA-seq data also provide opportunities to dissect the wiring and rewiring of cell states and identify the underlying TF and SIG drivers. However, inherent stochasticity and sparsity arising from variations and fluctuations among genetically identical cells, as well as low signal-to-noise resulting from the heterogeneity within populations of genetically similar cells present unique challenges in network and driver activity inference³⁵. A number of recent methods have been proposed to reconstruct TF regulatory networks from scRNA-seq data. For example, one of the most commonly used methods, SCENIC⁶, uses TF binding motif databases and co-expression analysis to reconstruct TF-target networks and infer TF activity that can be used for clustering analysis. Although SCENIC is broadly applicable for analysis of scRNA-seq data and inferring TF regulatory
+networks (TRNs) that define a cell state, it is restricted to the analysis of TF activity alone. Also, the TF cis-regulatory motif databases used for SCENIC are context-independent and incomplete, thus limiting the performance of this methodology. Furthermore, a recent benchmarking analysis of the state-of-the-art methods for TRN inference from scRNA-seq data revealed that all the algorithms analyzed have important limitations\(^7\), leaving an ongoing demand for robust tools. Additionally, there are currently no algorithms that can infer cell-type specific signaling networks from single-cell transcriptomics data.
+
+Another limitation is to accurately estimate cell-cell similarity and gene-gene dependency, which is critical but also challenging for clustering analysis and gene network inference from scRNA-seq data. Most existing single-cell clustering algorithms select highly variable genes first and then perform principal component analysis (PCA) dimension reduction followed by graph-based or consensus k-means clustering\(^5,8\). The selection of top variable features improves the clustering speed but is arbitrary and may lose the information that can distinguish close cell states. Furthermore, the linear-transformation of PCA and co-expression analysis using linear Pearson or Spearman correlations\(^6\) may not capture the nonlinear cell-cell distance and gene-gene correlations.
+
+To address the above challenges, we developed a mutual information (MI)-based integrative computational framework, termed single-cell Mutual Information-based Network Engineering Ranger (scMINER). ScMINER was designed to perform unsupervised clustering and reverse engineering of cell-type specific TF and SIG networks from scRNA-seq data. For this, we leveraged SJARACNe\(^9\), an MI-based algorithm for gene network reconstruction from bulk omics
+data\(^{13}\), to infer cluster-specific TF and SIG networks from scRNA-seq profiles. Based on the data-driven and cell-type specific networks, scMINER was able to transform the single-cell gene expression matrix into single-cell activity profiles and then identify cluster-specific TF and SIG drivers including hidden ones that show changes at the activity but not expression level. We benchmarked the clustering performance of scMINER in 11 scRNA-seq datasets against three widely-used tools (Seurat\(^{10}\), SC3\(^{11}\), and Scanpy\(^{12}\)), and showed that scMINER outperforms the other methods. In particular, scMINER improves the separation of similar cell types, thus significantly increasing the signal-to-noise-ratio for downstream cell-type specific network reconstruction and hidden driver identification. We demonstrated the power of scMINER in single-cell studies of immune cell diversity in peripheral blood mononuclear cells (PBMCs), exhausted T cell lineage differentiation, and tissue specification of regulatory T (Treg) cells.
+
+Results
+
+Overview of scMINER
+
+To characterize nonlinear relationships among cells and genes from single-cell omics data, we developed a MI-based scMINER workflow. In scMINER, we used nonlinear MI to measure cell-cell similarity for unsupervised clustering analysis and gene-gene correlation for reverse-engineering of cluster-specific intracellular networks from scRNA-seq data, which enables the identification of cell type-specific hidden drivers and their network rewiring events. Specifically, scMINER was designed to include two key components (**Fig. 1**): (i) Mutual Information-based Clustering Analysis (MICA) and (ii) Mutual Information-based Network Inference Engine (MINIE). We chose MICA because it uses MI to quantify cell-cell distance, which allows for
+characterization of the intrinsic nonlinear similarity of gene expression distributions among cells.
+
+To balance the efficiency and accuracy of clustering, we implemented MICA that combines two prevalent strategies for clustering analysis of scRNA-seq data\(^{5,8}\): a graph-based approach (e.g., Seurat\(^{10}\), Scanpy\(^{12}\)), which is fast and builds a heuristic cell-cell graph and applies community detection, and consensus k-means-based clustering (e.g., SC3\(^{11}\)), which is slower but more accurate, as it iteratively identifies the globally optimal k clusters and uses a consensus approach to increase the robustness. Thus, we took advantage of both strategies to balance the clustering stability and scalability, resulting in MICA that uses graph-based clustering when the cell number is large (default 5,000) and uses the k-means-based approach otherwise. We also employed nonlinear graph embedding (GE) in graph-based clustering and multidimensional scaling (MDS) in k-means-based clustering to reduce the noise arising from the intrinsic "dropout" effects in scRNA-seq data, as well as optimization of the number of dimensions used for clustering.
+
+MICA was integrated with MINIE that uses clustering results to reverse-engineer intracellular gene networks for each of the clusters by using a modified MI-based algorithm, SJARACNe\(^9\). Although originally developed to analyze bulk omics data, we re-parameterized SJARACNe to handle single-cell transcriptomics data. To overcome the sparseness of scRNA-seq data for gene network inference, we designed MINIE to employ a MetaCell\(^{13}\) approach by aggregating gene expression profiles of similar cells to reconstruct cluster-specific TF and SIG networks from scRNA-seq data. Furthermore, for each TF or SIG candidate driver, MINIE infers the cluster-specific gene activity based on the expression of its predicted regulon genes in the corresponding cluster. Taken together, the combination of non-linear nature of MICA clustering, and the
+activity-based analysis performed by MINIE is expected to overcome the dropout effects of scRNA-seq data and identify cluster-specific hidden drivers. Therefore, we propose that scMINER represents a robust platform for identification of cluster-specific hidden drivers and their target rewiring in lineage differentiation, tissue specification and many other biological processes.
+
+scMINER outperforms popular single-cell clustering tools
+To benchmark the clustering performance of scMINER, we considered the three widely-used methods: Seurat\(^{10}\) and Scanpy\(^{12}\), representing graph-based approaches, and SC3\(^{11}\) representing k-means-based algorithms. These methods were also among the top performers based on the previous evaluations\(^{14}\). We used 11 scRNA-seq datasets from different platforms with known cell-type labels and with various numbers of cells (Supplementary Table 1). These datasets consist of four gold-standard and three silver-standard datasets used for benchmarking SC3, as well as four additional large datasets with cell-type labels based on cell sorting markers and expert curations\(^{15,16}\). We used the Hubert-Arabie Adjusted Rand index (ARI), which ranges from 0 for random to 1 for identical matching, to quantify how well the inferred clusters by different methods recovered the reference labels.
+
+The benchmarking analysis indicated that MICA (in scMINER) consistently outperformed the other three methods with the highest ARI across all the datasets (Fig. 2a, Supplementary Fig. 1a), except for the Klein dataset, where the ARI of MICA, Seurat, and SC3 were almost identical and significantly higher than the ARI of Scanpy. Among the three benchmarking algorithms, there was no consistent winner: SC3 significantly outperformed graph-based Seurat and Scanpy
+in a few datasets with a small number of cells (e.g., Buettner and Pollen datasets), but failed for the two datasets with a large number of cells (e.g., Zheng and Bakke datasets); Seurat performed well in a few small datasets (e.g., Yan and Goolam datasets). Overall, MICA is the most consistent method with an average ARI value of 0.83 and the lowest variance (**Fig. 2b**). The superior performance of MICA was also confirmed by using an alternative metric, the Adjusted Mutual Information (AMI; **Supplementary Fig. 1b**).
+
+To evaluate MICA’s effect on visualization via UMAP, we calculated the silhouette index (SI)\(^{17}\) scores of 2d-UMAP visualization against the reference labels for each clustering method in all 11 benchmarking datasets. We observed that MICA exhibited much higher SI values than Seurat, SC3, and Scanpy (**Fig. 2c**), suggesting higher purity and closer to true biological cell types of MICA clustering than those of clustering by the other methods. Again, MICA is the most consistent method as shown by the lowest variance across all the datasets (**Fig. 2d**).
+
+We reasoned that the consistent superior clustering performance of MICA was because of the use of nonlinear metrics, including MI for quantifying cell-cell similarity and GE for dimension reduction. To investigate this further, we focused on the four gold-standard data sets with ground-truth data (Yan, Pollen, Kolodziejczyk, and Buettner datasets). First, we replaced the default MI metric with other widely-used distance metrics including Euclidean, Pearson, and Spearman correlation coefficients while keeping other steps of the MICA workflow the same. For each distance metric, we performed the clustering on the four gold-standard datasets for a range of MDS components from 1 to 50 (**Fig. 2e**, **Supplementary Fig. 2a**). MI-based clustering achieved consistently better performance than the other three metrics regardless of the number of
+components, which indicates that MI is more robust in capturing the actual cell-cell similarity, likely due to its non-linear nature.
+
+Similarly, we benchmarked MDS with three other commonly used dimension reduction methods: 1) Principal Component Analysis (PCA), 2) Laplacian, 3) Parallel PCA and Laplacian (Laplacian/PCA) by changing the dimension reduction metric only in the MICA-k-means pipeline. Clustering accuracy (ARI) was measured with the increment of selected components after reduction, ranging from the 1st to 50th, with downstream steps remaining the same. The results from the four gold-standard datasets showed that MDS reached its maximum accuracy during the process and remained stable with addition of more components, while the other three approaches reached their respective best ARI at different numbers of components and failed to maintain the optimal result when more components were involved (Fig. 2f, Supplementary Fig. 2b). This behavior of MDS enabled us to optimize the selection of components, a critical parameter for downstream k-means clustering, and we set 19 as the default in the MICA-MDS pipeline as this number ensured we reached the maximum accuracy in all datasets we have benchmarked.
+
+We also evaluated the computing resource usage of MICA-GE and its distribution in each step using the two largest Zheng and Bakken datasets (Supplementary Fig. 3a). The MI-kNN step used ~60% of the total time. We also evaluated the effects of GE parameters (e.g., number of workers, number of kNN neighbors, node2vec window size, etc) on clustering performance (Supplementary Fig. 3b), which helped to optimize the parameters. Taken together, scMINER-MICA is a robust, accurate, and efficient clustering algorithm.
+scMINER improves the clustering of ambiguous T-cell subpopulations in PBMCs
+
+To document the intrinsic clustering performance on a well-characterized mixed cell population, we compiled a training dataset with 14,000 PBMCs forming seven mutually exclusive cell types from the Zheng dataset\(^{15}\). We picked clustering resolution parameters for MICA and Seurat to produce the number of clusters based on the known number of cell types, and examined the true labels of the cells as defined by fluorescence-activated cell sorting (FACS) (**Fig. 3a**). Though CD4\(^+\) and CD8\(^+\) differences were well-recaptured by both MICA and Seurat, we found dramatic differences in identifying CD4\(^+\) cell subpopulations by MICA and Seurat (**Fig. 3b**, c).
+
+Specifically, MICA clearly identified a central memory T-cell population (CD4\(^+\)/CD45RO\(^+\) memory T) and a Treg population (CD4\(^+\)/CD25\(^+\) regulatory T), whereas Seurat generated two clusters (cluster 1 and 2) of CD4\(^+\) cells with mixed subpopulations (53% of CD4\(^+\) central memory cells and 45% of CD4\(^+\) Tregs, **Fig. 3d**). MICA identified three subpopulations of CD4\(^+\) T cells and one subpopulation of CD8\(^+\) naive cytotoxic T cells. In contrast, Seurat failed to separate the subpopulations of CD4\(^+\) T cells even after tuning the resolution parameter to produce 8 clusters. To avoid over-emphasizing the ground-truth labels which arises from the one or two surface-markers, we compiled a set of cell type specific signature genes and calculated the signature scores for each of the MICA and Seurat clusters (**Fig. 3c**). The signature scores show that Seurat identified two monocyte clusters and failed to identify pure clusters of CD4\(^+\) central memory T cells and CD4\(^+\) Tregs. Further, by comparing the two presumably Treg clusters, cluster 2 in MICA and cluster 1 in Seurat, we found that the number of cells with well-known Treg markers (FOXP3, IL2RA, TIGIT)\(^{18,19}\) in the MICA cluster is much higher than the Seurat cluster (**Fig. 3e**). The high signal-to-noise ratio highlights the advantage of MICA over Seurat to
+uncover cluster-specific signals for downstream network analysis. Additionally, we found that the high purity and the matching of the number of clusters to that of cell types are partially due to the amplified signals by MICA’s default count-per-million reads normalization approach (Fig. 3f, Supplementary Fig. 4).
+
+Every clustering approach has a few intrinsic parameters that could potentially change the clustering results. Therefore, it is instructive to examine the robustness of these parameters, such as the resolution parameter in the Louvain algorithm. We used CD4\(^+\) Tregs as a proxy to examine how the clusters vary across different resolutions and cluster counts (Supplementary Fig. 5). The analysis revealed that CD4\(^+\) Tregs spread across more Seurat clusters with increasing resolution, whereas most CD4\(^+\) Tregs form a single MICA cluster regardless of the resolution. Given that Seurat employs a variation-based gene selection step before PCA analysis, we examined whether the number of highly variable genes impacts the clustering performance and so no improvement on Seurat's ability to characterize CD4\(^+\) Treg cell similarities (Supplementary Fig. 6). Taken together, these studies indicate that scMINER achieves improved clustering of ambiguous cellular subpopulations.
+
+scMINER infers immune marker protein activity and improves clustering of PBMCs
+With improved clustering, we then applied the scMINER-MINIE workflow to map cell-type-specific intracellular TF and SIG networks from scRNA-seq data. Therefore, this process allowed us to transform the single-cell expression profiles into single-cell protein activity profiles, and identify hidden drivers underlying each cell type that expression may fail to capture. We continued the analysis of the PBMC dataset with 7 cell types – monocytes, B cells, NK cells,
+CD4^+^ T cells, and naïve CD8^+^ T cells (**Fig. 4a**). With MINIE, we first generated cell-type-specific TF and SIG networks based on scRNA-seq profiles of each of the seven sorted populations containing 2,000 cells (**Supplementary Fig. 7a**). We then inferred TF and SIG activities by taking the expression level of predicted targets into account, resulting in an activity matrix of 1,428 TFs and 3,382 SIGs. The activity matrix overcame the sparseness of scRNA-seq data; it satisfied a normal distribution, which drastically cut down the theoretical pre-requisite for any statistical testing.
+
+Unique molecular signatures have been used in literature to define different immune cells in PBMCs, including monocytes (LYZ, CD68, and CD14), B cells (CD19, MS4A1, and CD79A), Treg cells (CTLA4, TIGIT, and FOXP3), NK cells (GZMB, IL2RB, FCGR3A, and KLRB1) and naïve CD8^+^ T cells (CD8A, CD8B, SELL)^{20-22}. However, the expression level of a few markers cannot identify and separate immune cell subtypes, especially CD4^+^ T cell subsets in this PBMC dataset, possibly due to gene dropout (**Fig. 4b**). Compared to expression, the activity of classical immune markers can well separate these immune cell types (**Fig. 4b**). The dropout of both Treg marker FOXP3 and NK cell marker CD56 (encoded by NCAM1 gene) marker expression can be rescued by their effect on the UMAP (**Fig. 4c**), as well as other cell type-specific markers such as CD19, CD8A, and CD14 (**Supplementary Fig. 7b**). The activity of their signatures further separated the subsets of CD4^+^ T cells. For example, naïve CD4^+^ T cells showed higher FHIT and SATB1 activity and lower CXCR3 activity than CD4^+^ memory T cell subsets (**Fig. 4b and Supplementary Fig. 7c**). Compared with the widely used scRNA-seq regulon analysis method SCENIC (**Fig. 4d**), scMINER was able to identify Treg cells with FOXP3 activity with more specificity (**Fig. 4c**).
+The activity calculated from scMINER could also be used to improve clustering unbiasedly. We calculated the activity of the cell type signatures based on GRN generated from MetaCell\(^{13}\) using the total PBMC cells (**Fig. 4f**). We observed that MINIE-based activity clustering outperformed SCENIC-based activity clustering, in terms of recovering the reference labels. The separation of Treg cells from other T cells was further improved compared to gene expression-based clustering (**Fig. 4g**). Taken together, scMINER-inferred activity overcomes the “dropout” effects to improve marker protein identification and clustering from scRNA-seq data.
+
+**scMINER reveals drivers and their network rewiring in exhausted CD8\(^+\) T cell differentiation**
+
+Next, we demonstrated the power of scMINER to identify drivers in cell lineage and differentiation using a specific example of exhausted CD8\(^+\) T cell differentiation, a phenotype associated with severe infection, cancer and autoimmunity\(^{23-26}\). Previous studies have shown that the exhausted CD8\(^+\) T cells contain heterogeneous subpopulations with differential capability to respond to anti-PD1 therapy\(^{27-33}\). We performed scMINER clustering on scRNA-seq profiles of exhausted CD8\(^+\) T cells in mice chronically infected with lymphocytic choriomeningitis virus (LCMV) Clone 13 (Cl13) at a late stage (day 28)\(^{32}\). We recapitulated the 3 major subpopulations of exhausted CD8\(^+\) T cells defined by TCF-1 (encoded by *Tcf7* gene), CX3CR1, and TIM3 (encoded by *Hacvr2*\(^+\)): TCF-1\(^+\) exhaustion progenitor (Tpex), CX3CR1\(^+\) effector-like (Teff-like, effector-like Tex), and CX3CR1\(^-\)TIM3\(^+\) terminal exhausted T cells (Tex) (**Fig. 5a**). These three populations are distinct both phenotypically and functionally\(^{32, 34, 35}\).
+We then applied scMINER to delineate the transcription regulatory networks and underlying hidden drivers along the state changes from Tpex to Teff-like to Tex. Previous studies reported that TCF-1, FOXO1, ID3, LEF1, and NF-kB related transcriptional factors REL and NFKB1 are involved in Tpex regulation\(^{36,37}\), although the expression levels of these TFs didn’t show marked changes (**Fig. 5b**). In contrast, scMINER-inferred activities of these TF regulators based on cluster-specific regulatory networks uncovered their importance in Tpex (**Fig. 5b**). The surprising enrichment of NF-kB-related transcriptional factors suggested possible roles of NF-\( \kappa B \) signaling pathway in regulating the formation or maintenance of Tpex cells. For the Teff-like subpopulation, T-bet (encoded by *Tbx21*) is known to be important for the effector function of this population\(^{36}\) and indeed has heightened scMINER activity (**Fig. 5b and Supplemental Fig. 8a**). Other TFs such as KLF2/3, RUNX1, and ROR-\( \alpha \) (encoded by *Rora*) also have increased regulon activities in the Teff-like cluster, consistent with the prediction by SCENIC analysis in the literature\(^{36}\). Finally, the terminally exhausted Tex cells showed increased activity of NFATC1, BLIMP1 (encoded by *Prdm1*), and TOX, which were reported to promote exhaustion\(^{36,38-41}\). Notably, the increased scMINER activities for T-bet and BLIMP1 in Teff-like and Tex respectively are much more obvious than their expression. Although BATF function in terminal exhaustion and effector function is still debatable depending on the biological context\(^{36,42-45}\), overexpressed BATF has been shown to be critical for regulating effector function in adoptively transferred antigen-specific CD8\(^+\) T cells and CAR-T cells\(^{45,46}\). The scMINER analysis was able to accurately detect BATF activity that was missed by analysis of its expression pattern alone (**Supplementary Fig. 8a**).
+The TF transcriptional networks of these three CD8+ T cell exhaustion stages also captured known master TF drivers in CD8+ T cells. For example, in Tpex cells, the TCF-1 is predicted to directly promote expression of Cd9 and Ms4a4c (Supplementary Fig. 8b), while FOXO1 is known to promote Pdcd1 expression during exhaustion36, 47. In Teff-like cells, T-bet regulates Zeb2 expression, which has been reported to be critical for effector CD8+ cytotoxic cell differentiation48, 49. In terminal Tex cells, TOX regulates co-inhibitory molecular Lag3 expression50.
+
+To benchmark the performance of scMINER, we compared it with SCENIC6. SCENIC was applied to the exhausted CD8+ T cell dataset and was able to capture a few positive control drivers of T cell exhaustion, including REL, NFKB1, FOXO1, KLF2/3, RUNX1, T-bet, ROR-α, and E2F2, all of which were predicted by scMINER (Fig. 5c). However, SCENIC failed to predict TCF-1, ID3, LEF1, BATF, and TOX activity in this dataset based on their co-expressed regulons (filtered out in motif2tf step), among which TCF-1, BATF, and TOX are well-established TF regulators of exhausted T cell differentiation. This suggested that scMINER goes beyond the limitation of TF motif database and can predict a broader spectrum of TF drivers in exhausted T cell differentiation directly from scRNA-seq data. Intriguingly, we also found the TF regulons predicted by scMINER have a significant overlap with TF footprint genes detected by ATAC-seq analysis51 of Tpex and Tex cells. This suggested that scMINER regulons reflect true transcriptional targets of TFs in a context-specific fashion (Fig. 5d).
+
+Distinct from SCENIC that is focused on TF driver inference, scMINER can be used to reconstruct context-specific signaling networks and infer the activity of signaling factors. Indeed,
+scMINER successfully identified that memory-associated surface markers such as CCR7 and IL7R are uniquely activated in Tpex cells (Fig. 5e). CX3CR1, a surface hallmark for Teff-like cells, also exhibited higher activity in Teff-like cells. Effector function of CD8\(^+\) T cells is correlated with high mTOR activity\(^{34,52}\), and scMINER did capture that the activities of mTOR and its upstream regulator V-ATPases\(^{53}\) were high in Teff-like cells (Fig. 5e and Supplementary Fig. 8c). Further, genes that were reported to be highly expressed in terminal Tex cells such as \(Cd244\) (2B4)\(^{54}\) and \(Cd38^{55}\) exhibited the highest activity in Tex cluster (Fig. 5e). MAP4K1 (encoded by *Hpk1*) is known to promote terminal exhaustion\(^{56}\), and scMINER captured the most increased activity in terminal Tex cells. Notably, the selective kinase activity of mTOR and MAP4K1 in Teff-like and Tex could not be captured by their gene expression changes from scRNA-seq data (Fig. 5e). All of the above indicates that scMINER can capture context-dependent activity of signaling proteins, including surface receptors, intracellular enzymes, and kinases.
+
+By inferring cell-type-specific networks for various clusters, scMINER can uncover the regulon rewiring of drivers among cell types, and thus determine the transcription regulation during cell state transition. BATF has recently been identified to have a role in promoting Tpex to Teff-like transition via different regulons\(^{36}\). Indeed, scMINER network analysis captured that BATF regulon targets were significantly rewired among Tpex, effector-like Tex, and terminal Tex states (Fig. 5f). In the overlapped BATF regulons between Tpex and effector-like Tex, BATF regulates effector CD8\(^+\) T cell-associated oxidative phosphorylation and T cell receptor signaling pathway (Fig. 5g), which suggested BATF may promote metabolic rewiring to increase effector-like Tex and is consistent with the role of BATF reported in the literature\(^{45,46}\). In contrast, BATF
+regulons that are unique in Tpex cells were enriched in cytotoxic IFN-\( \alpha \) and IFN-\( \gamma \) response pathways while BATF regulons that are unique in Teff-like cells were enriched in cell cycle-related pathways (**Fig. 5g**). Together, these results indicated that BATF may alter its regulons in different cell subsets to tune their activity and exert their regulatory function during the process of CD8\(^+\) T cell exhaustion.
+
+Understanding complex transcriptional network changes in response to gene perturbation is among the biggest challenges for mechanism studies. Since TOX is a master TF regulator of T cell exhaustion, we analyzed scRNA-seq data (GSE119940) profiling wild-type (WT) and TOX knockout (KO) CD8\(^+\) T cells\(^{38}\) during chronic infection to examine whether scMINER can reveal the regulatory circuits of TOX in chronic infection (**Supplementary Fig. 8d**). TOX-KO CD8\(^+\) T cells exhibited reduced TOX activity compared to WT cells (**Fig. 5h**), indicating scMINER can correctly capture TOX activity in this biological context. *Tcf7* expression was reported to be downregulated upon TOX KO\(^{38,39}\), and we indeed found that TOX KO decreased both expression and activity of *Tcf7* (**Fig. 5h**). Since *Tcf7* marks the Tex cell precursors (Tpex), our results aligned with previous reports that the primary defect in TOX-KO exhausted T cells was the inability to rewire the transcriptional control of *Tcf7* after the initial development of Tpex. Apart from the reduction of *Tcf7* activity, TOX-KO CD8\(^+\) T cells were also accompanied by the reduced activity of BATF (**Fig. 5h**), which is required for sustaining antiviral CD8\(^+\) response during chronic infection\(^{57}\). TF motif enrichment analysis also validated the reduced activity of BATF in TOX-KO CD8\(^+\) T cells (**Supplementary Fig. 8e**). Moreover, the TOX-KO cells also increased the activity of effector-related transcription factor ZEB2 (**Fig. 5h**), in line with the increased effector T cell function in TOX-KO cells, which cannot be solely explained by loss of
+Tcf739. Moreover, other top TF and SIG drivers predicted by scMINER in TOX-KO CD8+ T cells were also enriched in the effector T cell signature but not exhausted T cell signature (Supplementary Fig. 8f). These results together highlighted that a complex transcription regulatory network, not just Tcf7 expression, is required for TOX-mediated effector function and exhaustion progression in CD8+ T cells during chronic infection.
+
+scMINER exposes drivers underlying Treg tissue specification
+
+While different types of T cells play different roles, the same type of T cell could have specific roles in specific tissues, driven by the underlying transcriptional regulatory networks58. For example, tissue specific Treg cells not only maintain immune tolerance but also promote homeostasis and regeneration after tissue damage59, 60. To examine this further, we used scMINER to dissect TF and SIG drivers underlying tissue specification of Treg cells. We performed scMINER clustering of scRNA-seq profiles of Treg cells from different tissues including spleen, lung, skin and visceral adipose tissue (VAT)61. Clustering results exhibited that Treg cells were well separated by their tissue origins. Skin and VAT Treg cells displayed high Cd44 and low Sell expression, while spleen and lung Treg cells showed the opposite (Fig. 6a). We then reconstructed tissue-specific regulatory networks of Treg cells to establish the regulons of TF drivers for their activity inference. Differential activity analysis by scMINER revealed that resting Treg cell-associated TFs (e.g., TCF-1, KLF2, SATB1, and BACH2) all have the highest activity in spleen and lung Treg cells (Fig. 6b and c). Endoplasmic reticulum (ER) stress is critical for normal skin function and associated with skin-related autoimmune disease62. Interestingly, Treg cells in the skin upregulate the activity of ER stress regulator ATF6, suggesting a possible influence from the skin microenvironment (Fig. 6b and c). VAT Treg is
+the most well-characterized tissue Treg with high activity of PPARG, FLI1, RORA, and RARA, consistent with the prediction based on motif enrichment analysis of ATAC-seq data\(^{63}\) and literature\(^{61}\) (**Fig. 6b right**). Notably, scMINER activity-based TF driver inference captured these tissue-specific drivers, which could not be clearly identified from their expression patterns (**Fig. 6b left**). Orthogonal scATAC-seq-based TF accessibility analysis (**Fig. 6c**) and SCENIC analysis (**Supplementary Fig. 9a**) captured differential tissue-selective activity of BACH2, KLF2, ATF6, and PPARG, but their signals were much weaker than scMINER-based activity analysis, and could not correctly predict the high FLI1, RORA, and RARA activity in VAT Treg cells (**Supplementary Fig. 9b**).
+
+The prediction of selective scMINER activity, but not expression, of *Bach2* and *Pparg* in spleen and VAT Treg cells could be validated by another independent scRNA-seq study that profiled spleen, colon, muscle, and VAT Treg cells\(^{61}\) (**Supplementary Fig. 9c, d**). This further indicates the robustness and reproducibility of scMINER in identifying regulators of tissue-specific Treg cells from different studies. Moreover, the top scMINER-predicted TF and SIG drivers from skin and VAT Treg cells were significantly enriched in the core tissue resident Treg signature. They were enriched in the skin and VAT-specific signatures, respectively (**Fig. 6d**). These results indicated the top TF and SIG drivers predicted by scMINER could faithfully reveal tissue Treg differentiation reported in the literature.
+
+To validate whether TF regulons predicted by scMINER also reflect TF transcriptional activity, we compared the scMINER-predicted regulons with footprint genes detected by ATAC-seq profiles of corresponding spleen and VAT Treg cells and indeed found a significant overlap of
+TFs between them (Supplementary Fig. 9e). Pparg is known as a master regulator of VAT Treg cells\(^{64, 65}\), and its transcription activity was correctly captured by scMINER in VAT (**Fig. 6c** and **Supplementary Fig. 9d**). Intriguingly, *Pparg* regulons are distinctly rewired in different tissues (**Fig. 6e**). The *Pparg* regulons in VAT Treg cells are significantly enriched in the VAT/Fat Treg signatures based on ATAC-seq analysis\(^{63}\) (**Fig. 6f**). Notably, predicted *Pparg* regulons in the spleen are also enriched in the core tissue Treg signature (**Fig. 6f**). This finding suggests *Pparg* may have an essential role in regulating early tissue Treg development and is consistent with previous studies\(^{66, 67}\). To further investigate this, we analyzed a scRNA-seq dataset of tissue Treg cell precursors (KLRG\(^{-}\)NFIL3\(^{+}\) and KLRG\(^{+}\)NFIL3\(^{+}\)) in the spleen\(^{66}\) by scMINER (**Fig. 6g**). Tissue Treg cell precursors also express higher *Pdcld1*, *Klr1g1* and *Nfil3* than KLRG\(^{-}\)NFIL3\(^{-}\) cells. *Batf* is known to regulate the generation of tissue Treg cell precursors\(^{66}\). scMINER identified increased activity of *Batf*, *Gata3*, and *Nfil3* in the two tissue Treg cell precursors, consistent with the original study\(^{66}\) (**Fig. 6h**). Indeed, *Pparg* activity was enhanced in these tissue Treg cell precursors despite its low expression, which supports that *Pparg* could regulate a common step of early tissue Treg cell generation in the spleen through its tuned regulons in the spleen, consistent with our observation above. Apart from *Pparg*, top TF and SIG drivers in the KLRG\(^{+}\)NFIL3\(^{+}\) tissue Treg precursors are enriched in the core tissue resident Treg cell signatures and *Pparg* related gene expression (**Fig. 6i**), indicating that scMINER can reveal the drivers underlying the early generation of tissue Treg cell precursors in the spleen.
+
+Similar to TF drivers, top SIG drivers for each tissue specific Treg cell are also highlighted (**Supplementary Fig. 9f**). Among these signaling drivers, *Ccr1* was demonstrated to possibly contribute to VAT Treg accumulation\(^{65}\), which was correctly captured by scMINER. In addition,
+a common epigenetic and transcriptional hallmark of tissue Treg cells is the upregulation of IL-33 receptor ST2 (*Il1rl1*)\(^{68}\). Treg cells from all three other Treg cells upregulated ST2 activity compared to the spleen. Still, VAT Treg cells have the highest ST2 activity (**Supplementary Fig. 9f**), which supports the critical role of the IL-33-ST2 axis in pan-tissue Treg cell generation. Moreover, other chemokine receptors such as *Ccr4* and *Ccr5*, which are essential in tissue Treg cell migration\(^{68,69}\), have also been uncovered by scMINER. Together, these results indicate that scMINER can capture the upstream signals that modulate tissue Treg cell specification.
+
+**Discussion**
+
+We have developed an integrative computational framework for unsupervised clustering and reconstruction of cell-type specific intracellular networks that enables the identification of hidden drivers directly from scRNA-seq data. Our scMINER framework takes advantage of mutual information for nonlinear measurements of intrinsic relationships among cells and genes. For clustering, scMINER also leverages an ensemble dimension reduction approach based on a reasonable assumption of the nature of biological dynamics: that a wider range of dynamics should be observed from a large population of cells of the same cell type. Using benchmarking datasets with ground-truth labels, we demonstrated that scMINER outperforms the state-of-the-art methods in single-cell clustering.
+
+From scRNA-seq data alone, scMINER is able to uncover hidden TF and SIG drivers underlying cell states, which have not been captured by differential gene expression analysis but have been experimentally validated as key drivers. Further, the scMINER-inferred TF regulons are significantly overlapped with the targets defined from ATAC-seq footprinting of the same cell
+type, suggesting high accuracy of the scMINER-derived TF networks. For TF driver prediction, we benchmark scMINER with SCENIC and demonstrate that scMINER identifies known TF drivers that SCENIC fails to reveal due to the lack of TF binding motif information or low expression of TFs. Importantly, scMINER is the only method that can predict SIG drivers from scRNA-seq data. Together, scMINER provides a new toolbox to dissect the TF regulatory and signaling networks and pinpoint hub drivers underlying cell lineage differentiation and specification from single-cell omics data.
+
+In addition to improving clustering accuracy, scMINER provides insights that could only be gleaned using an activity analysis pipeline. In particular, the established lineage markers of some subsets of lymphocytes, especially regulatory T cells, were missed in the conventional expression-based analysis, due to significant gene dropouts. In contrast, activity-based scMINER analyses rescue the dropout and reveal the hidden drivers and rewiring of their regulons in each cell state. Our results show that the importance of these cell-state drivers is consistent with their role reported in literature and these top drivers can be faithfully recapitulated in multiple scRNA-seq datasets profiled in similar experimental contexts. Moreover, scMINER provides quantitative activity assessment for > 6,000 TF and SIG proteins in a single experiment; it outperforms traditional low-throughput methods examining protein expression and activity, such as flow cytometry; and it overcomes the limitations of TF motif based SCENIC activity inference. Thus, activity-based scMINER analyses provide higher accuracy, reproducibility and scalability for inferring cellular transcriptional networks in each cell state from scRNA-seq data.
+Importantly, the reasons why activity-based scMINER analyses outperforms single cell expression-based analysis in the identification of multiple known transcription factors and signaling pathways go beyond the rescue of dropout. For instance, in regulating CD8\(^+\) T cell exhaustion and Treg cell tissue specification, *Batf* is an example of hidden driver because its expression is largely comparable among three subsets of CD8\(^+\) exhausted T cell subsets. However, its role acting in opposing Tpex generation is reported in the literatures\(^{33,45}\). Thus, the identification of *Batf* has a more important role for effector-like TCF1\(^-\)TIM3\(^+\) cells by scMINER, which stripped the disguise of its expression profile. The rewiring of the TF targets shown in different subsets of CD8\(^+\) T or Treg cells also suggests the necessity of studying cell-cluster specific TF regulons rather than the invariant TF regulons predicted by SCENIC, which could help in understanding unique transcriptional regulation in novel cell states and the molecular mechanism underlying the 'hidden' drivers. Since CD8\(^+\) T cell exhaustion and Treg cell development in tissues are both critical in regulating tumor and infection progression, targeting these top master regulators could help relieve these diseases and open the door for new combinational immunotherapies using current checkpoint blockade strategies.
+
+While scMINER is a robust and powerful tool for single-cell clustering and network analysis, it has several limitations. First, the nonlinear MI estimation of cell-cell or gene-gene similarities is time-consuming, especially with a large number of cells. For clustering, scMINER doesn't select top variable genes to retain information that can separate close cell states. Computing platforms supporting parallelism may help improve the efficiency. For network inference of big clusters, downsampling is one solution, but a MetaCell-type approach is preferred because it also helps improve the gene coverage by aggregating expression in multiple cells. Second, although
+scMINER provides silhouette analysis to guide selection of the optimal number of clusters, determining the number of clusters is still quite challenging, thus a manual and problem-dependent task.
+
+In summary, we report the development and application of a novel scRNA-seq analytic pipeline, which utilizes mutual information and network-based inference to complement gene expression for better clustering and predicting the importance of TF and SIG drivers in each cell type. The MICA clustering algorithm in scMINER can also be applied to other high-dimensional data, including scATAC-seq, bulk transcriptomics and proteomics, and spatial omics. While our examples focused on the immune system, the scMINER tool could be effectively applied to any other systems profiled by scRNA-seq.
+Methods
+
+Data compilation and preprocessing
+
+We summarize the 11 single-cell data sets used for accessing the clustering methods in Table 1. We filtered out genes detected in less than three cells, and cells that express less than 200 genes. The gold (Yan, Goolam, Pollen, Kolod) and silver standard data sets (Usoskin, Klein, Zeisel) were normalized using the same methods reported in SC3\(^{11}\). In addition, the Buettner data set was normalized using FPKM; Chung data set was normalized with TPM; all the UMI-based data sets were normalized to 10,000 reads per cell. We then performed a natural log transformation for all the normalized data. In addition, we extracted highly variable genes using the default parameters for the clustering analysis by Seurat and Scanpy as recommended in the tutorials for PCA dimension reduction. We only used the known cell labels afterward to access the clustering results.
+
+The dataset used in Fig. 3 was based on PBMC dataset generated by Zheng et al.\(^{15}\). It has 20,000 PBMCs purified via well-known cell surface markers with each subpopulation of 2,000 cells. To create a more purified simulation dataset, CD4+ T helpers, total CD8+ cytotoxic T, and CD34+ cells (HSPCs) were removed with the remaining 14,000 cells forming seven mutually exclusive cell types.
+
+Mutual information estimation
+
+Cell-to-cell distances are calculated using MI:
+
+\[
+I(C_i; C_j) = \sum_{y \in C_j} \sum_{x \in C_i} p_{(C_i,C_j)}(x, y) \log \frac{p_{(C_i,C_j)}(x,y)}{p_{C_i}(x)p_{C_j}(y)},
+\]
+where \( C_i \) and \( C_j \) are the \( i \)-th and \( j \)-th rows in matrix \( M \). Since normalized gene expression values are continuous, we use a binning approach\(^{70}\) for discretizing the expression values for the joint and marginal probability calculations, where the bin size \( b \) is defined as \( \sqrt[3]{n} \), n being the total number of genes. We then define a normalized distance between cells as
+
+\[
+D(C_i, C_j) = 1 - \frac{I(C_i;C_j)}{H(C_i,C_j)},
+\]
+
+where \( H(C_i, C_j) \) is the joint entropy of cells \( C_i \) and \( C_j \).
+
+**Ensemble dimension reduction**
+
+For data sets with more than t (default is 5,000) cells (according to the clustering performance evaluation), we first represent MI matrix \( M \) as a \( k \)-nearest neighbor graph \( G_1 \) and then adopted node2vec\(^{71}\) algorithm to embed \( G_1 \) to a \( d \) dimensional space, where \( k \) and \( d \) are predefined parameters to control the scale of the local structure to explore and the number of low dimensional components to transform, respectively. The embedding is performed for a range of \( d \) from 8 to 96 with step size four followed by consensus clustering to reduce the randomness caused by selecting a fixed \( d \) in a single clustering run. We use classical multidimensional scaling (MDS) to preserve the intercell distances for data sets with less than or equal t cells. We set the number of components to be a fixed number of 19, as explained in the Main section (**Fig. 2d**). As MDS requires storing the entire MI matrix in the memory, to enable MI estimation for large datasets, we parallelized the calculation in four steps: 1) partitioning \( M \) into \( M_{i,j} \) of a fixed number of cells, 2) MI estimation for every pair of \( M_{i,j} \) in parallel, 3) merging MI matrices, and 4) normalization using equation (1).
+
+**Cell clustering**
+To ensure reasonable running time, we build a k-nearest neighbor (kNN) graph \( G_2 \) again after embedding \( G_1 \) to a \( d \) dimensional space and use the Louvain algorithm as the default clustering method. Instead of using mutual information as the distance function, we use Euclidean distance to determine the similarity of cells on the \( d \) dimensional space. Euclidean distance has much fewer arithmetic operations than MI; thus, we adopt the KD-tree algorithm\(^{70}\) to construct an exact kNN graph \( G_2 \) instead of an approximate graph \( G_1 \). Similar to SC3, we use k-means clustering as the default method on the MDS transformed space. However, K-means clustering is sensitive to the centroid seed initialization and produces very different results for each run. To reduce randomness, we run k-means clustering ten times by default and use consensus clustering to aggregate multiple runs of k-means clustering results.
+
+**Determination of the optimal number of clusters**
+
+We compute a silhouette coefficient\(^{17}\) average over all the cells for the clustering results and rank the results by the coefficients. scMINER users may evaluate the top candidates to determine the optimal number of clusters with a priori knowledge of the biological context of the data set.
+
+**Determination of parameters for graph-embedding in MICA**
+
+With the increasing complexity and depth of cellular neighborhood in the cell-cell distance space for large datasets, we speculate that the ability to explore the diverse local neighborhoods in a non-linear fashion is important to the clustering performance. Therefore, we adopt node2vec\(^{71}\), a non-linear graph-based dimension reduction approach with the flexibility in exploring diverse neighborhoods, to maximize the likelihood of preserving local neighborhoods of cells. Most of the current dimension reduction techniques rely on eigendecomposition of the appropriate data
+matrix, which unsatisfies the scalability requirement for large datasets. A feasible solution is to explore and preserve the local neighborhood of cells approximated by a graph representation with each node representing a cell. node2vec’s random walk-based approach with flexible parameters, which allows for unsupervised exploration of the local neighbors in a graph and offers scalability for large datasets without sacrificing much clustering performance. We choose a subset of parameters critical to the dimension reduction performance and perform the grid searches over a predefined range for each parameter independently using the Zheng dataset. The default parameters are selected by considering the clustering performance in terms of ARI, the elapsed wall time and the highest memory consumption.
+
+Performance analysis and parameter tuning
+
+We compute the running time for each step of MICA for PBMC and Human Motor Cortex datasets using 25 CPU cores from a redhat linux machine (Supplementary Fig. 3a). The 1st step (MI-kNN) takes more than half of the total running time due to the number of arithmetic operations of mutual information calculation for each cell pair. We also perform parameter tunings by grid searching in a predefined range of selected parameters for PBMC clustering analysis (Supplementary Fig. 3b). The parameters in MI-kNN and node2vec steps have the greatest influence on the clustering performance and running time. We chose the default parameters to balance the clustering performance, running time and memory usage.
+
+Overview of MINIE
+
+MINIE allows users to reconstruct cell-type-specific GRNs for driver activity inference and target network rewiring analysis. MINIE takes inputs of a gene expression profile and cell cluster
+labels. It first filters the genes with all zero expressions on the cell cluster basis. Then MINIE invokes SJARACNe to reconstruct cell-type-specific transcriptional factor and signaling networks. While users can provide a list of known drivers (TFs or SIGs) as input, well-curated lists of drivers are included in the MINIE package for users' convenience. To resolve the sparseness of the networks due to the scRNA-seq dropout effect, we fine-tuned SJARACNE parameters (e.g., two p-value thresholds) to consider a series of network properties, including the median number of targets, a power law-like degree distribution, etc. Finally, with the predicted targets of a driver for a cell cluster, MINIE calculates the driver activity by performing a column-wise normalization to ensure each cell is on a similar expression level, followed by averaging the expression of the driver's target genes.
+
+Bulk ATAC-seq data analysis
+
+ATAC-seq analysis was performed as described previously. Briefly, two × 50-bp paired-end reads we obtained from public datasets were trimmed for Nextera adaptor by trimmomatic (v0.36, paired-end mode, with parameter LEADING:10 TRAILING:10 SLIDINGWINDOW:4:18 MINLEN:25) and aligned to mouse genome mm10 downloaded from gencode release M10 (https://www.gencodegenes.org/mouse/release_M10.html) by BWA (version 0.7.16, default parameters). Duplicated reads were then marked with Picard (v2.9.4), and only non-duplicated proper paired reads were kept by samtools (parameter '-q 1 -F 1804' v1.9). After adjustment of Tn5 shift (reads were offset by +4 bp for the sense strand and −5 bp for the antisense strand), we separated reads into nucleosome-free, mononucleosome, dinucleosome, and trinucleosome as previously described by fragment size and generated 'bigwig' files by using the centre 80-bp of fragments and scaled to \( 30 \times 10^6 \) nucleosome-free
+reads. We observed reasonable nucleosome-free peaks and a pattern of mono-, di- and tri-nucleosomes on IGV (v2.4.13). All samples in this study had approximately \(1 \times 10^7\) nucleosome-free reads, indicating good data quality. Next, peaks were called on nucleosome-free reads by MACS2 (v2.1.1.20160309, with default parameters with '-extsize 200--nomodel'). To assure reproducibility, we first finalized nucleosome-free regions for each sample and retained a peak only if it called with a higher cut-off (MACS2 -q 0.05). We further generated consensus peaks for each group by keeping peaks presenting in at least 50% of the replicates and discarding the remaining, non-reproducible peaks. The reproducible peaks were further merged between samples if they overlapped by 100-bp; we counted nucleosome-free reads from each sample by bedtools (v.2.25.0). To identify the differentially accessible open chromatin regions (OCRs), we first normalized raw nucleosome-free read counts per million (CPM) followed by differential accessibility analysis by implementing the negative binomial model in the DESeq2 R package\(^{72}\). FDR-corrected *P-value* < 0.05, \(|\log_2 \text{FC}| > 0.5\) were used as cut-offs for more- or less-accessible regions in TOX KO samples compared to their WT samples. Principal component analysis was performed using function prcomp in R. We then assigned the differentially accessible OCRs in the ATAC-seq data for the nearest genes to generate a list of DA genes using HOMER. This analysis identified 25,646 open chromatin regions (OCRs) with differential expression in TOX KO versus control cells (FDR < 0.05; \(|\log_2 \text{FC (TOX KO/WT)}| > 0.5\)).
+
+**Motif analysis and footprinting of transcription factor binding sites**
+
+For motif analysis, we further selected 1,000 unchanged regions log2 FC < 0.5 and FDR-corrected P-value > 0.5 as control regions. FIMO from MEME suite (v4.11.3, '-thresh 1e-4–motif-pseudo 0.0001')\(^{73}\) was used for scanning motif (TRANSFAC database release 2019, only
+included Vertebrata and not 3D structure-based) matches in the nucleosome-free regions, and two-tailed Fisher's exact test was used to determine whether a motif was significantly enriched in differentially accessible compared to the control regions. To perform footprinting analysis of transcription factor binding site, the RGT HINT application was used to infer transcription factor activity and plot the results\(^{51}\).
+
+Single-cell ATAC-seq processing and data analysis
+
+All preprocessing steps were performed using "Cell Ranger ATAC version 1.2.0" (10X Genomics). Read filtering, alignment, peak calling, and count matrix generation from fastq files were done per sample using 'cellranger-atac count'. Reference genome assemblies mm10 (refdata-cellranger-atac-mm10-1.2.0) provided by 10xGenomics were used for samples. All further analysis steps were performed in R (Version 4.0.0). Fragments were loaded into R using the package Seurat\(^{10}\). The R package Signac (version 1.3.0, https://github.com/timoast/signac) was used for normalization and dimensionality reduction. The peak-barcode matrix was then binarized and normalized using the implementation of the TF-IDF transformation described in (RunTFIDF (method = 1)). Subsequently, singular value decomposition was run (RunSVD) on the upper quartile of accessible peaks (FindTopFeatures (min.cutoff = 'q75')). The first 20 components from the SVD reduction were used for secondary dimensionality reduction with UMAP.
+
+Gene activity scores of scATAC-seq data
+
+To calculate gene activity scores, gene body coordinates were first obtained by using the command genes (TxDb.Mmusculus.UCSC.mm10.knownGene) from the package
+GenomicFeatures in R. The coordinates were filtered for normal chromosomes (keepStandardChromosomes (pruning.mode = 'coarse')) and extended by 2,000 bp upstream of the transcription start sites to include promoter regions (Extend(upstream = 2000)). Then, the command 'FeatureMatrix' from the Signac package was used with the 'features' parameter set to the extended gene coordinates, to sum up the number of unique reads within gene regions for each cell. The above steps can be performed using the wrapper function GeneActivity.
+
+Eventually, these gene activity scores were log-normalized and multiplied by the median read counts per cell (nCount_Reads) with the command NormalizeData(normalization.method = 'LogNormalize',scale.factor = median(nCount_Reads). Normalized gene activities were capped at the 95th quantile for plotting.
+
+Estimation of transcription factor activity with chromVAR
+
+Transcription factor (TF) activities for each cell were measured using chromVAR (Schep et al., 2017). TF position weight matrices were downloaded from the Homer website (http://homer.ucsd.edu/homer/custom.motifs). Signac was used to build a motif-peak matrix for all peaks in the murine and human datasets (CreateMotifMatrix) using reference genomes from the packages BSgenome.Mmusculus.UCSC.mm10 and BSgenome.Hsapiens.UCSC.hg19, respectively. After assembling and adding the Motif object to the Seurat object (CreateMotifObject, AddMotifObject), information on the base composition was calculated for each peak (RegionStats). Eventually, the wrapper function 'RunChromVAR' was called to obtain chromVAR deviation z-scores. ChromVAR deviation z-scores below the 5th and above the 95th quantile were capped for plotting.
+
+SCENIC regulon analysis
+Previously published scRNA-seq data of CD8+ T cells from LCMV infection model (GSE122712, GSE119940), tissue-specific Treg cells (GSE130879) were used for SCENIC analysis6, with raw count matrix as input. Briefly, the co-expression network was calculated by GRNBoost2, and RcisTarget identified the regulons. Next, the regulon activity for each cell was scored by AUCell. For some regulons, AUCell thresholds were manually adjusted as recommended by the SCENIC developers. Finally, the activity of each transcription factor was visualized by heatmap among all the cell clusters.
+
+Calculate activity from MetaCell
+
+Raw count matrix was imported by mcell_import_scat_tsv function in metacell R package and metacell membership was calculated by its default pipeline. Cells with Log2 (library normalized) gene expression was assigned the metacell membership and average gene expression of cells with the same membership was calculated to form a gene x metacell pseudobulk matrix. Based on the TF and SIG list in SJARACNE, the gene x metacell matrix was exported by generateSJARACNeInput function to for generating TF and SIG network by SJARACNE. The activity of each cell was further calculated with cal.Activity function with es.method='weightedmean'.
+
+Software packages
+
+For comparing the clustering performance with Seurat, SC3, and Scanpy, we used the following packages: (i) Seurat version 4.0.3 from CRAN (https://cran.r-project.org/web/packages/Seurat/index.html); (ii) SC3 version 1.18.0 from Bioconductor (https://bioconductor.org/packages/release/bioc/html/ SC3.html); (iii) Scanpy version 1.6.0 from
+GitHub (https://github.com/theislab/scanpy); for approximated nearest neighbor graph construction, we used PyNNDescent version 0.5.2 (https://github.com/lmcinnes/pynndescent), a Python implementation of NNDecent algorithm\(^{74}\); for graph embedding, we used PecanPy\(^{75}\), an efficient Python implementation of node2vec\(^{71}\); we used an open-source compiler Numba (http://numba.pydata.org/) for translation of our Python and NumPy implementation of mutual information calculation into fast machine code.
+Data availability
+
+All the data sets in Supplementary Tables 1 and 2 were downloaded from the accession numbers provided in the original publication.
+
+Code availability
+
+The source code for scMINER is available online at https://github.com/jyyulab/scMINER. The documentation with a tutorial is available online at https://jyyulab.github.io/scMINER.
+
+Acknowledgements
+
+We thank the members of the Yu Lab for testing and improving scMINER and Keith A. Laycock for scientific editing. This work was supported in part by National Institutes of Health grants R01GM134382 (to J.Y.), U01CA264610 (to J.Y.) and R35CA253188 (to H.C.), and by the American Lebanese Syrian Associated Charities. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health.
+
+Author contributions
+
+D.L., H.S., and J.Y. conceived the project. D.L. and H.S. designed the computational method, wrote software packages, and carried out analyses. C.Q. contributed to analyses and software development. C.B., J.P.V., A.K., M.R., and M.B. contributed to software development. Q.P., Y.D., Z.X., I.R., X.Y., X.H., and L.Y. assisted with analysis and software testing. K.K.Y. provided computational insights. H.C. provided biological insights. D.L., H.S., C.Q., and J.Y. wrote the manuscript. J.Y. supervised the project.
+Competing financial interests
+
+L.D. is currently an employee at Spatial Genomics Inc. All the other authors declare no competing financial interests.
+FIGURE LEGENDS:
+
+Figure 1: Overview of scMINER.
+
+scMINER is a system biology toolkit that has been separated into mutual information-based clustering analysis (MICA) and mutual information-based network inference engine (MINIE). Mutual information (MI) is first calculated from the gene count matrix from scRNA-seq to obtain a MI-based distance matrix. Multidimensional scaling (MDS) based dimension reduction is then performed followed by K-mean clustering. Cell state specific networks are constructed using SJARACNE to infer the regulons of transcription (TF) and signaling protein (SIG) drivers. The importance of each TF and SIG driver is measured by comparing between different cell states. The regulatory network re-wiring of these drivers in various cell states could be further captured, which serves the basis of identifying critical drivers in cell lineage differentiation and tissue specific specification. Moreover, the regulon activity could be further used to refine expression-based clustering (activity-based clustering).
+
+Figure 2: Evaluation of scMINER clustering performance.
+
+a, Clustering performance of scMINER, Seurat, SC3 and Scanpy measured by adjusted Rand index (ARI). b, The average ARIs and their variance (vertical segments). scMINER significantly outperforms other clustering methods (\( p = 0.0004 \) by the one-sided Wilcoxon test). c, UMAP and silhouette plots of the Zeisel and Klein datasets using scMINER, Seurat, and SC3. Silhouette index is reported (red dashed line) for each UMAP representation of clustering result. d, Average silhouette index values and their variance (vertical lines). scMINER significantly outperforms other clustering methods (\( p = 0.0019 \) by the one-sided Wilcoxon test). e, Clustering
+performance comparison using four distance metrics mutual information (MI), Spearman correlation, Pearson correlation and Euclidean distance as metrics. MI outperforms other linear metrics when the number of dimensions is greater than a fixed number. f, Clustering performance comparison using four dimension reduction approaches multidimensional scaling (MDS), principal component analysis (PCA), Laplacian, and PCA sequentially followed by Laplacian (LPCA).
+
+Figure 3: scMINER improves the clustering of ambiguous subpopulations in PBMCs in comparison with Seurat.
+
+a, UMAP and Sankey plots of scMINER and Seurat clustering results annotated using true labels. b, CD4TCM and CD4Treg cells (by true label) projected on scMINER and Seurat clustering UMAP plots. c, Signature score heatmap plots of scMINER and Seurat clusters calculated using curated markers for each cell type. d, Donut plots of scMINER cluster 1, 2 and Seurat cluster 1 to show the cell type compositions and the cluster purity. e, Comparison of the number of CD4Treg cells expressing master regulators FOXP3, IL2RA, and TIGIT on scMINER cluster 2 and Seurat cluster 1. f, MICA clustering performance comparison using CPM and CP10k normalization methods.
+
+Figure 4: Comparison of scMINER and SCENIC on activity-based mark identification and clustering of PBMC cell types.
+
+a, Unsupervised scMINER clustering of 7 clusters of sorted PBMC cell types on UMAP. b, Heatmap visualization of cell marker expression (left) and predicted activity (right) in each cell from sorted PBMC cell types. The regulatory networks are generated in cell-type specific
+manner. c, FOXP3 (left) and CD56 (encoded by NCAM1, right) expression and scMINER activity on UMAP. d, UMAP visualization of FOXP3 activity predicted by SCENIC pipeline. e, Unsupervised clustering of the 7 sorted PBMC cell types based on SCENIC and scMINER activity. The true labels of these 7 cell types are labeled. f, The Adjusted Rand Index (ARI) of clustering in e based on SCENIC and scMINER activity.
+
+Figure 5: scMINER captures cluster-specific drivers for CD8+ exhausted T cells.
+a, MICA MDS clustering of GP33-tetramer+ CD8+ T cells at day 28 from mice chronically infected with LCMV Clone 13 (GSE122712). The expression of Tcf7, Cx3cr1 and Haver2 is visualized on UMAP. b, Heatmap visualization of expression (left) and predicted activity (right) of selected TFs in each cell from 3 subsets of CD8+ T cells. c, Heatmap visualization of the average TF SCENIC activity in each cluster of CD8+ T cells. TFs without activity predicted by SCENIC are shown in light grey. d, Similarity of TF regulon in Tpex and Tex CD8+ T cells generated by SJARACNe and footprint genes detected by ATAC-seq data (GSE123236) in corresponding cell clusters. Expected number of genes in intersection of ATAC-seq footprints as reference (log10 scale, x axis) with regard to hypergeometric distribution vs. observed intersection (log10 scale, y axis). For all genes, the observed intersection is significantly higher than expectation (black line). The color of the dots represents –log_{10} (P-value) according to Fisher’s exact test. e, Heatmap visualization of cell marker expression (left) and predicted activity (right) of selected SIGs in each cell from 3 subsets of CD8+ T cells. f, The regulons of Batf in Tpex (red), Teff-like (green) and Tex (blue) cells. Regulons shared by 2 or more cell types are highlighted as yellow (Tpex and Teff-like), grey (Teff-like and Tex), magenta (Tex and Tpex), and turquoise (Tpex, Teff-like and Tex). g, Functional pathway enrichment of Batf
+regulons of Tpex and Teff-like cells and the one shared by Tpex and Teff-like. h, Violin plot of the expression (upper) and activity (lower) of Tox, Tcf7 and Batf in wild-type and Tox deficient CD8+ T cells.
+
+Figure 6: Tissue-specific differentiation of Treg identified by scMINER.
+
+a, MICA MDS clustering of mouse Foxp3+ regulatory CD4+ T cells (GSE130879) isolated from spleen, lung, skin and visceral adipose tissue (VAT). The expression of Cd44 and Sell is visualized by violin plots. b, Heatmap visualization of predicted activity of top TFs in each cell from spleen, muscle, colon and VAT Treg cells. c, Violin plot visualization of Bach2, Klf2, Atf6 and Pparg expression, scMINER activity, scATAC gene activity in spleen, muscle, colon and VAT Treg cells. scATAC gene activity was by signac R package based on GSE156112. d, Functional pathway enrichment of a union of top 50 TFs and top 200 SIGs in each tissue Treg cells based on t value from Student’s t test. e, The regulons of Pparg in spleen (red), lung (orange), skin (green) and VAT (blue) Treg cells. Regulons shared by 2 or more cell types are highlighted as pink. f, Functional pathway enrichment of Pparg regulons in spleen, muscle, colon and VAT Treg cells. g, MICA MDS clustering of mouse Klrg1-Nfil3-, Klrg1-Nfil3+, Klrg1+Nfil3+ Treg cells isolated from spleen (GSE130879). Pdcld1, Klrg1 and Nfil3 expression are visualized on UMAP. h, Violin plot visualization of Batf, Gata3, Nfil3 and Pparg expression and activity in spleen, muscle, colon and VAT Treg cells. i, Functional pathway enrichment of a union of top 50 TFs and top 200 SIGs in each stage of spleen Treg cells.
+Supplementary Information
+
+Supplementary Figures. 1–9.
+Supplementary Tables 1–2.
+Supplementary Note.
+References
+
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+Figure 1
+
+Pre-processed matrix
+Filtered genes
+N cells
+MI-based graph
+N nodes
+Graph embedding
+d2
+d1
+Embedded matrices
+N cells
+...
+Graph clustering
+Mutual information (MI) Estimation
+\( I(c_i, c_j) = \sum \sum p(c_i, c_j) \log \frac{p(c_i, c_j)}{p(c_i) p(c_j)} \)
+N <= M
+MI-based distance matrix
+N cells
+Multidimensional scaling
+N cells
+Consensus k-means
+Expression-based clustering
+A
+B
+C
+MICA
+Applications
+Lineage differentiation
+intermediate
+progenitor
+terminal
+Tissue specification
+tissue1
+tissue2
+tissue3
+Cluster-specific drivers
+Network rewiring
+Activity-based clustering
+Activity
+Cells
+Drivers
+MI-based gene network reverse-engineering
+A
+B
+C
+Cluster-specific networks
+MINIE
+Figure 2
+
+a
+
+![Line graph showing ARI (Adjusted Rand Index) for different methods across various datasets](page_120_120_1047_384.png)
+
+b
+
+![Bar chart comparing ARI for scMINER, Seurat, SC3, Scanpy](page_120_504_1047_192.png)
+
+c
+
+![Scatter plots and heatmaps for Zeisel and Hmab datasets for scMINER, Seurat, SC3](page_120_704_1047_192.png)
+
+d
+
+![Bar chart comparing Silhouette index for scMINER, Seurat, SC3, Scanpy](page_120_904_1047_192.png)
+
+e
+
+![Line graph showing ARI vs Number of components for MI, Spearman, Pearson, Euclidean](page_120_1104_1047_192.png)
+
+f
+
+![Line graph showing ARI vs Number of components for MDS, PCA, LaplacianPCA, Laplacian](page_120_1304_1047_192.png)
+Figure 3
+
+a
+
+![UMAP plots showing cell clusters labeled by scMINER and Seurat algorithms](page_120_120_670_480.png)
+
+b
+
+![UMAP plots showing CD4+ Treg true labels and CD4+ TCM true labels](page_120_600_670_480.png)
+
+c
+
+![Heatmap comparing scMINER and Seurat signature scores for various immune cell types](page_120_1080_670_480.png)
+
+d
+
+![Pie charts showing percentage distribution of clusters in scMINER and Seurat algorithms](page_800_120_670_480.png)
+
+e
+
+![Bar charts showing cell number for FOXP3+ cells, IL2RA+ cells, and TIGIT+ cells between scMINER cluster 2 and Seurat cluster 1](page_120_1560_670_480.png)
+
+f
+
+![Bar chart comparing ARI values for CP10k and CPM normalization methods](page_800_1560_670_480.png)
+Figure 4
+
+a
+1: Monocyte
+2: B
+3: CD4 Treg
+4: CD4 Naive T
+5: CD4 TCM
+6: NK
+7: CD8 Naive CTL
+
+b
+Expression
+Activity
+
+c
+FOXP3 Expression Activity
+CD56 (NCAM1) Expression Activity
+
+d
+FOXP3 SCENIC activity
+High
+Low
+
+e
+Activity-based clustering
+SCENIC
+scMINER
+True label
+1: Monocyte
+2: B cell
+3: CD4 Treg
+4: CD4 Naive T
+5: CD4 TCM
+6: NK
+7: CD8 Naive CTL
+
+f
+ARI
+SCENIC scMINER
+
+g
+Treg percentage
+Activity
+Expression
+True Label
+Figure 5
+
+a
+Tcfl7 Expression High
+Low
+UMAP_2
+UMAP_1
+Tpex
+Teff-like
+Tex
+Cx3cr1
+Hacvr2
+
+b
+TF expression
+TF activity
+Tpex  Teff-like  Tex
+Tpex  Teff-like  Tex
+
+c
+SCENIC
+Tcfl7
+Rbl (137g)
+Nkb1 (286)
+Foxo1 (536g)
+Id3
+Lef1
+Klf2 (313g)
+Klf3 (234g)
+Runx1 (65g)
+Tbx21 (304g)
+Ctnnα (14g)
+E2f2 (229g)
+Bhlhe40_extended (1299g)
+Irf1 (311g)
+Batf
+Prdm1_extended (131g)
+Tox
+Nat1ct (13g)
+
+d
+Tpex
+Tex
+Log_{10} (expectation) scMINER
+Log_{10} (expectation) ATAC
+
+e
+SIG expression
+SIG activity
+Tpex  Teff-like  Tex
+Tpex  Teff-like  Tex
+
+f
+Tex/Tpex  Batf TF targets rewiring
+Tex
+Tpex
+Tex/Teff-like
+Teff-like/Tpex
+Teff-like
+Tpex
+Tex
+Venn diagram: 63, 37, 32, 133
+
+g
+HALLMARK_DNA_REPAIR
+KEGG_CELL_CYCLE
+KEGG_CITRATE_CYCLE_TCA_CYCLE
+HALLMARK_UNFOLDED_PROTEIN_RESPONSE
+KEGG_UBIQUITIN_MEDiated_PROTEOLYSIS
+HALLMARK_IL2_STATS_SIGNALING
+HALLMARK_ADIPGENESIS
+KEGG_NATURAL_KILLER_CELL_MEDIATED_CYTOTOXICITY
+KEGG_LEUKOCYTE_TRANSDIFFERENTIATION
+HALLMARK_INTERFERENCE_ALPHA_RESPONSE
+HALLMARK_INTERFERENCE_GAMMA_RESPONSE
+KEGG_RIBOSOME
+KEGG_T_CELL_RECEPTOR_SIGNALING_PATHWAY
+HALLMARK_ALLOGRAFT_REJECTION
+KEGG_PROTEASOME
+KEGG_SPILOSOMES
+HALLMARK_MVC_TARGETS_V1
+KEGG_OXIDATIVE_PHOSPHORYLATION
+HALLMARK_OXIDATIVE_PHOSPHORYLATION
+Odds Ratio
+-log10(Adj_P)
+Tpex
+Teff-like
+Tpex
+Teff-like
+
+h
+Expression
+Activity
+Tox
+Tcfl7
+Batf
+Zeb2
+WT  Tox KO  WT  Tox KO  WT  Tox KO  WT  Tox KO
+Figure 6
+
+a
+
+VAT (1,329)
+Spleen (1,286)
+Lung (1,904)
+Skin (272)
+
+Expression
+Cd44
+Sell
+
+b
+TF expression
+TF activity
+
+c
+TF Expression
+TF activity (scMINER)
+TF activity (scATAC-seq)
+Bach2 (Spleen and lung)
+Klf2 (Lung)
+Atf6 (Skin)
+Pparg (VAT)
+
+d
+VAT TREG
+SKIN TREG
+SI 2016 TISSUE TREG
+GSE7852_LN_VS_FAT_TREG_UP
+GSE7852_LN_VS_FAT_TREG_DN
+GSE37532_WT_VS_PPARG_KO_VISCERAL_ADIOPOSE_TISSUE_TREG_UP
+
+e
+Pparg target rewiring
+Lung
+VAT
+Skin
+Spleen
+
+f
+GSE14350_IL2RB_KO_VS_WT_TREG_DN
+GSE20306_CD103_KLRG1_DP_VS_DN_TREG_UP
+GSE7852_LN_VS_FAT_TREG_UP
+GSE7852_THYMUS_VS_FAT_TREG_UP
+GSE14415_ACT_VS_CTRL_NATURAL_TREG_UP
+GSE42021_CD44H_VS_024LOW_TREG_UP
+GSE19364_PA_VS_UNTREATED_TREG_DN
+GSE14415_ACT_VS_CTRL_NATURAL_TREG_DN
+GSE51077_ETREG_SIGNATURE
+GSE14350_IL2RB_KO_VS_WT_TREG_UP
+GSE61077_CTREG
+GSE7852_LN_VS_FAT_TREG_DN
+GSE37532_VISCERAL_ADIOPOSE_TISSUE_VS_LN_DERIVED_TREG_CD4_TCELL_DN
+CORE_TR_TREG_SIGNATURE
+
+g
+UMAP_2
+UMAP_1
+Klr1-Nfil3*
+Klr1+Nfil3*
+Pdcd1
+Klr1
+Nfil3
+
+h
+Expression
+scMINER activity
+Batf
+Gata3
+Nfil3
+Pparg
+
+i
+GSE61077_ETREG_SIGNATURE
+GSE37532_WT_VS_PPARG_KO_VISCERAL_ADIOPOSE_TISSUE_TREG_UP
+GSE61077_CTREG
+Supplementary Files
+
+This is a list of supplementary files associated with this preprint. Click to download.
+
+• Supplementaryinformationv2.2.pdf

0c5a7af6bd9f4fbc811ddc8b633c0265f33543963fec69e508eee8501c4904ef/peer_review/peer_review.md

@@ -0,0 +1,43 @@
+Peer Review File
+
+Topographic representation of current and future threats in the mouse nociceptive amygdala
+Editorial Note: This manuscript has been previously reviewed at another journal that is not operating a transparent peer review scheme. This document only contains reviewer comments and rebuttal letters for versions considered at Nature Communications.
+
+REVIEWER COMMENTS</B>
+
+Reviewer #1 (Remarks to the Author):
+
+The authors have addressed my previous concerns and I support publication.
+
+Reviewer #3 (Remarks to the Author):
+
+1, I greatly appreciate that the authors plotted the locations of fiber placement for subjects. I also understand that the authors described the accuracy and efficiency of targeting the rostral vs. caudal Calcrl population in detail, as was also in response to Reviewer #2 point #2. As they used only the extreme ends of the CeA, and excluded the animals with fibers located >200 um from the desired coordinates (page 7, 2nd paragraph), I recommend analyzing the correlation between the location of fibers and the behaviors of these animals. This will reveal if the rCeA and cCeA are two distinct sub-nuclei or a continuous structure with a subtle gradient.
+
+2, My concern is still the definitions of rCeA and cCeA in this study. While I appreciate that the authors precisely controlled the stereotaxic coordinates, viral injection volumes, and expression levels, it still seems complicated to distinguish such small subregions. Because previous studies, including the authors’ own, have demonstrated many cell-type specific marker molecules, such as PKC delta, Somatostatin, and CRF, I recommend verifying the cell types in different coordinates using immunostaining or other methods.
+
+3, The response to Reviewer #1 point #14 was rather confusing to this reviewer. They found that the photoinhibition of either rCeA or cCeA Calcrl neurons during the foot shock delivery had no effect on fear learning (Extended Data Fig. 9i-j). The authors argue that these results suggest that while rCeA Calcrl neuron activity following the US conveys stimulus valence and promotes behavioral responses, the activity is not necessary for downstream associative processing. However, their previous work (Han et al., 2015) demonstrated that silencing Calcrl neurons in the CeA significantly attenuated fear learning. Are these potentially opposing results due to methodological differences (TeTx vs. GtACR2) or potential compensatory roles of rCeA and cCeA? Does silencing both rCeA and cCeA during the foot shock attenuate the fear learning?
+4, The response to my point #8 was not clear. The authors’ response to my comment says, “the bulk of the cells are located quite ventrally, over 1 mm deeper than our fiber tips in this stimulation experiment. Because of this, and the variability in fiber placement that results in locations slightly rostral or caudal from this AP level, we do not think that this is the reason for the difference in behavior in the place-aversion experiment. Additionally, these same animals were used in the conditioned place aversion study where cCeA stimulation led to enhanced place aversion.”
+
+The author’s group previously demonstrated that Calcrl neurons are more in rCeA, and stimulating Calcrl neurons in the CeA induces freezing behaviors and fear learning (Han et al., 2015). Do the authors suggest that the Calcrl neurons stimulated in the present study are different from those in the previous work by Han et al. because they reside deeper (over 1 mm deeper than our fiber tips)? Or are there distinct sub-regions of CeA along the DV axis as well?
+1, I greatly appreciate that the authors plotted the locations of fiber placement for subjects. I also understand that the authors described the accuracy and efficiency of targeting the rostral vs. caudal Calcrl population in detail, as was also in response to Reviewer #2 point #2. As they used only the extreme ends of the CeA, and excluded the animals with fibers located >200 um from the desired coordinates (page 7, 2nd paragraph), I recommend analyzing the correlation between the location of fibers and the behaviors of these animals. This will reveal if the rCeA and cCeA are two distinct sub-nuclei or a continuous structure with a subtle gradient.
+
+Thank you for the suggestion. We are inclined to regard the CeA as a continuous structure with a subtle gradient. As our dataset does not include any animals targeting the middle a simple correlation would be unable to reveal the entire relationship between phenotype and fiber placement (it would reveal two clusters best fit by a line, with an empty gap in the middle as in Extended Data Fig. 5d). However, several of our other studies involving anterograde and retrograde tracing involved variable expression distributions across the CeA. These reveal what appear to be a continuous distribution with smoothly varying relationship to various outcomes such as PBN connection strength (Extended Data Fig. 1f) and SI and BNST connectivity (Extended Data Fig. 3c-d). We were interested in what this gradient in connectivity might suggest functionally, so we specifically targeted the extremes of the distribution for manipulation. This allows us to understand the maximum likely differences to be observed biologically. We expect that under normal conditions, activity is balanced across the gradient to push behavior towards these different possibilities, as we describe in the discussion (lines 307-310), and now also explicitly mention as an important area of study in future (lines 339-340).
+
+2, My concern is still the definitions of rCeA and cCeA in this study. While I appreciate that the authors precisely controlled the stereotaxic coordinates, viral injection volumes, and expression levels, it still seems complicated to distinguish such small subregions. Because previous studies, including the authors’ own, have demonstrated many cell-type specific marker molecules, such as PKC delta, Somatostatin, and CRF, I recommend verifying the cell types in different coordinates using immunostaining or other methods.
+
+Thank you for the suggestion, we agree that identifying methods for isolating the topography of the CeA outside of targeted injections is crucial for others to leverage these findings in future work. Ours and others’ previous work identified a gradient of PKCδ and CRH expression across the CeA (Han et al. 2015, Kim et al. 2017, Sanford et al. 2017). We have added an additional experiment explicitly comparing expression of various cell-type markers in the rostral vs caudal CeA. We find that there are several genes co-expressed with Calcrl with significant spatial expression differences, with Drd2 co-expressed preferentially in the rCeA and Tacr1/Pkcd preferentially co-expressed caudally (new Extended Data Fig. 2, lines 111-119). These findings may be used in the future to aid targeting rostral vs. caudal CeA populations with a single viral injection.
+
+3, The response to Reviewer #1 point #14 was rather confusing to this reviewer. They found that the photoinhibition of either rCeA or cCeA Calcrl neurons during the foot shock delivery had no effect on fear learning (Extended Data Fig. 9i-j). The authors argue that these results suggest that while rCeA Calcrl neuron activity following the US conveys stimulus valence and promotes behavioral responses, the activity is not necessary for downstream associative
+processing. However, their previous work (Han et al., 2015) demonstrated that silencing CalcrI neurons in the CeA significantly attenuated fear learning. Are these potentially opposing results due to methodological differences (TeTx vs. GtACR2) or potential compensatory roles of rCeA and cCeA? Does silencing both rCeA and cCeA during the foot shock attenuate the fear learning?
+
+These apparent differences in findings can be resolved if the methodological differences are considered. TeTx expression in the study by Han et al. differed from our GtACR2 study in multiple ways. First, it silenced all CalcrI neurons across the entire CeA, second, it silenced CalcrI neurons both before, during, and after memory formation. Hence, this manipulation is unable to resolve whether activity of CalcrI neurons contributes to US encoding enabling memory formation, or consolidation to reinforce an association, or generation of the learned fear behavior (or all of the above). Our TeTx inhibition study silencing either the rostral or caudal CeA CalcrI+ neurons was most comparable to the study by Han et al.; in this case we replicated their findings (Fig. 5o-p). On the other hand, our GtACR2 study tested the specific question of whether activity in rostral or caudal CeA CalcrI+ neurons during the foot shock was specifically important for fear learning. In this case, neural activity was only affected for a total of 32 s, for 4 s each around each of the 8 conditioning foot shocks. In this case, fear learning was unaffected. This suggests that relay of the foot shock through CeA CalcrI+ neurons is not necessary for fear memory formation but does not account for whether their activity is important for consolidation or fear recall.
+
+4, The response to my point #8 was not clear. The authors’ response to my comment says, “the bulk of the cells are located quite ventrally, over 1 mm deeper than our fiber tips in this stimulation experiment. Because of this, and the variability in fiber placement that results in locations slightly rostral or caudal from this AP level, we do not think that this is the reason for the difference in behavior in the place-aversion experiment. Additionally, these same animals were used in the conditioned place aversion study where cCeA stimulation led to enhanced place aversion.”
+The author’s group previously demonstrated that CalcrI neurons are more in rCeA, and stimulating CalcrI neurons in the CeA induces freezing behaviors and fear learning (Han et al., 2015). Do the authors suggest that the CalcrI neurons stimulated in the present study are different from those in the previous work by Han et al. because they reside deeper (over 1 mm deeper than our fiber tips)? Or are there distinct sub-regions of CeA along the DV axis as well?
+
+We agree with the primary point that there are sections of the rostral CeA with greater numbers of CalcrI neurons than some sections of the caudal CeA. Our argument related to the probability that this difference in cell number could be responsible for our observed phenotypes. We argue that, since the cell density is comparable near the fiber tips in both placement conditions (the CeA is similarly wide/tall in the dorsal regions we targeted our fibers towards, but enlarges ventrally in rostral regions), that the delivered light would activate similar numbers of neurons in both scenarios. Regarding the question of sub-regions along the DV axis, our studies sought to disentangle rostral vs. caudal so we carefully maintained DV targeting to minimize variability outside the area of explicit inquiry. Hence, we cannot speak as to whether such a distinction exists. This could be a fruitful area of research for future study.
+REVIEWERS' COMMENTS
+
+Reviewer #2 (Remarks to the Author):
+
+The authors appropriately addressed all of my comments. I support the publication.

0cada618bb488f1258412c269438e0dbe8f9b287946d4660b5442737b0d7019d/peer_review/peer_review.md

@@ -0,0 +1,203 @@
+REVIEWER COMMENTS
+
+Reviewer #1 (Remarks to the Author):
+
+The present manuscript reports exploitation of Sondheimer oscillations as a method to obtain I_MR in micro/nano-devices. Basically, this report firmly establishes the methodology of Sondheimer oscillations, which is utilized in the analysis of electrical conduction of a micro/nano-device and allows for identification of its conduction regime and the extraction of conduction length scales. This methodology also overcomes the limitations of the analysis based on the Drude model in the micro/nano-devices and of SdH oscillations. Thus, the present study is of significance and widespread usage of this methodology as a tool to characterize the conduction mechanisms is expected to be made in the field of micro/nano-devices. As the manuscript is novel and no error was found in the analysis, I recommend the publication of the present manuscript in Nature Communications. A few typos should be corrected before publication.
+
+Reviewer #2 (Remarks to the Author):
+
+The paper by van Delft et al exploits Sondheimer oscillations (SO) to obtain the momentum relaxing mean-free path in microdevices. This is important for evaluating the quality of the quantum electronic devices after microfabrication; a step that can be harmful for intrinsic material properties. The evaluation of mean-free-path can also help to assign a transport regime (ohmic, ballistic or hydrodynamic), which the device operates in. The authors take WP2 material and fabricate a staircase device using focused ion beam technique. Such device geometry helps evaluating SO and the mean free path, which is in agreement with the bulk values of WP2. This serves as evidence that WP2 can be processed with FIB without degradation and the device can operate in a hydrodynamic regime. The paper can be interesting from the technical point of view, since it demonstrates evidences that WP2 can have good quality after FIB fabrication. However, the evaluation of the mean-free-path from SO is already well documented and the authors cite the previous works properly. Therefore, the proposal of this manuscript to use SO for mean-free-path evaluation is clearly not novel. The hydrodynamic transport regime of the fabricated device is also not demonstrated.
+
+New components of this work is the observation of SO oscillations in WP2 and, what I find appealing, is Fig 4c comparing different scattering times. Whether this is sufficient for publication in Nat Communications or is more suitable for a specialized community, I would like to leave it up to the Editor’s decision.
+
+1) I find the title is misleading, since it suggests that the type-II Weyl semimetal property is important for the effects reported here. However, the topological characteristics of the material are not a part of SO treatment; only a long I_MR is important. Whether the Weyl physics survives in FIB fabricated devices is yet to be demonstrated. The title “Sondheimer oscillations in FIB fabricated WP2 crystal” can better match the content of the presented manuscript.
+
+2)The emergence of oscillating Rxy behavior is not explained. The concept Figrue 1a is confusing and picks up only a particular electron velocity that moves on a spiral along the magnetic field. It looks like the device is insulating at this particular magnetic field, since the electrons are localized.
+
+3)It is unclear what frequency in Fig. 4a is taken for the analysis of scattering time. The notations for y-axis in Figures 4a and 4b are different, though these should be the same quantities.
+
+4)It would be interesting to add in Fig. 4c the scattering time evaluated from the sample resistance at
+zero field.
+
+5) I missed the discussion of the spectrum in Fig. 4a. What do the different frequencies correspond to?
+
+6) How large is the electrical current in the measurements? Do the devices have ohmic characteristics? The device dimensions reaching the regime when the size quantization can start become important. Did the author consider this possibility?
+
+7)The device dimensions should be given consistent throughout the paper. Sometimes the device dimension is given as 4.6um, in another figure it is 4.2um or even 4.3 um. This inconsistency appears for other sizes as well. Are these different devices? And what devices are used for evaluating the mean free path?
+
+8)Does the FIB fabrication change the charge carrier density? Is the charge carrier density the same in all segments of the staircase device?
+
+Reviewer #3 (Remarks to the Author):
+
+In their manuscript 'Sondheimer oscillations as a probe of non-ohmic flow in type-II Weyl semimetal WP2'. The authors report magneto-resistance measurements on high-quality micromachined WP2 crystals at various temperatures, aiming to discern different electronic transport regimes, namely ballistic and hydrodynamic.
+Using Sondheimer oscillation, they extract the electron momentum-relaxing scattering times, which:
+(1) in the ballistic regime is not limited by the device width and (2) is applicable at temperatures where hydrodynamic electron flow is claimed to appear. The measured electron scattering rates at high temperatures agree with a phonon-mediated hydrodynamic transport theory and previous studies (Gooth, J. et al.). However, no new information on the microscopic origin of hydrodynamic behavior in WP2 is provided.
+Nevertheless, the methodology presented in the manuscript for obtaining quantitative information on the momentum relaxing scattering times in working devices is essential when probing non-ohmic electron flow, particularly for any claim of hydrodynamic behavior - which is of current interest in the field.
+The paper is easy to read and clearly written. The conclusion that Sondheimer oscillations are useful in situ probe for non-ohmic electron transport in 3D conductors is convincing and will interest the community.
+Therefore, I recommend publication subject to a few comments/clarifications:
+(1) It would be instructive for the reader to compare the l_mr extracted form resistivity and Hall measurements to the SO extracted l_mr to clearly show the SO method advantage.
+(2) The maximum temperature probed appears to be 40 K for both figure 4 and S5. However, in the abstract and text, it is claimed 50 K. What is the maximum temperature you observe Sondheimer oscillations?
+(3) In Fig. 4C, the extracted scattering time is for which device thickness?
+(4) In Fig. S5, there is a missing legend for one of the data sets.
+(5) Line 29 in supplementary. The units of current are mislabeled 0.2 um, should be 0.2uA.
+Reviewer #1 (Remarks to the Author):
+
+The present manuscript reports exploitation of Sondheimer oscillations as a method to obtain I_MR in micro/nano-devices. Basically, this report firmly establishes the methodology of Sondheimer oscillations, which is utilized in the analysis of electrical conduction of a micro/nano-device and allows for identification of its conduction regime and the extraction of conduction length scales. This methodology also overcomes the limitations of the analysis based on the Drude model in the micro/nano-devices and of SdH oscillations. Thus, the present study is of significance and widespread usage of this methodology as a tool to characterize the conduction mechanisms is expected to be made in the field of micro/nano-devices. As the manuscript is novel and no error was found in the analysis, I recommend the publication of the present manuscript in Nature Communications. A few typos should be corrected before publication.
+
+Thank you for your encouraging words on our work!
+
+Reviewer #2 (Remarks to the Author):
+
+The paper by van Delft et al exploits Sondheimer oscillations (SO) to obtain the momentum relaxing mean-free path in microdevices. This is important for evaluating the quality of the quantum electronic devices after microfabrication; a step that can be harmful for intrinsic material properties. The evaluation of mean-free-path can also help to assign a transport regime (ohmic, ballistic or hydrodynamic), which the device operates in. The authors take WP2 material and fabricate a staircase device using focused ion beam technique. Such device geometry helps evaluating SO and the mean free path, which is in agreement with the bulk values of WP2. This serves as evidence that WP2 can be processed with FIB without degradation and the device can operate in a hydrodynamic regime. The paper can be interesting from the technical point of view, since it demonstrates evidences that WP2 can have good quality after FIB fabrication. However, the evaluation of the mean-free-path from SO is already well documented and the authors cite the previous works properly. Therefore, the proposal of this manuscript to use SO for mean-free-path evaluation is clearly not novel. The hydrodynamic transport regime of the fabricated device is also not demonstrated.
+
+New components of this work is the observation of SO oscillations in WP2 and, what I find appealing, is Fig 4c comparing different scattering times. Whether this is sufficient for publication in Nat Communications or is more suitable for a specialized community, I would like to leave it up to the Editor’s decision.
+
+Sondheimer oscillations pose a classical phenomenon in clean metals in high magnetic fields and have been discovered long ago. We have taken care, as noted, to cite the relevant works and give credits to the scientists discovering them. Please allow us to discuss the novel aspects which go well beyond the classical literature of SO. SO by itself is a rather exotic niche phenomenon that
+is not well-known outside of the expert community, unlike quantum oscillations (dHvA, SdH) which are taught in undergraduate courses. The simple reason is that while QO proved pivotal in developing our understanding of metals and their Fermi surfaces; SO failed to provide a use case. It had been proposed as a spectroscopic technique to learn about critical endpoints of the Fermi surface, yet it failed to deliver accuracy and to show new insights to be learned about a metal from the detailed knowledge of these curvature terms. The crux is of course the sensitivity of SO on the sample shape, the surface termination, and the roughness, which bulk quantization of QO is immune to. Attempts shifted to use it as a surface spectroscopy technique, determining the specularity coefficient, and even use it as sensors for adsorbed gasses on the surface. While SO by themselves were interesting manifestations of semi-classical dynamics of electrons at the time, none of this, to our knowledge, contributed significantly to our understanding of metals.
+
+This is the main conceptual point we make here. With the current developments of non-ohmic current flows, such as hydrodynamics and its platforms, the bulk mean free path and its relation to dynamic scattering scales (el-ph; el-el;...) as well as to the finite size of the metal becomes a critical parameter. Here, we point to the so-far overlooked critical advantage of SO as they sense the bulk mean-free-path even in strongly confined microdevices. This important transport length scale is commonly very different from the quantum mean free path probed by QO, largely due to the immunity of the former to small-angle scattering events. In classical SO experiments on bulk metallic crystals, the extracted scattering time is found to be highly consistent with the scattering times obtained from transport. This does not work anymore in complex and confining shapes. Pointing to this, and demonstrating an actual quantitative and model-parameter-free determination of a scattering mean free path more than 2 orders of magnitude larger than the size of the device, are the main observations going beyond the established SO literature.
+
+1) I find the title is misleading, since it suggests that the type-II Weyl semimetal property is important for the effects reported here. However, the topological characteristics of the material are not a part of SO treatment; only a long l_MR is important. Whether the Weyl physics survives in FIB fabricated devices is yet to be demonstrated. The title “Sondheimer oscillations in FIB fabricated WP2 crystal” can better match the content of the presented manuscript.
+
+This is of course a matter of taste. Please let us lay out the reasoning for our choice of title and why we prefer to keep the original title. The title you propose is a correct technical summary of the experiment, it states what has been done. Yet it does not convey the implications of the work, the meaning of the results, or their relevance for current research fields. Our target audience are researchers interested in novel transport regimes beyond ballistic/diffusive in solids. The manuscript is explicit in that the Weyl-II properties are not directly relevant to the observation. Yet mentioning it we feel is extremely helpful to point readers interested in this materials class to this work, making them aware of the experimental possibilities as well as inspiring theoretical works that could address SO in Weyl systems. Non-ohmic flow is a key research area of transport in topological systems, while the question of whether or not topology is a factor in obtaining hydrodynamic transport is open.
+Whether the Weyl physics survives in FIB fabricated devices is yet to be demonstrated.
+
+The SO are not impacted by Weyl physics, and whether or not to mention it in the title is clearly a matter of taste. However, regarding the science of Weyl-II in these structures, there is no evidence supporting or even suggesting a topological change in the microstructures. We conclusively demonstrate that neither the -very long- bulk mean free path nor the quantum oscillation spectrum is changed by the microfabrication. The micron-size of the structures is well beyond any finite size confinement or quantization effects (see discussion below). Given these observations, there seems little doubt about the survival of the bulk band structure and properties.
+
+2)The emergence of oscillating Rxy behavior is not explained.
+
+Although the initial prediction of Sondheimer oscillations did not extend to \( R_{xy} \), it has since been well established experimentally and theoretically that oscillations do occur in \( R_{xy} \) as well (see e.g. Munarin et al., Physical Review 172, 718-736 (1968)). As the physical mechanism is the same as for \( R_{xx} \), this is not explained separately in our manuscript. We have now changed our introduction of the origin of oscillatory behavior to mention transverse transport as well.
+
+The concept Figure 1a is confusing and picks up only a particular electron velocity that moves on a spiral along the magnetic field. It looks like the device is insulating at this particular magnetic field, since the electrons are localized.
+
+Indeed, we share that point fully and this figure was already before submission subject of intense discussions by the authors. However, we were not able to come up with a better version. The figure is intended to visualize why the electronic system may show commensurability oscillations. The only way to improve the figure we see involves drawing multiple spirals of different velocities that all match the criterion. This quickly gets crowded, and is also deceptive: Regardless of the Fermi surface shape, any metal features (not necessarily circular) spirals along the field. Yet SO only appear if there is an extended region of constant dA/dk which inevitably is lost in a set of differently sized spirals. This is the reason why we eventually kept this figure as it visualizes commensurability of an electron trajectory, despite all its shortcomings. Given that already in the classical papers on SO such spiral pictures were used (e.g. H.J. Trodahl, J.Phys. C: Solid St. Phys. 13, 1764-1777 (1971)), it may be fair to say that this problem does not have a simple visual solution. We would highly appreciate any concrete ideas how to improve clarity here.
+
+3)It is unclear what frequency in Fig. 4a is taken for the analysis of scattering time. The notations for y-axis in Figures 4a and 4b are different, though these should be the same quantities.
+
+The scattering time plotted in figure 4c was measured in a 4.3 \( \mu \)m thick section of a staircase device (data shown in figures 3b and 4a, left). We have adapted the figure caption to clarify this. As we also demonstrate in figure S5, this scattering time is consistent across several devices, with different thickness and orientation.
+Indeed, the y-axes of figures 4a and 4b represent the same quantity, and should have been labelled in the same way. We have corrected this in the manuscript.
+
+4) It would be interesting to add in Fig. 4c the scattering time evaluated from the sample resistance at zero field.
+
+We would love to do this, yet how could this be done? The main issue we address here is that the bulk scattering time is inaccessible by transport measurements. This material is so clean that the sample is 2 orders of magnitude smaller than the mean free path, and its resistance is (almost) entirely due to boundary scattering on a very complex shape – the role of bulk scattering in establishing voltage gradients in transport is negligibly small. The 3D ballistic regime is highly non-local and very difficult to tackle quantitatively, especially given the complex Fermi surface and the complex device shape. Even if that could be done by a Boltzmann approach, there is no hope to identify the few and very rare bulk scattering events in this situation – this is exactly why the SO are so powerful. Certainly, a model calculation is possible at very high temperatures (300 K) when the bulk mean free path is nanoscopic and a diffuse transport situation is established. There, a simple local diffusion equation can be trivially evaluated in any shape numerically. Yet once in the diffuse regime, we do not have any Sondheimer or QO values to compare it to.
+
+5) I missed the discussion of the spectrum in Fig. 4a. What do the different frequencies correspond to?
+
+We are sorry if the presentation caused any confusion. The frequency spectrum of Fig. 4a is exactly the same as in 3c, in which only the T=4 K curves of different thickness are plotted. From the position of the peak, the thickness dependence in 3d and the association with the Fermi surface lobes is done. Fig. 4a just shows the temperature dependence of the same data, which allows us to extract the temperature-dependent mean free path discussed in 4b,c. As there is only an amplitude reduction but no change in the spectra, we did not discuss this again. We have added a line into the caption.
+
+6) How large is the electrical current in the measurements? Do the devices have ohmic characteristics? The device dimensions reaching the regime when the size quantization can start become important. Did the author consider this possibility?
+
+Thank you for pointing this out, we have added a statement into the paper. We have used currents of 50 or 100 μA in our measurements. At these currents, the devices respond linearly (no higher harmonic generation), which excludes intrinsic or extrinsic non-linear transport, for example through self-heating. This should have been stated clearly, sorry.
+
+For size quantization, we are still quite large. WP$_2$ is a metal with Fermi-surfaces spanning a decent fraction of the Brillouin zone. The associated wavelength hence is a small number of unit cells, far from the micron-size we investigate here. Quantization is indeed most interesting, and as we now can confirm the bulk material quality, it is the goal of a separate research project to obtain <100nm class devices which may enter a quantized regime. This is not simple for various
+technical reasons. For example, the heat dissipation under ion irradiation is through the bulk of the target crystal. As one cuts the devices that thin, given that by design they are not coupled to a substrate directly, the thermal conductivity drops rapidly which leads to heat buildup and eventually chemistry. In the devices presented here, the observation of quantum oscillations in good agreement with bulk values excludes a significant band structure modification through quantization.
+
+7)The device dimensions should be given consistent throughout the paper. Sometimes the device dimension is given as 4.6um, in another figure it is 4.2um or even 4.3 um. This inconsistency appears for other sizes as well. Are these different devices? And what devices are used for evaluating the mean free path?
+
+The thickness of 4.3 \( \mu \)m corresponds to the middle section of the staircase device shown in figure 2. This was wrongly labelled within this figure as 4.2 \( \mu \)m (we have now corrected this). The thickness of 4.6 \( \mu \)m corresponds to a different device. Altogether, we have measured Sondheimer oscillations for thicknesses of 1.3, 1.9, 2.0, 2.7, 3.5, 4.3 and 4.6 \( \mu \)m. We have evaluated the mean free path for each of these, and found the results to be highly consistent. A statement on the range of thicknesses was added to the main text.
+
+8)Does the FIB fabrication change the charge carrier density? Is the charge carrier density the same in all segments of the staircase device?
+
+We do not see any evidence for charge carrier density changes. We know that there is no degradation of the bulk quantum or transport mean free path, hence it is reasonable not to expect chemical composition / doping changes in the bulk. Furthermore, WP$_2$ is a high carrier density material, and even if some amount of surface doping was active, it is unrealistic for it to change the bulk carrier density. As a general precaution, we fabricate these devices using a Xe beam. Xe has no implantation potential and completely leaves the sample after irradiation. This addresses a common issue of Ga surface implantation in FIB methods. Yet again, given the high carrier density even surface Ga implantation would be unlikely a source of carrier density variations. Indeed, experimentally we observe the same SdH frequencies of WP$_2$ bulk in the different segments, speaking against notable carrier density modulation in the devices.
+
+Reviewer #3 (Remarks to the Author):
+
+In their manuscript 'Sondheimer oscillations as a probe of non-ohmic flow in type-II Weyl semimetal WP2'. The authors report magneto-resistance measurements on high-quality micromachined WP2 crystals at various temperatures, aiming to discern different electronic transport regimes, namely ballistic and hydrodynamic. Using Sondheimer oscillation, they extract the electron momentum-relaxing scattering times, which: (1) in the ballistic regime is not limited by the device width and (2) is applicable at temperatures where hydrodynamic electron flow is claimed to appear. The measured electron
+scattering rates at high temperatures agree with a phonon-mediated hydrodynamic transport theory and previous studies (Gooth, J. et al.). However, no new information on the microscopic origin of hydrodynamic behavior in WP2 is provided.
+
+Nevertheless, the methodology presented in the manuscript for obtaining quantitative information on the momentum relaxing scattering times in working devices is essential when probing non-ohmic electron flow, particularly for any claim of hydrodynamic behavior - which is of current interest in the field.
+
+The paper is easy to read and clearly written. The conclusion that Sondheimer oscillations are useful in situ probe for non-ohmic electron transport in 3D conductors is convincing and will interest the community.
+
+We highly appreciate your supportive comments to our work, thank you.
+
+Therefore, I recommend publication subject to a few comments/clarifications:
+(1) It would be instructive for the reader to compare the l_mr extracted form resistivity and Hall measurements to the SO extracted l_mr to clearly show the SO method advantage.
+
+We would love to do this, yet how could this be done? The main issue we address here is that the bulk scattering time is inaccessible by transport measurements. This material is so clean that the sample is 2 orders of magnitude smaller than the mean free path, and its resistance is (almost) entirely due to boundary scattering on a very complex shape – the role of bulk scattering in establishing voltage gradients in transport is negligibly small. The 3D ballistic regime is highly non-local and very difficult to tackle quantitatively, especially given the complex Fermi surface and the complex device shape. Even if that could be done by a Boltzmann approach, there is no hope to identify the few and very rare bulk scattering events in this situation – this is exactly why the SO are so powerful. Certainly, a model calculation is possible at very high temperatures (300 K) when the bulk mean free path is nanoscopic and a diffuse transport situation is established. There, a simple local diffusion equation can be trivially evaluated in any shape numerically. Yet once in the diffuse regime, we do not have any Sondheimer or QO values to compare it to.
+
+(2) The maximum temperature probed appears to be 40 K for both figure 4 and S5. However, in the abstract and text, it is claimed 50 K. What is the maximum temperature you observe Sondheimer oscillations?
+
+The maximum temperature at which we observed Sondheimer oscillations was in fact 40 K. The 50 K mentioned in the text was an error that we have corrected in the new version of our manuscript.
+(3) In Fig. 4C, the extracted scattering time is for which device thickness?
+The scattering time plotted in figure 4c was measured in a 4.3 \( \mu \)m thick section of a staircase device (data shown in figures 3b and 4a, left). We have adapted the figure caption to clarify this.
+
+(4) In Fig. S5, there is a missing legend for one of the data sets.
+We have added the missing legend.
+
+(5) Line 29 in supplementary. The units of current are mislabeled 0.2 um, should be 0.2uA.
+We have corrected this mistake. Thank you!
+
+List of changes:
+
+• Caption of Fig. 4c: “Scattering times extracted for WP$_2$ using Eq. 2 and the Fermi velocity from Ref.18.” \( \rightarrow \) “Scattering times extracted for a 4.3 \( \mu \)m thick section of a WP$_2$ device using Eq. 2 and the calculated Fermi velocity, \( v_F = 3.6*10^5 \) m/s.”
+• Y-axis label of Fig 4b: “A (arb.u.)” \( \rightarrow \) “Amplitude (arb.u.)”
+• Label in Fig 2b: “4.2 \( \mu \)m” \( \rightarrow \) “4.3 \( \mu \)m”.
+• Added caption for the brown diamond symbols in figure S5.
+• Corrected line 29 of the SI: “0.2 \( \mu \)m” \( \rightarrow \) “0.2 \( \mu \)A”.
+• In the abstract: “up to T~50 K” \( \rightarrow \) “up to T~40 K”.
+• Line 188: “up to 50 K” \( \rightarrow \) “up to 40 K”.
+• Lines 70-72: “However, if the number of revolutions is non-integer, a net motion along the channel exists, delocalizing the carriers, resulting in oscillatory magnetotransport behavior.” \( \rightarrow \) “However, if the number of revolutions is non-integer, a net motion along or perpendicular to the channel exists, delocalizing the carriers, resulting in oscillatory longitudinal and transverse magnetotransport behavior.”
+• Line 132: “At high temperatures, the resistivity measured in \( \mu \)m-confined devices agrees well...” \( \rightarrow \) “We measure our \( \mu \)m-confined devices using standard lock-in techniques with applied currents of 50 or 100 \( \mu \)A, low enough to limit self-heating, and magnetic fields up to 18 T. At high temperatures, the measured resistivity agrees well...”
+• Lines 156-158, added: “We use Xe ions for the entire FIB fabrication process in order to avoid potential issues with Ga ion implantation leading to changes in the carrier density. Indeed, experimentally, we see no indication of any charge carrier modulation.”
+• Caption Fig. 4a, added: “The data at T=4 K is the same as that in Fig. 3c.”
+• Fig. 4a: exchanged labels “2.0 \( \mu m \)” and “4.3 \( \mu m \)”.
+• Line 204, added: “(between 1.3 and 4.6 \( \mu m \))”.
+• Line 69: “occur” \( \rightarrow \) “occurs”.
+• Abstract: “semi-metal” \( \rightarrow \) “semimetal”.
+• Line 134: “those”\( \rightarrow \) “that”.
+• Caption figure S5: “Device thickness, channel (Hall or longitudinal) and current direction (along the crystallographic a-axis, or between the b and c-axes.” \( \rightarrow \) “Device thickness, channel (Hall or longitudinal) and current direction (along the crystallographic a-axis, or between the b- and c-axes) do not affect the measured lifetime.”
+• Line 169: “Figs. 3f” \( \rightarrow \) “Fig. 3f”.
+• SI line 17: “phosphorous” \( \rightarrow \) “phosphorus”.
+• Lines 19, 50, 123, 134, 196, 235 and 241 and: “mean-free-path” \( \rightarrow \) ”mean free path”.
+REVIEWERS’ COMMENTS
+
+Reviewer #2
+
+I would like to thank the authors for addressing my comments and questions. Some issues have been clarified. I am particular thankful authors for discussing the novel aspects of their work, since I thought I may have missed some important arguments.
+
+Let me explain below the important points that I cannot agree.
+
+• The authors point to the “so-far overlooked critical advantage of SO as they sense the bulk mean-free-path even in strongly confined microdevices”. I cannot agree that this is something that has been overlooked. Reference 20 is from year 1979 and it is already stated there that: (i) the SO depends on the electron scattering in the volume, (ii) SO spectrum makes it possible to determine the mean free path. This paper and others make clear how the SO signal emerges. In fact, the nature of SO emergence requires some confinement. (The device size is comparable or smaller than the mean free path.) It is therefore unclear why the authors think that the “confinement” was overlooked. Because of the microstructure and the SO sensitivity to bulk scattering the authors can judge that the FIB seems not to affect the bulk part of WP2, at least in terms of the mean free path.
+
+The value of this MS can be that the authors re-introduce Sondheimer oscillations (40-50 years after their discovery), that remained largely unused so far. This MS does not show new aspects of SO phenomena. Neither the MS demonstrates anything on the hydrodynamic transport features and certainly does not probe non-ohmic flow.
+
+• I also cannot agree with the author’s approach on selecting the title. The current title misleads the reader and awakes wrong expectations. A reader anticipates type-II Weyl physics to come into play, but at the end the reader remains disappointed that Weyl is not important here. (Yes, the paper states in the text that Weyl is not important.) Any reference to Weyl is therefore inappropriate here. A material with a sufficiently large mean free path will show the same effect. Neither the MS demonstrates how the SO probes the non-ohmic flow. The SO probes only the mean free path in the bulk.
+The authors may anticipate implications of their work and discuss it in the text body. Whether this will then be realized at some point or not, is a different question. It will certainly be interesting to see in the future how the SO can probe the non-ohmic flow.
+One may also anticipate that, in the regime of hydrodynamic flow the emergence of SO may be altered, since the electron velocity changes gradually from the wall of the constriction to the bulk. Then the electron trajectory may be not a simple spiral as shown in Fig. 1, but may have some more complicated shape, which may change the oscillation frequency (?). Furthermore, a formation of a superconducting layer in the FIB fabricated WP2 microdevice hinders the studies of topological aspects of device performance, since the current distribution between the bulk and the surface will depend on temperature, magnetic field (?). At this moment it is unclear how the contribution of both can be clearly separated. Non-uniformity of the microdevice given by the amorphous surface can be unfavorable for studying the hydrodynamic flow. Hopefully, the future studies clarify how and whether this limitation can affect the transport phenomena.
+
+• I may have poorly formulated my original question about the spectrum in Figure 4a. Let me rephrased it. Every panel in Fig. 4a contains a dominating frequency and some side peaks with a lower intensity. Can the authors comment on the appearance of those side
+peaks? What can their origin be? Do they come from the inhomogeneity of the structure, such as density or structure size variation? Or does it have other origin?
+
+In overall, I find little novelty presented in this work, except the observation of Sondheimer oscillations in an FIB fabricated structures. The work did not give any new insights into SO or non-ohmic flow. In my opinion the work demonstrates an interesting technical progress, but in terms of physics the progress is not evident. Unjustified title misbalances the paper presentation and leaves an impression that the authors attempt to ascribe more value to their work, than it presents at the current stage of research.
+
+With this I would like to leave the decision to the editor whether this MS (after changing the title) can be suitable for the readership of Nature Communications.
+Reviewer #3 (Remarks to the Author):
+
+The authors addressed my questions. I have no further comments.
+I would like to thank the authors for addressing my comments and questions. Some issues have been clarified. I am particular thankful authors for discussing the novel aspects of their work, since I thought I may have missed some important arguments.
+Let me explain below the important points that I cannot agree.
+
+• The authors point to the “so-far overlooked critical advantage of SO as they sense the bulk mean-free-path even in strongly confined microdevices”. I cannot agree that this is something that has been overlooked. Reference 20 is from year 1979 and it is already stated there that: (i) the SO depends on the electron scattering in the volume, (ii) SO spectrum makes it possible to determine the mean free path. This paper and others make clear how the SO signal emerges. In fact, the nature of SO emergence requires some confinement. (The device size is comparable or smaller than the mean free path.) It is therefore unclear why the authors think that the “confinement” was overlooked. Because of the microstructure and the SO sensitivity to bulk scattering the authors can judge that the FIB seems not to affect the bulk part of WP2, at least in terms of the mean free path.
+
+Possibly our response was not worded as clearly as it should have. Indeed, it was already known in 1979 that SO require confinement and depend on the mean free path, in that sense confinement certainly was not overlooked but is at the heart of these classical explanations.
+
+However, these old works aimed at explaining the SO as an, at that time, novel physical phenomenon. We see this in complete analogy to quantum oscillations, in which the challenge lied in explaining why the magnetization and resistivity becomes oscillatory in high fields. Yet there is a key difference. As QO allowed to tomographically explore the Fermi surfaces of metals, it has become a cornerstone of our exploration of metals. SO depend on the sample geometry, and on non-extremal cross-section of a Fermi surface – facts that rendered the SO oscillations of little practical use.
+
+The value of this MS can be that the authors re-introduce Sondheimer oscillations (40-50 years after their discovery), that remained largely unused so far. This MS does not show new aspects of SO phenomena. Neither the MS demonstrates anything on the hydrodynamic transport features and certainly does not probe non-ohmic flow.
+
+Here we have a fully orthogonal viewpoint. Naturally SO is insensitive to small-angle MC-scattering and does not directly show hydrodynamic behavior. This has been done elsewhere (Nat. Comm. 9:4093 (2018) ). Here we address one of the main concerns in the community with that work, about if and how the scattering is changed by microfabrication. If microstructuring had significantly altered the material, these results may not have been based on confinement, but on sample modification. Before our work, there was no hope to disentangle these two parameters. Now by measuring I_MR independently in confined samples, we can settle this important question in the field of hydrodynamic transport. Hence we strongly disagree with the statement that this work does not contribute new insights to hydrodynamic transport in solids – quite the contrary.
+
+• I also cannot agree with the author’s approach on selecting the title. The current title misleads the reader and awakes wrong expectations. A reader anticipates type-II Weyl physics to come into play, but at the end the reader remains disappointed that Weyl is not important here. (Yes, the paper states in the text that Weyl is not important.) Any reference to Weyl is therefore inappropriate here. A material with a sufficiently large mean free path will show the same effect. Neither the MS demonstrates how the SO probes the non-ohmic flow. The SO probes only the mean free path in the bulk.
+In our previous response, we have outlined our reasoning for the choice of title. Although we disagree on this point, we accept to change the title and remove the mention of Weyl.
+
+The authors may anticipate implications of their work and discuss it in the text body. Whether this will then be realized at some point or not, is a different question. It will certainly be interesting to see in the future how the SO can probe the non-ohmic flow. One may also anticipate that, in the regime of hydrodynamic flow the emergence of SO may be altered, since the electron velocity changes gradually from the wall of the constriction to the bulk. Then the electron trajectory may be not a simple spiral as shown in Fig. 1, but may have some more complicated shape, which may change the oscillation frequency (?). Furthermore, a formation of a superconducting layer in the FIB fabricated WP2 microdevice hinders the studies of topological aspects of device performance, since the current distribution between the bulk and the surface will depend on temperature, magnetic field (?). At this moment it is unclear how the contribution of both can be clearly separated. Non-uniformity of the microdevice given by the amorphous surface can be unfavorable for studying the hydrodynamic flow. Hopefully, the future studies clarify how and whether this limitation can affect the transport phenomena.
+
+We agree that fully incorporating SO trajectories into hydrodynamic flow is the next challenge, and we work on this currently theoretically. It will remain to be seen how to explore these flow patterns. However, the situation is much more complex than sketched by the referee. The drift velocity v measures the net velocity at a point, in the spirit of a current density j=nev. It strongly differs from the velocity of the individual particle that enters the Lorentz force equation and hence leads to the spiral. Given that in a Fermi liquid particles are locked to velocities very close to vF in metals, one would not expect any sizable variation of the spiral itself. Rather, interspiral collisions will form a steady-state in which the net current density close to the boundary is suppressed – in the meaning of cancelling spirals.
+
+• I may have poorly formulated my original question about the spectrum in Figure 4a. Let me rephrased it. Every panel in Fig. 4a contains a dominating frequency and some side peaks with a lower intensity. Can the authors comment on the appearance of those side peaks? What can their origin be? Do they come from the inhomogeneity of the structure, such as density or structure size variation? Or does it have other origin?
+
+Unlike the main peaks, these side peaks are not reproducible. Regarding their origin, we can exclude variations in the structure. The required difference in size to produce a distinct frequency is large enough that we would be able to clearly observe this in SEM. We also know that our devices are made of high-quality single crystals, and inhomogeneity is unlikely. One should also consider the small window size accessible to experiments, from which low amplitude (sub-)harmonics naturally appear even if only one frequency is present.
+
+In overall, I find little novelty presented in this work, except the observation of Sondheimer oscillations in an FIB fabricated structures. The work did not give any new insights into SO or nonohmic flow. In my opinion the work demonstrates an interesting technical progress, but in terms of physics the progress is not evident. Unjustified title misbalances the paper presentation and leaves an impression that the authors attempt to ascribe more value to their work, than it presents at the current stage of research.
+With this I would like to leave the decision to the editor whether this MS (after changing the title) can be suitable for the readership of Nature Communications.

0d5d236ca2db4837436a59c800cfcd8d4634bf4e1db39c00ce4a07df353e91c4/peer_review/peer_review.md

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+Peer Review File
+Human centromere repositioning activates transcription and opens chromatin fibre structure
+
+Open Access This file is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. In the cases where the authors are anonymous, such as is the case for the reports of anonymous peer reviewers, author attribution should be to 'Anonymous Referee' followed by a clear attribution to the source work. The images or other third party material in this file are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.
+Editorial Note: This manuscript has been previously reviewed at another journal that is not operating a transparent peer review scheme. This document only contains reviewer comments and rebuttal letters for versions considered at Nature Communications
+
+REVIEWERS’ COMMENTS
+
+Reviewer #1 (Remarks to the Author):
+
+The authors have put a significant amount of effort addressing most of my comments and those of other reviewers- thank you.
+
+While I am not fully persuaded the key findings of this ms are strictu sensu novel, the premise of this work is novel, as it compares the same DNA sequence in two epigenetically distinct contexts in the powerful human/hamster system. In this, they do a very good job extending key findings from native centromeres to a new system that can be used experimentally to dissect questions in a cleaner manner than what the rest of us have been attempting to do with native human centromeres which are repetitive, dynamically shifting, and hard to analyze despite Karen Miga & T2T’s heroic tour-de-force filling of the genomic black hole.
+
+More to the point, the work is convincing that the 3q neoCEN does adopt an open, RNAP2 transcriptionally permissible domain once CENP-A/C have assembled upon it. This is a key piece of evidence that will be critical for the study of quasi-neocentromere domains in the context of chromosome fragility arising at breakpoints in human cancer, and also for karyotype evolution, where centromeres shift over time.
+
+In my view, these findings inform centromere biology and cancer biology fields, making it worthy of publication in Nat Comm.
+
+Reviewer #2 (Remarks to the Author):
+
+This is a revised manuscript from Naughton et al. addressing the chromatin structure induced by centromere formation. The manuscript takes a very powerful approach of deriving mouse:human hybrid cell lines containing the neocentromere chromosome to provide analysis of the neocentromere without complications of the presence of the homologous chromosome. The revised manuscript addresses most of the points raised in the initial review. However, one issue remains that I think is important for the impact of the manuscript. The revised manuscript provides further support that decompaction occurs at the neocentromere by including an analysis of Neo6 containing cell lines. This is an excellent inclusion, and I am not sure why these data are relegated to supplementary material. Analysis of the second Neocentromere 6 is critical to demonstrate these effects are due to the neocentromere, and not the process of creating the hybrid, which can lead to clonal selection (or idiosyncratic to this Neo3). This holds true for all the analysis. RNA pol II binding, histone PTMs, transcription and DNA supercoiling should all be analyzed on Neo6 (or independently derived clones of Neo3). Otherwise, it will be unclear if these are observations of this neocentromere derived mouse:human cell line, or general principles of neocentromere formation that will be of broad interest to the centromere community.
+REVIEWERS' COMMENTS
+
+Reviewer #1 (Remarks to the Author):
+
+The authors have put a significant amount of effort addressing most of my comments and those of other reviewers- thank you.
+
+While I am not fully persuaded the key findings of this ms are strictu sensu novel, the premise of this work is novel, as it compares the same DNA sequence in two epigenetically distinct contexts in the powerful human/hamster system. In this, they do a very good job extending key findings from native centromeres to a new system that can be used experimentally to dissect questions in a cleaner manner than what the rest of us have been attempting to do with native human centromeres which are repetitive, dynamically shifting, and hard to analyze despite Karen Miga & T2T's heroic tour-de-force filling of the genomic black hole.
+
+More to the point, the work is convincing that the 3q neoCEN does adopt an open, RNAP2 transcriptionally permissible domain once CENP-A/C have assembled upon it. This is a key piece of evidence that will be critical for the study of quasi-neocentromere domains in the context of chromosome fragility arising at breakpoints in human cancer, and also for karyotype evolution, where centromeres shift over time.
+
+In my view, these findings inform centromere biology and cancer biology fields, making it worthy of publication in Nat Comm.
+
+We thank the reviewer for acknowledging the significant efforts we undertook in addressing their comments and those of the other reviewers. We are delighted that the reviewer considers our findings worthy of publication in Nat comm and thank them for their time and input.
+
+Reviewer #2 (Remarks to the Author):
+
+This is a revised manuscript from Naughton et al. addressing the chromatin structure induced by centromere formation. The manuscript takes a very powerful approach of deriving mouse:human hybrid cell lines containing the neocentromere chromosome to provide analysis of the neocentromere without complications of the presence of the homologous chromosome. The revised manuscript addresses most of the points raised in the initial review. However, one issue remains that I think is important for the impact of the manuscript. The revised manuscript provides further support that decompaction occurs at the neocentromere by including an analysis of Neo6 containing cell lines. This is an excellent inclusion, and I am not sure why these data are relegated to supplementary material. Analysis of the second Neocentromere 6 is critical to demonstrate these effects are due to the neocentromere, and not the process of creating the hybrid, which can lead to clonal selection (or idiosyncratic to this Neo3). This holds true for all the analysis. RNA pol II binding, histone PTMs, transcription and DNA supercoiling should all be analyzed on Neo6 (or independently derived clones of Neo3). Otherwise, it will be unclear if these are observations of this neocentromere derived mouse:human cell line, or general principles of neocentromere formation that will be of broad interest to the centromere community.
+
+We agree with the reviewer that the data from the second neocentromere Neo6 is an excellent inclusion. We have added this data in revision and in supplementary as unfortunately there are no available human-hamster hybrid cell lines with this Neo6 centromere. This therefore prohibits further chromatin structural analysis of this neocentromere. We made several attempts to generate
+these human-hamster hybrid cell lines but it seems the Neo6 neocentromere is unstable. All attempts to select this chromosome into a hamster hybrid resulted in either loss of the Neo6 chromosome or breakage of the chromosome at the neocentromere followed by fusion to a hamster chromosome. We have added the following sentence to the discussion, “Although chromatin fibre decompaction was also observed at a second neocentromere (Neo6) (Supplementary Fig. 6) lack of available human-hamster hybrid cell lines prohibited further analysis of this neocentromere.” We thanks the reviewer for their time and helpful suggestions that have greatly improved our manuscript.

0d62870c95b96539354e1342ce7b4541a37c8df2c8571a011c7dc063baa3034a/peer_review/peer_review.md

@@ -0,0 +1,118 @@
+REVIEWER COMMENTS
+
+Reviewer #1 (Remarks to the Author):
+
+CRY2 is a light-labile photoreceptor that is rapidly degraded in blue light. Up to now, only COP1/SPA had been identified as a responsible E3 ubiquitin ligase. Here, the authors report an additional E3 ligase, the LRB family, and show that both COP1/SPA and LRBs are responsible for CRY2 degradation. LRBs were previously identified as an E3 ligase on PIFs and phyB. This manuscript provides very novel data in two-ways: it finally clarifies the E3 ligases that cause CRY2 degradation that have been long sought for; second, it demonstrates that LRBs are involved in both red light and blue light signaling.
+
+The results presented on CRY2 polyubiquitination and degradation are convincing and support the authors’ conclusions. The manuscript is well-written. The results will be of great interest to a larger readership, also beyond the photobiology community.
+
+I have two major comments:
+
+1. Most protein-protein interactions are shown in HEK cell expression systems. I would appreciate additional evidence that LRBs interact with CRY2 in vivo. BiFC is not very stringent (also, more negative controls using “empty vector” or unrelated fusion proteins should be included). The authors generated LRB CRY2 double transformants; hence, have they attempted in vivo coIPs?
+
+2. The authors show nicely that LRBs cause CRY2 degradation transiently after transfer of plants from darkness to light. It would be good if they could discuss why LRBs act transiently while COP1 acts short-term and long-term. Are LRBs instable in blue light? Does expression change?
+
+Minor comments:
+
+Fig 3a and b: what is the difference between the experiments shown in a and b? They appear identical, but PPK1 was pulled down by FLAG-LRB2 only in blue light (b) or in darkness and blue light (a).
+
+Fig. 5. Please indicate more clearly which duration of blue light irradiation (5, 10, 15 min?) was used in which subfigure. It is not clear from the legend.
+
+Fig. 4: Why is BiFC fluorescence intensity normalized to a nuclear stain? Normalizing to a co-expressed fluorescent marker would be useful to normalize for transfection efficiency. But how would normalizing for nuclear stain improve the data?
+
+Please provide more detailed information on the plasmid constructs used. The descriptions are very cryptic, e.g. vector backbones (citation possible?), primer sequences, etc.
+
+Reviewer #2 (Remarks to the Author):
+
+cry2 is a blue light photoreceptor crucial for photoperiodic flowering and light-mediated inhibition of cell elongation. Upon blue light activation, cry2 is phosphorylated by PPK kinases, followed by ubiquitination and proteasomal degradation. Previous work by the Lin lab has identified COP1/SPA as a E3 ubiquitin ligase complex that targets cry2 for ubiquitination and proteasomal degradation. In addition, cry2 is known as a negative regulator of COP1 activity, resulting in the stabilization of
+its substrates.
+As blue-light-dependent cry2 degradation was found to be only partially impaired in cop1 null mutants, the existence of additional E3 ubiquitin ligases targeting cry2 has been postulated. In this work, Yadi Chen et al describe the discovery of the CUL3-LRBs E3 ubiquitin ligases as key enzymes ubiquitinating cry2 and thereby targeting cry2 for proteasomal degradation. Interestingly, the authors find that COP1 determines cry2 protein abundance under steady state conditions during continuous blue light exposure (and not LRBs), whereas LRBs are responsible for the rapid blue light-induced cry2 degradation (and not COP1). The complementary of the two distinct ubiquitin ligases - one for the rapid ubiquitination and degradation of cry2, the other one for the slow or prolonged ubiquitination and degradation of cry2 - is very clearly illustrated by the cry2 stability in lrb1 lrb2 lrb3 cop1 quadruple mutants (Fig. 2e). This work provides very interesting and novel findings that significantly further our understanding of cry2 regulation. The manuscript is very well written and presented, with high quality experimental data supporting the conclusions.
+
+A few points to be addressed:
+
+1. cry2 uses a VP-motif to interact with COP1, as other COP1 substrates do. At present, the VP motif in photoreceptors has been mainly discussed as mimicking substrate interaction motifs, thereby resulting in COP1 target proteins to get stabilized (i.e. by competing off the COP1 substrates) (Ponnu et al., 2019; Lau et al., 2019). It would be interesting to discuss shortly that cry2 may function at the same time by inhibiting COP1, and as a COP1 substrate. It is not very clear how cry2 inhibits COP1 when it is ubiquitinated and degraded as any other substrate. It also is surprising that COP1 seems involved in late degradation of cry2. Is it that cry2 binds to COP1 inactivating it, but then only slowly becomes a substrate for COP1 ubiquitination? Any such mechanism known for any E3 ligase (different kinetics of ubiquitination after binding to an E3 ligase)? Could COP1 binding even protect a subfraction of cry2 from being targeted by LRBs? It may be interesting to shortly discuss.
+cry2P532L is thought to block interaction with COP1, and not LRBs (e.g. Fig. 6 e, f). It is not clear to me why degradation of cry2P532L then rather mimicks lrb mutants than cop1 mutants (compare Fig. 6c with Fig. 2e). P532L seems stabilized early and not late. Any explanation for that?
+
+2. Fig. 5d: long-exposure suggest that cry2 is even targeted in darkness by LRBs and COP1. It is less clear if that is reflected by cry2 protein levels in darkness (i.e. less cry2 in WT than in lrb1 lrb2 lrb3, cop1, and lrb1 lrb2 lrb3 cop1). Please mention and discuss shortly.
+
+3. cry2 is introduced as an important regulator of photoperiodic flowering (line 38). Is anything known about lrb5 and flowering? If data available, it would be great to add. If not, I think it would be good to shortly mention in the discussion that it will need to be investigated whether LRBs "only" with role for hypocotyl growth inhibition or also flowering time regulation; or whether such an involvement is not expected (at least not due to directly targeting cry2 for degradation).
+
+Minor:
+- lines 34, 249: protein name "Jetlag", not "Jetleg"
+- provide full name for TIM protein
+Authors’ responses:
+
+MS ID#: NCOMMS-20-45996
+Title: Regulation of Arabidopsis photoreceptor CRY2 by two distinct E3 ubiquitin ligases
+By: Yadi Chen, Xiaohua Hu, Siyuan Liu, Tiantian Su, Hsiaoichi Huang, Huibo Ren, Zhensheng Gao, Xu Wang, Deshu Lin, James A. Wohlschlegel, Qin Wang and Chentao Lin
+
+Reviewer #1:
+
+Major comments:
+
+1. Most protein-protein interactions are shown in HEK cell expression systems. I would appreciate additional evidence that LRBs interact with CRY2 in vivo. BiFC is not very stringent (also, more negative controls using “empty vector” or unrelated fusion proteins should be included). The authors generated LRB CRY2 double transformants; hence, have they attempted in vivo coIPs?
+
+Response:
+    We thank the reviewer for this insightful comment. We added results of two new in vivo experiments by split-LUC (Fig. 4b-c) and co-IP (Fig. 4d-e). The new results further support the CRY2/LRBs interaction argument.
+
+2. The authors show nicely that LRBs cause CRY2 degradation transiently after transfer of plants from darkness to light. It would be good if they could discuss why LRBs act transiently while COP1 acts short-term and long-term. Are LRBs instable in blue light? Does expression change?
+
+Response:
+    This is a very insightful comment that would significantly improve this paper. We added two discussions specifically to this issue (page 5, line 148-154; page 11, line 315-333), and we also added new data to show the photoresponsive LRB protein expression (Fig. 7b-e).
+
+Minor comments:
+
+Fig 3a and b: what is the difference between the experiments shown in a and b? They appear identical, but PPK1 was pulled down by FLAG-LRB2 only in blue light (b) or in darkness and blue light (a).
+
+Response:
+The experimental conditions for Fig. 3a and 3b are the same, except that 3a is for LRB1 and 3b is for LRB2. In the revision, we replaced PPK1 signal of Fig. 3b with a stronger exposure of the original experiment to minimize potential misleading impressions. It is possible that the affinity of PPK1 to CRY2 may be different in the presence of LRB1 or LRB2, but we do not wish to make this conclusion at present, and it seems irrelevant to our main conclusion.
+
+Fig. 5. Please indicate more clearly which duration of blue light irradiation (5, 10, 15 min?) was used in which subfigure. It is not clear from the legend.
+
+Response:
+We thank the reviewer for pointing out this oversight of ours. It is clarified in legend for the revision. We exposed seedlings with three different time treatment and mixed the seedling samples to see the overall light response.
+
+Fig. 4: Why is BiFC fluorescence intensity normalized to a nuclear stain? Normalizing to a co-expressed fluorescent marker would be useful to normalize for transfection efficiency. But how would normalizing for nuclear stain improve the data?
+
+Response:
+Our purpose is to normalize the background fluorescence, such as unknown source of autofluorescence, for BiFC signals. We tend to think that, as long as the transfection conditions are carefully controlled, the major artifacts of BiFC may be from the background autofluorescence, but not the common differential levels of protein expression encountered in the conventional fluorescence experiment. We agree that a better way is to include independent assays, so we added independent assays as the reviewer pointed out in the major comment (Fig. 4b-e).
+
+Please provide more detailed information on the plasmid constructs used. The descriptions are very cryptic, e.g. vector backbones (citation possible?), primer sequences, etc.
+
+Response:
+We now include two new supplemental figures to show the maps of the vectors used in this study (Supplementary Fig. 4, 5) and the primers used for plasmid construction are in Supplementary Table 2.
+Reviewer #2:
+
+Major comments:
+
+1. …It would be interesting to discuss shortly that cry2 may function at the same time by inhibiting COP1, and as a COP1 substrate….Is it that cry2 binds to COP1 inactivating it, but then only slowly becomes a substrate for COP1 ubiquitination? Any such mechanism known for any E3 ligase (different kinetics of ubiquitination after binding to an E3 ligase)? Could COP1 binding even protect a subfraction of cry2 from being targeted by LRBs? ….cry2P532L is thought to block interaction with COP1, and not LRBs (e.g. Fig. 6 e, f). It is not clear to me why degradation of cry2P532L then rather mimicks lrb mutants than cop1 mutants (compare Fig. 6c with Fig. 2e). P532L seems stabilized early and not late. Any explanation for that?
+
+Response:
+    We thank the reviewer for these insightful comments. We added additional discussion to specifically address the reviewer’s questions (page 5, line 148-154; page 10, line 291-305; page 11-12, line 315-352).
+    We agree with the reviewer that different role of COP1 and LRB in CRY2 signaling is likely one of the explanations. We are not aware of any other E3 ligase acts this way (substrate inhibits its own E3 ligase). However, our new results (Fig. 7b-e) included in the revision is consistent with this comment by the reviewer, and it suggests a possible mechanism. Thus, we tempt to make this speculative proposition that COP1 may suppress LRB by facilitating its degradation in the dark, similar to other proteins, such as HY5. It is also possible that COP1 binds subclass of CRY2 with different consequences, and we emphasize in the revision the difference between COP1 and LRB with respect to their interaction with different structural elements of CRY2.
+    We added new Fig. 6g-j, which may partially explain the unusual behavior of CRY2^{P532L}. Namely, the VP mutation may alter the photochemistry of this mutant to change its degradation behavior. Although the exact photochemical mechanism of this is out of the scope of this study, we emphasize this unexpected results and possible explanations in the revision (page 10, line 291-305).
+
+2. Fig. 5d: long-exposure suggest that cry2 is even targeted in darkness by LRBs and COP1. It is less clear if that is reflected by cry2 protein levels in darkness (i.e. less cry2 in WT than in lrb1 lrb2 lrb3, cop1, and lrb1 lrb2 lrb3 cop1). Please mention and discuss shortly.
+
+Response:
+    The reviewer raised an excellent question. We now include a short discussion about this complex result (page 8, line 237-241).
+3. cry2 is introduced as an important regulator of photoperiodic flowering (line 38). Is anything known about lrbs and flowering? If data available, it would be great to add. If not, I think it would be good to shortly mention in the discussion that it will need to be investigated whether LRBs "only" with role for hypocotyl growth inhibition or also flowering time regulation; or whether such an involvement is not expected (at least not due to directly targeting cry2 for degradation).
+
+Response:
+    The reviewer raised a relevant and excellent question. We include the flowering data in the revision (Supplementary Fig. 1) and a brief discussion (page 3, line 90-96).
+
+Minor:
+- lines 34, 249: protein name "Jetlag", not "Jetleg"
+- provide full name for TIM protein
+
+Response:
+    We made these corrections in the revision.
+REVIEWERS' COMMENTS
+
+Reviewer #1 (Remarks to the Author):
+
+The authors did an excellent job in revising the manuscript. Hence, all my comments were addressed very well.
+
+Reviewer #2 (Remarks to the Author):
+
+The authors satisfactorily responded to all my requests and comments.

0d62870c95b96539354e1342ce7b4541a37c8df2c8571a011c7dc063baa3034a/preprint/preprint.md

@@ -0,0 +1,368 @@
+Regulation of Arabidopsis photoreceptor CRY2 by two distinct E3 ubiquitin ligases
+
+Yadi Chen
+Fujian Agriculture and Forestry University
+Xiaohua Hu
+Fujian Agriculture and Forestry University
+Siyuan Liu
+Fujian Agriculture and Forestry University
+Tiantian Su
+University of California, Los Angeles
+Hsiaochi Huang
+University of California, Los Angeles
+Huibo Ren
+Fujian Agriculture and Forestry University
+Zhensheng Gao
+Fujian Agriculture and Forestry University
+Xu Wang
+University of California, LA
+Deshu Lin
+Fujian Agriculture and Forestry University
+Qin Wang (qinwangCRY@163.com)
+Fujian Agriculture and Forestry University https://orcid.org/0000-0002-9202-8005
+Chentao Lin
+University of California, Los Angeles https://orcid.org/0000-0002-0004-8480
+
+Article
+
+Keywords: cryptochromes, Arabidopsis, E3 ubiquitin ligases
+
+Posted Date: December 2nd, 2020
+
+DOI: https://doi.org/10.21203/rs.3.rs-110165/v1
+
+License: This work is licensed under a Creative Commons Attribution 4.0 International License.
+Read Full License
+Version of Record: A version of this preprint was published at Nature Communications on April 12th, 2021. See the published version at https://doi.org/10.1038/s41467-021-22410-x.
+Regulation of Arabidopsis photoreceptor CRY2 by two distinct E3 ubiquitin ligases
+
+Yadi Chen1,3, Xiaohua Hu1,3, Siyuan Liu1, Tiantian Su2, Hsiaoichi Huang2, Huibo Ren1, Zhensheng Gao1, Xu Wang1,2, Deshu Lin1, Qin Wang1,*, and Chentao Lin2
+
+1. College of Life Sciences, Basic Forestry and Proteomics Research Center, Fujian Agriculture and Forestry University, Fuzhou 350002, China; 2. Department of Molecular, Cell & Developmental Biology, University of California, Los Angeles, CA 90095, USA; 3. These authors contributed equally to this work.
+*. For correspondence: qinwangCRY@163.com.
+
+Abstract
+
+Cryptochromes (CRYs) are photoreceptors or components of the molecular clock in various evolutionary lineages, and they are commonly regulated by polyubiquitination and proteolysis. Multiple E3 ubiquitin ligases regulate CRYs in animal models, and previous genetics study also suggest existence of multiple E3 ubiquitin ligases for plant CRYs. However, only one E3 ligase, Cul4COP1-SPAs, has been reported for plant CRYs so far. Here we show that Cul3LRBs is the second E3 ligase of CRY2 in Arabidopsis. We demonstrated the blue light-specific and CRY-dependent activity of LRBs (Light-Response Bric-a-Brack/Tramtrack/Broad 1, 2 & 3) in blue-light regulation of hypocotyl elongation. LRBs physically interact with photoexcited and phosphorylated CRY2 to facilitate polyubiquitination and degradation of CRY2 in response to blue light. We propose that Cul4COP1-SPAs and Cul3LRBs E3 ligases interact with CRY2 via different structure elements to regulate the abundance of CRY2 photoreceptor under different light conditions, facilitating optimal photoresponses of plants grown in nature.
+
+CRYs are photolyase-like flavoproteins that act as photoreceptors in plants or core components of the molecular clock in mammals1-3. Regulation of CRY abundance is an important mechanism to control cellular photo-responses and chrono-responses. For example, two cullin 1 family E3 ubiquitin ligases, SCFFBXL3 and SCFFBXL21, regulate
+ubiquitination and degradation of mCRYs to govern the circadian clock in mammals\(^{4-8}\).
+Similarly, a cullin 1-based E3 ubiquitin ligase receptor, Jetleg, and a cullin 4-based E3 ubiquitin ligase receptor, Brwd3, bind to dCRY to regulate ubiquitination of Tim and dCRY in *Drosophila*\(^{9,10}\).
+
+*Arabidopsis* cryptochrome 2 (CRY2) is one of the best studied plant CRYs that mediate blue light inhibition of cell elongation and photoperiodic promotion of floral initiation\(^{11,12}\). These physiological activities of CRY2 are regulated by at least three blue light-dependent mechanisms. Firstly, CRY2 undergoes blue light-dependent oligomerization to become active tetramers\(^{13-17}\). The BIC1 and BIC2 (Blue-light Inhibitors of Cryptochromes 1 and 2) proteins interact with photoexcited CRY2 to negatively regulate CRY2 photo-oligomerization in light, whereas the active CRY2 homooligomers may also undergo thermal relaxation to become inactive monomers in the absence of light\(^{14-17}\). Secondly, the activity of CRY2 homooligomers are positively regulated by protein phosphorylation reactions catalyzed by four related protein kinases PPKs (Photoregulatory Protein Kinases 1-4)\(^{18-20}\). Thirdly, the photoexcited CRY2 proteins undergo polyubiquitination catalyzed by the E3 ubiquitin ligase Cul4\(^{\text{COP1-SPAs}}\) and subsequently degraded by the 26S proteasome\(^{11,21,22}\). Like animal CRYs, the abundance and overall cellular activity of plant CRYs are regulated by phosphorylation, ubiquitination, and proteolysis\(^{3}\). However, only a cullin 4 family E3 ubiquitin ligase, Cul4\(^{\text{COP1-SPAs}}\), is presently known to regulate ubiquitination and degradation of plant CRYs\(^{3}\), raising the question how the highly conserved CRYs are differentially regulated in different evolutionary lineages.
+
+Under nature light conditions, plants rely on the coaction of blue light receptors CRYs and the red/far-red light receptors phytochromes (phys)\(^{23,24}\) to achieve the optimal photoresponses\(^{25}\). Mechanistically, the CRY-phy coaction could be achieved by different photoreceptors physically complexing with the same signaling proteins, such as bHLH transcription factors Phytochrome Interacting Factors (PIF1-8)\(^{26}\), Photoregulatory Protein Kinases (PPK1-4)\(^{20,27}\), the substrate receptor of a Cul4 E3 ligase Constitutive Photomorphogenic 1 (COP1)\(^{28}\), and Suppressors of PHYA-105 1 family members (SPA1-4) that act as COP1 activators\(^{29}\). For example, CRY2 interacts with PPKs, which catalyzes blue light-dependent phosphorylation of CRY2 to positively regulate the
+functions, polyubiquitination, and degradation of CRY2^{20}. On the other hand, PPKs interact with the phyB-PIF3 complex to negatively regulate the function of phyB by the so-called “mutually assured destruction” mechanism^{27,30}. According to this hypothesis, the photoexcited phyB interacts with PIF3, recruiting PPKs to phosphorylate PIF3; phosphorylated PIF3 interact with the substrate receptors of the Cul3^{LRBs}, Light-Response Bric-a-Brack/Tramtrack/Broad (LRB 1-3), which catalyze polyubiquitination and degradation of PIF3 that also leads to phyB degradation^{27}. Arabidopsis genome encodes three LRBs, LRB1, LRB2, and LRB3^{30,31}. LRB1 and LRB2 share higher homology and higher levels of mRNA expression than LRB3, and they act redundantly to suppress phyB-dependent photoresponses^{31}. It has not been reported whether Cul3^{LRBs} play other roles in addition to its important function regulating PIF3 ubiquitination and phyB-dependent red-light responses.
+
+Results
+
+LRBs are required for the CRY-dependent blue light responses
+
+We have previously shown that the blue light-dependent ubiquitination and proteolysis of CRY2 is diminished but not completely abolished in the cop1 null mutant^{22}, suggesting the existence of another E3 ubiquitin ligase in addition to Cul4^{COP1-SPAs}. Because LRB2 was identified as a putative CRY2-associated protein in our prior IP-MS (Immunoprecipitation-Mass Spectrometry) analyses of CRY2 complexomes purified from transgenic Arabidopsis plants overexpressing GFP-CRY2^{20} (Supplementary Table 1), we first tested whether LRBs play a role in blue light-dependent seedling development. As reported previously^{30}, the lrb123 triple mutant showed little apparent abnormality when grown in darkness or far-red light, but it exhibited a dramatic short-hypocotyl phenotype when grown in continuous red light (Fig. 1a-b). The lrb123 triple mutant also showed short-hypocotyl phenotype when grown in both long-day and short-day photoperiods illuminated with white light (Fig. 1a-b). These results are consistent with the established function of LRBs regulating red light-dependent activities of phyB^{30,31}. When grown in continuous blue light, the cry1cry2 mutant developed long hypocotyl phenotype as previously reported^{32}, whereas the lrb123 showed hypocotyls modestly shorter than
+that of the wild-type seedlings (Fig. 1c-d). The short hypocotyl phenotype of \( lrb123 \) mutant in blue light can be rescued by constitutively overexpressing LRB2 protein in \( lrb123 \) mutant (Supplementary Fig. 1). The short-hypocotyl phenotype of the \( lrb123 \) mutant seedlings (6-day-old) is more apparent in seedlings grown in blue light of the light intensities higher than 10 \( \mu \)mol m\(^{-2}\) s\(^{-1}\) (Fig. 1d), which is consistent with the previous report that showed hardly distinguished phenotype of the wild-type and the \( lrb12 \) double mutant (4-day-old) grown in continuous blue light with the light intensities of 10 \( \mu \)mol m\(^{-2}\) s\(^{-1}\) or lower\(^{31}\). These results argue for a light intensity-dependent function of LRBs in blue light. To examine the functional relationship between CRYs and LRBs, we prepared the \( cry1cry2lrb123 \) quintuple mutant and compared the hypocotyl phenotype of the quintuple mutant with its parents (Fig. 1e-f). When grown under continuous blue light, the \( cry1cry2 \) mutant and the \( lrb123 \) mutant exhibit long or short hypocotyl phenotype, respectively. However, the \( cry1cry2lrb123 \) quintuple mutant shows the long hypocotyl phenotype indistinguishable to that of the \( cry1cry2 \) mutant parent in blue light (Fig. 1e-f), but not in other light conditions (Fig. 1a-b). This result clearly demonstrates that the function of LRBs in blue light is dependent on the activity of the blue-light receptor CRYs.
+
+Comparing to the \( lrb123 \) parent, the \( lrb123cop1 \) quadruple mutant shows de-etiolated phenotype of the \( cop1 \) parent in darkness but a slight additive effect of both parents in blue light (Fig. 1g-h). Taken together, these results argue that LRBs regulate plant development by controlling not only the red light-dependent activity of phytochromes but also the blue light-dependent activity of cryptochromes.
+
+LRBs are required for the blue light-dependent CRY2 degradation
+
+We next tested how LRBs regulate cryptochrome activity by examining the blue light-dependent degradation of CRY2 in the \( lrb123 \) mutants. Results shown in Fig. 2 demonstrate that LRBs are required for the blue light-induced degradation of CRY2. The CRY2 protein level decreased by at least 70% (in 30 minutes) to 85% (in 60 minutes) in etiolated wild-type seedlings transferred to blue light (30 \( \mu \)mol m\(^{-2}\) s\(^{-1}\)) (Fig. 2a-b). In contrast, levels of the CRY2 protein exhibited little change in one \( lrb123 \) triple mutant allele (\( lrb1lrb2-1lrb3 \)) or less than 50% decrease in the second \( lrb123 \) triple mutant allele (\( lrb1lrb2-2lrb3 \)) under the same condition (Fig. 2a-b). This result indicates that
+lrb1lrb2-1lrb3 is a slightly stronger allele in comparison to lrb1lrb2-2lrb3. We then compared the blue light-induced CRY2 degradation in lrb123, cop1, and lrb123cop1 quadruple mutant in seedlings grown in continuous dark or blue light (Fig. 2c-d). Results of this experiment suggest that COP1, but not LRBs, determines abundance of the CRY2 protein in this steady-state condition, suggesting that LRBs are responsible for the rapid blue light response of CRY2 proteolysis but not the prolonged photoresponse of CRY2 proteolysis, whereas COP1 is required for the prolonged photoresponse of CRY2 proteolysis. To test this hypothesis, we compared the photoresponsive CRY2 proteolysis in etiolated seedlings transferred to blue light from 30 minutes to 14 hours (Fig. 2e-f). Results of this experiment show that the lrb123 mutants are clearly defective for the blue light-induced CRY2 degradation within two hours of light exposure, whereas the cop1 mutant shows defect in CRY2 degradation primarily during prolonged light exposure. As expected, little CRY2 degradation was detected in the lrb123cop1 quadruple mutant for both short or long exposure of blue light. We concluded that LRBs and COP1 are both required for the blue light-induced CRY2 degradation.
+
+LRBs interact with phosphorylated CRY2 to catalyze its polyubiquitination
+
+Given that a substrate receptor of E3 ubiquitin ligases must physically interact with the substrate, we examined the CRY2-LRB interaction (Fig. 3), using the co-immunoprecipitation (co-IP) assays of proteins co-expressed in the heterologous HEK293T (Human Embryo Kidney) cells as we previously reported14. Because we have previously shown that the blue light-induced phosphorylation of CRY2 is required for CRY2 ubiquitination and degradation, and that PPK1 is one of the four related protein kinases that specifically phosphorylate photoexcited CRY218,20, we tested LRB-CRY2 interaction in the presence of the wild-type PPK1 in response to blue light in HEK293T cells. LRB1 and LRB2 preferentially interact with phosphorylated CRY2 in HEK293T cells co-expressing PPK1, but only when cells were exposed to blue light (Fig. 3a-b). The light dependence of LRB-CRY2 interaction is confirmed by the result that LRB2 failed to interact with the photo-insensitive CRY2D387A mutant that does not bind the FAD (Flavin Adenine Dinucleotide) chromophore33 (Fig. 3c). The phosphorylation dependence of LRB-CRY2 interaction was confirmed by the result that LRB2 failed to
+interact with CRY2 in light-treated HEK293T cells co-expressing the catalytically inactive PPK1^{D267N} (Fig. 3d). These results demonstrate that LRBs directly and specifically interact with photoexcited and phosphorylated CRY2. We next examined LRB1-CRY2 and LRB2-CRY2 interactions in vivo, using the BiFC (Bimolecular Fluorescence Complementation) assay in Arabidopsis cells^{34}. In this experiment, Arabidopsis leaves were transiently transformed by infiltration of Agrobacterium cells harboring plasmids expressing the indicated BiFC pairs of recombinant proteins^{34}, and the direct protein-protein interactions between the BiFC pairs were analyzed by the BiFC assay. Figure 4 shows strong BiFC signals between CRY2 and LRB1 or CRY2 and LRB2. In contrast, no BiFC signal was detected between the photo-insensitive CRY2^{D387A} and LRB1 or CRY2^{D387A} and LRB2. These results clearly demonstrate the direct interaction of CRY2 and LRB proteins in vivo.
+
+To further test the hypothesis that the Cul3^{LRBs} and Cul4^{COP1-SPAs} E3 ubiquitin ligases catalyze blue light-dependent CRY2 ubiquitination, we performed three independent experiments to investigate the activity of LRBs and COP1 in the blue light-induced polyubiquitination of CRY2, using the IP/immunoblot assays. In the first two experiments, we prepared transgenic plants overexpressing Flag-GFP-tagged CRY2 (FGFP-CRY2) in the wild-type (WT), the strong (lrb1lrb2-1lrb3) or weak (lrb1lrb2-2lrb3) alleles of the lrb123 triple mutant (Fig. 5a-b,d), and the cop1 mutant backgrounds (Fig. 5c-d). In the third experiment, we prepared double-tagged transgenic lines that overexpress FGFP-CRY2 with either the Myc-tagged LRB (Myc-LRB1, Myc-LRB2) or the Myc-tagged COP1 (Myc-COP1) (Fig. 5e). In the first experiment, polyubiquitinated proteins of samples were indiscriminately precipitated using the TUBE2 (Tandem Ubiquitin Binding Entity 2)-conjugated beads^{35}, and the TUBE2-enriched proteins were analyzed by immunoblots probed with the anti-ubiquitin or anti-CRY2 antibodies (Fig. 5a-c). This experiment detected a high level of polyubiquitination of CRY2 in blue light-treated wild-type background seedlings (Fig. 5a-c). However, little ubiquitinated CRY2 was detected in etiolated seedlings or in blue light-treated lrb123 or cop1 mutant background seedlings (Fig. 5a-c). In the other two experiments, FGFP-CRY2 were immunoprecipitated by the GFP-trap beads, and the level of polyubiquitination of FGFP-CRY2 was analyzed by immunoblots probed against anti-ubiquitin antibody (Fig.
+5d-e). In etiolated seedlings exposed to blue light, a high level of ubiquitinated FGFP-CRY2 was detected in the wild-type seedlings overexpressing FGFP-CRY2. In contrast, a lower level of ubiquitinated FGFP-CRY2 was detected in \( lrb1lrb2-2lrb3 \) weak allele, whereas almost no ubiquitinated FGFP-CRY2 was detected in the \( lrb1lrb2-1lrb3 \) strong allele or the cop1 mutant seedlings transgenically overexpressing FGFP-CRY2 (Fig. 5d). In comparison to FGFP-CRY2 overexpressed in the wild-type background, the blue light-induced polyubiquitination of GFP-CRY2 is enhanced in plants co-overexpressing LRB1, or LRB2, or COP1 (Fig. 5e). Taken together, results of those three independent experiments all support the hypothesis that two distinct E3 ubiquitin ligases, Cul3\(^{LRBs}\) and Cul4\(^{COP1-SPAs}\), can both catalyze blue light-dependent polyubiquitination of CRY2 *in vivo*.
+
+**COP1 and LRBs interact with different structure elements of CRY2**
+
+Because the LRBs and COP1 proteins share little sequence or structural similarity, we reasoned that they are unlikely to interact with the identical structure elements of CRY2. The VP motif is a conserved COP1-binding motif of many substrates of the Cul4\(^{COP1-SPAs}\) E3 ligase, including CRY2\(^{36,37}\). We previously reported that the CRY2\(^{P532L}\) mutation impaired at the VP motif (Fig. 6a) loses all the physiological activities tested but retains many photochemical properties of CRY2, including blue light-induced oligomerization, phosphorylation, ubiquitination, and degradation\(^{15}\). We first compared the relative activity of FGFP-CRY2 and FGFP-CRY2\(^{P532L}\), using the hypocotyl inhibition assay in transgenic plants expressing the respective recombinant protein at similar levels in the *cry1cry2* mutant background (Supplementary Fig. 2a). Transgenic seedlings expressing FGFP-CRY2\(^{P532L}\) showed no obvious activity mediating light inhibition of hypocotyl elongation under all light intensities of blue light tested (Fig. 6b, Supplementary Fig. 2b). This result confirmed our previous report that *CRY2*\(^{P532L}\) is a loss-of-function mutation\(^{15}\). We then compared the kinetics of blue light-induced degradation of FGFP-CRY2 and FGFP-CRY2\(^{P532L}\), using the same transgenic lines (Fig. 6c-d). Although FGFP-CRY2\(^{P532L}\) is degraded in response to blue light as we previously reported\(^{15}\), this recombinant CRY2 mutant protein appears to degrade slower than its wild-type counterpart (Fig. 6c-d). The apparent half-life of FGFP-CRY2\(^{P532L}\) is more than
+twice that of FGFP-CRY2 (Fig. 6d). Because the LRBs only interact with phosphorylated CRY2 whereas COP1 interacts with both phosphorylated and unphosphorylated CRY2 (Fig. 6e), we examined the phosphorylation activity of the CRY2P532L mutant protein in HEK293T cells co-expressing the CRY2 kinase PPK1. CRY2P532L mutant undergoes blue light- and PPK1-dependent phosphorylation (Fig. 6e-f). Neither the unphosphorylated CRY2D387A control or the phosphorylated CRY2P532L mutant protein interacts with COP1 or SPA1 in response to blue light (Fig. 6e). Because the CRY2P532L mutant does not interact with COP1, its blue light-induced degradation is most likely dependent on another E3 ligase, such as LRBs. Consistent with this hypothesis, the photoexcited and phosphorylated CRY2P532L mutant protein interacts with LRB2 with no discernable difference in comparison to the wild-type CRY2 (Fig. 6f). This result explains why CRY2P532L that does not interact with COP1 or SPA1 can still be degraded in plants (Fig. 6c). Taken together, the results of our experiments argue that two types of substrate receptors, COP1 and LRBs, interact with CRY2 via distinct structural elements of CRY2 to enable the blue light-induced CRY2 ubiquitination and degradation by the respective E3 ubiquitin ligases, Cul3LRBs and Cul4COP1-SPAs.
+
+Discussion
+
+In this study, we demonstrate that, in addition to Cul4COP1-SPAs, the E3 ubiquitin ligases Cul3LRBs is required for blue light regulation and function of CRY2. We demonstrate that Cul3LRBs is responsible for the rapid ubiquitination and degradation of CRY2, whereas Cul4COP1-SPAs is responsible for the slow or prolonged ubiquitination and degradation of CRY2. We show that LRBs and COP1 interact with CRY2 via different structural elements: LRBs interacts with photoexcited and phosphorylated CRY2, but COP1 interacts with CRY2 regardless of its phosphorylation states. It is interesting that plants evolved with two distinct E3 ubiquitin ligases to regulate a CRY photoreceptor by different modes of interaction under different light conditions. In mammals, two related Cul1-based E3 ligases, SCF^FBXL3 and SCF^FBXL21, act to promote ubiquitination and degradation of CRYs in the nucleus and cytoplasm, respectively, to control the period of the circadian clock8. In Drosophila, Jetleg of a Cul1-based E3 ligase and Brwd3 of a
+Cul4-based E3 ligase regulate ubiquitination and degradation of dCRY-dependent circadian rhythm\(^{9,10}\). Cul4\(^{\text{Brwd3}}\) mediates light-dependent ubiquitination and degradation of dCRY, whereas Cul1\(_{\text{Jetlag}}\) interacts with dCRY to catalyze ubiquitination of the dCRY-interacting protein TIM\(^{10,38}\). Decreased TIM may enhance interaction of dCRY with its E3 ligases to accelerate its degradation in light. These studies demonstrate that multiple E3 ligases are needed to regulate the activity of a CRY to control the circadian clock. The results of this study argue that plant CRY2 is also controlled by two distinct E3 ligases, and that the delicate control of the abundance of CRYs is evolutionarily conserved for not only circadian rhythms in animals but also photomorphogenesis in plants. Our finding that Cul3\(^{\text{LRBs}}\) or Cul4\(^{\text{COP1-SPAs}}\) catalyze CRY2 ubiquitination in different light conditions to promote rapid or slow degradation of CRY2, respectively, highlights the importance of photosensitivity to photomorphogenesis of plants. The complex mechanism regulating CRY2 turnover is likely evolved to optimize photomorphogenesis under natural light conditions. In this regard, it is particularly interesting that Cul3\(^{\text{LRBs}}\) has been previously shown to be the E3 ligase of PIF3 and critical for the function of phyB and phytochrome-dependent photoresponses\(^{30,31}\). Our finding that Cul3\(^{\text{LRBs}}\) also catalyzes blue light-dependent ubiquitination of CRY2 to regulate blue light-dependent photomorphogenesis argues for a previously unrecognized mechanism toward a better understanding of how plants respond to light in the nature white light conditions.
+
+Methods
+
+Plasmid construction
+
+Plasmid constructs in this study were generated by In-Fusion Cloning methods. The insertions were all verified by Sanger sequencing. The mammalian cell expression vectors used in this study were pQCMV-Flag-GFP, pQCMV-GFP and pCMV-Myc. pQCMV-Flag-GFP vector, driven by CMV promoter and with 1x Flag and GFP tags, was modified from pEGFP-N1 (Clontech). pQCMV-GFP vector, driven by CMV promoter and with a GFP tag, was modified from pQCMV-Flag-GFP. pCMV-Myc vector, driven by CMV promoter and with a 1x Myc tag, was described previously\(^{20}\). To generate plasmids expressing Flag-LRB1, Flag-LRB2, Flag-CRY2 and Flag-CRY2\(^{D387A}\), the CDS regions of
+respective genes were amplified either from Arabidopsis cDNA or previous plasmids, and in-fusion into Spel/KpnI-digested pQCMV-Flag-GFP vector, resulting a Flag tag at the N-terminus of genes. Myc-LRB1, Myc-LRB2, Myc-CRY2, Myc-SPA1 and Myc-COP1 plasmids were prepared by cloning CDS into the BamHI site of pCMV-Myc vector, resulting a Myc tag at the N-terminus of genes. The CDS of PPK1 and PPK1^{D267N} were amplified from previous plasmids by using the primers containing 2x HA coding sequences at the 5' end of forward primers, and in-fusion into Spel/KpnI-digested pQCMV-GFP vector to generate HA-PPK1 and HA-PPK1^{D267N}.
+
+For BiFC constructs, the vectors used in this study were described previously^{39}. The coding sequences of LRB1 (AT2G46260), LRB2 (AT3G61600), CRY2 (AT1G04400) and CRY2^{D387A} were amplified and cloned into pDONR/Zeo entry vector. The entry constructs were then introduced into the destination vector pX-nYFP (N-terminus of YFP fused to C-terminus of genes) or pcCFP-X (C-terminus of CFP fused to N-terminus of genes) by LR reaction.
+
+pFGFP and pDT1H binary vectors were used for creating overexpression transgenic lines. The pFGFP binary vector, driven by Actin2 promoter and with 2x Flag and GFP tags, was modified from pCambia3301^{20}. The pDT1H binary vector, possessing two expression cassettes which can sequentially insert two genes into one vector, was modified from previously published vector pDT1^{40} by replacing the BAR gene with HPT gene which converts basta resistance to hygromycin resistance in plants. The CDS of LRB2, CRY2 and CRY2^{P532L} were cloned into BamHI-digested pFGFP vector to generate FGFP-LRB2, FGFP-CRY2, FGFP-CRY2^{P532L} with 2x Flag and GFP tags fused to N-terminus of the genes. The CDS regions of LRB1, LRB2 and COP1 (AT2G32950) were cloned into the BamHI site of pDT1H vector to produce Myc-LRB1, Myc-LRB2 and Myc-COP1 with 4x Myc tags fused to N-terminus of the genes.
+
+Plant materials and growth conditions
+
+All mutants used in this study are in the Arabidopsis thaliana Columbia ecotype background. The cry1cry2 double mutant were described as previously^{32}. The lrb1lrb2-1lrb3 (lrb1, Salk_145146; lrb2-1, Salk_001013; lrb3, Salk_082868) and lrb1lrb2-2lrb3 (lrb2-2, Salk-044446) triple mutants were gifts from Dr. Peter Quail and as described previously^{30,31}. cop1-4 and cop1-6 are weak mutant alleles of COP1 as
+previously described\(^{41}\). *cry1cry2lrb1lrb2-2lrb3* and *lrb1lrb2-2lrb3cop1-4* mutants were generated by crossing. The genotypes of *lrb123* mutants were verified by PCR using the primers listed in Supplementary Table 2. *cop1-4* mutant was verified by PCR using the primers listed in Supplementary Table 2, followed by Sanger sequencing to confirm the point mutation of COP1. *cry1cry2* mutant was verified by western blots using antibodies against CRY1 and CRY2 proteins.
+
+All transgenic lines were generated via *Agrobacterium tumefaciens*-mediated floral-dip method\(^{42}\). The wild-type plants used for transformation in this study are *rdr6-11*, which suppresses gene silencing\(^{43}\). For *in vivo* ubiquitination study, *FGFP-CRY2* was introduced into *rdr6-11*, *lrb1lrb2-1lrb3*, *lrb1lrb2-2lrb3*, and *cop1-6* background. The *FGFP-CRY2/Myc-LRB1* double-overexpression lines were prepared by introducing *FGFP-CRY2* into *Myc-LRB1/rdr6-11* plants. The transgenic T1 populations were screened on MS plates containing 25 mg/L Glufosinate-ammonium (cat # CP6420, Bomei Biotechnology) and 25 mg/L hygromycin (cat # 10843555001, Roche), and western blots were performed to confirm the expression of both proteins. The same method was used for generating *FGFP-CRY2/Myc-LRB2* and *FGFP-CRY2/Myc-COP1* double-overexpression lines. For experiments comparing the hypocotyl phenotype and protein degradation kinetics of FGFP-CRY2 and FGFP-CRY2\(^{P532L}\), *FGFP-CRY2* and *FGFP-CRY2^{P532L}* were introduced into *cry1cry2rdr6* background. The *cry1cry2rdr6* were generated by crossing *cry1-304*\(^{32}\), *cry2-112*, and *rdr6-11*\(^{43}\). The transgenic lines were screened on MS plates with 25 mg/L Glufosinate-ammonium, and lines with similar protein expression level of FGFP-CRY2 and FGFP-CRY2\(^{P532L}\) were used for analysis.
+
+For *lrb123* mutant blue-light hypersensitivity phenotype rescue experiments, *FGFP-LRB2* and *Myc-LRB2* were transformed into *lrb1lrb2-2lrb3* background.
+
+For routine maintenance, *Arabidopsis thaliana* were grown under long day conditions (16 hours light / 8 hours dark) at 22°C. For hypocotyl phenotype analysis, seedlings were grown on MS plates with 3% sucrose at 20-22°C for 6 days under different light conditions. Light-emitting diode (LED) was used to obtain monochromatic light (blue light, peak 465 nm, half-bandwidth of 25 nm; red light, peak 660 nm, half-bandwidth of 20 nm; far-red light, peak 735 nm, half-bandwidth of 21 nm). For endogenous CRY2 degradation analysis in WT, *lrb123*, *cop1* and *lrb123cop1* mutants, seedlings were grown in darkness
+on MS plates with 3% sucrose for 7 days, then subjected to 30 \( \mu \)mol m\(^{-2}\) s\(^{-1}\) blue light for the indicated time. For FGFP-CRY2 and FGFP-CRY2\(^{P532L}\) degradation analysis, seedlings were grown in darkness on MS plates with 3% sucrose for 7 days, then subjected to 100 \( \mu \)mol m\(^{-2}\) s\(^{-1}\) blue light for the indicated time. For immunoprecipitation of polyubiquitinated proteins, 7-day-old etiolated seedlings grown on MS medium containing 3% sucrose were treated with 50 \( \mu \)M MG132 (Cat # S2619, Selleck) in liquid MS in the dark overnight with gentle shaking, and then moved to 30 \( \mu \)mol m\(^{-2}\) s\(^{-1}\) blue light for 5, 10 and 15 minutes before harvest.
+
+Blue-light-induced CRY2 degradation assays
+
+For endogenous CRY2 degradation analysis, seedlings were grown in the dark for seven days and then treated with 30 \( \mu \)mol m\(^{-2}\) s\(^{-1}\) of blue light for indicated time. For FGFP-CRY2 and FGFP-CRY2\(^{P532L}\) degradation analysis, seedlings were treated with 100 \( \mu \)mol m\(^{-2}\) s\(^{-1}\) of blue light. Tissues were homogenized by TissueLyser (QIAGEN). Proteins were extracted in equal tissue volume of protein extraction buffer [120mM Tris pH 6.8, 100mM EDTA, 4% w/v SDS, 10% v/v beta-mercaptoethanol, 5% v/v Glycerol, 0.05% w/v Bromophenol blue]\(^{44}\), heated at 100\(^\circ\)C for 8 minutes, centrifuged at 16000 rcf for 10 minutes, and analyzed by western blot. Proteins were separated in 10% SDS-PAGE gels, and transferred to nitrocellulose membranes (Pall Life Sciences).
+
+For immunoblot signals detected by enhance conventional chemiluminescent (ECL) method, membranes were blocked with 5% non-fat milk in PBST for 1 hour, blotted with anti-CRY2 primary antibody (1:3000, homemade) in PBST for 1.5 hours, washed 8 minutes x 3 times with PBST, blotted with anti-Rabbit-HRP (1:10000, cat # 31460, ThermoFisher) secondary antibody in PBST for 1.5 hours, washed 8 minutes x 3 times with PBST and then incubated with ECL solution for X-ray film development. The membranes were then stripped with stripping buffer [0.2 M Glycine, pH 2.5] and re-probed with anti-HSP82 (1:10000, cat # AbM51099-31-PU, Beijing Protein Innovation) primary antibody and anti-Mouse-HRP (1:10000, cat # 31430, ThermoFisher) secondary antibody. Anti-HSP82 antibody from Oryza sativa can also recognized Arabidopsis HSP90 protein\(^{45}\). Three independent blots were performed in parallel for quantification analysis. The quantification of protein intensity of ECL immunoblots was performed by ImageJ.
+For immunoblot signals detected by Odyssey CLx Infrared Imaging System (Li-COR), membranes were blocked with 0.5% casein in PBS for 1 hour, blotted with anti-CRY2 (1:3000) and anti-HSP82 (1:10000) mixed primary antibodies in PBST with 0.5% casein for 1.5 hours, washed 8 minutes x 3 times with PBST, blotted with Donkey anti-rabbit 790 (1:15000, cat # A11374, ThermoFisher) and Donkey anti-mouse 680 (1:15000, cat # A10038, ThermoFisher) mixed secondary antibodies in PBST with 0.5% casein for 1.5 hours, washed 8 minutes x 3 times with PBST and then signals were captured with Odyssey CLx by Image Studio Lite software. Three independent blots were performed in parallel for quantification analysis. Quantification of signals were processed with Image Studio Lite software. CRY2 degradation curves were indicated by CRY2 (B/D) ratio, calculated as CRY2 (B/D) = [CRY2/HSP90]^{blue} / [CRY2/HSP90]^{dark}, and analyzed with one phase decay of nonlinear regression.
+
+Protein expression and co-immunoprecipitation in HEK293T cells
+
+Human embryonic kidney (HEK) 293T cells were cultured in Dulbecco's modified Eagle's medium (DMEM) supplemented with 10% (v/v) FBS, 100 mg/L streptomycin and 100 IU penicillin, in humidified 5% (v/v) CO_2 air at 37°C. Cells were seeded at a density of approximately 8 x 10^5 cells/6-cm plate and the transfection were carried out with a calcium phosphate precipitation protocol. Briefly, different combinations of plasmid DNA (2~5 µg / construct) were mixed with 30 µl 2.5 M CaCl_2 and ddH_2O to a total volume of 300 µl, then 300 µl of 2x HeBS [250 mM NaCl, 10 mM KCl, 1.5 mM Na_2HPO_4, 12 mM Dextrose and 50 mM HEPES, adjust the pH of the final solution to 7.05] was added drop by drop with vortex, and kept at room temperature for 5 minutes before applying to cells. The media were aspirated from each plate, DNA mixtures were gently added into plates and the plates were rotated gently to allow the mixtures to coat the entire plate. 3 ml of fresh media containing 25 µM chloriquine (cat # C6628, Sigma) were added to each plate and the plates were kept in the CO_2 incubator overnight. The next day, the media were changed with 3 ml of fresh media without chloriquine. 36-48 hours after transfection, the cells were subjected to blue light treatment for indicated time, washed twice with cold PBS buffer and then harvested in liquid nitrogen for co-immunoprecipitation.
+
+Cells transfected with different plasmid DNA were lysed in 800 µl 1% Brij buffer [1% Brij-35, 50 mM Tris-HCl pH 8.0, 150 mM NaCl, 1 mM EDTA,1x Protease inhibitor cocktail,
+and 1x phosphatase inhibitor PhosSTOP] with rotating at 4°C for 20 minutes. Cell lysates were centrifuged at 16,000 rcf for 10 minutes at 4°C, and the supernatants were incubated with 20 µl Anti-FLAG M2 affinity gel (Cat. # F2426, Sigma) at 4°C for 2 hours with rotation. Beads were washed with 1% Brij buffer for 5 times. Proteins were competed from the beads with 35 µl 3xFlag peptide solution [500 ng/µl in 1% Brij buffer] for 30 minutes at room temperature with mixing. Elution was transferred to a new tube, mixed with 4XSDS sample buffer, denatured at 100 °C for 4 minutes and subjected to western blot analysis. Western blots were performed as described above. Primary antibodies used here were anti-Flag (1:1500, cat # F1804, Sigma), anti-Myc (1:5000, cat # 05-724, Millipore) and anti-HA (1:5000, cat # 12013819001, Roche), and secondary antibodies used were anti-Mouse-HRP (1:10000, cat # 31430, ThermoFisher) and anti-Rabbit-HRP (1:10000, cat # 31460, ThermoFisher).
+
+Bimolecular fluorescence complementation (BiFC) assay
+
+BiFC assays in Arabidopsis plants were performed as previously described methods with minor modifications34. Briefly, Agrobacteria AGL0 transformed with BiFC plasmids were grown in LB medium with 40 µM Acetosyringone and 1% Glucose in 28°C shaker overnight. Agrobacteria were centrifuged at 5000 rcf for 10 minutes, washed once with washing buffer [10 mM MgCl2, 100 µM Acetosyringone] and resuspended in infiltration buffer [1/4 MS pH 6.0, 1% sucrose, 100 µM Acetosyringone and 0.01% Silwet L-77] to 0.5 of OD600. The agrobacteria were infiltrated into 3-4 weeks old Arabidopsis leaves with syringe. Each BiFC assay was performed with at least 3 independent plants with 2-3 leaves infiltrated for each. Plant leaves were dried before kept in the dark for 24 hours, and then moved back to long day conditions (16 h light/8 h dark) to grow for two more days. The infiltrated leaf samples were analyzed under a Leica TCS SP8X confocal microscope. Hoechst 33342 was used for nuclei staining. The quantification of fluorescence intensity was performed by ImageJ. Briefly, the images of GFP and Hoechst 33342 channels from the same field were stacked first, then the regions of nuclei were selected on the image of Hoechst 33342 channel. The integrated intensity of the selected regions over the entire stack were measured. The BiFC ratio of the selected regions were calculated as [GFP intensity]^{nuclei} / [Hoechst 33342 intensity]^{nuclei} for each
+image. Four to nine images (~40-100 nuclei in total) for each BfC assay were used for quantification and the BiFC ratios were presented as mean ± SD (standard deviation).
+
+Immunoprecipitation of ubiquitinated proteins in Arabidopsis
+
+7-day-old etiolated seedlings were treated with 50 μM MG132 in liquid MS in the dark overnight with gentle shaking, and then treated with 30 μmol m^{-2} s^{-1} blue light for 5, 10 and 15 minutes before harvest. For each immunoprecipitation, about 3 g of seedlings were used. Seedlings were ground in liquid nitrogen and homogenized in 1.5x tissue volume of IP buffer [50 mM Tris-HCl pH 7.5, 150 mM NaCl, 1 mM EDTA, 1% Triton X-100, 20 mM NaF and 1x Protease inhibitor cocktail] at 4°C for 20 minutes with mixing. Lysates were centrifuged at 16000 rcf for 15 minutes at 4°C. 100 μl of supernatant were saved as inputs.
+
+For total ubiquitinated protein purification, the supernatant were incubated with 30 μl Agarose-TUBE2 beads (cat # UM402M, LifeSensors) for 2 hours at 4°C with rotating. After binding, beads were pelleted and washed 4 times with ice-cold IP buffer (without inhibitors). Total ubiquitinated proteins were eluted with 2XSDS sample buffer, denatured at 100 °C for 4 minutes and subjected to western blot analysis. Anti-ubiquitin antibody (α-Ubq, cat # 14-6078-80, Thermofisher) was used to detect total ubiquitinated proteins, and homemade anti-CRY2 antibody was used to detect CRY2 protein.
+
+For FGFP-CRY2 protein purification, the supernatant were incubated with 50 μl GFP-trap agarose beads (homemade or cat # gta-20, Chromotek) and rotated at 4°C for 2 hours. Beads were pelleted and washed 4 times with IP buffer (without inhibitors). Proteins were eluted with 2XSDS sample buffer by heating at 100 °C for 4 minutes and subjected to western blot analysis. Anti-Flag antibody was used to detect FGFP-CRY2 (IP) fusion protein, and anti-ubiquitin antibody was used to detect ubiquitinated CRY2.
+
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+
+Acknowledgments
+The authors thank Dr. Peter Quail for providing the lrb123 mutant alleles. Works in the authors’ laboratories are supported in part by the National Natural Science Foundation of China (31970265 to Q.W.), Natural Science Foundation of Fujian Province (2019J06014 to Q.W.), FAFU-ICE fund (KXGH17011 to Q.W.) and the National Institutes of Health (GM56265 to C.L.). The UCLA-FAFU Joint Research Center on Plant Proteomics provided the institutional supports.
+
+Author contributions
+Y.C. and X.H. conducted most of the experiments. S.L. and T.S. performed some biochemical experiments in HEK293T. H.H. and H.R. prepared some genetic materials. S.L. and Z.G. helped with BiFC experiments. X.W. and D.L. provided critical feedback. C.L. and Q.W. conceived the project, designed the experiments, and wrote the manuscript.
+Figures
+
+Fig. 1 LRBs are required for blue light responses.
+
+Fig. 2 LRBs and COP1 regulate fast or slow proteolysis of CRY2, respectively.
+
+Fig. 3 LRBs interact with phosphorylated Arabidopsis CRY2 expressed in the HEK293T cells.
+
+Fig. 4 LRBs interact with CRY2 in vivo.
+
+Fig. 5 LRBs and COP1 are both required for CRY2 ubiquitination.
+
+Fig. 6 The VP motif of CRY2 is required for the CRY2-COP1 interaction but not the CRY2-LRB interaction.
+Fig. 1 LRBs are required for blue light responses. a, 6-day-old seedlings grown in darkness, red light (20 \( \mu \)mol m\(^{-2}\) s\(^{-1}\)), far-red light (6 \( \mu \)mol m\(^{-2}\) s\(^{-1}\)), long day (16h light / 8h dark), or short day (8h light / 16h dark). b, Hypocotyl length of indicated genotypes of (a). c, 6-day-old seedlings grown in darkness or blue light (10 \( \mu \)mol m\(^{-2}\) s\(^{-1}\)). d, Hypocotyl length of indicated genotypes grown under blue light of different intensities (0, 5, 10, 20, 40 \( \mu \)mol m\(^{-2}\) s\(^{-1}\)) for 6 days. e-g, 6-day old seedlings grown in darkness or blue light (20 \( \mu \)mol m\(^{-2}\) s\(^{-1}\)). f-h, Hypocotyl length of indicated genotypes as in (e) and (g). Standard deviations (n\( \geq \)20) are shown.
+Fig. 2 LRBs and COP1 regulate fast or slow proteolysis of CRY2, respectively. a-b, Representative immunoblots (a) and a quantitative analysis (b, n=3) showing the endogenous CRY2 in the 7-day-old etiolated lrb123 mutants irradiated with 30 μmol m^{-2} s^{-1} blue light for the indicated time. c-d, Representative immunoblots (c) and a quantitative analysis (d, n=3) showing the endogenous CRY2 in seedlings of indicated genotypes grown in darkness (D) or continuous blue light (cB, 30 μmol m^{-2} s^{-1}). e, Representative immunoblots showing degradation of the endogenous CRY2 in 7-day-old etiolated seedlings irradiated with 30 μmol m^{-2} s^{-1} of blue light. f, Quantitative results of CRY2 degradation from
+immunoblots in (e), analyzed with one phase decay of nonlinear regression.
+
+CRY2 (B/D) = [CRY2/HSP90]^{blue} / [CRY2/HSP90]^{dark}. CRY2 and HSP90 were probed with anti-CRY2 antibody and anti-HSP90 antibody. HSP90 is a loading control. Arrows indicate phosphorylated CRY2.
+
+Figure 3
+
+![Co-immunoprecipitation results showing LRBs interacting with phosphorylated Arabidopsis CRY2](page_481_670_1017_563.png)
+
+Fig. 3 LRBs interact with phosphorylated Arabidopsis CRY2 expressed in the HEK293T cells. a-d, Co-immunoprecipitation results showing the blue light-dependent interaction of LRBs and phosphorylated CRY2 in heterologous HEK293T cells. HEK293T cells co-transfected with indicated plasmids were either kept in the dark (-) or treated with 100 μmol m^{-2} s^{-1} blue light for 2 hours (+). Immunoprecipitations were performed with Flag-conjugated beads. CRY2^{D387A} and PPK1^{D267N} are inactive mutants of CRY2 and PPK1, respectively. Anti-Flag antibody, anti-Myc antibody or anti-HA antibody were used for detecting respective tagged proteins. Arrows show phosphorylated CRY2.
+Figure 4
+
+![Confocal microscopy images showing BiFC of indicated protein pairs transiently expressed in Arabidopsis plants.](page_232_186_1107_393.png)
+
+<table>
+  <tr>
+    <th></th>
+    <th>CRY2-nYFP cCFP-CRY2</th>
+    <th>LRB1-nYFP cCFP-CRY2</th>
+    <th>LRB2-nYFP cCFP-CRY2</th>
+    <th>CRY2D387A-nYFP cCFP-CRY2D387A</th>
+    <th>LRB1-nYFP cCFP-CRY2D387A</th>
+    <th>LRB2-nYFP cCFP-CRY2D387A</th>
+  </tr>
+  <tr>
+    <th>BiFC (GFP)</th>
+    <td></td><td></td><td></td><td></td><td></td><td></td>
+  </tr>
+  <tr>
+    <th>Hoechst 33342</th>
+    <td></td><td></td><td></td><td></td><td></td><td></td>
+  </tr>
+  <tr>
+    <th>Merge</th>
+    <td></td><td></td><td></td><td></td><td></td><td></td>
+  </tr>
+  <tr>
+    <th>BiFC ratio (mean ± SD)</th>
+    <td>0.5497 ± 0.0320</td>
+    <td>0.8417 ± 0.0378</td>
+    <td>0.5228 ± 0.0175</td>
+    <td>0.0462 ± 0.0210</td>
+    <td>0.0406 ± 0.0207</td>
+    <td>0.0266 ± 0.0081</td>
+  </tr>
+  <tr>
+    <th>Image #</th>
+    <td>4</td>
+    <td>4</td>
+    <td>6</td>
+    <td>8</td>
+    <td>9</td>
+    <td>6</td>
+  </tr>
+  <tr>
+    <th>Nuclei #</th>
+    <td>92</td>
+    <td>43</td>
+    <td>99</td>
+    <td>61</td>
+    <td>59</td>
+    <td>41</td>
+  </tr>
+</table>
+
+Fig. 4 LRBs interact with CRY2 in vivo. Confocal microscopy images showing BiFC of indicated protein pairs transiently expressed in Arabidopsis plants. The Hoechst 33342 (nuclei) and GFP (BiFC) signals are shown. The relative activity of CRY2-LRB interaction was presented as BiFC ratio, calculated as BiFC ratio = [GFP intensity]^{nuclei} / [Hoechst 33342 intensity]^{nuclei}, quantified from each image (n≥4). Total number of quantified images and nuclei in the images is indicated underneath. CRY2^{D387A} inactive mutant is used as the negative control. Standard deviations (n≥4 images) are shown. Scale bars, 10 μm.
+Figure 5
+
+Fig. 5 LRBs and COP1 are both required for CRY2 ubiquitination.
+Immunoblots showing the ubiquitination of FGFP-CRY2 in indicated genotypes.
+7-day-old etiolated seedlings constitutively expressing FGFP-CRY2 in indicated genotypes, pretreated with MG132, were kept in the dark (D) or exposed to 30 μmol m^{-2} s^{-1} blue light for 5, 10 and 15 minutes (B) before harvest for IP assays.
+a-c, Total ubiquitinated proteins were purified by TUBE2-conjugated beads. Immunoprecipitated proteins were analyzed by immunoblots probed with anti-ubiquitin antibody (α-Ubq) or anti-CRY2 antibody (α-CRY2). The extent of CRY2 ubiquitination were shown underneath, calculated as [CRY2-Ubq intensity]IP / [Ubq intensity]IP. d-e, FGFP-CRY2 proteins were purified with GFP-trap beads. Immunoprecipitated proteins were analyzed by immunoblots probed with anti-ubiquitin antibody (α-Ubq), anti-Flag antibody (α-Flag) or anti-Myc antibody (α-Myc) for respective epitope-tagged proteins. The extent of CRY2 ubiquitination is calculated by [CRY2-Ubq intensity]IP / [Flag intensity]IP with the short exposure immunoblots and shown underneath. S. exp or L. exp: short or long chemiluminescence exposures of immunoblots.
+Fig. 6 The VP motif of CRY2 is required for the CRY2-COP1 interaction but not the CRY2-LRB interaction. a, A schematic diagrams depicting the CRY2^{P532L} mutation. PHR, photolyase homologous region; CCE, CRY C-terminal extension; DQQVPSAV, VP motif in CRY2; numbers, amino acid positions. b, Hypocotyl length of 6-day-old seedlings of indicated genotypes grown under blue light of different light intensities (0, 10, 30, 60, 100 μmol m^{-2} s^{-1}). FGFP-CRY2 and FGFP-CRY2^{P532L} were constitutively expressed in cry1cry2dr6. Standard deviations (n≥20) are shown. c, Immunoblots showing degradation of FGFP-CRY2 or FGFP-CRY2^{P532L} in 7-day-old etiolated transgenic seedlings
+irradiated with blue light (100 \( \mu \)mol m\(^{-2}\) s\(^{-1}\)) for the indicated time. Immunoblots were probed with anti-CRY2 and anti-HSP90 antibodies. HSP90 is a loading control. **d**, Quantitative results of CRY2 degradation from immunoblots in (c), analyzed with one phase decay of nonlinear regression. CRY2 (B/D) = [CRY2/HSP90]\(^{\text{blue}}\) / [CRY2/HSP90]\(^{\text{dark}}\). T\(_{1/2}\) indicates the time required for 50% degradation. **e-f**, Co-IP assays showing the lack of CRY2\(^{P532L}\)-COP1 interaction (**e**) and the the blue light- and phosphorylation-dependent CRY2\(^{P532L}\)-LRB2 interaction (**f**) in heterologous HEK293T cells. HEK293T cells co-transfected with indicated plasmids were either kept in the dark (-) or treated with 100 \( \mu \)mol m\(^{-2}\) s\(^{-1}\) blue light for 2 hours (+). Immunoprecipitations were performed with Flag-conjugated beads. CRY2\(^{D387A}\) is a negative control. Anti-Flag antibody, anti-Myc antibody or anti-HA antibody were used for detecting respective tagged proteins. Arrows indicate phosphorylated CRY2.
+Figures
+
+![A set of panels showing various experimental results and graphs related to plant growth under different light conditions and genetic backgrounds.](page_120_180_1347_1012.png)
+
+Figure 1
+
+[Please see the manuscript file to view the figure caption.]
+Figure 2
+
+[Please see the manuscript file to view the figure caption.]
+
+Figure 3
+[Please see the manuscript file to view the figure caption.]
+
+![BiFC and Hoechst staining images and corresponding BiFC ratios for various constructs](page_120_120_1347_682.png)
+
+<table>
+  <tr>
+    <th>BiFC ratio (mean ± SD)</th>
+    <th>CRY2-nYFP cCFP-CRY2</th>
+    <th>LRB1-nYFP cCFP-CRY2</th>
+    <th>LRB2-nYFP cCFP-CRY2</th>
+    <th>CRY2<sup>D387A</sup>,nYFP cCFP-CRY2<sup>D387A</sup></th>
+    <th>LRB1-nYFP cCFP-CRY2<sup>D387A</sup></th>
+    <th>LRB2-nYFP cCFP-CRY2<sup>D387A</sup></th>
+  </tr>
+  <tr>
+    <td>Image #</td>
+    <td>4</td>
+    <td>4</td>
+    <td>6</td>
+    <td>8</td>
+    <td>9</td>
+    <td>6</td>
+  </tr>
+  <tr>
+    <td>Nuclei #</td>
+    <td>92</td>
+    <td>43</td>
+    <td>99</td>
+    <td>61</td>
+    <td>59</td>
+    <td>41</td>
+  </tr>
+  <tr>
+    <td>0.5497 ± 0.0320</td>
+    <td>0.8417 ± 0.0378</td>
+    <td>0.5228 ± 0.0175</td>
+    <td>0.0462 ± 0.0210</td>
+    <td>0.0406 ± 0.0207</td>
+    <td>0.0266 ± 0.0081</td>
+  </tr>
+</table>
+
+Figure 4
+
+[Please see the manuscript file to view the figure caption.]
+Figure 5
+
+[Please see the manuscript file to view the figure caption.]
+Figure 6
+
+[Please see the manuscript file to view the figure caption.]
+
+Supplementary Files
+
+This is a list of supplementary files associated with this preprint. Click to download.
+
+• LRBsup.pdf

0dbf2481fcf07fc6fd0e01821e9109b6f6dfa78793e31b5946d85a21c8c5a94b/peer_review/peer_review.md

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+Peer Review File
+
+Potential global impacts of alternative dosing regimen and rollout options for the ChAdOx1 nCoV-19 vaccine
+
+Open Access This file is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. In the cases where the authors are anonymous, such as is the case for the reports of anonymous peer reviewers, author attribution should be to 'Anonymous Referee' followed by a clear attribution to the source work. The images or other third party material in this file are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.
+REVIEWER COMMENTS
+
+Reviewer #1 (Remarks to the Author):
+
+Comments for Author
+
+This paper uses static agent-based transmission modelling to explore circumstances under which allocating of a single or a double dose of the ChAdOx1 nCoV-19 vaccine will have higher vaccine effectiveness across different settings. The authors use data from the clinical trials of this vaccine, and combine it with a static transmission model to explore how vaccine effectiveness is affected by a) the characteristics of the vaccine quantified by the ratio of the efficacy of single dose vs double dose of the vaccine and the efficacy waning over time and b) the administration of the vaccine including the proportion of people receiving the second dose, the delivery speed and the time interval between the two doses and c) the settings profile defined by the demographic profile – specifically the proportion of the population that is 65+-, the vaccine availability and the attack rate of the virus in the setting. The results showcase the different trade-offs between a)-c) need to be considered for decision making around how this vaccine roll-out is delivered across different countries. For example, one of the main analysis scenarios suggests that if the number of doses available is not sufficient to cover all 65+ (considered people at highest risk) with two doses, then allocation of a single vaccine to twice as many individuals or extending the time interval between doses may be necessary. This is dependent how effective I the first dose vs the second dose and the results are not surprising. While, this is a very valuable study, I have some reservations in accepting this manuscript as it is and would suggest some changes are necessary before it is accepted.
+
+Major comments:
+
+1) The simulations at the core of this work is a static (time-invariant) transmission model. I feel that having a static model is not sufficiently robust for this analysis and suggest using a dynamic agent-based model that simulates the individuals with infection attributes (susceptible, infectious, hospitalised etc) that change over time, in addition to the belonging in different society layers (home, work, etc). The force of infection \( \lambda \) will then not only depend on age but also on time and also possibly on the viral profile- as for example captured within the dynamic agent-based model, for example. https://www.medrxiv.org/content/10.1101/2020.05.10.20097469v3
+2) The vaccine drop out rate modelled is 5%. I would like to see a sensitivity analysis on this value and especially in light of possible vaccine hesitancy towards ChAdOx1 nCoV-19 vaccine in different settings.
+3) Important characteristics of a vaccine against COVID-19 is the reduction in severity from vaccination – quantified by reduced hospitalisations and deaths- but also the impact of onwards transmission. The authors here assume that the vaccine efficacy against infection is 5% and they do not untangle the relationship between vaccine allocation and effectiveness of the vaccine on transmission. Decisions of rolling out vaccination in younger age groups, or in settings with younger population, is crucially depended on this and any informed evidence on vaccine allocation has to address this issue. My suggestion would be to include sensitivity analysis on this parameter and reproduce Figures 1-3 for different values of this parameter.
+
+Minor comments
+
+1) Please give more detail on why the booster dose interval is following a specific beta distribution – and explain why variation of this is not considered in additional sensitivity analysis.
+Reviewer #2 (Remarks to the Author):
+
+This is an interesting paper that explores some trade-offs with dosing strategies for the ChAdOx1 vaccine. The authors find that, under conditions of constrained supply, in some situations it is optimal to give a single dose to as large a section of the population as possible (starting from elderly and working down) and in other situations prioritising two doses works better. This trade-off depends on the size of the supply population age structure in a relatively simple way -- clearly explained in the discussion.
+
+While I suspect that the trade-off is described in a way that is qualitatively accurate, I would take the specific numbers obtained with a grain of salt for methodological reasons as I will explain. The identification of this tradeoff and its qualitative nature is a valuable contribution and I therefore recommend acceptance subject to revisions.
+
+The authors explain, "the methodology employed was very specifically tailored to the research question and its context." However no source code is available for inspection from what I can tell. This is a serious issue for evaluating the model, for transparency and reproducibility. I always recommend against publication of papers based on models where the source code is not publicly available.
+
+The authors use an individual based model which in principle could be an unconstrained computer program that does anything, however there is a hint that it is much simpler than that: individuals are described by a tuple of attributes which are modified in a uniform way. This is good because it suggests that the model is just a stochastic rewriting system perhaps equivalent to a rule-based model or a coloured Petri net. I would find this more convincing than a tailored, bespoke, ad-hoc model because it means that we know how to understand the conceptual framework where it sits.
+
+The equation in "transmission and clinical cascade". Please number your equations. \( \lambda \) is a function age \( \rightarrow \mathbb{R} \). However age (a) does not appear on the right hand side. I think it perhaps corresponds to the "\( l \)" subscript in the numerator but as written this appears to be a constant vector-valued function of age which is clearly not what is intended.
+
+However, this definition of \( \lambda \) is motivated by computational simplification because the simulation is expensive. It is unclear why the simulation should be so expensive. In particular, the authors say that the daily risk of infection is a function of time and is adjusted (how?) such that the correct attack rate is obtained. In the absence of a transmission model, what is the correct attack rate? How is this obtained? Surely it is itself influenced by vaccination which reduces the chance of infection. The mechanism here is unclear and is the main reason why I say that quantitative results obtained in this way should be taken with a grain of salt.
+
+Is it perhaps feasible, given that parameter regimes of interest have been identified using the relatively inexpensive model, to then explore those interesting regimes with a more fully-fledged model containing transmission? That would be my preferred approach over a static model.
+
+Vaccine efficacy decays exponentially (next equation). This doesn't seem biologically realistic. At t = 0 I would expect efficacy to be zero and for it to increase to some maximum over a period of time and then to reach a plateau (probably not a sharp peak) and thereafter to slowly decay. This could to matter because the time to reach the plateau is on a similar scale to the serial interval.
+
+Ideally I would like to see the effect of the vaccine on transmission incorporated here though I
+understand if the authors feel that it is out of scope. For countries with high rates of vaccination this is clearly important as we are already seeing in the USA and the UK. For countries that are severely supply constrained such as the LMICs that are really the main focus of this paper, this effect may not be so strong. At a minimum this should be discussed.
+
+The observation of the threshold value for choosing between strategies corresponding to the curve whose integral is the is the proportion of the population over 65 mentioned in the caption of Fig 3 could usefully be emphasised. This seems to be the main result, actually, and it is mentioned almost in passing at the end of the Results section. However, it is not clear to me how the integral is defined because the curves are not functions (there are multiple "y" values for some "x"). Please clarify this and explain.
+
+Reviewer #3 (Remarks to the Author):
+
+This article uses static transmission modelling to predict the impact of ChAdOx1 vaccine rollout in limited-resource scenarios, altering parameters such as the timing of vaccine rollout and administering one vs. two doses of vaccine. This work is timely, important, and makes an important acknowledgment of the hard decisions surrounding vaccine allocation that will continue to be made in the coming months.
+
+The authors have taken the trouble to quantify an answer for vaccine allocation that may largely be intuitive: that the greatest number of COVID-19 cases are averted with high vaccine coverage that is rolled out as quickly as possible. Additionally intuitive may be the finding that, as long as VE for one dose is at least 51% of the VE for two doses, a greater number of illnesses may be averted if twice the people receive half the doses. It is reassuring to see that these back-of-napkin, informal calculations hold up when additional, formal model considerations are added. I believe it will be helpful for the authors to more clearly highlight circumstances under which these “intuitive” findings could be violated. If there is time and space, it would be extraordinarily helpful to identify how these assumptions could change under additional scenarios, potentially including:
+1. ChAdOx1 VE against circulating variants of concern, especially in LMIC settings where VOCs may cause the majority of cases
+2. National regulatory agencies’ decision-making process regarding ChAdOx1 vaccine safety in younger populations, and how this could influence age-based prioritization and/or speed of rollout
+3. Alternate scenarios in which (usually younger) healthcare workers are prioritized for vaccination alongside older adults; this may be of special interest given SAGE recommendations for vaccine prioritization and given new safety outcomes of interest in Europe
+
+Additional minor comments are listed below.
+• Page 4, paragraph 1: It would be helpful for the purposes of contrast to also list the estimated efficacy for ChAdOx1, since it is listed for the Pfizer and Moderna vaccines, and to specify the outcomes for which efficacy was measured (for all vaccines)
+• Page 4, paragraph 2: As a point of clarification, when the authors say “suffer complex vaccine responses”, are they referring to vaccine safety/adverse event outcomes?
+• The authors note a hospitalization fatality rate; perhaps they could note which proportion of COVID-19 deaths in low-resource settings they assume to occur outside the hospital.
+• Page 9, paragraph 5: By “an individual with baseline status i”, do the authors mean “baseline vaccination status”?
+• At the end of the discussion section, it could be helpful to briefly mention which additional observational data (e.g., VE estimations from Canada which will now include a 4-month delay between dose 1 and dose 2) will be helpful to update these calculations
+• In Figure 1, is the top bar x-axis representing VE? If so, it would be helpful to provide that information in the axis title or labels. Similarly, it can be challenging to flip back and forth between Table 1 and Figure 1; it would be helpful to include the abbreviations in row titles in Figure 1 as a footnote as well.
+• In Figure 2, if I understand the figure correctly, I recommend the vertical bar on the right side be removed and rotated 90 degrees so that it reads more as a “legend” than as a secondary y-axis. (Again, if I do not understand correctly, my apologies.)
+• In Figure 2, it is not clear to me what the decimal represents for “dose allocation”—does this represent the percentage of the population vaccinated, the percentage of total doses that are given in a 6 month time frame, or other?
+REVIEWER 1 COMMENTS:
+Major comments:
+
+1. The simulations at the core of this work is a static (time-invariant) transmission model. I feel that having a static model is not sufficiently robust for this analysis and suggest using a dynamic agent-based model that simulates the individuals with infection attributes (susceptible, infectious, hospitalised etc) that change over time, in addition to the belonging in different society layers (home, work, etc). The force of infection \( \lambda \) will then not only depend on age but also on time and also possibly on the viral profile- as for example captured within the dynamic agent-based model, for example. https://www.medrxiv.org/content/10.1101/2020.05.10.20097469v3
+
+Author response: We have explained in the paper that the methodology employed was specifically tailored to the research question (prioritising single-dose vs double dose vaccine coverage) and its context (using the ChAdOx1 nCoV-19 vaccine in a top-down age priority schedule). The ChAdOx1 nCoV-19 Phase 3 vaccine clinical trials were the only Phase 3 trials to present infection as one of the tracked outcomes. No evidence was found for a transmission-blocking effect (VE = 3.8% [−72.4 to 46.3]) both overall and at any stage of follow-up. Given the broad confidence intervals, there could be an argument that some indirect effects might be accrued. We demonstrate in the methods section (Box 1), that given the low values of coverage explored here, the vaccine would need to have a very high infection blocking profile for indirect effects to be significant in our simulations, which would be against the evidence produced by the clinical trials. Also, there is no scope to vaccinate younger individuals (where indirect effects could play a larger role) since the vaccine prioritisation schedule was fixed to mimic the UK vaccine rollout (which is similar to most HICs), and thus, the potential for reductions in transmission were assumed negligible throughout our simulations. This is further elaborated at the beginning of the methods section and illustrated with two supplementary figures. In addition, given that vaccine production rates are likely to be insufficient to meet the demand generated by a global pandemic in the short term, even if the vaccines did have some infection prevention properties, vaccine coverage would not be able to reach the high rates needed to achieve significant herd effects. We therefore purposefully implemented an individual-based, age-dependent, static transmission model to predict the number of infections, clinical cases, and deaths expected to occur within the first 6 months of the vaccination programme rollout.
+
+A recent paper¹ employed a dynamic model to explore optimal vaccination schedules in the UK specifically and concluded that even under the most optimistic scenario for protection against new infections (85%), vaccinations would
+not reduce the reproduction number \( R \) below 1, and that the most beneficial strategy would always be to vaccinate the elderly first, regardless of indirect effects. We have now provided figures that highlight the analytical reasoning behind this and justify the methodology employed and choice of model given the context and vaccination characteristics.
+
+1 Moore S, Hill EM, Dyson L, Tildesley MJ, Keeling MJ (2021) Modelling optimal vaccination strategy for SARS-CoV-2 in the UK. PLOS Computational Biology 17(5): e1008849. https://doi.org/10.1371/journal.pcbi.1008849
+
+2. The vaccine drop-out rate modelled is 5%. I would like to see a sensitivity analysis on this value and especially in light of possible vaccine hesitancy towards ChAdOx1 nCoV-19 vaccine in different settings.
+
+Author response: The 5% vaccine dropout rate was obtained from the Voysey et al. paper\(^2\) and conforms to the rates of refusal observed in the UK vaccination rollout\(^3\). Note that this is not a relevant parameter for our analyses (which is why we ignored it), since it is only a significant concern for younger people (not reached in our simulations given the limited dose allocation), and the core issue remains whether it would be better to vaccine more people with a singe dose or less people with two doses when the number of available doses is limited.
+
+2 Voysey, M., et al., Single dose administration, and the influence of the timing of the booster dose on immunogenicity and efficacy of ChAdOx1 nCoV-19 (AZD1222) vaccine Lancet, 2021.
+
+3 https://www.ons.gov.uk/releases/coronavirusandvaccinehesitancygreatbritain31marchto25april2021
+
+3. Important characteristics of a vaccine against COVID-19 is the reduction in severity from vaccination – quantified by reduced hospitalisations and deaths- but also the impact of onwards transmission. The authors here assume that the vaccine efficacy against infection is 5% and they do not untangle the relationship between vaccine allocation and effectiveness of the vaccine on transmission. Decisions of rolling out vaccination in younger age groups, or in settings with younger population, is crucially depended on this and any informed evidence on vaccine allocation has to address this issue. My suggestion would be to include sensitivity analysis on this parameter and reproduce Figures 1-3 for different values of this parameter.
+
+Author response: As addressed in point 1, the ChAdOx1 nCoV-19 Phase 3 vaccine clinical trials found no statistically significant transmission-blocking effect (VE = 3.8% [−72.4 to 46.3]) both overall and at any stage of follow-up. We demonstrate in the methods section (Box 1) that for the low values of coverage explored here, the vaccine would need to have a very high infection blocking profile for indirect effects to be significant in our simulations, which would be against the evidence produced by the clinical trials. Also, there is no scope to vaccinate younger individuals (where indirect effects could play a larger role) since the vaccine prioritisation schedule was fixed to mimic the UK vaccine rollout (which was similar to most of the HICs), and thus, the potential for reductions in transmission was assumed to
+be negligible throughout our simulations. Given that age is by far the most significant covariate to explain risk of deaths from infection, no country has of yet, decided to not prioritise the elderly population, since vaccinating them promptly is guaranteed to yield the most efficiency per dose. In addition, given that vaccine production rates are likely to be insufficient to meet the demand generated by a global pandemic in the short term, even if the vaccines have some infection prevention properties, the coverage of the vaccine in populations would not be able to reach the high rates needed to achieve significant transmission blocking.
+
+Minor comments
+
+5. Please give more detail on why the booster dose interval is following a specific beta distribution – and explain why variation of this is not considered in additional sensitivity analysis.
+
+Author response: We chose a beta distribution due to its appropriateness as a continuous probability distribution. With it we can easily define the proportion of individuals receiving the second vaccine dose a certain number of days after the first dose. We should note that this is not a random distribution but one that conforms with the second dose delay distribution in the ChAdOx1 nCoV-19 Phase 3 vaccine clinical trial. The distribution has a flat tail, i.e., delay times are spread out across the interval boundaries, which is realistic for a vaccine rollout programme where most people are likely to receive the second dose exactly X days after the first dose, but where others are likely to make other arrangements to receive the vaccine at their convenience over a longer time scale. We now provide a plot of the delay distribution for transparency – Figure S9.
+
+Reviewer 2 COMMENTS:
+
+6. The authors explain, "the methodology employed was very specifically tailored to the research question and its context." However, no source code is available for inspection from what I can tell. This is a serious issue for evaluating the model, for transparency and reproducibility. I always recommend against publication of papers based on models where the source code is not publicly available.
+
+Author response: The source code was made available in a GitHub repository as indicated in the paper under the heading “data sharing” as required by Nature Communications: https://github.com/ricardoaguas/como-ChAdOx1-vaccine-. We can only assume this was not removed from the version the reviewer was provided.
+
+7. The authors use an individual based model which in principle could be an unconstrained computer program that does anything, however there is a hint that it is much simpler than that: individuals are described by a tuple of attributes which are modified in a uniform way. This is good because it suggests that the model is just a stochastic rewriting system perhaps equivalent to a rule-based model or a coloured
+Petri net. I would find this more convincing than a tailored, bespoke, ad-hoc model because it means that we know how to understand the conceptual framework where it sits.
+
+Author response: We thank the reviewer for this comment and agree that indeed the model framework used facilitates understanding of the processes involved and is invaluable for consistently comparing different scenarios assuming different attack rates. We should note that this is perhaps the most pertinent criticism the other reviewers have raised, so we really appreciate that this reviewer sees the value in the approach taken.
+
+8. The equation in "transmission and clinical cascade". Please number your equations. \( \lambda \) is a function age \( \rightarrow \mathbb{R} \). However, age (a) does not appear on the right hand side. I think it perhaps corresponds to the "I" subscript in the numerator but as written this appears to be a constant vector-valued function of age which is clearly not what is intended.
+
+Author response: We thank the reviewer for the suggestion and have now numbered the equations in the methods section. However, we don’t quite understand how there could be confusion regarding the force of infection equation. The text following the equation clearly defines \( c_{ij} \) as the daily number of contacts between age groups i and j for a particular country and \( P_j \) as the population age distribution. Since there are two age indices, we decided not to use the letter a (which is typically associated with age), in the right-hand side of the equation, to avoid any confusion. Clearly, we were not successful, and thus decided to change the notation based on this comment.
+
+9. However, this definition of \( \lambda \) is motivated by computational simplification because the simulation is expensive. It is unclear why the simulation should be so expensive. In particular, the authors say that the daily risk of infection is a function of time and is adjusted (how?) such that the correct attack rate is obtained. In the absence of a transmission model, what is the correct attack rate? How is this obtained? Surely it is itself influenced by vaccination which reduces the chance of infection. The mechanism here is unclear and is the main reason why I say that quantitative results obtained in this way should be taken with a grain of salt. Is it perhaps feasible, given that parameter regimes of interest have been identified using the relatively inexpensive model, to then explore those interesting regimes with a more fully-fledged model containing transmission? That would be my preferred approach over a static model.
+
+Author response: We considered a range of attack sizes (proportion of the population infected) during the six-month period which accounts for all non-pharmaceutical interventions in that timeframe. Mathematical models have been notoriously poor at predicting the future dynamics of the epidemic even in the medium-term. To avoid making extreme assumptions about what the future would look like, we opted to explore all possible realistic burdens within a 6 months’
+time window, ignoring the minutia of the daily shape of the epidemic curve. To do that, we calibrate the model without vaccination to establish the daily risk of infection (same every day) for each level of attack rate – this is now clearly explained in the methods section. We then run model simulations with those daily risks of infection for the vaccine model and compare the outcome metrics of interest (deaths, clinical cases, and infections), thus establishing vaccine effectiveness as defined by equation (3) in the methods section. As mentioned in points 1 and 4 above, the vaccination campaigns simulated here can only have a very marginal impact on transmission since direct vaccine efficacy against infection is very low and there is a fixed rollout schedule that prioritised high-risk individuals who don’t contribute very much to onwards transmission (Box 1). We have now also included Supplementary Figures 7 and 8 to clarify these effects.
+
+10. Vaccine efficacy decays exponentially (next equation). This doesn't seem biologically realistic. At t = 0 I would expect efficacy to be zero and for it to increase to some maximum over a period of time and then to reach a plateau (probably not a sharp peak) and thereafter to slowly decay. This could to matter because the time to reach the plateau is on a similar scale to the serial interval.
+
+Author response: As indicated on page 9, we imposed a stepwise increase in post-dose two vaccine efficacy across an 8-week booster dose interval, as observed in the clinical trial¹. Furthermore, the trial revealed a slow decrease in protection following the first dose (in those that received one dose only) in agreement with an exponential decay. Note that the maximum interval between doses allowed in the model is 55 days, which is much lower than the lowest mean duration of vaccine protection explored.
+
+¹ Voysey, M., et al., Single dose administration, and the influence of the timing of the booster dose on immunogenicity and efficacy of ChAdOx1 nCoV-19 (AZD1222) vaccine Lancet, 2021.
+
+11. Ideally, I would like to see the effect of the vaccine on transmission incorporated here though I understand if the authors feel that it is out of scope. For countries with high rates of vaccination this is clearly important as we are already seeing in the USA and the UK. For countries that are severely supply constrained such as the LMICs that are really the main focus of this paper, this effect may not be so strong. At a minimum this should be discussed.
+
+Author response: Please see our responses under 1, 4, and 9 above justifying the use of static model vs a transmission model. We have extended the methods section to provide more detail on the robustness of our assumptions and added some of those elements to the discussion as well, as suggested by the reviewer.
+12. The observation of the threshold value for choosing between strategies corresponding to the curve whose integral is the is the proportion of the population over 65 mentioned in the caption of Fig 3 could usefully be emphasised. This seems to be the main result, actually, and it is mentioned almost in passing at the end of the Results section. However, it is not clear to me how the integral is defined because the curves are not functions (there are multiple "y" values for some "x"). Please clarify this and explain.
+
+Author response: This integral is calculated from its sensu strictu definition of the area under the curve, the curve being the contour line with value 1. Note that these are surface plots, in which the contour line is defined by the mean of the Z values (relative vaccine effectiveness of single vs double dose regimens) for each combination of X and Y, as explained in Figure 2. This was outlined in the legend for Figure 3, but we have made the link clearer. Essentially if one dosing regimens were always superior to two dose regimens, the area under the curve would be 1, i.e., 100% of the surface plot area.
+
+Reviewer 3 COMMENTS:
+
+13. ChAdOx1 VE against circulating variants of concern, especially in LMIC settings where VOCs may cause the majority of cases.
+
+Author response: The reviewer raises an interesting point that is, however, outside the scope of this paper. We address the optimal logistical deployment of a vaccine campaign based on the immunological profile of the ChAdOx1 vaccine. Given that data on ChAdOx1 vaccine efficacy results against VOCs are speculative at best, these have not been included. We did however consider that efficacy could potentially be lower than the estimate presented in the original clinical trial, thus accounting for some viral immune escape over time. Note that the lowest vaccine efficacy values explored in the sensitivity analysis are 32.5% after the first dose and 65% after the second dose, which is constitutes a 24-50% decrease in efficacy from the best-case efficacy scenario.
+
+14. National regulatory agencies’ decision-making process regarding ChAdOx1 vaccine safety in younger populations, and how this could influence age-based prioritization and/or speed of rollout. Alternate scenarios in which (usually younger) healthcare workers are prioritized for vaccination alongside older adults; this may be of special interest given SAGE recommendations for vaccine prioritization and given new safety outcomes of interest in Europe.
+
+Author response: We do not address that issue as there was no scope to vaccinate younger individuals (where indirect effects could play a larger role) since the vaccine prioritisation schedule was fixed to mimic the UK vaccine rollout (which is similar to most of the HICs). Crucially, this work tries to provide insights into the potential value of vaccinating those
+at higher risk of death with a single dose vs a double dose under very strict dosing availability scenarios. Additionally, we consistently argue that direct vaccine protection against deaths is dominant unless a very large proportion of the younger population (responsible for most infectious contacts) could be targeted. Other modelling groups have tackled the age prioritisation issue and have reached the same conclusion¹ – that the highest risk group (elderly) should always be prioritised first if the aim is to reduce the mortality burden.
+
+¹ Moore S, Hill EM, Dyson L, Tildesley MJ, Keeling MJ (2021) Modelling optimal vaccination strategy for SARS-CoV-2 in the UK. PLOS Computational Biology 17(5): e1008849. https://doi.org/10.1371/journal.pcbi.1008849
+
+Additional minor comments are listed below.
+
+**15. Page 4, paragraph 1: It would be helpful for the purposes of contrast to also list the estimated efficacy for ChAdOx1, since it is listed for the Pfizer and Moderna vaccines, and to specify the outcomes for which efficacy was measured (for all vaccines)**
+
+Author response: We did not include this as this vaccine estimated efficacy is one of the parameters explored in our sensitivity analysis. Granted, in our sensitivity analysis we generate uncertainty around the estimate provided in the OVG paper (Voysey et al)², so we have taken the reviewers suggestion and added this to the introduction/background section of the paper.
+
+² Voysey, M., et al., Single dose administration, and the influence of the timing of the booster dose on immunogenicity and efficacy of ChAdOx1 nCoV-19 (AZD1222) vaccine Lancet, 2021.
+
+**16. Page 4, paragraph 2: As a point of clarification, when the authors say “suffer complex vaccine responses”, are they referring to vaccine safety/adverse event outcomes?**
+
+Author response: We thank the reviewer for picking up on this poor choice of wording. The statement refers to immunogenicity of the vaccine in populations with high levels of malnutrition and other infectious diseases’ incidence. This has been clarified in the text.
+
+**17. The authors note a hospitalization fatality rate; perhaps they could note which proportion of COVID-19 deaths in low-resource settings they assume to occur outside the hospital.**
+
+Author response: This is an interesting point that we have tackled continuously with in other work (see
+https://como.bmj.com/). Ultimately, we have found that deaths tend to be under-reported in LMICs, but that the magnitude of that bias is very difficult to quantify. Here, we assume that differences in fatality across countries are only a reflection of their age structure, rather than differences in population frailty. Also note that the numbers of infections, cases and deaths in our results pertain to “true” outcomes and not what would be reported by the health system. In conclusion, we do not take country level access issues into account beyond age structure and “availability” as defined by the maximum population that would be covered by COVAX.
+
+18. Page 9, paragraph 5: By “an individual with baseline status i”, do the authors mean “baseline vaccination status”?
+
+Author response: We adopted the standard nomenclature used in vaccine trials, defining individuals as previously exposed or naïve at enrolment (baseline). The baseline status is then the susceptibility status of population (immune vs. non-immune) before the vaccination campaign starts. This has been made clearer in the methods section.
+
+19. At the end of the discussion section, it could be helpful to briefly mention which additional observational data (e.g., VE estimations from Canada which will now include a 4-month delay between dose 1 and dose 2) will be helpful to update these calculations
+
+Author response: We agree that including these elements is a valuable addition and have made the appropriate changes in the discussion.
+
+20. In Figure 1, is the top bar x-axis representing VE? If so, it would be helpful to provide that information in the axis title or labels. Similarly, it can be challenging to flip back and forth between Table 1 and Figure 1; it would be helpful to include the abbreviations in row titles in Figure 1 as a footnote as well.
+
+Author response: We are unsure what the reviewer means by “top bar x-axis”. The figure legend and title clearly mention that the boxplots show the median and interquartile ranges of the predicted vaccine effectiveness (VE) on each of the outcomes (Deaths, Clinical cases, and Infections). We fully agree that adding the abbreviations as a footnote might facilitate reading and have made the appropriate changes.
+21. In Figure 2, if I understand the figure correctly, I recommend the vertical bar on the right side be removed and rotated 90 degrees so that it reads more as a “legend” than as a secondary y-axis. (Again, if I do not understand correctly, my apologies.)
+
+Author response: The vertical bar is the colour legend. This is a standard presentation of a surface plot, with a figure legend on the right-hand side. We have left an empty space between the plot and the colour-bar to avoid any confusion.
+
+22. In Figure 2, it is not clear to me what the decimal represents for “dose allocation”—does this represent the percentage of the population vaccinated, the percentage of total doses that are given in a 6 month time frame, or other?
+
+Author response: This is simply a different numerical representation of a percentage value (0.3 = 30%). As defined in the Vaccination delivery and vaccine efficacy section of the Methods section and in Table 1, this represents the allocation range, i.e., the number of doses available as a percentage of the total population. For example, for a population of 10 million people that has 1 million doses available, that would correspond to 10% dose allocation.
+REVIEWER COMMENTS
+
+Reviewer #1 (Remarks to the Author):
+
+Overall, the authors have taken in consideration my comments and responded adequately to the points I have raised. I am happy to recommend acceptance of this paper for publications following this revision.
+
+Below are couple of suggestions to improve the timeliness of this work in light of the ongoing vaccine rollout:
+
+1) An extra analysis that would be nice to include is additional third dose of the vaccine - as a booster vaccine. Exploring whether this additional vaccine would improve outcomes would be interesting, If the authors feel this is better suited to future analysis, maybe they can add a paragraph on this in the discussion instead.
+
+2) Updating the model parameters for effectiveness of this vaccine on onwards transmission - in light of recent PHE work that onwards transmission can be reduced by 49% in vaccinated people with this vaccine
+https://khub.net/documents/135939561/390853656/Impact+of+vaccination+on+household+transmission+of+SARS-COV-2+in+England.pdf/35bf4bb1-6ade-d3eb-a39e-9c9b25a8122a?t=1619601878136- would also be a useful discussion point.
+Reviewer #2 (Remarks to the Author):
+
+I thank the authors for their detailed responses. Whilst I still believe that a dynamic transmission model would be better, I accept that it was the authors’ express intention to implement a static one due to a lack of evidence for transmission blocking effects of vaccine and the focus being on low resource settings where coverage can be expected to be low. All of my concerns have been addressed except one, as well as a minor point.
+
+Eq. 1 – Force of Infection, \( \lambda(a) \)
+
+Also thanks for adjusting the notation for \( \lambda(a) \) (Equation 1). It is now clearer though I still have a minor niggle. The authors write,
+
+\[
+\lambda(a) = k_\lambda \sum_{w=1}^N c_{aw} \frac{\sum_{a=1}^N c_{aw}}{\sum_{a=1}^N \sum_{w=1}^N c_{aw}}
+\]
+
+this is ambiguous because the \( a \) that represents the argument to the function is only the \( a \) in the first \( c_{aw} \) term and is not the same \( a \) as appears in the sums. To fix this, just choose a different symbol in the sums, e.g.,
+
+\[
+\lambda(a) = k_\lambda \sum_{w=1}^N c_{aw} \frac{\sum_{v=1}^N c_{vw}}{\sum_{v=1}^N \sum_{w=1}^N c_{vw}}
+\]
+
+Fig. 3 – Areas under curves
+
+The authors respond that they are computing the area under the curves in this figure. I queried what this could mean because the curves are not functions so the integral is not defined, and the authors replied that they are using the definition of an integral that means the area under the curve. This is still not satisfactory. I have annotated the figure to help explain the problem. The usual way of understanding area under the curve is to take the limit of a sum of small area elements, say of width
+
+![Areas under curves figure showing three curves labeled f(x), g(x), h(x) with axes labeled Dose Allocation - maximum number of doses available vs Efficacy of Single dose vs Double dose regimen](page_489_1047_627_495.png)
+δ.
+
+\[
+\int_{0.5}^{1} f(x)dx = \lim_{\delta \to 0} \sum_{n=0}^{\frac{0.5}{\delta}} [f(0.5 + (n+1)\delta) - f(0.5 + n\delta)] \delta
+\]
+
+The problem is, what is the value of \( f(x) \) and \( g(x) \) where they intersect the red line? \( f(x) \) would have *three* distinct values and \( g(x) \) would have five. That means that the sum above is not defined and neither is the area.
+
+Based on the authors’ response, I *think* what is meant is the fraction of the surface area enclosed by the curves (and, implicitly, both axes). This makes sense but is a very different concept from area under the curve. For this to make sense, the treatment of the two excursions (circled in red) needs to be specified. I believe that the authors mean the area enclosed by the main \( h(x) \) cirve and the axes, minus the area of the small excursions. This could be written as,
+
+\[
+\int_{0}^{0.3} \int_{0.5}^{1} f'(x, y)dxdy
+\]
+
+where,
+
+\[
+f'(x, y) = \begin{cases}
+1 & f(x, y) \leq 1 \\
+0 & \text{otherwise}
+\end{cases}
+\]
+
+and I have taken \( y \) to be the “Dose allocation” axis.
+
+If this is right, the general idea would be better conveyed as “the area enclosed by the curves”. Writing what is meant in math, correctly, is good to make sure the meaning is clear. The term “area under the curve” should not be used because (a) it is incorrect as I show above and (b) it is very confusing as this exchange shows.
+Reviewer #3 (Remarks to the Author):
+
+I thank the authors for the time spent revising this article, which I do believe has important value for vaccine implementation programs. However, there are challenges to the manuscript interpretation which still remain after revision, and which would be good to address before the manuscript is published. These fall into two main categories, described below:
+
+1. Considerations for other environments/epidemiological contexts. The authors have made an effective argument for the analysis they have completed, and acknowledge that adjustment of existing parameters or addition of new ones—while likely helpful for different contexts—is outside the scope of the paper. I understand this, but would then appreciate more mention in the discussion of how these factors could change policy decisions based on their findings and other literature that has been published in the meantime. The authors noted that calculated VE for ChAdOx1 against variants of concern is “speculative at best”, which may have been true when the response was written; but they will hopefully be able to provide preliminary estimates from Public Health England and other groups at this point.
+
+2. Interpretation of figures and tables. The authors have noted that the figures are standard and should be able to be interpreted easily, but unfortunately, the paper will be most effective if the figures are explained to the lowest common denominator (a group which certainly must include myself). It is still unclear to me how to interpret the third column in Figure 1, but it appears to show an estimated VE against SARS-CoV-2 infections of 0.4%. This seems low, given existing literature on this topic. Similarly, it would be helpful to change the y-axis title in Figure 2 to the more accurate phrase “Dose allocation – maximum doses available per population”. The current description, “number of doses available,” is not strictly accurate; the value shown is not a number but a proportion.
+Author’s note:
+We appreciate the reviewers’ constructive comments and feel the revised manuscript should clarify all the concerns raised and be a lot clearer to a wider audience. All new sources of data and code used to generate the results in the detailed response to reviewer’s comments below can be found in the github repository that accompanied the original submission: https://github.com/ricardoaguas/como-ChAdOx1-vaccine-.
+Reviewer 1
+
+1.1. An extra analysis that would be nice to include is additional third dose of the vaccine - as a booster vaccine. Exploring whether this additional vaccine would improve outcomes would be interesting, if the authors feel this is better suited to future analysis, maybe they can add a paragraph on this in the discussion instead.
+
+Author response: We appreciate the reviewer’s positive feedback and are very happy to respond to their comments. Recent discussions have focused on the potential population-level impact of an additional third booster dose of the vaccine, with Israel even implementing a third round of vaccinations without FDA approval. We feel that the lack of clinical data on the potential additional benefits of a third dose warrants further research especially given the uncertainty in the duration of the vaccine’s protective effective following the second dose. Additional data from trials would enable us to the conduct post hoc analyses on optimal dosage strategies including a third dose in a variety of demographic settings. We have included this additional commentary in the discussion section of the manuscript.
+
+1.2. Updating the model parameters for effectiveness of this vaccine on onwards transmission - in light of recent PHE work that onwards transmission can be reduced by 49% in vaccinated people with this vaccine https://khub.net/documents/135939561/390853656/Impact+of+vaccination+on+household+transmission+of+SARS-COV-2+in+England.pdf/35bf4bb1-6ade-d3eb-a39e-9c9b25a8122a?t=1619601878136- would also be a useful discussion point.
+
+Author response: We thank the reviewer for this observation. We have been attentively following the literature on the population level impact of vaccination rollout, with a special interest in Israel and the UK. In the UK there have been a series of epidemiological studies trying to determine how community and household transmission is being modulated by vaccination1,2. These studies suffer from a series of sampling and frame of reference issues which result in the highest level of protection from the vaccine being found in the days immediately following vaccination – when antibody levels induced by vaccination are known to be negligible3.
+
+1 https://www.nejm.org/doi/full/10.1056/NEJMc2107717
+2 https://www.medrxiv.org/content/10.1101/2021.03.11.21253275v1
+3 https://www.thelancet.com/journals/lancet/article/PILS0140-6736(20)31604-4/fulltext#seccetitle150
+Regardless, we do believe an argument can be made for lower infectivity of vaccinated individuals as a consequence of lower viral loads following infection (we still assume risk of infection following vaccination is largely unchanged). Thus, we now calculate a daily modulator \( (\overline{vb}) \) of the risk of infection that accounts for the vaccine impact on onwards transmission depending on the proportion of people in the population with \( j \) doses of the vaccine:
+
+\[
+\overline{vb}(t) = 1 - \frac{\sum_{i=0}^{N} v_{impact}^j}{N}
+\]
+
+Consistent with the remaining vaccine efficacy parameters, we assumed there is a boost in vaccine impact on transmission with increasing number of doses given by parameter D2B. In plain terms, under homogeneous transmission assumptions, the overall impact on transmission of vaccinating a proportion of the population is equal to the mean decrease in transmission across all individuals. To circumvent this limitation, we assume that the mean impact on transmission changes daily to reflect how the network of contacts on a given day might contain different proportions of vaccinated people. This is done by sampling a population level impact on transmission \( vb \) assuming a Beta distribution with overdispersion \( \sigma \):
+
+\[
+vb(t) \sim \beta(\overline{vb}(t), \sigma)
+\]
+
+This parameter \( vb \) changes daily as more people get vaccinated and modulates the population force of infection (\( \lambda(a) \)) directly:
+
+\[
+\lambda(a, t) = \lambda(a) \cdot vb(t)
+\]
+
+We performed similar sensitivity analyses as the ones in the main manuscript that include vaccine impact on infectivity and retrieve the results in Figure 1 below.
+
+The methodological description above along with the additional sensitivity analysis (with maximal values for vaccine impact on infectivity of 25% and 50%) are now provided in the supplementary materials (Supplementary Figure 10) and referenced to in the discussion.
+Figure 1. Sensitivity analysis mimicking that in Figure 1 of the previous submission, now including a max vaccine effect on transmission given by parameter RT.
+
+2. Reviewer 2
+
+2.1. Eq. 1 (Force of infection, \( \lambda(a) \)). The \( a \) that represents the argument to the function is only the \( a \) in the first \( c_{aw} \) term and is not the same \( a \) as appears in the sums. To fix this, just choose a different symbol in the sums.
+
+Author response: We thank the review for calling our attention to this potential source of confusion and have made the appropriate changes as shown below and on page 8.
+
+\[
+\lambda(a) = k_\lambda \sum_{w=1}^N c_{aw} \frac{\sum_{v=1}^N c_{vw}}{\sum_{v=1}^N \sum_{w=1}^N c_{vw}}
+\]
+
+2.2. Fig. 3 – Areas under curves. The authors respond that they are computing the area under the curves in this figure. I queried what this could mean because the curves
+are not functions so the integral is not defined, and the authors replied that they are using the definition of an integral that means the area under the curve. This is still not satisfactory.
+
+Author response: We apologize for not being clearer in our response. To be very specific, we take the contour lines of the linearly interpolated outcome values for each combination of x and y values. We then vectorize each contour line to obtain the y-values at which the contour line is crossed for evenly spaced x-values (taking the highest y-value for duplicates). The resulting vector is then run through a composite trapezoid rule algorithm that computes the area under the curve (auc function in the MESS R package). This is now made more explicit in the caption for figure 3 in the manuscript.
+
+3. Reviewer 3
+
+3.1. Considerations for other environments/epidemiological contexts. The authors have made an effective argument for the analysis they have completed and acknowledge that adjustment of existing parameters or addition of new ones—while likely helpful for different contexts—is outside the scope of the paper. I understand this but would then appreciate more mention in the discussion of how these factors could change policy decisions based on their findings and other literature that has been published in the meantime. The authors noted that calculated VE for ChAdOx1 against variants of concern is “speculative at best”, which may have been true when the response was written; but they will hopefully be able to provide preliminary estimates from Public Health England and other groups at this point.
+
+Author response: We appreciate the reviewer’s positive feedback. We are cognisant of the influence of diverse environments and epidemiological settings on vaccine effectiveness. However, to fully evaluate the specific impacts, additional research is needed on the implications of the epidemiological and health system contexts - particularly in LMICs. We have updated the discussion, highlighting the importance of understanding how the impact of vaccinating specific population sub-groups is a product of a trade-off between the relative proportion of those at highest risk vs. those that contribute the most to onwards transmission which is balanced by the magnitude of the impact of vaccination on transmission (page 12, second paragraph).
+We maintain that our intention in this study is to investigate optimal dosing strategies for a specific vaccine delivery strategy (vaccinating the high-risk groups first) under different dose availability and population structure constraints. However, we have expanded the discussion to provide examples of ongoing studies addressing other health contexts and related themes, and how to interpret our results in light of those studies.
+
+3.2. Interpretation of figures and tables. The authors have noted that the figures are standard and should be able to be interpreted easily, but unfortunately, the paper will be most effective if the figures are explained to the lowest common denominator (a group which certainly must include myself). It is still unclear to me how to interpret the third column in Figure 1, but it appears to show an estimated VE against SARS-CoV-2 infections of 0.4%. This seems low, given existing literature on this topic. Similarly, it would be helpful to change the y-axis title in Figure 2 to the more accurate phrase “Dose allocation – maximum doses available per population”. The current description, “number of doses available,” is not strictly accurate; the value shown is not a number but a proportion.
+
+Author response: We should stress that the analyses contained in the original submission assumed that the vaccine infection blocking effect was at most 5% at the individual level. As a consequence, the population level impact on infections of vaccinating at most 30% of people with a single dose is negligible. However, in the revised manuscript we now provide an additional analysis accounting for vaccine induced reduction in infectivity (Supplementary Figure 10). Please refer to our response to point 1.2 above for a comprehensive description of the methodology.
+
+Regarding the second half of the comment, we appreciate the suggestion and have changed the axis label in Figure 2 to “Dose allocation – maximum doses available per population”.
+REVIEWERS’ COMMENTS
+
+Reviewer #1 (Remarks to the Author):
+
+I am very pleased that the authors have successfully addressed both of my comments and I am content to recommend acceptance of this manuscript.
+
+On the first comment: adding a discussion paragraph on the addition booster vaccine, while awaiting further results from trials, suffices my first comments.
+
+On the second comment: The extra analysis that they have undertaken on the boost of vaccine efficacy with an increasing number of people in the population being vaccinated and hence reliant on the population network structure, together with the sensitivity analysis of 25% and 50% vaccine effect on infectivity, are very good additions to the paper methods. These two parts have sufficiently answered my query.
+
+One additional point that the authors could add to the discussion is the avenue of further work where this analysis is complemented with analysis looking at waning of immunity from vaccination: both the time and the shape of the distribution and how this differs in a one-dose, two-dose and three-dose regime.
+
+Reviewer #2 (Remarks to the Author):
+
+I thank the authors for taking the time to address my concerns. All of my concerns have been addressed and I am happy to recommend the article for publication.
+Author’s note:
+We appreciate the reviewers’ constructive comments and feel the revised manuscript should clarify all the concerns raised and be a lot clearer to a wider audience. All new sources of data and code used to generate the results in the detailed response to reviewer’s comments below can be found in the github repository that accompanied the original submission: https://github.com/ricardoaguas/como-ChAdOx1-vaccine_ (doi:10.5281/zenodo.5522794).
+Reviewer 1
+
+Comment: I am very pleased that the authors have successfully addressed both of my comments and I am content to recommend acceptance of this manuscript.
+
+1.1. On the first comment: adding a discussion paragraph on the addition booster vaccine, while awaiting further results from trials, suffices my first comments.
+
+We thank the reviewer for acknowledging the addition.
+
+1.2. On the second comment: The extra analysis that they have undertaken on the boost of vaccine efficacy with an increasing number of people in the population being vaccinated and hence reliant on the population network structure, together with the sensitivity analysis of 25% and 50% vaccine effect on infectivity, are very good additions to the paper methods. These two parts have sufficiently answered my query.
+
+We thank the reviewer for acknowledging the addition.
+
+1.3. One additional point that the authors could add to the discussion is the avenue of further work where this analysis is complemented with analysis looking at waning of immunity from vaccination: both the time and the shape of the distribution and how this differs in a one-dose, two-dose and three-dose regime.
+
+We have included this addition in the last paragraph of the discussion.
+
+Reviewer 2
+
+Comment: I thank the authors for taking the time to address my concerns. All of my concerns have been addressed and I am happy to recommend the article for publication.
+
+We thank the reviewer for acknowledging the revisions and for recommending the article for publication.

0dbf2481fcf07fc6fd0e01821e9109b6f6dfa78793e31b5946d85a21c8c5a94b/preprint/preprint.md

@@ -0,0 +1,359 @@
+An analysis of the potential global impact of dosing regimen and rollout options for the ChAdOx1 nCoV-19 vaccine
+
+Ricardo Aguas
+University of Oxford
+Anouska Bharath
+University of Oxford
+Lisa White
+University of Oxford   https://orcid.org/0000-0002-6523-185X
+Bo Gao
+University of Oxford
+Merryn Voysey
+Oxford Vaccine Group, Department of Paediatrics, University of Oxford, United Kingdom
+Andrew Pollard
+University of Oxford   https://orcid.org/0000-0001-7361-719X
+Rima Shretta ( rima.shretta@ndm.ox.ac.uk )
+University of Oxford   https://orcid.org/0000-0001-5011-5998
+
+Article
+
+Keywords: COVID-19, coronavirus, vaccine
+
+Posted Date: March 11th, 2021
+
+DOI: https://doi.org/10.21203/rs.3.rs-296726/v1
+
+License: This work is licensed under a Creative Commons Attribution 4.0 International License.
+Read Full License
+
+Version of Record: A version of this preprint was published at Nature Communications on November 4th, 2021. See the published version at https://doi.org/10.1038/s41467-021-26449-8.
+An analysis of the potential global impact of dosing regimen and rollout options for the ChAdOx1 nCoV-19 vaccine
+
+Ricardo Aguas¹, Anouska Bharath¹, Lisa J White¹, Bo Gao¹, Andrew J Pollard², Merryn Voysey², Rima Shretta*¹
+
+¹ Nuffield Department of Medicine, University of Oxford: R. Aguas PhD, A. Barath PhD, L.J. White PhD, B. Gao PhD, R. Shretta PhD
+² Oxford Vaccine Group, Department of Paediatrics, University of Oxford: A. J. Pollard FMedSci, M. Voysey DPhil.
+
+*Corresponding author
+Rima Shretta
+Nuffield Department of Medicine
+University of Oxford
+Old Road Campus
+Headington, Oxford OX3 7LF
+United Kingdom
+rima.shretta@ndm.ox.ac.uk
+Summary
+
+Background
+
+The ongoing COVID-19 pandemic has placed an unprecedented health and economic burden on countries at all levels of socioeconomic development, emphasizing the need to evaluate the most effective vaccination strategy in multiple, diverse environments. The high reported efficacy, low cost, and long shelf-life of the ChAdOx1 nCoV-19 vaccine positions it well for evaluation in different settings.
+
+Methods
+
+Using data from the ongoing ChAdOx1 nCoV-19 clinical trials, an individual-based model was constructed to predict the 6-month population-level impact of vaccine deployment. A detailed probabilistic sensitivity analysis (PSA) was developed to evaluate the importance of epidemiological, demographic, immunological, and logistical factors in determining vaccine effectiveness. Using representative countries, logistical plans for vaccination rollout at various levels of vaccine availability and delivery speed, conditional on vaccine efficacy profiles (efficacy of the booster dose, time interval between doses, and relative efficacy of the first dose) were explored.
+
+Findings and Interpretation
+
+Our results highlight how expedient vaccine delivery to high-risk groups is critical in mitigating COVID-19 disease and mortality. In scenarios where the number of vaccine doses available is insufficient for high-risk groups (those aged more than 65 years) to receive two vaccine doses, administration of a single dose of vaccine is optimal. This effect is consistent even when vaccine efficacy after one dose is just 75% of the levels achieved after two doses. These findings offer a nuanced perspective of the critical drivers of COVID-19 vaccination effectiveness and can inform optimal allocation strategies. These are relevant to high-income countries with a large high-risk group population as well as to low-income countries with younger populations, where the cost and logistical challenges of procuring and delivering two doses for each citizen represent a significant challenge.
+Funding
+
+Bill and Melinda Gates Foundation (OPP1193472); Li Ka Shing Foundation; Oxford University COVID-19 Research Response Fund (ref: 0009280).
+
+The funders played no role in the design or outcomes of this work.
+
+Contributors
+
+RA, AB, LJW, and RS conceived the paper and contributed to the analysis. RA developed the model and wrote the code. BG ran the PSA and contributed to data processing. MV and AP provided the data, discussed the analysis, and commented on the draft. All authors have read, contributed to, and approved the final version of the manuscript.
+
+Declaration of interests
+
+The authors declare no conflict of interest.
+
+Data Sharing
+
+The data used to inform this analysis have been published and are available in the public domain. The code used is available at: https://github.com/ricardoaguas/como-ChAdOx1-vaccine-.
+
+Acknowledgements
+
+LJW is funded by the Li Ka Shing Foundation. RA is funded by the Bill and Melinda Gates Foundation (OPP1193472). The Covid-19 Modelling Consortium has support from the Oxford University COVID-19 Research Response Fund (ref: 0009280). The authors have not been paid to write this article by a pharmaceutical company or other agency. The authors are grateful to Adam Bodley for proofreading the final draft.
+Introduction
+
+As of March 2nd 2021, almost 115 million people have been diagnosed with COVID-19 worldwide, and in excess of 2.5 million confirmed deaths have been reported\(^{2,3}\). Vaccination is a critical strategy to control the spread of SARS-CoV-2, the virus that causes COVID-19, and to reduce the severity of symptomatic disease. Three vaccines have already received emergency use authorization in the United Kingdom (UK). The developers of two of these vaccines have reported efficacies of 95% for their vaccines in their respective Phase 3 trials (Pfizer/BioNTech and Moderna)\(^{4}\). The third vaccine, ChAdOx1 nCoV-19, jointly developed by Oxford University and AstraZeneca, demonstrated an acceptable safety profile and efficacy against symptomatic COVID-19, with no hospital admissions or severe cases of disease reported in the intervention arm during Phase 3 trials conducted in three countries. This vaccine can be stored and distributed at 2–8°C and will be made available at a lower cost than the other vaccines, making it suitable for global access, particularly in low- and middle-income countries (LMICs)\(^{5-7}\).
+
+While clinical trials have validated the efficacy of the ChAdOx1 nCoV-19 vaccine in reducing symptomatic infection, appropriate national vaccination strategies across the world must consider heterogeneity among populations as well as the diverse demographic and socioeconomic environments of affected countries. In particular, the younger population typically present in LMICs justifies the need to assess the effects of associated behaviours and health profiles on vaccine effectiveness. These countries exhibit competing health, social, and economic challenges owing to inadequate healthcare infrastructure and a high prevalence of immunocompromising and infectious diseases. In these settings, individuals could also suffer complex vaccine responses when compared with responses in individuals in more developed economies\(^{8,9}\). At the same time, many LMICs have been unable to secure vaccine doses in advance from potential suppliers and thus are likely to have incomplete coverage of their populations, particularly in the short-term. The global COVID-19 vaccine alliance, COVAX, has pledged to procure and distribute vaccines equitably to LMICs; however, this will cover a maximum of 20% of the total population in each country\(^{10}\). Although the University of Oxford and AstraZeneca have made the largest supply commitment to LMICs at more affordable prices than other vaccine manufacturers, there is a need to evaluate the impact of a range of factors on vaccine effectiveness\(^{11-13}\).
+Due to shortages in supply, the UK government has instituted a policy of administering the booster dose of the vaccine at up to 12 weeks following the initial dose, prompting a debate among scientists, manufacturers, and governments on optimal dosing intervals for COVID-19 vaccines\(^{14,15}\). The purpose of this analysis is therefore to evaluate the efficacy of the ChAdOx1 nCoV-19 vaccine in countries with different demographic profiles, as a function of vaccine efficacy, dosage regime (interval between initial and booster doses, or no booster at all), coverage, and immunity wane rate. Given the differences in healthcare infrastructure and vaccine access around the world, decision-makers should consider the effect of these factors on population-level impact to determine the most effective strategy for their context\(^{13}\).
+
+Where vaccination programmes have begun, priority has so far been given to older age groups, individuals with co-morbidities, and frontline medical staff. The model developed therefore considers a simplified system where the vaccine is delivered to age groups in descending order while supplies are available. As there is limited evidence of indirect effects, that is, the potential for reductions in transmission, this vaccine effect was assumed to be negligible for the purposes of this analysis.
+
+Methods
+
+The methodology employed was very specifically tailored to the research question and its context. Vaccine production rates are always going to be insufficient to meet the demand generated by a global pandemic. In a context of limited vaccine dose availability, it is imperative to prioritize those individuals who would yield the greatest epidemiological benefit. Assuming the most pressing need is to reduce hospitalization rates and deaths, the initial targeting of those at higher risk for these outcomes seems logical, given that the alternative of immunizing sufficient people at lower risk for the indirect benefits to outweigh the direct benefits of a vaccine targeted at those at higher risk is not feasible with the number of vaccines available in the short-term. Even the UK, where mass production of the AztraZeneca vaccine has enabled 20% of the population to be vaccinated within 3 months, opted to prioritize the high-risk groups (those aged more than 65 years), partially because of the uncertainty around vaccine efficacy against infection. The ChAdOx1 nCoV-19 vaccine
+clinical trials were the only Phase 3 trials in which infection was evaluated as an outcome. No evidence was found for a transmission reduction effect (VE = 3.8% [–72.4 to 46.3])\textsuperscript{7}, but important questions were raised about how to allocate a limited number of doses to optimize the impact on symptomatic disease, given that a single-dose regimen could offer prolonged protection and thus a delay of the second dose could be warranted.
+
+We began from the premise laid out above and implemented an individual-based, age-dependent, static transmission model to predict the number of infections, clinical cases, and deaths expected to occur within 6 months of vaccination programme rollout. Individuals are simulated as autonomous systems, each with a set of attributes, informing their serostatus, vaccination uptake history (number of doses and dosing interval), and age. Box 1 details how the dynamics processes inherent to disease transmission and vaccination campaign logistics are considered in the model.
+Box 1. Consider a hypothetical scenario where the number of SARS-CoV-2 infections over 6 months in an unvaccinated population is 100,000. Policymakers could opt for one of two alternative options with very different direct benefit outlooks when deciding on how to allocate the limited number of vaccine doses available to them.
+
+Option 1: Vaccinate high contact groups (aged 25–40 years) (36% of all infections, 10% of all hospitalizations, 1% of all deaths)¹
+
+Predicted infections:
+
+\( 100,000*36\%*[1\text{-vaccine direct effect on infection}] + 100,000*64\%*[1\text{-vaccine indirect effect on infection}] \)
+
+Predicted hospitalizations:
+
+Predicted infections*10%*[1-vaccine direct effect on hospitalization] + Predicted infections *90%*[ 1-vaccine Indirect effect on hospitalizations]
+
+Predicted deaths:
+
+Predicted infections*1%*[1-vaccine direct effect on deaths] + Predicted infections*99%*[ 1-vaccine indirect effect on deaths]
+
+Option 2: Vaccinate high risk groups (aged >65 years) (10% of all infections, 66% of all hospitalizations, 90% of all deaths)¹
+
+Predicted infections:
+
+\( 100,000*10\%*[1\text{-vaccine direct effect on infection}] + 100,000*90\%*[1\text{-vaccine indirect effect on infection}] \)
+
+Predicted hospitalizations:
+
+Predicted infections *66%*[1-vaccine direct effect on hospitalization] + Predicted infections *34%*[ 1-vaccine indirect effect on hospitalizations]
+
+Predicted deaths:
+
+Predicted infections*90%*[1-vaccine direct effect on deaths] + Predicted infections*10%*[ 1-vaccine indirect effect on deaths]
+
+Thus, vaccines targeting high-contact groups would have to provide indirect effects in the order of 80% (80% reduction in risk in the untargeted population) to prevent an approximate number of deaths similar to that which would be provided by targeting the high-risk group with a direct vaccine effect against death of 85%.
+Transmission and clinical cascade
+
+The spread of COVID-19 is sensitive to the underlying network of contacts between infectious and susceptible individuals in their various societal spheres (home, work, public transport, etc). For a given population, we can summarize the number of contacts per day as an age-dependent force of infection \( \lambda(a) \), i.e. a daily risk of acquiring an infection given age \( a \). The age-dependent risk of infection can then be defined as:
+
+\[
+\lambda(a) = k_\lambda \frac{\sum_{j=1}^N c_{ij} P_j}{\sum_{i=1}^N (\sum_{j=1}^N c_{ij} P_j)}
+\]
+
+Where \( c_{ij} \) is the daily number of contacts between age groups \( i \) and \( j \) for a particular country, \( P_j \) is the population age distribution, \( N \) is the total number of age categories, and \( k_\lambda \) is the overall daily risk of infection (which is informed by the number of infectious people in the population). Here, we decided to simplify the transmission process by making the daily risk of infection constant over time, thus having a static transmission model. When evaluating different epidemiological scenarios with different levels of population attack size over the 6-month period explored here, we simply changed the daily risk of infection parameter until the correct attack rate was obtained. Without this constraint, computation of the very high number of simulations required to perform the sensitivity analyses presented here would be virtually impossible.
+
+The risk of developing severe disease and possibly dying as a consequence of infection was informed by age-dependent infection hospitalization (IHR) and hospitalization fatality (HFR) ratios, published in\(^{16}\). Thus, the modelled daily risk that an individual will develop severe disease is given by \( \lambda(a) IHR(a) \), whereas the risk of dying is approximately \( \lambda(a) IHR(a) HFR(a) \). The timing of these events and the lag between infection and clinical outcome are not relevant, as we are only making comparisons between synthetic populations, as detailed below.
+
+Vaccination delivery and vaccine efficacy
+
+Different vaccine dose allocation schemes were simulated, by limiting the number of doses distributed in 6 months, as well as allowing for different dosing intervals (delaying the second
+dose) and dosing splits (giving one dose vs two doses). The allocation of doses was always prioritized to the oldest age groups. Individuals were assigned vaccine doses in descending order of age until the maximum number of doses had been allocated.
+
+Given a fixed number of available doses, one can calculate the target recipient population by looking at the dose-split proposal. If all doses are given as single doses in 6 months, then the target population for vaccination is equal to the number of available doses. At the other extreme, where all vaccinees receive two doses, the number of recipients would be half the number of available doses. Within the group that is meant to receive two doses of the vaccine, a 5% dropout rate (vaccine refusal) was imposed, and a range of booster dose intervals was explored.
+
+We implemented three different logistical implementations of a vaccine campaign rollout: constant effort, frontloaded, and backloaded. The distinction was in the speed at which the target population received vaccine doses during the initial 2 months. As individuals were assigned a vaccine, the number of doses received would be determined by a draw from a uniform distribution according to the desired dose split. Individuals given two doses would be assigned a booster dose interval following a beta distribution with \( \alpha = 0.15 \) and \( \beta = 0.95 \).
+
+Although vaccine efficacy was explored in the sensitivity analyses presented here, we centred the explored ranges around the point estimates presented in\(^{17}\). Vaccine efficacy, \( V_e(t) \), was treated as a direct modulator of the risk of infection, clinical disease, and death; it was then defined for each individual, at each timestep of the simulation, as:
+
+\[
+V_e(t) = V_i^j e^{-\delta t}
+\]
+
+, where V is the vaccine efficacy in an individual with baseline status \( i \) that received dose number \( j \) a \( t \) number of days ago, while \( \delta \) is the rate of loss of vaccine-induced immunity.
+
+Throughout this paper, we present a sensitivity analysis of the post-dose two maximum efficacy, the relative efficacy of dose one vs dose two, and the booster dose interval. While doing so, we constrain vaccine efficacy against clinical disease to be the same as that against death, while vaccine efficacy against infection is fixed at 5%\(^{7}\). We also imposed a stepwise increase in post-dose two vaccine efficacy across an 8-week booster dose interval, as observed in the clinical trial\(^{17}\). This means that giving the second vaccine dose less than 8
+weeks after the first dose will result in a 25% lower post-dose two efficacy relative to the maximum assumed vaccine efficacy.
+
+Vaccine effectiveness
+
+The vaccination campaign population impact is referred to throughout as vaccine effectiveness and was defined as:
+
+\[
+V_{eff} = 100 \frac{AR_v - AR_u}{AR_u}
+\]
+
+, where \( AR_v \) is the attack rate (over 6 months) in the vaccinated population, and \( AR_u \) is the attack rate in a population that mirrors the vaccinated population in all aspects except vaccination. We thus have a pair of populations for each parameter set in our analyses and calculate the expected vaccine effectiveness for each parameter set as the relative difference in occurrence of each of the disease endpoints (infection, clinical symptoms, and death).
+
+Results
+
+We conducted an extensive initial sensitivity analysis to determine how the impact of rolling out a COVID-19 vaccination campaign in the UK depends on epidemiological, logistical, and immunological factors. The sensitivity of the modelled vaccine effectiveness to the variables explored is illustrated in Figure 1. It is clear that the prospects for vaccine impact are most sensitive to the number of vaccine doses available within 6 months, the speed of delivery within the same timeframe, and the vaccine efficacy (both the maximum efficacy post-dose two and the relative efficacy of dose one compared with dose two). Interestingly, for the same inputs, the median expected vaccine effectiveness is greater for deaths than it is for clinical cases.
+
+From this first exploratory analysis one could immediately suggest that, for maximum effectiveness, a vaccine campaign should aim to vaccinate as many people as possible (thus governments/policymakers should procure the maximum number of doses possible), in the shortest time possible. These are by far the two variables the model outputs are most sensitive to, as can clearly be seen in Supplementary Figures 1 and 2. These figures also reveal
+a very interesting interaction between the vaccine efficacy profile and an actionable decision of how the first available doses are to be distributed. In the frontloaded scenario, where the speed of vaccine delivery is maximal during the early stages of the 6-month vaccination campaign, a single-dose regimen is expected to perform significantly worse if vaccine efficacy post-dose one is 50% lower than vaccine efficacy post-dose two (top row). However, if the vaccine efficacy after both doses is the same (bottom row), a single-dose regimen can actually be preferable, especially if the number of vaccine doses available is small.
+
+These initial results prompted further investigation of the possible interactions and trade-offs between the vaccine efficacy profiles and logistical implementation variables. In this detailed analysis, the population attack size was fixed at 12%, delivery speed to frontloaded, and vaccine-induced protection to last 360 days. The results are summarized in Supplementary Figure 3. As determined by the initial sensitivity analysis, vaccine effectiveness is quite sensitive to the number of available doses, the maximum post-dose two efficacy, and the efficacy of the first dose relative to the second.
+
+Two interesting results pertain to the sensitivity of the model to changes in the dose number split and the interval in days between doses for the two-dose regimen recipients. While giving everyone two doses, irrespective of all other variables, seems to be preferable to the single-dose option, the length of the whiskers suggests there might be a parameter space for which the single-dose option is optimal, as seen in Supplementary Figures 1 and 2. Increasing the time interval between doses generally produces improved vaccine effectiveness, although a slight decrease in median effectiveness can be observed after an 8-week (56 day) interval. This is further investigated in Supplementary Figures 4 and 5, revealing an interesting trade-off, with a large increase in predicted effectiveness after 7 to 8 weeks, followed by a small decrease as the booster dose interval expands, but only if the efficacy of the first dose is low. If the efficacy of the first dose is similar to the efficacy of the second, increasing the interval between doses up to 12 weeks does not decrease vaccine effectiveness.
+
+Interestingly, we find a non-linear increase in effectiveness for large values of dose availability, which can be explained by the markedly non-linear risk of severe disease and death with age. As the number of available doses increases, a larger proportion of the population will receive a vaccine dose. However, since vaccines are allocated in descending order of age, as a larger proportion of the population is reached, more and more low-risk
+individuals are vaccinated, for whom the vaccine accrued benefits are smaller and smaller. It is then advisable to investigate these relationships for different settings.
+
+We proceeded to investigate what factors could potentially influence the decision-making process regarding the distribution of doses during the first 6 months of vaccine programme rollout. We thus evaluated the relative predicted effectiveness of the single-dose versus the double-dose regimen, for different countries with potentially different dose availability, and assuming different vaccine efficacy profiles (Figure 2). For very high levels of dose allocation (high y-axis values), a two-dose regimen is clearly optimal. This starts to become less evident for scenarios where the protection conferred by the first dose gets closer to the post-dose two efficacy (moving right along the x-axis). Interestingly, when the number of available doses is small, the single-dose regimen will become more effective than the double-dose regimen, as the thick black line is crossed. The parameter combinations defining the line where there is a shift in strategy positioning are country dependent, with countries with older populations having a larger parameter space in which a single-dose option is preferable, as shown in Figure 3.
+
+Discussion
+
+The SARS-CoV-2/COVID-19 pandemic has created an unprecedented public health challenge, spurring a global race to develop and distribute viable vaccines. A vaccine that creates broad immunity against the SARS-CoV-2 virus could be the only effective means to control the pandemic and allow a return to “normalcy”. To have a significant impact on the disease, a critical mass of the global population at risk will need to be vaccinated. However, many high-income countries have secured more than half of the available vaccine doses for themselves, leaving LMICs, which make up more than 85% of the global population, to find their own solutions18. To address the problem of equitable access, WHO, Gavi, and the Coalition for Epidemic Preparedness Innovations (CEPI) established COVAX, a global alliance that has pledged to pool investment and allocate and distribute COVID-19 vaccines equitably, particularly in LMICs 10. However, COVAX is currently under-resourced and the doses secured are insufficient to achieve the coverage levels needed19. Supply constraints and new variants of SARS-CoV-2 are steering countries towards strategies that counter low
+access with dosing patterns or volumes to maximize the impact of the vaccines. Data from the ChAdOx1 nCoV-19 vaccine trials have allowed us to explore potential strategies to inform optimal allocation programmes, particularly in contexts where the cost and logistics of implementing multiple doses within a short timeframe may be challenging.
+
+Our findings indicate that vaccine effectiveness is dependent upon (i) the country context, which includes the demographic profile, the attack rate of the virus, and the amount of vaccine that is available (which influences the proportion of the population that is vaccinated); ii) the characteristics of the vaccine, which include the efficacy of a single dose relative to a double dose and the waning of efficacy over time; and iii) the proportion of the population receiving the second dose, the time interval between doses, and the delivery speed.
+
+Our analysis demonstrates that in scenarios where the number of vaccine doses available is insufficient for the highest risk groups (aged >65 years) to receive two doses, the allocation of a single vaccine dose is optimal. This effect is consistent even when the vaccine efficacy of a single dose is just 75% of the levels achieved after a double dose, until allocation drops to a population coverage of 10%, after which vaccinating only the high-risk individuals, with two doses, is more effective. In scenarios where the number of doses available to the country is sufficiently high, or if the relative single-dose efficacy is low (50% or less), providing a booster dose within 8 weeks would be preferable. Apart from these specific conditions, the results indicate that providing individuals with two doses of vaccine would have a similar effectiveness to the use of a single dose given to twice the number of individuals.
+
+The speed at which the high-risk population is vaccinated greatly influences the expected vaccine effectiveness in preventing clinical cases and death. This is particularly true if the transmission rate is high, with faster vaccination reducing the number of infections in groups awaiting their first dose during the rollout. Distributing the vaccine very slowly provides an effectiveness of less than 10%, regardless of the number of doses and allocations. The impact of allocation on outcomes is also greater when the population is vaccinated rapidly over a six-month period. In both of these scenarios, providing a single dose is preferable.
+An interesting trade-off was found between the booster dose interval and the relative vaccine efficacy of a single dose. For vaccines with large differences between first and second dose efficacy, delaying the booster dose interval past 8 weeks after the first dose was found to be detrimental. However, if a single dose provided at least 75% of the protection conferred by a double dose, delaying the booster dose interval to 12 weeks had a negligible impact on the number of cases and deaths. Given the similar reported efficacies of single and double doses of ChAdOx1 nCoV-19, a 12-week interval is the optimal scenario for this vaccine\(^{17}\). However, this finding may not be applicable to other COVID-19 vaccines.
+
+These differences are more profound when considering the demographic characteristics of a population. In high-income countries, which have a larger older population (>65 years), a single-dose regimen will allow the vaccination of more individuals more quickly, with a correspondingly greater impact on cases and deaths. In the UK, the six-month allocation threshold above which a two-dose regimen would be preferred was found to be about 16.5%.
+
+The six-month allocation threshold above which a two-dose regimen would be preferred is much lower in LMICs, mainly due to mortality in the younger population. In these contexts, decision-makers will need to consider the affordability, availability, and logistical constraints and feasibility of implementing a single or a double dose, the dosage intervals, and delivery speed. Most LMICs lack the digital databases necessary to manage patient data, reliably track vaccine inventories, keep track of who has received which vaccine, and inform people where and when they are due for a booster. Governments would also need to ensure that they reserve sufficient stocks to allow the administration of booster doses. In these cases, a robust cost–benefit analysis of each option will need to be considered.
+
+The dosing interval for COVID-19 vaccines has been a subject of debate among scientists, regulators, and governments around the world following the UK government’s decision to prioritize administering the first dose of vaccine to as many at-risk people as possible and increasing the interval between the two doses to up to 12 weeks\(^{14,15,20}\). A one-dose vaccine regimen or a two-dose regimen with longer time intervals may be sufficient to reduce symptoms of COVID-19 in the most vulnerable individuals and ultimately slow the pandemic, given that the time difference between first and second doses was shown to have a negligible effect on overall vaccine effectiveness (clinical cases, infections, and
+deaths). Indeed, a recent WHO notification stated that some countries are facing “exceptional circumstances” and may want to delay second doses to “allow for a higher initial coverage”. Other exceptional circumstances may involve trade-offs around the relative size of the highest risk population in a country and the currently unknown potential for a vaccine to reduce transmission, which may lead to some countries targeting high-contact groups to benefit from any potential indirect effects.
+
+Nevertheless, these thresholds are likely to differ depending on the country context. For example, smaller countries may be able to rapidly rollout the vaccine to a higher percentage of their population compared with the speed at which larger countries can do this. It should be noted that an implementation strategy is determined at a country level. The assumptions made in this work are based on the association of certain parameters with the health infrastructure and existing population of certain country groups defined by income level.
+
+Published clinical data were used to inform the parameters used in the model described in this paper. These data provide an aggregate efficacy of the ChAdOx1 nCoV-19 vaccine among people of a wide range of ages living in different countries. However, there were limited data available for assessing the effects of certain parameters (such as the effect of the dosing interval on post-dose two efficacy) on vaccine efficacy, which begat the need to conduct the post hoc exploratory analysis presented here.
+
+Conclusion
+
+This analysis demonstrates that in scenarios where the number of vaccine doses available is insufficient for the highest risk groups (>65 years of age) to receive two vaccine doses, allocation of a single vaccine dose to twice the number of individuals or extending the time interval between doses may be more optimal strategies. In contexts without supply constraints, or if the single-dose efficacy is low, providing a booster dose would be preferable. Apart from these specific conditions, the results indicate that providing individuals with two doses of vaccine would have a similar effectiveness to the use of a single dose in twice the number of individuals. In an ideal world, decisions about vaccination strategies would be made within the exact parameters of the trials that have been
+conducted. However, the limited availability of resources, and specific country contexts, may require decision-makers to consider alternative strategies.
+Tables and Figures
+
+Table 1: Model parameters.
+
+<table>
+  <tr>
+    <th>Parameter</th>
+    <th>Model term</th>
+    <th>Range</th>
+    <th>Description</th>
+  </tr>
+  <tr>
+    <td><b>Population attack size (% of the population)</b></td>
+    <td>ATT</td>
+    <td>(4; 12; 20)</td>
+    <td>This is the percentage of the population infected within the 6-month study period</td>
+  </tr>
+  <tr>
+    <td>Vaccine allocation (% of the population during study period)</td>
+    <td>TRG</td>
+    <td>(5; 10; 20; 30)</td>
+    <td>Allocation range was based on the assumed administration speed. Using current data, we assumed that higher-income countries could reach a maximum speed, allowing 30% coverage of the population within 6 months</td>
+  </tr>
+  <tr>
+    <td><b>Second dose administered (% of the vaccinated population administered a second dose)</b></td>
+    <td>DSP</td>
+    <td>(0; 25; 50; 75; 100)</td>
+    <td>This is the percentage of the vaccinated population that are administered a second (booster) dose</td>
+  </tr>
+  <tr>
+    <td>Interval between first dose and booster dose</td>
+    <td>BTI</td>
+    <td>(4 weeks; 7 weeks; 12 weeks)</td>
+    <td>The interval between doses can affect vaccine efficacy; the range chosen was based on available clinical trial data</td>
+  </tr>
+  <tr>
+    <td><b>Vaccine delivery speed</b></td>
+    <td>DEL</td>
+    <td>(fixed; frontloaded; backloaded)</td>
+    <td>The speed of vaccine delivery to the population – see Supplementary figure 6</td>
+  </tr>
+  <tr>
+    <td>Vaccine efficacy after the second dose</td>
+    <td>PD2</td>
+    <td>(65; 75; 85)</td>
+    <td>Maximum efficacy following the second dose</td>
+  </tr>
+  <tr>
+    <td><b>Vaccine efficacy of the first dose compared with the second dose (%)</b></td>
+    <td>D2B</td>
+    <td>(50; 75; 100)</td>
+    <td>Effect of the first dose compared with the second dose</td>
+  </tr>
+  <tr>
+    <td>Immunity wane rate (days following last dose)</td>
+    <td>VCW</td>
+    <td>(90; 180; 360; 540)</td>
+    <td>Vaccine protection decay post-last dose</td>
+  </tr>
+</table>
+Fig. 1: Overall sensitivity analysis of vaccine effectiveness, based on UK data.
+
+![Overall sensitivity analysis of vaccine effectiveness, based on UK data. Three boxplots showing sensitivity to various parameters across Deaths, Clinical Cases, and Infections.](page_246_357_957_682.png)
+
+The boxplots show the median and interquartile ranges of the predicted vaccine effectiveness on each of the outcomes for specific parameters. They were generated by aggregating all model simulations for each of the parameters, with each boxplot summarizing the variance in predicted vaccine efficacy for all possible combinations of the other parameters. The full list of parameters explored and their descriptions can be found in Table 1.
+Fig. 2: Optimal dose allocation.
+
+![Three contour plots showing optimal dose allocation for UK, Brazil, and Uganda, with axes labeled 'Efficacy of Single dose vs Double dose regimen' and 'Dose Allocation - maximum number of doses available'. The color bar indicates 'Double dose vaccine effectiveness compared to single dose effectiveness'.](page_184_357_1082_393.png)
+
+The coloured surfaces and respective contour lines indicate the ratio between the predicted vaccine effectiveness for a double-dose regimen vs a single-dose regimen. This ratio is a mean ratio, obtained by averaging out the ratios obtained in all model runs assuming the corresponding x and y parameter values and thus are not expected to be regular. Contour line 1 (thicker black line) indicates the parameter combinations for which there is no expected difference between giving everyone a single dose vs giving everyone two doses. For values greater than 1 (hot colours), a two-dose regimen is preferable, and for values less than 1 (cold colours), a single-dose regimen is preferable.
+Fig. 3: Dose allocation thresholds in different countries.
+
+![Dose allocation thresholds in different countries](page_246_312_957_682.png)
+
+The figure illustrates the parameter combinations that define the allocation threshold above which a two-dose regimen would be preferred over a single-dose regimen. The areas under the curves are 16.5%, 8%, and 3.8% for the UK, Brazil, and Uganda, respectively, which correlates almost perfectly with the proportion of the population above the age of 65 years in those countries.
+Supplementary Fig. 1: Impact of vaccine delivery speed, dose split, and dose availability on vaccine effectiveness as a measure of reduction in clinical cases.
+
+![Impact of vaccine delivery speed, dose split, and dose availability on vaccine effectiveness as a measure of reduction in clinical cases. Three panels showing Vaccine Effectiveness on Clinical Cases vs Dose Allocation - maximum number of doses available for Linear Delivery, Front Loaded Delivery, and Back Loaded Delivery. Each panel shows three lines representing different dose splits (0, 0.5, 1).](page_184_320_1080_670.png)
+
+The white number on the black background in each panel defines the vaccine efficacy of the first dose relative to the second dose. Lines represent the mean effectiveness calculated using all runs, where the parameters are those defined by each figure, irrespective of all remaining parameters. Lines are coloured according to the dose split, i.e. the proportion of individuals receiving two vaccine doses. These results are based on the UK population structure.
+Supplementary Fig. 2: Impact of vaccine delivery speed, dose split, and dose availability on vaccine effectiveness as a measure of reduction in deaths.
+
+![Impact of vaccine delivery speed, dose split, and dose availability on vaccine effectiveness as a measure of reduction in deaths. Three panels showing vaccine effectiveness on deaths versus dose allocation for Linear Delivery, Front Loaded Delivery, and Back Loaded Delivery, each with three dose split lines (0, 0.5, 1).](page_184_370_1080_670.png)
+
+The white number on the black background in each panel defines the vaccine efficacy of the first dose relative to the second dose. Lines represent the mean effectiveness calculated using all runs, where the parameters are those defined by each figure, irrespective of all remaining parameters. Lines are coloured according to the dose split, i.e. the proportion of individuals receiving two vaccine doses. These results are based on the UK population structure.
+Supplementary Fig. 3: Detailed sensitivity analysis of vaccine effectiveness for the most sensitive parameters, based on UK data.
+
+![Boxplots showing detailed sensitivity analysis of vaccine effectiveness for the most sensitive parameters, based on UK data.](page_184_256_1080_768.png)
+
+The boxplots show the median and interquartile ranges of the predicted vaccine effectiveness on each of the outcomes for specific parameters. They were generated by aggregating all model simulations for each of the parameters, with each boxplot summarizing the variance in predicted vaccine efficacy for all possible combinations of the other parameters.
+Supplementary Fig. 4: Impact of vaccine booster dose interval on vaccine effectiveness as a measure of reduction in clinical cases.
+
+![Impact of vaccine booster dose interval on vaccine effectiveness as a measure of reduction in clinical cases. Three panels showing vaccine effectiveness vs. dose allocation for boost intervals of 28 days, 56 days, and 84 days. Each panel contains three lines representing different dose splits (0, 0.5, 1).](page_184_312_1080_670.png)
+
+The white number on the black background in each panel defines the vaccine efficacy of the first dose relative to the second dose. Lines represent the mean effectiveness calculated using all runs, where the parameters are those defined by each figure, irrespective of all remaining parameters. Lines are coloured according to the dose split, i.e. the proportion of individuals receiving two vaccine doses. These results are based on the UK population structure.
+Supplementary Fig. 5: Impact of vaccine booster dose interval on vaccine effectiveness as a measure of reduction in deaths.
+
+![Impact of vaccine booster dose interval on vaccine effectiveness as a measure of reduction in deaths.](page_184_232_1080_670.png)
+
+The white number on the black background in each panel defines the vaccine efficacy of the first dose relative to the second dose. Lines represent the mean effectiveness calculated using all runs, where the parameters are those defined by each figure, irrespective of all remaining parameters. Lines are coloured according to the dose split, i.e. the proportion of individuals receiving two vaccine doses. These results are based on the UK population structure.
+Supplementary Fig. 6: Vaccine delivery speed.
+
+![Line graph showing vaccine delivery speed over time for Linear Delivery, Front Loaded, and Back Loaded scenarios](page_184_320_1087_563.png)
+
+The figure shows the number of vaccine doses administered over the course of the vaccination campaign (6 months).
+References
+
+1. Office for National Statistics. Coronavirus (COVID-19) weekly insights: latest health indicators in England, 12 February 2021. February 12, 2021 ed. United Kingdom; 2021.
+2. Dong E, Du H, Gardner L. An interactive web-based dashboard to track COVID-19 in real time. Lancet Infect Dis 2020; 20(5): 533-4.
+3. Johns Hopkins University. COVID-19 Dashboard. 2020. https://coronavirus.jhu.edu/map.html (accessed June 2020.
+4. Pfizer. Pfizer and BioNtech announce vaccine candidate against Covid-19 achieved success in first interim analysis from phase 3 study. 2020.
+5. Folegatti PM, Ewer KJ, Aley PK, et al. Safety and immunogenicity of the ChAdOx1 nCoV-19 vaccine against SARS-CoV-2: a preliminary report of a phase 1/2, single-blind, randomised controlled trial. Lancet 2020; 396(10249): 467-78.
+6. Ramasamy MN, Minassian AM, Ewer KJ, et al. Safety and immunogenicity of ChAdOx1 nCoV-19 vaccine administered in a prime-boost regimen in young and old adults (COV002): a single-blind, randomised, controlled, phase 2/3 trial. Lancet 2021; 396(10267): 1979-93.
+7. Voysey M, Clemens SAC, Madhi SA, et al. Safety and efficacy of the ChAdOx1 nCoV-19 vaccine (AZD1222) against SARS-CoV-2: an interim analysis of four randomised controlled trials in Brazil, South Africa, and the UK. Lancet 2021; 397(10269): 99-111.
+8. MacLennan CA. Vaccines for low-income countries. Seminars in Immunology 2013; 25(2): 114-23.
+9. Rodrigues CMC, Plotkin SA. Impact of Vaccines; Health, Economic and Social Perspectives. Frontiers in Microbiology 2020; 11(1526).
+10. WHO. Fair allocation mechanism for COVID-19 vaccines through the COVAX Facility. Geneva: WHO, 2020.
+11. Davies NG, Klepac P, Liu Y, Prem K, Jit M, Eggo RM. Age-dependent effects in the transmission and control of COVID-19 epidemics. Nat Med 2020; 26(8): 1205-11.
+12. Pullano G, Valdano E, Scarpa N, Rubrichi S, Colizza V. Evaluating the effect of demographic factors, socioeconomic factors, and risk aversion on mobility during the COVID-19 epidemic in France under lockdown: a population-based study. The Lancet Digital Health 2020; 2(12): e638-e49.
+13. Wang W, Wu Q, Yang J, et al. Global, regional, and national estimates of target population sizes for covid-19 vaccination: descriptive study. BMJ 2020; 371: m4704.
+14. Iacobucci G, Mahase E. Covid-19 vaccination: What’s the evidence for extending the dosing interval? BMJ 2021; 372: n18.
+15. Mahase E. Covid-19: Medical community split over vaccine interval policy as WHO recommends six weeks. BMJ 2021; 372: n226.
+16. Brazeau N, Verity R, Jenks S, et al. COVID-19 Infection Fatality Ratio Estimates from Seroprevalence. London: Imperial College London, 2020.
+17. Voysey M, Clemens SAC, Madhi SA, et al. Single dose administration, and the influence of the timing of the booster dose on immunogenicity and efficacy of ChAdOx1 nCoV-19 (AZD1222) vaccine Lancet 2021.
+18. Twohey M, Collins K, Thomas K. With First Dibs on Vaccines, Rich Countries Have ‘Cleared the Shelves’. New York Times. 2020 December 15, 2020.
+19. UN News. COVID-19 vaccines: donors urged to step up funding for needy countries. New York: UN News; 2020.
+20. Davis N. Vaccine experts call for clarity on UK’s 12-week Covid jab interval. The Guardian. 2021 January 25, 2021.
+Figures
+
+![Boxplots showing sensitivity analysis of vaccine effectiveness for deaths, clinical cases, and infections across various parameters](page_184_232_1207_693.png)
+
+Figure 1
+
+Overall sensitivity analysis of vaccine effectiveness, based on UK data. The boxplots show the median and interquartile ranges of the predicted vaccine effectiveness on each of the outcomes for specific parameters. They were generated by aggregating all model simulations for each of the parameters, with each boxplot summarizing the variance in predicted vaccine efficacy for all possible combinations of the other parameters. The full list of parameters explored and their descriptions can be found in Table 1.
+Figure 2
+
+Optimal dose allocation. The coloured surfaces and respective contour lines indicate the ratio between the predicted vaccine effectiveness for a double-dose regimen vs a single-dose regimen. This ratio is a mean ratio, obtained by averaging out the ratios obtained in all model runs assuming the corresponding x and y parameter values and thus are not expected to be regular. Contour line 1 (thicker black line) indicates the parameter combinations for which there is no expected difference between giving everyone a single dose vs giving everyone two doses. For values greater than 1 (hot colours), a two-dose regimen is preferable, and for values less than 1 (cold colours), a single-dose regimen is preferable.
+
+![Contour plot showing optimal dose allocation for three regions: UK, Brazil, Uganda. The plot compares the efficacy of single vs double dose vaccine regimens based on dose allocation and vaccine effectiveness.](page_68_120_1447_563.png)
+![Line graph showing dose allocation thresholds for UK, Brazil, and Uganda, with efficacy of single vs double dose regimen on the x-axis and maximum number of doses available on the y-axis.](page_120_186_1047_654.png)
+
+Figure 3
+
+Dose allocation thresholds in different countries. The figure illustrates the parameter combinations that define the allocation threshold above which a two-dose regimen would be preferred over a single-dose regimen. The areas under the curves are 16.5%, 8%, and 3.8% for the UK, Brazil, and Uganda, respectively, which correlates almost perfectly with the proportion of the population above the age of 65 years in those countries.
+
+Supplementary Files
+
+This is a list of supplementary files associated with this preprint. Click to download.
+
+• SupplementaryFigures.pdf

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+Peer Review File
+
+Knowledge-graph-based cell-cell communication inference for spatially resolved transcriptomic data with SpaTalk
+
+Open Access This file is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. In the cases where the authors are anonymous, such as is the case for the reports of anonymous peer reviewers, author attribution should be to 'Anonymous Referee' followed by a clear attribution to the source work. The images or other third party material in this file are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.
+REVIEWER COMMENTS
+
+Reviewer #1 (Remarks to the Author):
+
+In this manuscript, the authors present a novel method for inference of cell-cell communication networks from spatial transcriptomics data. The method considers both the spatial proximity and activated downstream signalling in the target cell for inference of relevant ligand-receptor interactions. The spatial proximity is implemented using a knn graph and permutations to calculate significant cell proximity enrichment, in a similar way as other methods such as Giotto, however the authors in addition consider ligand-receptor-target co-expression to score the ligand-receptor interactions that activate downstream signalling, in a similar way as NicheNet. The method is especially relevant for spot-based spatial data where the authors combine deconvolution of cell types in each spot and then inference of cell-cell communication, however some details of the method were not clear to me with regards to spot-based data. In addition, some improvements and additions would make the method more usable and some issues with the comparison with other similar methods should be addressed.
+
+Major comments:
+
+- I was a bit confused with the description about the KNN distance graph. Since the interaction score here is calculated only based on the distance between two cell types from what I understood, this would be the same score for all ligand-receptor pairs between two cell types (sender and receiver). It could be better explained that the inter-cellular score is only calculated based on distance and is not per ligand-receptor pair, but per sender-receiver cell type pair. This is very similar to what is implemented in Giotto and should be acknowledged.
+
+- It was not quite clear to me how spatial coordinates are assigned to each cell type within a spot, could you please explain this part in more details? What does this mean for the knn graph, I saw that you use K=10 in your code, if you consider 30 cells in each spot, does that mean that some of them are directly connected between each other in the knn graph and other not, and how are they connected with cells from other spots? Related to this, how is the downstream signalling implemented for spot-based data where there are multiple different cell types within a spot, which would lead to multiple signalling pathways and targets activated for each of those different cell types? How do the results compare when used on scRNA-seq data instead of spatial data without considering spatial proximity?
+
+- It would increase the usability of the method if there is an option for the user to use a method for deconvolution of ST data of their choice and then only use the second component for inference of cell-cell communication.
+
+- Is there an option to change the default number of expected cells in each spot from 30 to another number? The user should be able to change this depending on previous knowledge or whether they can use segmentation to estimate the number.
+
+- Was the same LR database (CytoTalkDB) used for comparison of the performance of different cell-cell communication platforms? I could not find this information in the Methods. Otherwise, it would be difficult to compare the results.
+
+- Cell2location was not used in the benchmarking for the deconvolution step.
+
+Reviewer #2 (Remarks to the Author):
+
+In this manuscript, Shao, Li and Yang et al. introduced a method (SpaTalk) to use single-cell RNA-seq
+references to decompose spatial transcriptomic data and infer short-range cell-cell signalling and their downstream regulatory networks. They also benchmarked their method against existing tools with similar goals using published data.
+
+Major concerns:
+
+1. In Figure 3, the authors used STARmap brain data to infer short-range signaling between neurons and other cells based on the locations of cell bodies captured by STARmap. However, due to the shape of neurons, interactions can usually happen far away from the cell bodies through axons and synapses that current segmentation methods cannot well capture. The authors should address that point or may consider focusing on other tissues.
+
+2. The authors compared their method against multiple decomposition and cell-cell interaction algorithms. However, cell2location (decompostion), cellphoneDB (interaction) and cellchat(interaction) have been missed. These packages have been widely used. It would be more convincing to benchmark against them, especially cell2location.
+
+3. The authors should also compare computational time between SpaTalk and other methods.
+
+4. For spot-based spatial data, the authors introduced arbitrarily generated locations of single-cells (x,y) around each spot (x0,y0) (Figure 6c, Line 598-600) which increases the noise of the data. Is it a must? Could neighbor spots around each spot also be used to help decide alpha and theta?
+
+5. Handling biological replicates is a key challenge for signaling inference that spatial algorithms start to meet (One example is the multinichenetr algorithm being developed https://github.com/saeyslab/multinichenetr). How would the cell decomposition step and the graph learning step handle replicates and how robust will it be?
+
+Minor:
+
+1. Fig 1c: “siganling” should be “signaling”
+
+2. For visualizing cell-cell crosstalks, the arrows on top of cells are very difficult to see (such as Fig 4g, 6g, and supplementary Fig 6). The authors can consider just using lines without arrowheads since the two colors can already indicate directionality.
+
+3. Figure 5b: should choose a different color scheme to better visualize cell types and compositions
+
+4. Figure 5e: the legend is missing
+
+5. Figure 6a,b: The two matrices seem to have the same sets of ligands and receptors on rows and columns. The authors may consider merging the two matrices into one with different markings to separate FB and Endo instead of duplicating the axes.
+
+6. In Line 411, the authors mentioned: “receptors that promote the proliferation and differentiation of TSKs”. Any GO analysis? Those receptors contributing to proliferation and differentiation should be highlighted with asterisks in Figure 6b.
+
+7. Line 659-661 is really confusing in terms of the definition of a,b and c.
+
+8. Supplementary Figure 2d legend: “umber” should be “Number”
+
+9. Supplementary Figure 4b-d: the color scheme makes the scores very difficult to see
+Response to Reviewers
+
+Overview of Changes
+
+We greatly appreciate the reviewers’ concerns and insightful feedback. Our work has been much improved due to their valuable suggestions. We attempted to address every concern by either making appropriate changes to our work or by providing a thorough explanation for our decision. The most significant changes to the manuscript are as follows:
+
+• We have additionally evaluated the performance of Cell2location, CellPhoneDB, and CellChat over the benchmarked datasets, wherein SpaTalk outperforms these methods, consistent with the previous findings.
+
+• We have optimized the algorithms of generating the spatial location of cells by letting the neighbor spots help decide alpha and theta, and added the details about this step.
+
+• We have benchmarked our SpaTalk with other methods with the same LRI database, i.e., CellTalkDB, CytoTalkDB, CellCallDB, CellChatDB, and CellPhoneDB. Concordantly, the superior performance of SpaTalk was observed.
+
+• We have compared computational time between SpaTalk and other methods, wherein the computation time of SpaTalk was within minutes for the decomposition step and the inferring cell-cell communication step, outperforming most deconvolution and signaling inference methods.
+
+• We have added details about the calculation of inter-cellular and intra-cellular scores, and several parameters and functions allowing users to select deconvolution methods, to change the default number of expected cells in each spot, and to show the arrows or not for plotting spatial LRI pairs.
+• We have selected the kidney tissue as another application of SpaTalk in replacement of the brain tissue, as suggested by Reviewer#2. Consistent with the previous findings in literature, SpaTalk identified the known intraglomerular communications.
+
+• We have demonstrated the robustness of SpaTalk for signaling inference with the different Slides of the human and mouse kidney tissue (Slide-seq v2), and different patients of SCC (10X Visium).
+
+Please find detailed responses to each concern below.
+
+Reviewer #1
+
+Major comments:
+
+- I was a bit confused with the description about the KNN distance graph. Since the interaction score here is calculated only based on the distance between two cell types from what I understood, this would be the same score for all ligand-receptor pairs between two cell types (sender and receiver). It could be better explained that the inter-cellular score is only calculated based on distance and is not per ligand-receptor pair, but per sender-receiver cell type pair. This is very similar to what is implemented in Giotto and should be acknowledged.
+
+Response: Thanks for your careful review. We are sorry that the previous description of SpaTalk algorithm makes you misunderstand the inter-cellular scores, which are actually different for all ligand-receptor pairs between two cell types (sender and receiver) in SpaTalk. For a given ligand \( i \) of the sender (cell type A) and a given receptor \( j \) of the receiver (cell type B), the number of ligand-receptor co-expressed cell-cell pairs (\( C_{Ai,Bj} \)) was obtained from the graph network by counting the 1-hop neighbor nodes of receivers for each sender, resulting in the different number of cell-cell pairs for a given LRI pair between the sender cell type A and the receiver cell type B. In other words, assuming that there is a total of \( C_{A,B} \) cell-cell pairs between the sender cell type A and the receiver cell type B, the \( C_{Ai,Bj} \) depends on the number of co-
+expressed LRI among the \( C_{A,B} \) cell-cell pairs and it must be less than \( C_{A,B} \) as shown in Fig. 1 below. We have revised the Methods and Results sections about this part as described above, and we have also revised the Fig. 1c about the process of ‘(i) Inter-cellular score’ in the revised manuscript, in order to avoid the misunderstanding.
+
+Indeed, we are inspired by the implementation in Giotto when developing the SpaTalk method, hence we have added the ‘inspired by Giotto’ in the corresponding Methods and Results section about the incorporation of KNN distance graph to calculate the inter-cellular score. Besides, we have acknowledged the Giotto in Acknowledgements section in the revised manuscript.
+
+![Process of calculating the inter-cellular and intra-cellular scores with KNN and knowledge graph from the single-cell ST data.](page_324_670_1097_282.png)
+
+Fig. 1 Process of calculating the inter-cellular and intra-cellular scores with KNN and knowledge graph from the single-cell ST data.
+
+- It was not quite clear to me how spatial coordinates are assigned to each cell type within a spot, could you please explain this part in more details? What does this mean for the knn graph, I saw that you use K=10 in your code, if you consider 30 cells in each spot, does that mean that some of them are directly connected between each other in the knn graph and other not, and how are they connected with cells from other spots? Related to this, how is the downstream signalling implemented for spot-based data where there are multiple different cell types within a spot, which would lead to multiple signalling pathways and targets activated for each of those different cell types? How do the results compare when used on scRNA-seq data instead of spatial data without considering spatial proximity?
+
+Response: Thanks for your comment. As you know, inference of cell-cell communications for spot-based ST data requires the single-cell profiling and
+coordinates as the input. However, current deconvolution methods can only dissect the percentage of various cell types. Thus, we proposed the step of spatial mapping to realize the reconstruction of spatial transcriptomics at single-cell resolution. In order to assign a coordinate \( (\hat{x}, \hat{y}) \) for each mapped cell in the given spot \( (x_0, y_0) \), we applied following equation to locate the cell into the space:
+
+\[
+\begin{align*}
+\hat{x} &= x_0 + \alpha d_{min} \cos(\theta \pi / 180) / 2 \\
+\hat{y} &= y_0 + \alpha d_{min} \sin(\theta \pi / 180) / 2
+\end{align*}
+\]
+
+where \( d_{min} \) represents the spatial distance of the closest neighbor spot, and \( \alpha \in (0, 1] \) and \( \theta \in (0, 360] \) mean the weight for \( d_{min} \) and the angle towards the spot center \( (x_0, y_0) \), respectively.
+
+![Schematic diagram for the generation of spatial coordinates (a) and KNN distance graph (b).](page_374_563_1092_312.png)
+
+Fig. 2 Schematic diagram for the generation of spatial coordinates (a) and KNN distance graph (b).
+
+As shown in Fig. 2a above, each sampled cell was distributed around the spot center. In the previous version, a random \( \alpha \) and \( \theta \) were used, which might increase the noise of the data as stated by Review #2. Therefore, we proposed a probabilistic distribution for a given cell in each spot \( (x_0, y_0) \) by considering the ratio \( (R) \) of the same cell type in \( Q \) neighbor spots as the probability to locate the cell into the space instead of the random distribution, wherein the \( \theta \) were first determined by the following probability equation:
+
+\[
+\hat{P}(\theta) = \frac{R_q + 1}{\sum_{i=1}^Q (R_i + 1)}, \theta \in (90q - 90, 90q]
+\]
+
+where \( q \) represents the \( q_{th} \) neighbor spot in \( Q \), which was set to 4 in practice denoting that the space centered the spot were split into four areas and the nearest neighbor in each area was filtered. After determining the \( \theta \), the corresponding neighbor spot \( (x_\theta, y_\theta) \) was selected to determine the probabilistic distribution of \( \alpha \)
+by the following equation:
+
+\[
+\hat{P}(\alpha) = \begin{cases}
+(R_{x_0,y_0} + 1)/(R_{x_0,y_0} + R_{x_\theta,y_\theta} + 2), & \alpha \in (0, 0.5] \\
+(R_{x_\theta,y_\theta} + 1)/(R_{x_0,y_0} + R_{x_\theta,y_\theta} + 2), & \alpha \in (0.5, 1]
+\end{cases}
+\]
+
+where \( R_{x_0,y_0} \) and \( R_{x_\theta,y_\theta} \) represent the ratio of the given cell type in each spot and its neighbor spot.
+
+Given the KNN graph, your understanding is right that some of them are directly connected between each other in the KNN graph and other not in each spot with 30 cells. However, because the generated cells are distributed around the spot center, some cells distributed in the border of the neighbor spots might also be connected as the condition shown in Fig. 2b above. We have added the details about how spatial coordinates are assigned to each cell type within a spot to the Methods section as described above and revised the corresponding Result section in the revised manuscript.
+
+Indeed, we agree with you that there are multiple different cell types within a spot and multiple signaling pathways as well as targets activated for each of those different cell types as you mentioned. For spot-based ST data, we first transformed it into single-cell ST data and find the significantly proximal LR pairs between senders and receivers. Then, our SpaTalk filters the LR pairs with known activated downstream signals which are successfully propagated from the receptor to its downstream transcriptional factor (TF) and its target gene in the receiver cell type, because the LRI that mediates the cell-cell communication is supposed to activate at least one TF and its target gene in the receiver cell type as the principle summarized in the recent review (*Nat Rev Genet*, 2021). In detail, we first use knowledge graph to model the ligand-receptor-target (LRT) signaling network with the known regulatory relationship from KEGG and Reactome, then we use a random walk algorithm to determine and score the activated TF and its target gene for a given ligand-receptor pair by using the gene expressed percent among cells of the receiver cell type as the weight of edges in the LRT knowledge graph. As the goal of SpaTalk is to filter and score the LR pairs that mediate the spatially proximal cell-cell communication, the downstream co-expressed TFs and target genes are both used to calculate the final score of each inferred LR pair
+(Fig. 1 above), and the greater number of co-expressed TFs and their target genes will lead to a higher score for a given LR pair between the sender cell type and the receiver cell type. We have supplemented the details about the intracellular signal propagation process as described above and revised the Fig. 1c about the process of ‘(ii) Intracellular score’ in the revised manuscript, in order to make it clear.
+
+In terms of the comparison of the inferred cell-cell communication results on scRNA-seq data without spatial coordinates, it is hard to evaluate the results for the methods that only consider the ligands and receptors. However, some methods like NicheNet, CytoTalk, and CellCall incorporate the downstream targets to infer the cell-cell communications, which not only infer the significantly enriched LR pairs but also the downstream activated targets triggered by the LRI. For these methods, the result can be compared based on the principle summarized in the recent review (Nat Rev Genet, 2021) that the LRI mediating cell-cell communications is supposed to activate the downstream signal pathways, TFs, and their targets. Therefore, we reasoned that a more accurate method would be more likely to enrich the receptor-related biological processes or pathways using the inferred downstream target genes in the receiver cell type, which can be applied to compare the results when used on scRNA-seq data instead of spatial data without considering spatial proximity as you stated. As shown in Fig. 3 below, we benchmarked SpaTalk with NicheNet, CytoTalk, and CellCall using the evaluation index of significance of the enriched ligand-receptor-related pathways based on the inferred targets in the receiver cell type with the Fisher’s exact test.
+
+![Schematic illustration for compare the result on scRNA-seq data (left) and the performance comparison of SpaTalk with NicheNet, CytoTalk, and CellCall over the STARmap and seqFISH+ datasets without considering the spatial proximity (right).](page_184_1092_1082_276.png)
+
+Fig. 3 Schematic illustration for compare the result on scRNA-seq data (left) and the performance comparison of SpaTalk with NicheNet, CytoTalk, and CellCall over the STARmap and seqFISH+ datasets without considering the spatial proximity (right).
+
+- It would increase the usability of the method if there is an option for the user to use a method for deconvolution of ST data of their choice and then only use the second component for inference of cell-cell communication.
+Response: Thanks for your valuable comment. As you suggested, we have added two new parameters named ‘method’ and ‘dec_result�� in the ‘dec_celltype()’ function for users to select deconvolution methods including the NNLM of SpaTalk, RCTD, Seurat, SPOTlight, deconvSeq, Stereoscope, and cell2location, or directly use the deconvolution results from other upcoming methods (Fig. 4 below), followed by the second component for inference of cell-cell communication. We have updated the codes and documents on GitHub, and added a tutorial of this part in the Wiki page.
+
+<table>
+  <tr>
+    <th>method</th>
+    <td>1 means using the SpaTalk deconvolution method, 2 means using RCTD, 3 means using Seurat, 4 means using SPOTlight, 5 means using deconvSeq, 6 means using stereoscope, 7 means using cell2location</td>
+  </tr>
+  <tr>
+    <th>env</th>
+    <td>When method set to 6, namely use stereoscope python package to deconvolute, please define the python environment of installed stereoscope. Default is the 'base' environment. Anaconda is recommended.</td>
+  </tr>
+  <tr>
+    <th>anaconda_path</th>
+    <td>When use python package, please define the path to anaconda, default is ~/anaconda3</td>
+  </tr>
+  <tr>
+    <th>dec_result</th>
+    <td>A matrix of deconvolution result from other upcoming methods, row represents spots or cells, column represents cell types of scRNA-seq reference. See demo_dec_result</td>
+  </tr>
+</table>
+
+Fig. 4 New parameters in the ‘dec_celltype()’ function.
+
+- Is there an option to change the default number of expected cells in each spot from 30 to another number? The user should be able to change this depending on previous knowledge or whether they can use segmentation to estimate the number.
+
+Response: Thanks for your helpful suggestion and we agree with you that the user should be able to change the estimated cell number in each spot. As you suggested, we have provided a parameter named ‘spot_max_cell’ for users to change the default number of expected cells in each spot when creating the SpaTalk object (Fig. 5 below).
+
+createSpaTalk(st_data, st_meta, species, if_st_is_sc, spot_max_cell)
+
+Arguments
+st_data A data frame or matrix or dgCMatrix containing counts of spatial transcriptomics, each column representing a spot or a cell, each row representing a gene.
+st_meta A data frame containing coordinate of spatial transcriptomics with three columns, namely 'spot', 'x', 'y' for spot-based spatial transcriptomics data or 'cell', 'x', 'y' for single-cell spatial transcriptomics data.
+species A character meaning species of the spatial transcriptomics data 'Human' or 'Mouse'.
+if_st_is_sc A logical meaning if it is single-cell spatial transcriptomics data. TRUE is FALSE.
+spot_max_cell A integer meaning max cell number for each plot to predict. If if_st_is_sc FALSE, please determine the spot_max_cell. For 10X (55um), we recommend 30. For Slide-seq, we recommend 1.
+
+Fig. 5 Parameters in the ‘createSpaTalk()’ function.
+
+set the expected cell in SpaTalk object
+
+Usage
+set_expected_cell(object, value)
+
+Arguments
+object SpaTalk object
+value The number of expected cell for each spot, must be equal to the spot number.
+
+Fig. 6 A new function named ‘set_expected_cell ()’.
+In addition, we have added a new function named ‘set_expected_cell()’ to define the variable number of cells in each spot given the situation as you stated (Fig. 6 above). We have updated the codes and documents on GitHub, and added a tutorial of this part in the Wiki page.
+
+- Was the same LR database (CytoTalkDB) used for comparison of the performance of different cell-cell communication platforms? I could not find this information in the Methods. Otherwise, it would be difficult to compare the results.
+
+Response: Thanks for your comment and you raise an important point. As you suggested, we have benchmarked our SpaTalk with other methods with the same LRI database, i.e., CellTalkDB, CytoTalkDB, CellCallDB, CellChatDB, and CellPhoneDB. As shown in Fig. 7 below, SpaTalk obtained the most times of the first place across the benchmarked datasets and the underlying LRI databases, outperforming other existing methods for inference of spatially proximal LR pairs that mediating cell-cell communication in space.
+
+![Three line plots comparing performance of SpaTalk and other methods across three datasets: STARmap, seqFISH+ OB, and seqFISH+ SVZ. Each plot shows median log10P and median co-expression percent for various methods.](page_324_1012_1097_246.png)
+
+Fig. 7 Superior performance of SpaTalk over existing methods. The asterisk represents the top-ranked method for each used LRI database. The times of the first place was labelled beside each method.
+
+However, it is worth to point that several methods also showed decent performance on some individual LRI databases. For example, Giotto obtained the highest median –log_{10}P among all methods over the STARmap dataset based on CellPhoneDB and CellCallDB, while CytoTalk is the top-ranked method over the STARmap dataset based on CellPhoneDB and CellChatDB considering the median co-expression percent. Over the seqFISH+ OB dataset based on CellChatDB, both of CellPhoneDB and CellChatDB perfectly identified the significantly proximal LRIs in space. For SpaOTsc, it exhibited the highest median co-expression percent over the seqFISH+ SVZ dataset across all LRI databases. We have added the comparison as
+described above to the Result section and revised the corresponding Methods section about details of the process of comparison in the revised manuscript.
+
+- Cell2location was not used in the benchmarking for the deconvolution step.
+
+Response: Thanks for your comment. As you suggested, we have also compared the performance of Cell2location in our benchmark. Consequently, although the majority of existing cell-type deconvolution methods can achieve a decent correlation coefficient and low RMSE on spot deconvolution, SpaTalk outperformed these methods on most benchmark datasets with the top-ranked performance (Fig. 8 below), except for the evaluation indices on the MERFISH dataset and the mean RMSE on the STARmap dataset, which is consistent with the previous conclusion. We have updated the corresponding Result section and figures in the revised manuscript.
+
+![Performance comparison of SpaTalk with other existing cell-type deconvolution methods (RCTD, Seurat, SPOTlight, deconvSeq, Stereoscope, Cell2location). The asterisk represents the top-ranked method for each dataset. NA, not available.](page_374_693_1097_180.png)
+
+Fig. 8 Performance comparison of SpaTalk with other existing cell-type deconvolution methods (RCTD, Seurat, SPOTlight, deconvSeq, Stereoscope, Cell2location). The asterisk represents the top-ranked method for each dataset. NA, not available.
+Reviewer #2
+
+Major concerns:
+
+1. In Figure 3, the authors used STARmap brain data to infer short-range signaling between neurons and other cells based on the locations of cell bodies captured by STARmap. However, due to the shape of neurons, interactions can usually happen far away from the cell bodies through axons and synapses that current segmentation methods cannot well capture. The authors should address that point or may consider focusing on other tissues.
+
+Response: Thanks for your comment and we agree with you that interactions can usually happen far away from the cell bodies through axons and synapses due to the shape of neurons. As the current segmentation methods only provide the coordinate of the cell location, it is hard to capture these types of interactions for neurons. As you suggested, we have selected the kidney tissue as another application of SpaTalk in replacement of the brain tissue. Consistent with the previous findings in literature, SpaTalk identified the intraglomerular communications among glomerular cells in kidney as shown in Fig. 1 below. We have revised the Result section in the revised manuscript as follows:
+
+“Identification of signal transmission among glomerular cells in kidney. SpaTalk was then applied to investigate and visualize the intraglomerular communications over the Slide-seq ST dataset (v2) of the mouse kidney (Fig. 1a), including data of 20591 sequenced genes for 27044 spots in space covering the spatial axis of collecting duct intercalated cells (CD-IC), collecting duct principal cells (CD-PC), distal convoluted tubules (DCT), endothelial cells (Endo), fibroblasts (FB), granular cells (GC), macrophages (Macro), mesangial cells (MC), immune cells, proximal convoluted tubules (PCT), podocytes (Pod), thick ascending limb (TAL), and vascular smooth muscle cells (vSMC) from cortex of kidney to renal medulla. As shown in Fig. 1b, SpaTalk identified the spatial signal transmission among Pod, MC, and Endo in glomerulus. For example, the direct cell-cell communication mediated by the pleiotrophin (Ptn) and protein tyrosine phosphatase receptor type B (\( Ptprb \))
+interaction was observed from MC and Pod to Endo, wherein Ptn is a secreted growth factor that can bind Ptprb, which is known to be involved with adherens junction stimulating endothelial cell migration and maintaining proper glomerular function. Besides, collagen and Notch signaling were also identified forming the matrix that provides structural support for the glomerulus, which are necessary for proper glomerular basement membrane formation and glomerular development. Concordantly, these identified LRIs among glomerular cells are associated with multiple biological processes and pathways that play vital roles in the regulation of physiological kidney development and glomerular filtration function in the urinary system, including tube morphogenesis, positive regulation of cell adhesion, urogenital system development, and morphogenesis of a branching epithelium (Fig. 1c).
+
+Notably, the Pod-Endo communication mediated by vascular endothelial growth factor a (Vegfa) signaling was significantly enriched in space, in accordance with the fact that Vegfa is vital for the formation and maintenance of select microvascular beds within the kidney. It is known that Vegfa, normally produced by healthy podocytes, has been shown to be a critical regulator of glomerular development and function and precise expression of the amount of Vegfa is required for adequate barrier function. As the kinase insert domain receptor (Kdr) of Vegfa, Kdr functions as the main mediator of VEGF-induced endothelial proliferation, survival, migration, tubular morphogenesis and sprouting. Concordantly, the Pod-Endo communication mediated by Vegfa-Kdr was also identified in other mouse kidney ST data. In addition, most shared LRIs mediating the intraglomerular communications in space were also observed across slides of human and mouse kidney, suggesting the robustness and universality of the spatially resolved cell-cell communications inferred by SpaTalk.
+
+We then applied SpaTalk to another spot-based ST dataset of the mouse kidney (10X Visium), reaching up to 19,465 unique genes among 3,124 spots in space (Fig. 1f). Leveraging previously published adult mouse kidney cell taxonomy by single-nucleus RNA-seq data (Supplementary Fig. 5c), SpaTalk reconstructed the spatial transcriptomics atlas at the single-cell resolution for Slide-seq data, which showed consistent spatial localization of glomerular and other cells (Fig. 1f).
+Fig. 1 Identification of spatial signal transmission among glomerular cells in kidney.
+a Slide-seq (v2) ST dataset of the mouse kidney involving 27044 spots and 20591 genes. CD-IC, collecting duct intercalated cells; CD-PC, collecting duct principal cells; DCT, distal convoluted tubules; Endo, endothelial cells; FB, fibroblasts; GC, granular cells; Macro, macrophages; MC, mesangial cells; PCT, proximal convoluted tubules; Pod, podocytes; TAL, thick ascending limb; vSMC, vascular smooth muscle cells. b Significantly enriched LRs that mediate cell-cell communications among MC, Endo, and Pod inferred by SpaTalk with \( P < 0.05 \). The \( P \) value represents the significance of spatial proximity of LRs using the permutation test. Top 20 LRI pairs were plotted for Pod-Endo communications. c Significantly enriched GO biological processes determined with the Metascape web tool for the ligands and receptors from MC and Pod to Endo inferred by SpaTalk. d Spatial distribution of the Vegfa–Kdr pairs between the Pod senders and Endo receivers. e Number of Vegfa–Kdr pairs from Pod to Endo in space across other slides of mouse kidney. f Mouse kidney ST dataset generated from 10X Visium involving 3124 spots and 19465 genes and the reconstructed single-cell ST data by SpaTalk. The percent of MC, Endo, and Pod as well as the expression of the corresponding known markers were plotted. LHDL, loop of Henle descending loop;
+LHAL, loop of Henle ascending loop. g Significantly enriched LRIs that mediate Pod-Endo communications. Top 20 LRIs (left) and spatial distribution of the Angpt1-Tek pairs between the Pod senders and Endo receivers were plotted. h Communications of Endo-MC mediated by the Pdgfb–Pdgfrb interaction in space and the spatial distances of Pdgfb–Pdgfrb in Endo-MC and all cell-cell pairs, respectively. P values were calculated with the Wilcoxon test.
+
+Compared to Slide-seq (v2) data, loop of Henle descending loop (LHDL) and loop of Henle ascending loop (LHAL) were also observed in the 10X Visium data. Consistently, most LRIs mediating intraglomerular communications in Slide-seq (v2) data were also found in 10X Visium data (Fig. 1g). Similar to the Vegfa paracrine system, Angiopoietin-1 (Angpt1) is expressed by podocytes and its cognate tyrosine kinase receptor (Tek) is expressed by the glomerular endothelial cells, which plays an indispensable role in glomerular health and maintenance of the filtration barrier in physiological conditions. Moreover, the direct communication between Endo to MC mediated by platelet-derived growth factor B and its receptor (Pdgfb-Pdgfrb) was significantly enriched (Fig. 1h), in accordance with the classical studies that have delineated a key role for the Pdgfb in communication between the glomerular endothelium and nearby mesangial cells.”
+
+2. The authors compared their method against multiple decomposition and cell-cell interaction algorithms. However, cell2location (decompostion), cellphoneDB (interaction) and cellchat(interaction) have been missed. These packages have been widely used. It would be more convincing to benchmark against them, especially cell2location.
+
+Response: Thanks for your comment. As you suggested, we have also compared the performance of Cell2location in our benchmark. Consequently, although the majority of existing cell-type deconvolution methods (RCTD, Seurat, SPOTlight, deconvSeq, Stereoscope, and Cell2locatoion) can achieve a decent correlation coefficient and low RMSE on spot deconvolution, SpaTalk outperformed these methods on most benchmark datasets with the top-ranked performance (Fig. 2a-b below), except for the evaluation indices on the MERFISH dataset and the mean RMSE on the STARmap dataset, which is consistent with the previous conclusion.
+Fig. 2 Comparison of SpaTalk with other methods. a Schematic diagram for generating simulated spot data. Cells were split according to the fixed spatial distance and then merged for the single-cell ST data with known cell types. b Performance comparison of SpaTalk with other existing cell-type deconvolution methods (RCTD, Seurat, SPOTlight, deconvSeq, Stereoscope, Cell2location). The asterisk represents the top-ranked method for each dataset. NA, not available. c Schematic illustration of the procedure and rationale for single-cell ST data to evaluate predicted LRIs that mediate spatially resolved cell–cell communications. d and e Performance comparison of SpaTalk with existing cell–cell communication inference methods (Giotto, SpaOTsc, NicheNet, CytoTalk, CellCall, CellPhoneDB, and CellChat) on the STARmap and seqFISH+ datasets. The \( P \) value represents the difference of spatial distances between sender–receiver and all cell–cell pairs assessed with the Wilcoxon test.
+
+In terms of the CellPhoneDB and CellChat, we have also evaluated the performance of them over the benchmarked datasets. As shown in Fig. 2c-d above, although most LRIs inferred by other methods showed significantly closer spatial distances between sender-receiver pairs than that between all cell-cell pairs, superior performance of SpaTalk was observed, ranking first for both evaluation indices for STARmap datasets. Similarly, SpaTalk obtained a higher median –\( \log_{10}P \) value and co-expression percent on the seqFISH+ OB and SVZ datasets but not for SpaOTsc, CellPhoneDB, and CellChat on individual evaluation indices (Fig. 2e above), which is consistent with the previous conclusion. We have revised the corresponding Result section by additionally evaluating the performance of Cell2location, CellPhoneDB, and CellChat as described above in the revised manuscript.
+3. The authors should also compare computational time between SpaTalk and other methods.
+
+Response: Thanks for your comment. As you suggested, we have compared computational time between SpaTalk and other methods in terms of the decomposition and the inferring cell-cell communication steps. For the decomposition step, SpaTalk and other deconvolution six methods were compared over four simulated (STARmap, MERFISH, seqFISH+ OB and SVZ) and one real spot-based (10X Visium) ST datasets, wherein the computation time of SpaTalk was within minutes similar to RCTD and Seurat, outperforming SPOTlight, deconvSeq, Stereoscope, and Cell2location (Table 1 below).
+
+Table 1. Computation time of the deconvolution step.
+
+<table>
+  <tr>
+    <th rowspan="2">Methods</th>
+    <th colspan="4">Simulated spot data</th>
+    <th rowspan="2">Real spot data</th>
+  </tr>
+  <tr>
+    <th>STARmap</th>
+    <th>MERFISH</th>
+    <th>seqFISH OB</th>
+    <th>seqFISH SVZ</th>
+    <th>10X Visium</th>
+  </tr>
+  <tr>
+    <td>SpaTalk</td>
+    <td>0.13min</td>
+    <td>0.08min</td>
+    <td>2.18min</td>
+    <td>3.05min</td>
+    <td>6.23min</td>
+  </tr>
+  <tr>
+    <td>RCTD</td>
+    <td>1.35min</td>
+    <td>0.65min</td>
+    <td>1.20min</td>
+    <td>3.80min</td>
+    <td>3.33min</td>
+  </tr>
+  <tr>
+    <td>Seurat</td>
+    <td>0.22min</td>
+    <td>0.18min</td>
+    <td>0.90min</td>
+    <td>0.55min</td>
+    <td>2.47min</td>
+  </tr>
+  <tr>
+    <td>SPOTlight</td>
+    <td>1.68min</td>
+    <td>0.32min</td>
+    <td>4.30min</td>
+    <td>10.92min</td>
+    <td>26.83min</td>
+  </tr>
+  <tr>
+    <td>deconvSeq</td>
+    <td>2.18min</td>
+    <td>NA</td>
+    <td>25.85min</td>
+    <td>17.52min</td>
+    <td>NA</td>
+  </tr>
+  <tr>
+    <td>Stereoscope</td>
+    <td>56.58min</td>
+    <td>205.53min</td>
+    <td>359.20min</td>
+    <td>67.02min</td>
+    <td>604.58min</td>
+  </tr>
+  <tr>
+    <td>Cell2location</td>
+    <td>35.13min</td>
+    <td>20.30min</td>
+    <td>25.25min</td>
+    <td>30.02min</td>
+    <td>31.03min</td>
+  </tr>
+</table>
+
+NA, not available.
+
+Table 2. Computation time of the inferring cell-cell communication step.
+
+<table>
+  <tr>
+    <th rowspan="2">Methods</th>
+    <th>STARmap</th>
+    <th>seqFISH OB (FOVO)</th>
+    <th>seqFISH SVZ(FOVO)</th>
+    <th>10X Visium (TSK-Endo)</th>
+  </tr>
+  <tr>
+    <td></td>
+    <td></td>
+    <td></td>
+    <td></td>
+  </tr>
+  <tr>
+    <td>SpaTalk</td>
+    <td>0.47min</td>
+    <td>3.40min</td>
+    <td>22.05min</td>
+    <td>4.72min</td>
+  </tr>
+  <tr>
+    <td>Giotto</td>
+    <td>5.02min</td>
+    <td>5.06min</td>
+    <td>3.99min</td>
+    <td>37.11min</td>
+  </tr>
+  <tr>
+    <td>SpaOTsc</td>
+    <td>0.08min</td>
+    <td>0.09min</td>
+    <td>0.11min</td>
+    <td>26.70min</td>
+  </tr>
+  <tr>
+    <td>NicheNet</td>
+    <td>19.39min</td>
+    <td>13.09min</td>
+    <td>11.00min</td>
+    <td>4.59min</td>
+  </tr>
+  <tr>
+    <td>CytoTalk</td>
+    <td>42.03min</td>
+    <td>&gt;12h</td>
+    <td>&gt;12h</td>
+    <td>123.68min</td>
+  </tr>
+  <tr>
+    <td>CellCall</td>
+    <td>2.34min</td>
+    <td>12.66min</td>
+    <td>16.26min</td>
+    <td>14.86min</td>
+  </tr>
+  <tr>
+    <td>CellPhoneDB</td>
+    <td>1.57min</td>
+    <td>1.67min</td>
+    <td>3.69min</td>
+    <td>11.30min</td>
+  </tr>
+  <tr>
+    <td>CellChat</td>
+    <td>0.69min</td>
+    <td>67.65min</td>
+    <td>123.90min</td>
+    <td>41.48min</td>
+  </tr>
+</table>
+
+For the inferring cell-cell communication step, SpaTalk and other seven methods were benchmarked over three single-cell ST datasets (STARmap, seqFISH+ OB and SVZ)
+and one reconstructed single-cell ST dataset (10X Visium) with SpaTalk. As shown in Table 2 above, the computation time of SpaTalk, Giotto, SpaOTsc, NicheNet, CellCall, and CellPhoneDB were all within minutes, superior to that of CytoTalk and CellChat. We have added the comparison to the Result section as described above in the revised manuscript.
+
+4. For spot-based spatial data, the authors introduced arbitrarily generated locations of single-cells (x,y) around each spot (x0,y0) (Figure 6c, Line 598-600) which increases the noise of the data. Is it a must? Could neighbor spots around each spot also be used to help decide alpha and theta?
+
+Response: Thanks for your helpful suggestion and we totally agree with your point. In our pipeline, it is a must to generated locations of single cells in each spot sinc it is the foundation for the subsequent inference of spatially resolved cell-cell communications over the spot-based ST data. However, it is indeed not a must to arbitrarily generate locations, which might increase the noise of the data as you stated. Inspired by your idea, we reason that the higher ratio of the same cell type in the neighbor spot will lead to the closer distance for a given cell towards the corresponding neighbor spot, namely letting the neighbor spots help decide alpha and theta as you suggested. To be more specific, we have proposed a probabilistic distribution for a given cell in each spot \((x_0,\ y_0)\) by considering the ratio \((R)\) of the same cell type in \(Q\) neighbor spots as the probability to assign a coordinate \((\hat{x},\ \hat{y})\) for each sampled cell with the following function:
+
+\[
+\begin{align*}
+\hat{x} &= x_0 + \alpha d_{min} \cos(\theta \pi / 180)/2 \\
+\hat{y} &= y_0 + \alpha d_{min} \sin(\theta \pi / 180)/2
+\end{align*}
+\]
+
+where \(d_{min}\) represents the spatial distance of the closest neighbor spot, and \(\alpha \in (0, 1]\) and \(\theta \in (0,\ 360]\) mean the weight for \(d_{min}\) and the angle towards the spot center \((x_0,\ y_0)\), respectively. In detail, the \(\theta\) were first determined by the following probability equation:
+
+\[
+\hat{P}(\theta) = \frac{R_q + 1}{\sum_{i=1}^Q (R_i + 1)}, \theta \in (90q - 90, 90q]
+\]
+
+where \(q\) represents the \(q_{th}\) neighbor spot in \(Q\), which was set to 4 in practice
+denoting that the space centered the spot were split into four areas and the nearest neighbor in each area was filtered. After determining the \( \theta \), the corresponding neighbor spot (\( x_\theta,\ y_\theta \)) was selected to determine the probabilistic distribution of \( \alpha \) by the following equation:
+
+\[
+\hat{P}(\alpha) = \begin{cases}
+(R_{x_0,y_0} + 1)/(R_{x_0,y_0} + R_{x_\theta,y_\theta} + 2), & \alpha \in (0, 0.5] \\
+(R_{x_\theta,y_\theta} + 1)/(R_{x_0,y_0} + R_{x_\theta,y_\theta} + 2), & \alpha \in (0.5, 1]
+\end{cases}
+\]
+
+where \( R_{x_0,y_0} \) and \( R_{x_\theta,y_\theta} \) represent the ratio of the given cell type in each spot and its neighbor spot.
+
+We have revised the Method section as described above in the revised manuscript and updated the corresponding codes and documents on GitHub.
+
+5. Handling biological replicates is a key challenge for signaling inference that spatial algorithms start to meet (One example is the multinichenetr algorithm being developed https://github.com/saeyslab/multinichenetr). How would the cell decomposition step and the graph learning step handle replicates and how robust will it be?
+
+Response: Thanks for your comment and you raise an important point. We agree with you that handling biological replicates has been always the key challenge for signaling inference methods including the single-cell algorithms over scRNA-seq data and the spatial algorithms over ST data with growing concern. To make the signaling inference as replicable as possible, we used the normalized expression of all detected genes instead of the count and partial genes, e.g., differentially expressed genes (DEGs) or marker genes, to dissect the cell-type composition, in order to mitigate the influence of highly variable genes and different platforms, individuals, and batches in the cell decomposition step. Given the inference of spatially resolved cell-cell communication mediated by ligand-receptor interactions, we used the co-expression of ligands and receptors over the KNN distance graph instead of the significantly high expression of ligands/receptors to mitigate the influence of variably expressed ligands and receptors. In the same way, we used the co-expression of receptors, transcriptional factors (TFs), and target genes among all receiver cells instead of using the absolute expression to mitigate the influence of variably expressed TFs and their target genes in the graph
+learning step.
+
+As you suggested, we have evaluated the robustness of SpaTalk for signaling inference. First, we applied SpaTalk to the human and mouse kidney tissues with multiple slides sequenced by Slide-seq v2 (iScience, 2022), wherein we selected slides with at least 15 MCs to infer the cell-cell communications. As shown in Fig. 3 below, several known LRIs that have been widely reported to mediate the intraglomerular communications for maintaining proper glomerular function were identified such as VEGFA and PTN signaling, which were shared in most slides. Although the total number of inferred LRI pairs were different across nine slides, more than half of significantly enriched LRI pairs for each slide were existed in other slides with the median percent of shared LRI pairs reaching up to 75% and 65% for human and mouse slides, respectively.
+
+![Cell-cell communication inference among the glomerular cells in kidney by SpaTalk. Inferred LRI pairs mediating the intraglomerular communications across different slides of human and mouse kidney sequenced by Slide-seq (v2). Shared LR pairs among different slides were plotted.](page_349_682_1047_324.png)
+
+Fig. 3 Cell-cell communication inference among the glomerular cells in kidney by SpaTalk. Inferred LRI pairs mediating the intraglomerular communications across different slides of human and mouse kidney sequenced by Slide-seq (v2). Shared LR pairs among different slides were plotted.
+
+In addition, we compared the significantly enriched LRI pairs mediating the stroma-TSK communications of human SCC ST datasets from two patients, namely P. 2 and P .10 as shown in Fig. 4 below. Concordantly, a substantial shared LRI pairs and downstream TFs were identified between P. 2 and P. 10. For P. 2, the median percent of shared LRI pairs and TFs reach 82% and 77%, respectively. For P. 10, the percent of shared LRI pairs and TFs range from 86% to 96% and from 93% to 99%, respectively. The present results indicate that SpaTalk is a relatively robust method with high
+biological replicability for signaling inference across different slides and individuals. We have also revised the Resection about the two applications of SpaTalk as described above in the revised manuscript.
+
+![Venn diagrams comparing inferred LRI pairs and TFs by SpaTalk over 10X Visium ST datasets from two SCC patients (P. 2 and P. 10).](page_346_370_1057_388.png)
+
+Fig. 4 Comparison of inferred LRI pairs and TFs by SpaTalk over 10X Visium ST datasets from two SCC patients (P. 2 and P. 10). The percent of shared LRI pairs and TFs for each patient was labeled beside the total number of inferred LRI pairs and TFs.
+
+Minor:
+
+1. Fig 1c: “siganling” should be “signaling”
+
+Response: Thanks for your careful review. We have revised the typo of Fig. 1c in the revised manuscript.
+
+2. For visualizing cell-cell crosstalks, the arrows on top of cells are very difficult to see (such as Fig 4g, 6g, and supplementary Fig 6). The authors can consider just using lines without arrowheads since the two colors can already indicate directionality.
+
+Response: Thanks for your useful suggestion. As you suggested, we have revised the visualization of cell-cell crosstalks by using lines instead of arrowheads in Fig.4g, 6g, and supplementary Fig. 6, e.g., Fig. 5 below. Besides, we have added a new parameter named ‘if_show_arrow’ in the plotting functions allowing users to show the directionality or not inspired by your suggestion. We have also updated the code and document on Github and the Wiki page.
+Fig. 5 Communications from EMT-like and EMT-unlike TSKs to CAFs mediated by the MMP1–CD44 interaction in space.
+
+3. Figure 5b: should choose a different color scheme to better visualize cell types and compositions
+
+Response: Thanks for your comment. We have changed a different color scheme to visualize cell type s and compositions (Fig. 6 below) and updated the corresponding figure in the revised manuscript.
+
+Fig. 6 Spatial characterization of tumor and stromal cells in human squamous cell carcinoma Visium data with SpaTalk. a Visium spot-based ST dataset of human skin SCC in patient 2 with the matched scRNA-seq dataset involving the main keratinocytes (KC), stromal cells, and immune cells. b Cell-type decomposition by SpaTalk. Cyc, cycling; Diff, differentiating; NK, natural killer; FB, fibroblast. c TSK percent and TSK score across spatial spots. The expression of known TSK markers is plotted. d Pearson’s
+correlation coefficient between the TSK percent and TSK score. e Cell-type decomposition by SpaTalk at single-cell resolution for the spot-based human skin SCC ST data. f Contour plot of TSK, FB, and Endo based on the reconstructed single-cell ST atlas by SpaTalk.
+
+4. Figure 5e: the legend is missing
+
+Response: Thanks for your careful review. We have added the legend for Fig. 5e in the revised manuscript as follows: e Cell-type decomposition by SpaTalk at single-cell resolution for the spot-based human skin SCC ST data. (Fig. 6 above)
+
+5. Figure 6a,b: The two matrices seem to have the same sets of ligands and receptors on rows and columns. The authors may consider merging the two matrices into one with different markings to separate FB and Endo instead of duplicating the axes.
+
+Response: Thanks for your comment. As you suggested, we have revised the Fig. 6a and 6b by merging the two matrices into one with different markings to separate FB and Endo instead of duplicating the axes (Fig. 7 below) and updated the corresponding figure in the revised manuscript.
+
+![Two heatmaps showing inferred LRs that mediate cell–cell communication from the TSK senders to the FB and Endo receivers and from the FB and Endo senders to TSK receivers](page_328_1042_1092_246.png)
+
+Fig. 7 Top 20 inferred LRIs that mediate cell–cell communication from the TSK senders to the FB and Endo receivers and from the FB and Endo senders to TSK receivers. The number sign represents the receptor contributing to the proliferation and differentiation of TSK.
+
+6. In Line 411, the authors mentioned: “receptors that promote the proliferation and differentiation of TSKs”. Any GO analysis? Those receptors contributing to proliferation and differentiation should be highlighted with asterisks in Figure 6b.
+
+Response: Thanks for your comment. As you suggested, we have supplemented GO analysis on the TSK receptors that promote the proliferation and differentiation of TSKs
+triggered by the MDK, HGF, HMGB1, and THBS1 ligands (Table 3 below). From the GO analysis, the PTPRZ1, SDC1, and ITGA6 are highly related with the cell development, differentiation, and migration, consistent with the characteristics of TSK. Also, we have highlighted those receptors contributing to proliferation and differentiation with number sign. We have updated the corresponding figure and figure legend in the revised manuscript.
+
+Table 3 GO analysis of TSK receptors
+
+<table>
+  <tr>
+    <th>Gene</th>
+    <th>GO_ID</th>
+    <th>GO_term</th>
+  </tr>
+  <tr>
+    <td>PTPRZ1</td>
+    <td>GO:0007417</td>
+    <td>central nervous system development</td>
+  </tr>
+  <tr>
+    <td>PTPRZ1</td>
+    <td>GO:0002244</td>
+    <td>hematopoietic progenitor cell differentiation</td>
+  </tr>
+  <tr>
+    <td>PTPRZ1</td>
+    <td>GO:0048709</td>
+    <td>oligodendrocyte differentiation</td>
+  </tr>
+  <tr>
+    <td>PTPRZ1</td>
+    <td>GO:0048714</td>
+    <td>positive regulation of oligodendrocyte differentiation</td>
+  </tr>
+  <tr>
+    <td>PTPRZ1</td>
+    <td>GO:0070445</td>
+    <td>regulation of oligodendrocyte progenitor proliferation</td>
+  </tr>
+  <tr>
+    <td>SDC1</td>
+    <td>GO:0060070</td>
+    <td>canonical Wnt signaling pathway</td>
+  </tr>
+  <tr>
+    <td>SDC1</td>
+    <td>GO:0016477</td>
+    <td>cell migration</td>
+  </tr>
+  <tr>
+    <td>SDC1</td>
+    <td>GO:0050900</td>
+    <td>leukocyte migration</td>
+  </tr>
+  <tr>
+    <td>SDC1</td>
+    <td>GO:0048627</td>
+    <td>myoblast development</td>
+  </tr>
+  <tr>
+    <td>SDC1</td>
+    <td>GO:0060009</td>
+    <td>Sertoli cell development</td>
+  </tr>
+  <tr>
+    <td>SDC1</td>
+    <td>GO:0055002</td>
+    <td>striated muscle cell development</td>
+  </tr>
+  <tr>
+    <td>SDC1</td>
+    <td>GO:0001657</td>
+    <td>ureteric bud development</td>
+  </tr>
+  <tr>
+    <td>ITGA6</td>
+    <td>GO:0098609</td>
+    <td>cell-cell adhesion</td>
+  </tr>
+  <tr>
+    <td>ITGA6</td>
+    <td>GO:0007160</td>
+    <td>cell-matrix adhesion</td>
+  </tr>
+  <tr>
+    <td>ITGA6</td>
+    <td>GO:0050900</td>
+    <td>leukocyte migration</td>
+  </tr>
+  <tr>
+    <td>ITGA6</td>
+    <td>GO:0050873</td>
+    <td>brown fat cell differentiation</td>
+  </tr>
+  <tr>
+    <td>ITGA6</td>
+    <td>GO:0010668</td>
+    <td>ectodermal cell differentiation</td>
+  </tr>
+  <tr>
+    <td>ITGA6</td>
+    <td>GO:0030198</td>
+    <td>extracellular matrix organization</td>
+  </tr>
+  <tr>
+    <td>ITGA6</td>
+    <td>GO:0022409</td>
+    <td>positive regulation of cell-cell adhesion</td>
+  </tr>
+  <tr>
+    <td>ITGA6</td>
+    <td>GO:0030335</td>
+    <td>positive regulation of cell migration</td>
+  </tr>
+  <tr>
+    <td>ITGA6</td>
+    <td>GO:0035878</td>
+    <td>nail development</td>
+  </tr>
+</table>
+
+7. Line 659-661 is really confusing in terms of the definition of a,b and c.
+
+Response: Thanks for your comment. We have added a more clear description and a table (Table 4 below) about the pathway enrichment analysis with Fisher’s exact test, wherein \( a \) is the number of inferred target genes (interested genes) that match a given pathway; \( b \) is the number of a given pathway’s genes that exclude \( a \), namely the uninterested genes that match a given pathway; \( c \) is the number of inferred
+target genes (interested genes) that unmatch a given pathway; \( d \) is the number of all genes excluding \( a, b, \) and \( c \), namely the uninterested genes that unmatch a given pathway. We have revised the Methods section about the pathway enrichment analysis with Fisher’s exact test as described above in the revised manuscript.
+
+Table 4. Pathway enrichment analysis with Fisher’s exact test
+
+<table>
+  <tr>
+    <th></th>
+    <th>Interested genes</th>
+    <th>Uninterested genes</th>
+  </tr>
+  <tr>
+    <td>Genes matching the pathway</td>
+    <td>\( a \)</td>
+    <td>\( b \)</td>
+  </tr>
+  <tr>
+    <td>Genes unmatching the pathway</td>
+    <td>\( c \)</td>
+    <td>\( d \)</td>
+  </tr>
+</table>
+
+8. Supplementary Figure 2d legend: “umber” should be “Number”
+
+Response: Thanks for your careful review. We have revised the typo in Supplementary Figure 2d legend.
+
+9. Supplementary Figure 4b-d: the color scheme makes the scores very difficult to see
+
+Response: Thanks for your comment. As you suggested, we have tried a different color schemes, but the result seems the same (Fig. 8 below). We find the reason is that the scores and percent of these non-hepatocyte cell types in most spots are very low, which makes them hard to distinguish from hepatocytes. Besides, we have provided the Source Data as a single Excel file related to this figure.
+Fig. 8 Cell-type decomposition on the mouse liver ST data of Slide-seq. a Mouse liver scRNA-seq reference integrating the non-parenchymal cells from the mouse cell atlas (MCA) and the parenchymal hepatic cells from GSE12568847, which contains 6,029 cells involving the major immune cells and the pericentral and periportal hepatocytes, etc. b-d Expression of known marker gene (up) and the percent (down) for Endo, B cell, DC, Epithelia, Erythroblast, granulocyte, Kupffer cell, Macro, neutrophil, stromal cell, and T cell. e Percent of cell types across 25,595 spots of Slide-seq data.
+REVIEWERS’ COMMENTS
+
+Reviewer #1 (Remarks to the Author):
+
+The authors addressed all of my comments.
+
+Reviewer #2 (Remarks to the Author):
+
+Shao, Li, and Yang et al. have addressed most of my concerns. The manuscript and the algorithm have both improved a lot.
+
+The only minor concern left is the visibility of Supplementary Figure 4. It may be possible to make the signals visible by enlarging the dots with non-zero values and allowing partial overlaps - but that's totally optional.
+Point-by-point response to the reviewers' comments
+
+Reviewer #1:
+
+The authors addressed all of my comments.
+
+Response: Thanks for your positive comment.
+
+Reviewer #2
+
+Shao, Li, and Yang et al. have addressed most of my concerns. The manuscript and the algorithm have both improved a lot.
+
+The only minor concern left is the visibility of Supplementary Figure 4. It may be possible to make the signals visible by enlarging the dots with non-zero values and allowing partial overlaps - but that's totally optional.
+
+Response: Thanks for your helpful suggestion. As you suggested, we have made the signals visible by enlarging the dots with non-zero values and allowing partial overlaps and changed a visible color scheme to improve the visibility of Supplementary Figure 4 (see Fig. 1 below), which was also done to improve the visibility for Figure 5 in the revised manuscript.
+Fig. 1 Cell-type decomposition on the mouse liver ST data of Slide-seq. a Mouse liver scRNA-seq reference integrating the non-parenchymal cells from the mouse cell atlas (MCA) and the parenchymal hepatic cells from GSE125688, which contains 6,029 cells involving the major immune cells and the pericentral and periportal hepatocytes, etc. b-d Expression of known marker gene (up) and the percent (down) for Endo, B cell, DC, Epithelia, Erythroblast, granulocyte, Kupffer cell, Macro, neutrophil, stromal cell, and T cell. e Percent of cell types across 25,595 spots of Slide-seq data. For the boxplots (minima, 25th percentile, median, 75th percentile, and maxima), the numbers of data points for each box are 25,595. PC, pericentral; PP, periportal; Hep, hepatocytes; Endo, endothelial cells; DC, dendritic cells; Macro, macrophages.

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+Peer Review File
+
+Electrochemically induced crystalline-to-amorphization transformation in sodium samarium silicate solid electrolyte for long-lasting sodium metal batteries
+
+Open Access This file is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. In the cases where the authors are anonymous, such as is the case for the reports of anonymous peer reviewers, author attribution should be to 'Anonymous Referee' followed by a clear attribution to the source work. The images or other third party material in this file are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.
+REVIEWER COMMENTS
+
+Reviewer #1 (Remarks to the Author):
+
+In Na5SmSi4O12-based ceramics, the authors have achieved an excellent critical current density and cycle properties in plating/stripping reactions against Na electrodes, together with a high conductivity of 3 x 10-3 Scm-2 at room temperature. An electrochemically induced amorphization is proposed as the origin for the excellent properties, and have been verified by theoretical calculations. The facts that the amorphization extends over the entire ~1mm-thick sample and that the total conductivity is mostly maintained after the amorphization are interesting new findings.
+
+The novelty of the present study relies on this amorphization. Thus, sufficient experimental demonstration about the amorphization, its mechanism, and its contribution to the enhanced properties in the Na anode junction are supposed to be required.
+
+(1) With regard to the amorphization, there is no doubt that the samples in the present study became at least partially amorphous. But it is not fully convinced, since quantitative information is lacking like: at what volume fraction, to where in a solid electrolyte sample and by what kinetics (e.g. as a function of the Na stripping/plating reaction) the amorphization is taking place. Such quantitative estimation is required, even partially.
+
+The deduction of the mechanism of amorphization by experimental and theoretical collaboration in the Li system is interesting and convincing. However, since the authors have not attributed this knowledge to amorphization in the Na-SE interface, some conclusion is necessary, even speculatively. Why are the volume change and resultant strain induced in the Na-SE interface, as well? For example, does it allow excess Na to be inserted into the SE lattice near the Na interface, and does this induce a strain? If so, how does amorphization propagate into the interior of a sample? If it is not simply induced by an ionic current, does amorphization not occur, for example, in an NVP|SE|NVP cell?
+
+The most basic and convenient way to quantify the weight fraction of amorphization would be to mix an internal standard (e.g. CeO2) and perform Rietveld analysis. However, in this case, the sample is destroyed by crushing and only an averaged information is available.
+(2) The conductivity of SE obtained by the authors, although notably high, is well foreseeable from the results presented in the pioneering work of Shannon et al. Inorg. Chem. (1978). This study should be properly cited and introduced (as in the authors' earlier paper) in the manuscript.
+
+(3) Although the critical current density (CCD) is accepted as a measure of the 'goodness' of a SE and Na-SE interface, I consider not only the CCD but also the integrated current density per cycle, i.e., the critical charge density (unfortunately the abbreviation is the same), is important. In this respect, I agree that the authors have presented a well-defined integrated current density. I would like to know whether the critical integrated current density in this study is sufficiently high as compared to other similar studies to date.
+
+(4) In the previous paper (Sun et al., Energy Storage Mater. 2021), the authors introduced an organic electrolyte into the NVP cathode, as in the present study, and it appears to have been titled "quasi"-solid-state battery. I think that removing "all-solid-state" from the original title may work well here.
+
+(5) Minor points.
+
+Line 4, page 12: "etc." has two citation numbers. It would be preferable to describe the materials.
+
+The words of "ultarastable" or "ultraconformal" are somewhat exaggerated for a scientific paper.
+
+Cell notation should be, for example, Na|Na5SmSi4O12|Na3V2(PO4)3. The phase boundary is represented by a single line (not a double line as there is no salt bridge, etc.), and an anode is on the left side.
+
+There are several values where the significant figures are too large. For example, a = b = 22.14609 A (7 digits may require a temperature control of 0.01 K level) , 2.90 x 10-3 S cm-1 (requires very precise measurement of sample and electrode dimensions).
+
+The crystalline system of space group R-3c is rhombohedral, not hexagonal; I understand that the lattice constants are in a hexagonal "setting". "Hexagonal" is found in the text and in Supplemental Table 2. In addition, "Y1" is supposed to be "Sm1".
+
+Page 11, line 19: "holes" may be changed to "pores".
+
+Reviewer #2 (Remarks to the Author):
+The authors presented an interesting paper titled “Electrochemically induced crystalline-to-amorphization transformation in sodium samarium silicate solid electrolyte for long-lasting all-solid-state sodium metal batteries”. This paper suggests the advantages of Na<sub>5</sub>SmSi<sub>4</sub>O<sub>12</sub> solid electrolyte for long-life all-solid-state sodium metal batteries. However, due to the following reasons, I believe that Nature Communications cannot accept it as it is.
+
+The authors claim to report a new member of the Na<sub>5</sub>MSi<sub>4</sub>O<sub>12</sub> family with M=Sm. However, solid electrolytes of this composition have been reported for a long time. For example, the following have been previously reported.
+
+1. Solid State Ionics, Volumes 86–88, Part 1, July 1996, Pages 511-516
+
+Synthesis and conduction properties of Na<sup>+</sup> superionic conductors of sodium samarium silicophosphates
+
+2. Journal of the European Ceramic Society, Volume 26, Issues 4–5, 2006, Pages 619-622
+
+Superionic conducting Na<sub>5</sub>SmSi<sub>4</sub>O<sub>12</sub>-type glass-ceramics: Crystallization condition and ionic conductivity
+
+3. Journal of Electroceramics, Volume 24, 2010, Pages 83–90
+
+Na<sup>+</sup>-fast ionic conducting glass-ceramics of silicophosphates
+
+4. Solid State Ionics, Volume 262, 1 September 2014, Pages 604-608
+
+Synthesis and Na<sup>+</sup> conduction properties of Nasicon-type glass–ceramics in the system Na<sub>2</sub>O–Y<sub>2</sub>O<sub>3</sub>–R<sub>2</sub>O<sub>3</sub>–P<sub>2</sub>O<sub>5</sub>–SiO<sub>2</sub> (R = rare earth) and effect of Y substitution
+
+5. Solid State Ionics, Volume 285, February 2016, Pages 143-154
+
+Na<sup>+</sup> superionic conducting silicophosphate glass-ceramics – Review
+
+6. Materials, 15, 2022, 1104. https://doi.org/10.3390/ma15031104
+
+Influence of R=Y, Gd, Sm on Crystallization and Sodium Ion Conductivity of Na<sub>5</sub>Rsi<sub>4</sub>O<sub>12</sub> Phase
+
+I feel that there is a lack of data on the subject of long life as a solid-state battery. The changes at the electrode-electrolyte interface after repeated charging and discharging of the battery over a long period of time and the results of analysis near the surface of the solid electrolyte should be presented.
+The mechanism of conduction has also been reported since the 1980s, and the authors' previous report "Na<sub>5</sub>YSi<sub>4</sub>O<sub>12</sub>: A sodium superionic conductor for ultrastable quasi solid-state sodium-ion batteries. batteries. Energy Storage Mater. 41, 196-202 (2021)" also discusses the same issues as in the present study.
+
+The other figures are considered unnecessary as they are not very relevant and are not beyond the scope of the previous report.
+Response to the Referees for Nature Communication
+
+We would like to express our sincere gratitude to the editor and reviewers for their valuable contributions towards this report. We are truly grateful for the opportunity to address and clarify certain issues of interest in the revised manuscript. With this in mind, we have carefully reviewed and responded to each of the referee’s comments point-to-point. All revisions have been highlighted in red in the uploaded manuscript.
+
+Reviewer #1 (Remarks to the Author):
+In Na5SmSi4O12-based ceramics, the authors have achieved an excellent critical current density and cycle properties in plating/stripping reactions against Na electrodes, together with a high conductivity of \(3 \times 10^{-3}\) S cm\(^{-1}\) at room temperature. An electrochemically induced amorphization is proposed as the origin for the excellent properties, and have been verified by theoretical calculations. The facts that the amorphization extends over the entire ~1 mm-thick sample and that the total conductivity is mostly maintained after the amorphization are interesting new findings. The novelty of the present study relies on this amorphization. Thus, sufficient experimental demonstration about the amorphization, its mechanism, and its contribution to the enhanced properties in the Na anode junction are supposed to be required.
+
+Author’s Response: We would like to extend our sincere gratitude to the reviewer for his/her positive evaluation of our manuscript and invaluable suggestions. These suggestions play a crucial role in enhancing the overall quality of our work. We have diligently incorporated your feedback into our revision process, and we strongly believe that our detailed responses have addressed any potential concerns you may have had.
+
+(1) With regard to the amorphization, there is no doubt that the samples in the present study became at least partially amorphous. But it is not fully convinced, since quantitative information is lacking like: at what volume fraction, to where in a solid electrolyte sample and by what kinetics (e.g. as a function of the Na stripping/plating
+reaction) the amorphization is taking place. Such quantitative estimation is required, even partially.
+
+Author’s Response: Thank you for the kind advice. To confirm the crystalline-to-amorphous (CTA) transformation of Na5SmSi4O12, X-ray diffraction was utilized to monitor the structural changes at various polishing depths, as depicted in Figure R1a. The analysis reveals that the solid electrolyte (SE) pellet, after undergoing 100 hours of plating/stripping at 0.15 mA cm\(^{-2}\), exhibits a lack of reflections, which suggests complete amorphization near the surface of the Na5SmSi4O12 SE. As the polishing depths increased, a limited number of weak reflections of Na5SmSi4O12 emerge, indicative of a gradual amorphization process from the surface to the bulk. Upon polishing to a depth of 0.15 mm, sharp reflections are observed, suggesting that the crystalline SE may constitute the majority of the volumetric ratio within the entire Na5SmSi4O12 pellet.
+
+![Schematic diagram showing X-ray tube, detector, and sample with labeled polishing depth](page_370_682_393_180.png)
+
+Figure R1. (a) Schematical and (b) XRD patterns of the Na5SmSi4O12 polished to different depths after cycling 100 h at 0.15 mA cm\(^{-2}\).
+
+According to the reviewer’s suggestion, we have employed the internal standard method to quantitatively assess the volume fraction of amorphous Na5SmSi4O12. This involves mixing CeO2 with the Na5SmSi4O12 solid electrolyte (SE) at different plating/stripping stages. Figure R2 illustrates that the weight fraction of amorphization is directly proportional to both the cycling time (h) and current density (mA cm\(^{-2}\)). This correlation aligns with the time-resolved XRD results presented in Figure R1. It is observed that an increase in cycling time leads to a higher weight fraction of the amorphous phase. Similarly, at the same cycling time, a higher applied current density accelerates the amorphization process of the solid electrolyte. In the revised manuscript,
+we have discussed this phenomenon as “To further assess the amorphous depth of Na5SmSi4O12, XRD was utilized to monitor the structural changes at various polishing depths, as depicted in Supplementary Fig. 10. The analysis reveals that the SE pellet, after undergoing 100 hours of cycling at 0.15 mA cm\(^{-2}\), exhibits no reflections, indicating complete amorphization near the surface of the Na5SmSi4O12 SE. As the polishing depths increased, a limited number of weak reflections of Na5SmSi4O12 emerge, which suggests a gradual amorphization process from the surface to the bulk. Upon polishing to a depth of 0.15 mm, sharp reflections appear which means the crystalline SE may constitute the majority of the volumetric ratio within the entire Na5SmSi4O12 chip. To quantify the weight fraction of amorphization in an SE sample and by what kinetics, the internal standard method was employed to further assess the CTA transformation process, by mixing CeO2 with the Na5SmSi4O12 SE at different plating/stripping stages. The Rietveld refinements and the corresponding results are summarized in Supplementary Fig. 11 and Fig. 12, respectively, which clearly reveal the weight fraction of amorphization is strongly related to both the cycling time and current density. With increasing the cycling time, a higher weight fraction of the amorphous phase can be realized and a higher applied current density can accelerate the amorphization process.” from line 6 to 22 on Page 11, and line 1 on Page 12.
+
+![Bar charts showing weight fraction (%) vs. cycling time (h) and current density (mA cm^{-2}) for Na5SmSi4O12](page_370_1092_803_312.png)
+
+Figure R2. The amorphization weight fraction of Na5SmSi4O12 determined by the internal standard method for different (a) cycling times and (b) current densities.
+
+The deduction of the mechanism of amorphization by experimental and theoretical collaboration in the Li system is interesting and convincing. However, since the authors
+have not attributed this knowledge to amorphization in the Na-SE interface, some conclusion is necessary, even speculatively. Why are the volume change and resultant strain induced in the Na-SE interface, as well? For example, does it allow excess Na to be inserted into the SE lattice near the Na interface, and does this induce a strain? If so, how does amorphization propagate into the interior of a sample? If it is not simply induced by an ionic current, does amorphization not occur, for example, in an NVP[SE]NVP cell?
+
+Author’s Response: We thank the reviewer for the insightful suggestion. In the crystal structure of Na5SmSi4O12 (Figure R3a), vacancies at Na4, Na5 and Na6 sites are observed, which may facilitate the insertion of additional Na+ ions. Therefore, Na5SmSi4O12 is investigated as an anode material to validate this possible insertion. The discharge capacity of Na5SmSi4O12 is demonstrated in Figure R3b. Such result is without the contribution from Super P, indicating that the SE possesses additional sites capable of accommodating Na+ ions. Furthermore, EDS mapping was employed to monitor the changes in element ratios before and after cycling. A comparison of the data in Table R1 reveals an increase in Na content, supporting the speculation that the insertion of Na+ ions into the vacancies leads to changes in size effect, resulting in lattice stress. As stress accumulates, the internal strain field leads to a gradual transformation of the material into an amorphous state. In the revised manuscript, we have discussed this phenomenon as “As presented in the schematic crystal structure of Na5SmSi4O12 (Supplementary Fig. 21a), vacancies are observed at Na4, Na5 and Na6 sites, which may accommodate additional Na ions’ insertion and thus induce local variance. This possible insertion can be confirmed by the presence of the initial discharge capacity of Na5SmSi4O12 (Supplementary Fig. 21b) and an increase in the Na content after cycling (EDS mapping, Supplementary Table 8). As the local stress accumulates, the internal strain field leads to the CTA transformation.” between line 4 and 10, page 19.
+Figure R3. (a) Schematical crystal structure of Na5SmSi4O12; The initial charge-discharge profile of (b) Na5SmSi4O12:Super P (7:2) and (c) Super P as the anode in the Na metal half cell.
+
+Table R1. The comparison of element ratios of Na5SmSi4O12 before and after cycling.
+
+<table>
+  <tr>
+    <th></th>
+    <th>Na</th>
+    <th>Sm</th>
+    <th>Si</th>
+    <th>O</th>
+  </tr>
+  <tr>
+    <th>Before cycling</th>
+    <td>4.9</td>
+    <td>1.0</td>
+    <td>4.2</td>
+    <td>12.1</td>
+  </tr>
+  <tr>
+    <th>After cycling</th>
+    <td>6.1</td>
+    <td>1.0</td>
+    <td>4.1</td>
+    <td>12.2</td>
+  </tr>
+</table>
+
+The most basic and convenient way to quantify the weight fraction of amorphization would be to mix an internal standard (e.g. CeO2) and perform Rietveld analysis. However, in this case, the sample is destroyed by crushing and only an averaged information is available.
+
+Author’s Response: Thank you for the insightful advice. According to the reviewer’s suggestion, we performed the internal standard method to evaluate the relationship between the weight fraction of amorphization and Na deposition/stripping, and the results are displayed in Figure R2. It can be seen that an increase in cycling time leads to a higher weight fraction of the amorphous phase. Similarly, at the same cycling time, a higher applied current density accelerates the amorphization process of the solid electrolyte. In the revised manuscript, we have added discussions as “To quantify the weight fraction of amorphization in an SE sample and by what kinetics, the internal standard method was employed to further assess the CTA transformation process, by mixing CeO2 with the Na5SmSi4O12 SE at different plating/stripping stages. The Rietveld refinements and the corresponding results are summarized in Supplementary Fig. 11
+and Fig. 12, respectively, which clearly reveal the weight fraction of amorphization is strongly related to both the cycling time and current density. With increasing the cycling time, a higher weight fraction of the amorphous phase can be realized and a higher applied current density can accelerate the amorphization process.” between line 14 and 22 on Page 11 and line 1 on Page 12.
+
+(2) The conductivity of SE obtained by the authors, although notably high, is well foreseeable from the results presented in the pioneering work of Shannon et al. Inorg. Chem. (1978). This study should be properly cited and introduced (as in the authors' earlier paper) in the manuscript.
+
+Author’s Response: Thank you for the suggestion. In the revised manuscript, we have cited Shannon et al.’s work and revised the manuscript accordingly as “In 1978, Shannon et al. first reported the synthesis of a new inorganic material Na5MSi4O12 and found that the ionic conductivity gradually increases with the increase of M^{3+} ionic radius with ionic conductivity of \(10^{-1}\) S cm\(^{-1}\) at 200 °C\(^{16}\).” in page 3.
+
+(3) Although the critical current density (CCD) is accepted as a measure of the 'goodness' of a SE and Na-SE interface, I consider not only the CCD but also the integrated current density per cycle, i.e., the critical charge density (unfortunately the abbreviation is the same), is important. In this respect, I agree that the authors have presented a well-defined integrated current density. I would like to know whether the critical integrated current density in this study is sufficiently high as compared to other similar studies to date.
+
+Author’s Response: Based on the reviewer’s suggestions, we conducted a comparison between our reported critical integrated current density and the values obtained by other researchers[1-11], as presented in Table R2. By utilizing the amorphous Na5SmSi4O12, we are able to achieve a significantly enhanced critical current density (CCD) of 1.4 mA cm\(^{-2}\). This improvement is in stark contrast to the lower initial crystalline stage CCD of 0.4 mA cm\(^{-2}\). Our findings demonstrate that the amorphous Na5SmSi4O12 enables a more intimate contact between the solid electrolyte (SE) and Na metal,
+resulting in superior performance compared to oxide SEs that lacks interfacial modification with SE/Na metal anodes. In the revised manuscript, we have also added discussion as “As displayed in Fig. 3a and Supplementary Fig. 16, the amorphous Na5SmSi4O12 facilitates intimate contact of SE with Na metal and brings essentially improved critical current density (CCD) of 1.4 mA cm^{-2} in comparison with the initial crystalline stage (0.4 mA cm^{-2}). This behavior is mainly because the uneven metal deposition leads to rapid growth of sodium dendrites along the crystalline Na5SmSi4O12 grain boundary with a large deposition current and hence results in the short circuit rapidly. The result is also much higher than most reported values based on oxide SEs without and with SE/Na metal anode interfacial modification (Supplementary Table 6), indicating the superiority of amorphous SE interfaces.” between line 11 and 15 on Page 13 and line 1 to 4 on Page 14.
+
+Table R2. A survey of critical current density of Na-based oxide solid-state electrolytes.
+
+<table>
+  <tr>
+    <th>Electrolytes</th>
+    <th>Operating temperature</th>
+    <th>Critical current density</th>
+    <th>Deposited capacity</th>
+    <th>Ref.</th>
+  </tr>
+  <tr>
+    <td><b>amorphous Na<sub>5</sub>SmSi<sub>4</sub>O<sub>12</sub></b></td>
+    <td>25 °C</td>
+    <td><b>1.4 mA cm<sup>-2</sup></b></td>
+    <td><b>1.4 mA h cm<sup>-2</sup></b></td>
+    <td>This work</td>
+  </tr>
+  <tr>
+    <td>crystalline Na<sub>5</sub>SmSi<sub>4</sub>O<sub>12</sub></td>
+    <td>25 °C</td>
+    <td>0.4 mA cm<sup>-2</sup></td>
+    <td>0.4 mA h cm<sup>-2</sup></td>
+    <td>[1]</td>
+  </tr>
+  <tr>
+    <td>Na<sub>4.9</sub>Sm<sub>0.3</sub>Y<sub>0.2</sub>Gd<sub>0.2</sub>La<sub>0.1</sub>Al<sub>0.1</sub>Zr<sub>0.1</sub>Si<sub>4</sub>O<sub>12</sub></td>
+    <td>25 °C</td>
+    <td>0.6 mA cm<sup>-2</sup></td>
+    <td>0.6 mA h cm<sup>-2</sup></td>
+    <td>[1]</td>
+  </tr>
+  <tr>
+    <td>Na<sub>3.2</sub>Zr<sub>1.9</sub>Mg<sub>0.1</sub>Si<sub>2</sub>PO<sub>12</sub></td>
+    <td>25 °C</td>
+    <td>0.5 mA cm<sup>-2</sup></td>
+    <td>0.08 mA h cm<sup>-2</sup></td>
+    <td>[2]</td>
+  </tr>
+  <tr>
+    <td>AlF<sub>3</sub>-Na<sub>3</sub>Zr<sub>2</sub>Si<sub>2</sub>PO<sub>12</sub></td>
+    <td>60 °C</td>
+    <td>1.2 mA cm<sup>-2</sup></td>
+    <td>2.4 mA h cm<sup>-2</sup></td>
+    <td>[3]</td>
+  </tr>
+  <tr>
+    <td>Na<sub>3</sub>Zr<sub>2</sub>Si<sub>2</sub>PO<sub>12</sub>-10 wt.% Na<sub>2</sub>B<sub>4</sub>O<sub>7</sub></td>
+    <td>25 °C</td>
+    <td>0.55 mA cm<sup>-2</sup></td>
+    <td>0.275 mA h cm<sup>-2</sup></td>
+    <td>[4]</td>
+  </tr>
+  <tr>
+    <td>Na<sub>3</sub>Zr<sub>2</sub>Si<sub>2</sub>PO<sub>12</sub></td>
+    <td>60 °C</td>
+    <td>0.6 mA cm<sup>-2</sup></td>
+    <td>0.5 mA h cm<sup>-2</sup></td>
+    <td>[5]</td>
+  </tr>
+  <tr>
+    <td>Na<sub>3.4</sub>Mg<sub>0.1</sub>Zr<sub>1.9</sub>Si<sub>2.2</sub>P<sub>0.8</sub>O<sub>12</sub></td>
+    <td>60 °C</td>
+    <td>2.0 mA cm<sup>-2</sup></td>
+    <td>0.5 mA h cm<sup>-2</sup></td>
+    <td>[5]</td>
+  </tr>
+  <tr>
+    <td>Na<sub>3.2</sub>Hf<sub>1.9</sub>Ca<sub>0.1</sub>Si<sub>2</sub>PO<sub>12</sub>@SnO<sub>2</sub></td>
+    <td>60 °C</td>
+    <td>1.9 mA cm<sup>-2</sup></td>
+    <td>0.475 mA h cm<sup>-2</sup></td>
+    <td>[6]</td>
+  </tr>
+  <tr>
+    <td>Na<sub>3.2</sub>Hf<sub>1.9</sub>Ca<sub>0.1</sub>Si<sub>2</sub>PO<sub>12</sub>@SnO<sub>2</sub></td>
+    <td>25 °C</td>
+    <td>1.2 mA cm<sup>-2</sup></td>
+    <td>0.3 mA h cm<sup>-2</sup></td>
+    <td>[6]</td>
+  </tr>
+  <tr>
+    <td>Na<sub>3</sub>Zr<sub>2</sub>Si<sub>2</sub>PO<sub>12</sub></td>
+    <td>25 °C</td>
+    <td>0.4 mA cm<sup>-2</sup></td>
+    <td>0.4 mA h cm<sup>-2</sup></td>
+    <td>[7]</td>
+  </tr>
+  <tr>
+    <td>Na<sub>3.2</sub>Hf<sub>1.9</sub>Ca<sub>0.1</sub>Si<sub>2</sub>PO<sub>12</sub>-CuO</td>
+    <td>25 °C</td>
+    <td>0.6 mA cm<sup>-2</sup></td>
+    <td>0.6 mA cm<sup>-2</sup></td>
+    <td>[8]</td>
+  </tr>
+  <tr>
+    <td>Na<sub>3</sub>Zr<sub>2</sub>Si<sub>2</sub>PO<sub>12</sub></td>
+    <td>25 °C</td>
+    <td>0.15 mA cm<sup>-2</sup></td>
+    <td>0.15 mA h cm<sup>-2</sup></td>
+    <td>[8]</td>
+  </tr>
+</table>
+<table>
+  <tr>
+    <th>Na<sub>3</sub>Zr<sub>2</sub>Si<sub>2</sub>PO<sub>12</sub></th>
+    <th>25 °C</th>
+    <th>0.1 mA cm<sup>-2</sup></th>
+    <th>0.017 mA h cm<sup>-2</sup></th>
+    <th>[9]</th>
+  </tr>
+  <tr>
+    <th>Na<sub>3</sub>Zr<sub>2</sub>Si<sub>2</sub>PO<sub>12</sub>-SnO<sub>x</sub>/Sn</th>
+    <th>25 °C</th>
+    <th>1.0 mA cm<sup>-2</sup></th>
+    <th>0.17 mA h cm<sup>-2</sup></th>
+    <th>[9]</th>
+  </tr>
+  <tr>
+    <th>Na<sub>3</sub>Zr<sub>2</sub>Si<sub>2</sub>PO<sub>12</sub>-TiO<sub>2</sub></th>
+    <th>25 °C</th>
+    <th>1.0 mA cm<sup>-2</sup></th>
+    <th>0.08 mA h cm<sup>-2</sup></th>
+    <th>[10]</th>
+  </tr>
+  <tr>
+    <th>Na<sub>3</sub>Zr<sub>2</sub>Si<sub>2</sub>PO<sub>12</sub></th>
+    <th>25–27 °C</th>
+    <th>0.6 mA cm<sup>-2</sup></th>
+    <th>0.3 mA h cm<sup>-2</sup></th>
+    <th>[11]</th>
+  </tr>
+</table>
+
+references
+
+[1] Sun G, et al. High-Entropy Solid-State Na-Ion Conductor for Stable Sodium-Metal Batteries. Chem. Eur. J. **29**, e202300413 (2023).
+
+[2] Fu H, et al. Reducing Interfacial Resistance by Na-SiO<sub>2</sub> Composite Anode for NASICON-Based Solid-State Sodium Battery. ACS Mater. Lett. **2**, 127-132 (2019).
+
+[3] Miao X, et al. AlF<sub>3</sub>-modified anode-electrolyte interface for effective Na dendrites restriction in NASICON-based solid-state electrolyte. Energy Storage Mater. **30**, 170-178 (2020).
+
+[4] Zhao Y, Wang C, Dai Y, Jin H. Homogeneous Na<sup>+</sup> transfer dynamic at Na/Na<sub>3</sub>Zr<sub>2</sub>Si<sub>2</sub>PO<sub>12</sub> interface for all solid-state sodium metal batteries. Nano Energy **88**, 106293 (2021).
+
+[5] Shen L, Yang J, Liu G, Avdeev M, Yao X. High ionic conductivity and dendrite-resistant NASICON solid electrolyte for all-solid-state sodium batteries. Mater. Today Energy **20**, 100691 (2021).
+
+[6] Tian H, Liu S, Deng L, Wang L, Dai L. New-type Hf-based NASICON electrolyte for solid-state Na-ion batteries with superior long-cycling stability and rate capability. Energy Storage Mater. **39**, 232-238 (2021).
+
+[7] Wang C, Jin H, Zhao Y. Surface Potential Regulation Realizing Stable Sodium/Na<sub>3</sub>Zr<sub>2</sub>Si<sub>2</sub>PO<sub>12</sub> Interface for Room-Temperature Sodium Metal Batteries. Small **17**, e2100974 (2021).
+
+[8] Sun Z, et al. Active Control of Interface Dynamics in NASICON-Based Rechargeable Solid-State Sodium Batteries. Nano Lett. **22**, 7187-7194 (2022).
+
+[9] Yang J, et al. Improving Na/Na<sub>3</sub>Zr<sub>2</sub>Si<sub>2</sub>PO<sub>12</sub> Interface via SnO<sub>x</sub>/Sn Film for High-Performance Solid-State Sodium Metal Batteries. Small Methods **5**, e2100339
+(2021).
+[10] Gao Z, et al. TiO₂ as Second Phase in Na₃Zr₂Si₂PO₁₂ to Suppress Dendrite Growth in Sodium Metal Solid-State Batteries. Adv. Energy Mater. **12**, 2103607 (2022).
+[11] Wang X, Chen J, Wang D, Mao Z. Improving the alkali metal electrode/inorganic solid electrolyte contact via room-temperature ultrasound solid welding. Nat. Commun. **12**, 7109 (2021).
+
+*(4) In the previous paper (Sun et al., Energy Storage Mater. 2021), the authors introduced an organic electrolyte into the NVP cathode, as in the present study, and it appears to have been titled "quasi"-solid-state battery. I think that removing "all-solid-state" from the original title may work well here.*
+
+**Author’s Response:** In accordance with the reviewer’s advice, we have made a modification throughout the manuscript, revising the term “all-solid-state batteries” into “quasi-solid-state batteries”.
+
+*(5) Minor points.
+
+Line 4, page 12: "etc." has two citation numbers. It would be preferable to describe the materials.
+
+The words of "ultarastable" or "ultraconformal" are somewhat exaggerated for a scientific paper.
+
+Cell notation should be, for example, Na|Na₅SmSi₄O₁₂|Na₃V₂(PO₄)₃. The phase boundary is represented by a single line (not a double line as there is no salt bridge, etc.), and an anode is on the left side.
+
+There are several values where the significant figures are too large. For example, \( a = b = 22.14609\ \text{Å} \) (7 digits may require a temperature control of 0.01 K level), \( 2.90 \times 10^{-3}\ \text{S cm}^{-1} \) (requires very precise measurement of sample and electrode dimensions).
+
+The crystalline system of space group R-3c is rhombohedral, not hexagonal; I understand that the lattice constants are in a hexagonal "setting". "Hexagonal" is found in the text and in Supplemental Table 2. In addition, "Y1" is supposed to be "Sm1".
+
+Page 11, line 19: "holes" may be changed to "pores".*
+Authors’ Response: We sincerely appreciate the valuable advice provided by the reviewer, which has significantly enhanced the accuracy and clarity of our manuscript. We have diligently addressed all the previously identified errors, appropriately highlighted in red within the revised manuscript.
+
+<table>
+  <tr>
+    <th>Original content</th>
+    <th>Revised content</th>
+    <th>Location</th>
+  </tr>
+  <tr>
+    <td>etc<sup>28, 29</sup></td>
+    <td>AlF<sub>3</sub><sup>28</sup> and polymer with intrinsic nanoporosity<sup>29</sup></td>
+    <td>Page 4</td>
+  </tr>
+  <tr>
+    <td>ultrastable</td>
+    <td>stable</td>
+    <td>Page 5</td>
+  </tr>
+  <tr>
+    <td>ultraconformal</td>
+    <td>compact</td>
+    <td>Page 11, 17</td>
+  </tr>
+  <tr>
+    <td>Na<sub>3</sub>V<sub>2</sub>(PO<sub>4</sub>)<sub>3</sub>||Na<sub>5</sub>SmSi<sub>4</sub>O<sub>12</sub>||Na</td>
+    <td>Na|Na<sub>5</sub>SmSi<sub>4</sub>O<sub>12</sub>|Na<sub>3</sub>V<sub>2</sub>(PO<sub>4</sub>)<sub>3</sub></td>
+    <td>in full text</td>
+  </tr>
+  <tr>
+    <td>Na||Na<sub>5</sub>SmSi<sub>4</sub>O<sub>12</sub>||Na</td>
+    <td>Na|Na<sub>5</sub>SmSi<sub>4</sub>O<sub>12</sub>|Na</td>
+    <td>in full text</td>
+  </tr>
+  <tr>
+    <td>Li||Na<sub>5</sub>SmSi<sub>4</sub>O<sub>12</sub>||Li</td>
+    <td>Li|Na<sub>5</sub>SmSi<sub>4</sub>O<sub>12</sub>|Li</td>
+    <td>in full text</td>
+  </tr>
+  <tr>
+    <td>\(a = b = 22.14609\) Å,\(c = 12.68858\) Å</td>
+    <td>\(a = b = 22.15\) Å,\(c = 12.69\) Å</td>
+    <td>Page 6</td>
+  </tr>
+  <tr>
+    <td>2.90 \times 10^{-3}\) S cm\(^{-1}</td>
+    <td>2.9 \times 10^{-3}\) S cm\(^{-1}</td>
+    <td>in full text</td>
+  </tr>
+  <tr>
+    <td>hexagonal</td>
+    <td>rhombohedral</td>
+    <td>Page 5, 6, 21</td>
+  </tr>
+  <tr>
+    <td>Y1</td>
+    <td>Sm1</td>
+    <td>Page 33 in SI</td>
+  </tr>
+  <tr>
+    <td>holes</td>
+    <td>pores</td>
+    <td>Page 10</td>
+  </tr>
+</table>
+Reviewer #2 (Remarks to the Author):
+The authors presented an interesting paper titled “Electrochemically induced crystalline-to-amorphization transformation in sodium samarium silicate solid electrolyte for long-lasting all-solid-state sodium metal batteries”. This paper suggests the advantages of Na5SmSi4O12 solid electrolyte for long-life all-solid-state sodium metal batteries. However, due to the following reasons, I believe that Nature Communications cannot accept it as it is.
+The authors claim to report a new member of the Na5MSi4O12 family with M=Sm. However, solid electrolytes of this composition have been reported for a long time. For example, the following have been previously reported.
+1. Solid State Ionics, Volumes 86–88, Part 1, July 1996, Pages 511-516
+Synthesis and conduction properties of Na+ superionic conductors of sodium samarium silicophosphates
+2. Journal of the European Ceramic Society, Volume 26, Issues 4–5, 2006, Pages 619-622
+Superionic conducting Na5SmSi4O12-type glass-ceramics: Crystallization condition and ionic conductivity
+3. Journal of Electroceramics, Volume 24, 2010, Pages 83–90
+Na+-fast ionic conducting glass-ceramics of silicophosphates
+4. Solid State Ionics, Volume 262, 1 September 2014, Pages 604-608
+Synthesis and Na+ conduction properties of Nasicon-type glass–ceramics in the system Na2O–Y2O3–R2O3–P2O5–SiO2 (R = rare earth) and effect of Y substitution
+5. Solid State Ionics, Volume 285, February 2016, Pages 143-154
+Na+ superionic conducting silicophosphate glass-ceramics – Review
+6. Materials, 15, 2022, 1104. https://doi.org/10.3390/ma15031104
+Influence of R=Y, Gd, Sm on Crystallization and Sodium Ion Conductivity of Na5RSi4O12 Phase
+
+Author’s Response: Thank you for the insightful comment and we acknowledge that Na5MSi4O12 is not a new family of ionic conductors. However, earlier research has primarily focused on reporting the ionic conductivity of these materials at high
+temperatures, while what we reported here focuses on the crystalline-to-amorphous (CTA) transition and its stabilization of the interface for solid-state batteries. Accordingly, we have modified our statements. It is worthwhile to note that, to meet the eager demand for low-cost and high-safety batteries, solid-state sodium metal batteries appear as promising devices for future energy storage systems. So far, the reported Na-based SE is limited to Na-β'/β"-Al2O3, NASICON-type materials, Na3PS4 system, Na11Sn2PS12 system, etc. Na5MSi4O12 is a promising type of Na+ ionic conductor with high ionic conductivity above \(10^{-3}\) S cm\(^{-1}\), while there are rare studies on their application in solid-state sodium metal batteries. In our earlier study in Energy Storage Material[1], we report the synthesis and ionic transfer mechanism, which opens a new application area for such kind of material. In this manuscript, we not only realize a higher ionic conductivity in Na5SmSi4O12 with a lower reaction temperature but also discover a CTA transition during Na+ plating/stripping processes, which may propose a mechanism to achieve a conformal interface between Na metal and SE in the solid-state battery assembly. These discoveries can further propel the application of Na5MSi4O12 materials in solid-state batteries.
+
+[1] Sun G, et al. Na5YSi4O12: A sodium superionic conductor for ultrastable quasi-solid-state sodium-ion batteries. Energy Storage Mater. **41**, 196-202 (2021).
+
+*I feel that there is a lack of data on the subject of long life as a solid-state battery. The changes at the electrode-electrolyte interface after repeated charging and discharging of the battery over a long period of time and the results of analysis near the surface of the solid electrolyte should be presented.*
+
+Author’s Response: According to the reviewer’s suggestion, we have included the cycle lives of the state-of-the-art solid-state full cell in Table R3. It is obvious that our proposed Na|Na5SmSi4O12|Na3V2(PO4)3 batteries demonstrate very comparative cycle lives in state-of-the-art solid-state batteries[1-12]. In the revised Supplementary material, we have added this table as Supplementary Table 7 and discussed it accordingly.
+
+Table R3. A survey of cycle performance of oxide electrolytes-based solid-state cells.
+<table>
+  <tr>
+    <th>Solid-state cells description</th>
+    <th>Operating temperature</th>
+    <th>Cycle performance</th>
+    <th>Ref.</th>
+  </tr>
+  <tr>
+    <td><b>Na|Na<sub>5</sub>SmSi<sub>4</sub>O<sub>12</sub>|Na<sub>3</sub>V<sub>2</sub>(PO<sub>4</sub>)<sub>3</sub></b></td>
+    <td><b>25 °C</b></td>
+    <td><b>4000 cycles 100%</b></td>
+    <td><b>This work</b></td>
+  </tr>
+  <tr>
+    <td>Na|Na<sub>5</sub>YSi<sub>4</sub>O<sub>12</sub>|Na<sub>3</sub>V<sub>2</sub>(PO<sub>4</sub>)<sub>3</sub></td>
+    <td>25 °C</td>
+    <td>500 cycles 100%</td>
+    <td>[1]</td>
+  </tr>
+  <tr>
+    <td>Na/β"-Al<sub>2</sub>O<sub>3</sub>/NaTi<sub>2</sub>(PO<sub>4</sub>)<sub>3</sub></td>
+    <td>25 °C</td>
+    <td>50 cycles 75.1%</td>
+    <td>[2]</td>
+  </tr>
+  <tr>
+    <td>Na/β"-Al<sub>2</sub>O<sub>3</sub>/Na<sub>0.66</sub>Ni<sub>0.33</sub>Mn<sub>0.67</sub>O<sub>2</sub></td>
+    <td>70 °C</td>
+    <td>10000 cycles 90%</td>
+    <td>[3]</td>
+  </tr>
+  <tr>
+    <td>Na/Na<sub>3</sub>Zr<sub>2</sub>(Si<sub>2</sub>PO<sub>12</sub>)/NVP</td>
+    <td>50 °C</td>
+    <td>100 cycles 98%</td>
+    <td>[4]</td>
+  </tr>
+  <tr>
+    <td>Na/Na<sub>3</sub>Zr<sub>2</sub>Si<sub>2</sub>PO<sub>12</sub>/Na<sub>2</sub>MnFe(CN)<sub>6</sub></td>
+    <td>60 °C</td>
+    <td>200 cycles 89.2%</td>
+    <td>[5]</td>
+  </tr>
+  <tr>
+    <td>Na/beta-alumina/PTO</td>
+    <td>60 °C</td>
+    <td>50 cycles 80%</td>
+    <td>[6]</td>
+  </tr>
+  <tr>
+    <td>Na/Na<sub>3.2</sub>Zr<sub>1.8</sub>Ca<sub>0.1</sub>Si<sub>2</sub>PO<sub>12</sub>/NVP</td>
+    <td>25 °C</td>
+    <td>500 cycles 98%</td>
+    <td>[7]</td>
+  </tr>
+  <tr>
+    <td>Na/Na<sub>3.4</sub>Zr<sub>1.8</sub>Mg<sub>0.2</sub>PO<sub>12</sub>/NaCrO<sub>2</sub></td>
+    <td>25 °C</td>
+    <td>1755 cycles 87%</td>
+    <td>[8]</td>
+  </tr>
+  <tr>
+    <td>Na/polydopamine-Na<sub>3.4</sub>Zr<sub>1.9</sub>Zn<sub>0.1</sub>Si<sub>2.2</sub>P<sub>0.8</sub>O<sub>12</sub>/FeS<sub>2</sub></td>
+    <td>60 °C</td>
+    <td>300 cycles 73.3%</td>
+    <td>[9]</td>
+  </tr>
+  <tr>
+    <td>UW-Na/Na<sub>3</sub>Zr<sub>2</sub>Si<sub>2</sub>PO<sub>12</sub>/NVP</td>
+    <td>25–27 °C</td>
+    <td>900 cycles 89.8%</td>
+    <td>[10]</td>
+  </tr>
+  <tr>
+    <td>Na/Na<sub>3.3</sub>Zr<sub>1.7</sub>La<sub>0.3</sub>Si<sub>2</sub>PO<sub>12</sub>/IL/NVP</td>
+    <td>25 °C</td>
+    <td>10000 cycles 100%</td>
+    <td>[11]</td>
+  </tr>
+  <tr>
+    <td>Na/Na<sub>3</sub>Zr<sub>2</sub>Si<sub>2</sub>PO<sub>12</sub>/NVP</td>
+    <td>25 °C</td>
+    <td>100 cycles 97%</td>
+    <td>[12]</td>
+  </tr>
+</table>
+
+references
+
+[1] Sun G, et al. Na<sub>5</sub>YSi<sub>4</sub>O<sub>12</sub>: A sodium superionic conductor for ultrastable quasi-solid-state sodium-ion batteries. Energy Storage Mater. **41**, 196-202 (2021).
+
+[2] Zhao K, et al. A room temperature solid-state rechargeable sodium ion cell based on a ceramic Na-β"-Al<sub>2</sub>O<sub>3</sub> electrolyte and NaTi<sub>2</sub>(PO<sub>4</sub>)<sub>3</sub> cathode. Electrochem. Commun. **69**, 59-63 (2016).
+
+[3] Liu L, et al. Toothpaste-like Electrode: A Novel Approach to Optimize the Interface for Solid-State Sodium-Ion Batteries with Ultralong Cycle Life. ACS Appl. Mater. Interfaces **8**, 32631-32636 (2016).
+
+[4] Gao H, Xue L, Xin S, Park K, Goodenough JB. A Plastic-Crystal Electrolyte Interphase for All-Solid-State Sodium Batteries. Angew. Chem. Int. Ed. Engl. **56**, 5541-5545 (2017).
+
+[5] Gao H, Xin S, Xue L, Goodenough JB. Stabilizing a High-Energy-Density Rechargeable Sodium Battery with a Solid Electrolyte. Chem **4**, 833-844 (2018).
+[6] Chi X, et al. A high-energy quinone-based all-solid-state sodium metal battery. Nano Energy **62**, 718-724 (2019).
+
+[7] Lu Y, Alonso JA, Yi Q, Lu L, Wang ZL, Sun C. A High-Performance Monolithic Solid-State Sodium Battery with Ca^{2+} Doped Na_{3}Zr_{2}Si_{2}PO_{12} Electrolyte. *Adv. Energy Mater.* **9**, 1901205 (2019).
+
+[8] Wang C, *et al*. Grain Boundary Design of Solid Electrolyte Actualizing Stable All-Solid-State Sodium Batteries. *Small* **17**, e2103819 (2021).
+
+[9] Yang J, *et al*. Ultrastable All-Solid-State Sodium Rechargeable Batteries. *ACS Energy Lett.* **5**, 2835-2841 (2020).
+
+[10] Wang X, Chen J, Wang D, Mao Z. Improving the alkali metal electrode/inorganic solid electrolyte contact via room-temperature ultrasound solid welding. *Nat. Commun.* **12**, 7109 (2021).
+
+[11] Zhang Z, *et al*. A Self-Forming Composite Electrolyte for Solid-State Sodium Battery with Ultralong Cycle Life. *Adv. Energy Mater.* **7**, 1601196 (2017).
+
+[12] Yang J, *et al*. Improving Na/Na_{3}Zr_{2}Si_{2}PO_{12} Interface via SnO_{x}/Sn Film for High-Performance Solid-State Sodium Metal Batteries. *Small Methods* **5**, e2100339 (2021).
+
+In addition, the changes in the electrode-electrolyte interface and SE surface were studied in detail. First, the Nyquist plots of the symmetric Na|Na_{5}SmSi_{4}O_{12}|Na cell were recorded after different cycling times to reveal the changes in the internal resistance (Fig. 2b and Supplementary Table 4). As the sodium plating/stripping proceeds, the resistance of SE (both R_{b} and R_{GB}) remains nearly unchanged, while the interfacial resistance (R_{int}) between sodium metal and electrolyte decreases at an initial few cycles and then stabilizes at a relatively low value, demonstrating good compatibility between Na_{5}SmSi_{4}O_{12} and sodium metal. To reveal the interfacial morphology evolution, SEM images of the electrode-electrolyte interface at different plating/stripping stages (Fig. 2c and 2d) were further recorded, indicating the disappearance of interface gap between Na and Na_{5}SmSi_{4}O_{12} SE with the result of increased contact areas after cycling.
+
+Furthermore, XRD patterns of Na_{5}SmSi_{4}O_{12} show a CTA transition after cycling
+for 200 h (Fig. 2e). To further confirm this CTA transition, HRTEM and SAED measurements before and after cycling were recorded (Supplementary Fig. 9). There are no observed lattice fringes (Fig. 2f) and diffraction spots (Fig. 2g) for the cycled SE sample, confirming the CTA transition once more. Owing to the intrinsic characteristics of the amorphous materials, it is difficult to determine the possible local coordination based on XRD measurement. Therefore, Raman spectra were then used to examine the potential short-range vibration changes in the chemical bonding. As expected, the amorphous Na5SmSi4O12 SE maintains nearly all the vibrational peaks without new vibrations confirming no chemical reaction between the interface of SE and Na metal (Supplementary Fig. 10). While the disappearance of the peak at 1041 cm^{-1} might be related to the damage of the fracture of Si-O bond by the amorphous transition. Furthermore, X-ray photoelectron spectroscopy (Supplementary Fig. 11) suggests that there is no change in the Sm 3d, Na 1s and Si 2p XPS spectra after cycling, indicative of no redox reaction occurred between sodium metal and Na5SmSi4O12 once more.
+
+Moreover, the improved properties of bulk materials and amorphous interface can be understood in terms of the following two aspects: On one hand, the ionic conductivity of bulk material was improved. Figure 4a shows the \(^{23}\)Na NMR spectra before and after metallic Na cycling by using crystalline Na5SmSi4O12 as an electrolyte. The \(^{23}\)Na NMR spectrum did not change significantly before and after the Na cycling, indicating the stability of the structure. The changes for Na4, Na5, and Na6 are obvious, indicating their redistribution upon cycling. In addition, the activation energy of the mobile Na of the cycled Na5SmSi4O12 is 0.07 eV (Fig. 4b), which is much lower than that of the pristine state (0.13 eV in Fig. 1k), indicating the amorphous interface and bulk materials greatly reduces the activation energy, further resulting in higher conductivity of crystalline Na5SmSi4O12. On the other hand, the interfacial issues, such as high interfacial resistance and metal dendrite growth, are strongly alleviated. The amorphous Na5SmSi4O12 could enhance the wettability with significantly reduced interface resistance by reducing the interface energy between Na and Na5SmSi4O12 since amorphous Na5SmSi4O12 exhibits lower interfacial energy of 0.33 J m^{-2} with sodium than crystalline Na5SmSi4O12 (0.56 J m^{-2}) (Supplementary Fig. 16). In addition,
+Young’s modulus \( E \) and hardness \( H \) of the amorphous Na$_5$SmSi$_4$O$_{12}$ are calculated to be ~79.9 GPa and ~3.8 GPa, respectively, higher than the crystalline Na$_5$SmSi$_4$O$_{12}$ (~72.6 GPa and ~2.8 GPa), beneficial to inhibiting the dendrite growth.
+
+*The mechanism of conduction has also been reported since the 1980s, and the authors' previous report "Na$_5$YSi$_4$O$_{12}$: A sodium superionic conductor for ultrastable quasi solid-state sodium-ion batteries. batteries. Energy Storage Mater. 41, 196-202 (2021)" also discusses the same issues as in the present study.*
+*The other figures are considered unnecessary as they are not very relevant and are not beyond the scope of the previous report.*
+
+Author’s Response: Thank you for the reviewer’s kind suggestion. Besides the reports on the synthesis and ionic conducting mechanism, the most interesting finding in our manuscript is the discovery of “crystalline-into-amorphous transition” in Na$_5$SmSi$_4$O$_{12}$ SE during Na plating/stripping, which leads to faster ionic transport and superior interfacial properties.
+
+We fully agree with the review’s comment and revise Figure 1 and the corresponding discussion part in the revised manuscript.
+
+![Five subfigures showing XRD patterns, energy vs diffusion coordinate plots, Na shift spectra, saturation recovery curves, and Arrhenius plot](page_320_1042_1002_370.png)
+
+Fig. 1. Crystal structure and sodium-ion conduction characteristic of crystalline Na$_5$SmSi$_4$O$_{12}$. **a** Rietveld refinement based on the powder XRD. **b** Minimum potential
+energy path along Na^+ diffusion route in crystalline Na_5SmSi_4O_{12}. **c** Solid-state \(^{23}\)Na NMR spectrum and its simulation for the crystalline Na_5SmSi_4O_{12}. The gray line is experimental data and the green-dashed line is the sum of simulation. **d** Saturation recovery fitting curve for the data obtained at room temperature. **e** Temperature dependence of \(^{23}\)Na NMR relaxation rate as a function of temperature in K^{-1}. The solid line is the fit according to Eq. (1). The derivation of the data is not used for the fit.
+REVIEWERS' COMMENTS
+
+Reviewer #1 (Remarks to the Author):
+
+The authors responded well to the review comments, and the revised manuscript and study are considered more complete. I especially appreciate the deeper discussion on critical 'charge' density.
+
+One small point, in response to my comment about the number of digits of lattice constants, the revised version employs four digits, a = b = 22.15, c = 12.69 A, which I think is too few as a result of the analysis; it would be appropriate to report around 5 or 6 digits.
+
+Reviewer #2 (Remarks to the Author):
+
+Since you have responded to my comments, I think I can accept the manuscript of this paper.
+Response to the Referees for Nature Communication
+
+We would like to express our sincere gratitude for the decision to accept our manuscript after revision. We deeply appreciate the time and effort the editor and the reviewers have dedicated to reviewing and providing constructive feedback on our work. We've carefully addressed the suggested revisions, which are highlighted in red in the revised manuscript. We look forward to the final publication and hope that our work will contribute to the broader scientific community.
+
+Reviewer #1 (Remarks to the Author):
+The authors responded well to the review comments, and the revised manuscript and study are considered more complete. I especially appreciate the deeper discussion on critical 'charge' density.
+One small point, in response to my comment about the number of digits of lattice constants, the revised version employs four digits, \( a = b = 22.15, c = 12.69\ \text{\AA} \), which I think is too few as a result of the analysis; it would be appropriate to report around 5 or 6 digits.
+
+Author’s Response: We are very grateful for your valuable comments, which have been instrumental in refining our manuscript and enhancing its quality. According to your suggestion, we have kept 6 digits for the lattice constant and revised the manuscript as “All the diffraction peaks can be indexed into a rhombohedral system with space group R-3c, and the lattice parameters are calculated as \( a = b = 22.1461\ \text{\AA},\ c = 12.6886\ \text{\AA} \)” on page 6.
+
+Reviewer #2 (Remarks to the Author):
+Since you have responded to my comments, I think I can accept the manuscript of this paper.
+
+Author’s Response: Thank you very much for your positive feedback and for agreeing to accept our manuscript. We appreciate the time and effort you have invested in reviewing our work.

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+Peer Review File
+
+Interrogating Site Dependent Kinetics over SiO2-Supported Pt Nanoparticles
+
+Open Access This file is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. In the cases where the authors are anonymous, such as is the case for the reports of anonymous peer reviewers, author attribution should be to 'Anonymous Referee' followed by a clear attribution to the source work. The images or other third party material in this file are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.
+REVIEWER COMMENTS
+
+Reviewer #1 (Remarks to the Author):
+
+The manuscript of Kim et al. presents the study of the site-dependent kinetics of CO oxidation over SiO2-supported Pt nanoparticles. The experimental results are solid, novel, and clearly described. The used methods are insightful and quantitative. I have some doubts, however, if the paper is of broad interest... maybe it can be improved by showing more concrete perspectives. Based on it, I recommend major revision. The detailed comments are listed below:
+
+1. I am not sure that the perspectives on the use of this methodology for other catalytic systems, beyond CO oxidation, are sufficiently presented. I think it would be interesting to know what are the limitations of the methods, and for which other catalytic systems and processes they can be applied. Somehow, I do not see a direct link to operando catalysis, due to the pressure gap, but see perspectives in bridging the gap between the single crystal model catalysts and realistic powder catalysts and comparing the structure of powder catalysts (not necessarily operando) prepared by different methods and different supports.
+
+2. Only one Pt/SiO2 catalyst is studied. The conclusions could become more significant if the Pt particle size were varied or different supports could be compared. Currently, there is a curious result but I do not see the impact of the obtained knowledge on the catalytic science.
+
+3. Considering the previous literature, were different pathways of CO oxidation on platinum nanoparticles ever considered or observed? What do the authors think about this paper claiming room temperature CO oxidation on Pt particles (https://www.nature.com/articles/ncomms9675 ) or maybe other literature?
+
+4. I do not understand why the term “operando” is used in this paper. This term is typically reserved for the methods providing direct information about the structure of a catalyst. I believe, TAP with all its uniqueness still provides indirect information, as it analyses the gas phase composition, and DRIFTS is done in situ.
+
+5. Minor comment: On page 3, it is mentioned that the reaction order in CO is 1.02. I believe it should be negative.
+
+Reviewer #2 (Remarks to the Author):
+
+Concept on manuscript 447948: Interrogating Site Dependent Kinetics over SiO2-Supported Pt Nanoparticles
+General concept
+This is a very interesting paper that claims “Herein, we can bypass the pressure, materials, and temperature gaps, resolving and quantifying two distinct pathways for CO oxidation over SiO2-supported 2 nm Pt nanoparticles under operando conditions.” Therefore, new venues for kinetic analysis may be open if this study is further corroborated independently. However, there are several aspects of the work that need careful consideration to properly sustain such a claim. Please find them below:
+1. My main concern with the presented results is the possible influence of transport artifacts on the measurement of reaction rates and further modelling of the kinetic data. On the one hand, the authors do not provide any information whatsoever on the porosity of their catalyst. Ideally, if the authors are ascribing all catalysis to the metal, the latter should be fully exposed at the external surface of the SiO2 support. For this, the support should either be macroporous or non-porous. Which of these instances apply here? On the other hand, CO oxidation is a highly exothermic reaction thus eliminating temperature gradients during catalytic tests is hard to accomplish. Therefore, in my opinion, the authors must present a rigorous evaluation of the possible influence of mass and heat transport limitations in the paper to validate the claims that they are making.
+2. I am also concerned about the possible influence of impurities from the SiO2 support on the catalytic activity. Particularly, commercial SiO2 samples tend to be contaminated with traces of Na. Furthermore, the authors used NaOH for the preparation of the catalyst. The authors must then present a full chemical analysis (both bulk and surface) of the composition of the catalyst to discard undesired effects on the measured kinetics. In this sense, I couldn’t find results of blank tests that serve to discard effects from the diluent of the catalyst and from the SiO2 support. These results must be included in the Supplementary information of the paper.
+3. Quantification by mass spectrometry is complex. According to the manuscript, the authors normalized the signals from the mass spectrometer with the Ar signal. However, when MS analysis is made, the amount of substance of the analyte may strongly influence quantification; particularly when the sum of the stoichiometric numbers of the reaction is not zero; which is the case for CO oxidation. This causes an increase in the pressure which combined with the fact that tests are being performed at ramped temperatures may strongly affect quantification. Therefore, the authors must discuss the latter in the experimental section of the paper and should discuss how this can affect their data analysis.
+4. Although the authors made a reduction treatment of their catalyst, no evidence of the full reduction of the metal is presented. In addition, literature has presented evidence on the fact that traces of carbonaceous species may remain tightly bound to supported noble metal catalysts even after oxidation treatments. In particular, unpublished results from our lab have shown supported platinum catalysts that undergo oxidation treatments followed by reductions treatments produce methane during the latter. This can, of course, be due to impurities in the gas fed to the reactor. The authors should then ensure that such effects are not affecting their analysis.
+5. According to the paper, catalytic tests were made with an O2 to CO ratio ~ 2 which is four times higher than the stoichiometric ratio for the reaction. Why did you make this choice? What would be effect of changing this ratio on the presented conclusions? Would the two claimed mechanisms exist under both the stoichiometric and an under-stoichiometric reaction ratio?
+6. The data for the apparent activation energy presented in Figure 2a suggests an alternative interpretation from the one provided by the authors. Indeed, the authors claim that all their data is fitted by a linear curve, but the dispersion of the data is strong starting around 1/RT ~ 0.282 mol/kJ. On the
+one hand, this suggests that the statistics of the data after such a value require very careful checking of influence of the correlation effects over the data. On the other hand, this indicates that reaction regime is modified after some temperature. This does not necessarily imply a new mechanism because heat transport artifacts may strongly influence the measured kinetics. And, in the case of the observed effect in Figure 2a, the existence of two different mechanisms when changing the temperature of the catalytic tests seems to contradict the claim of the authors.
+Other minor concerns are:
+(i) The description of the experiments is often times incomplete so one may have problems trying to reproduce the work of the authors. First, although the techniques used for the characterization of the catalyst are kind of rutinary for catalysis researchers, every laboratory uses some slight modifications when performing them and this hinders reproducibility. Therefore, I recommend including full details of the presented experiments in the Supplementary Information of the paper. Please, do not make the reader read other papers to understand and reproduce your experiments.
+(ii) The “error” bars presented for the data in Supplementary Figures does not allow understanding the data. Please, make these plots clearer. Also, you may include a Table for reporting the statistics of the measurements.
+(iii) How did you measure the flux of the products of the reactor? Typically, flux refers to a quantity per area of flow. What was the area of flow?
+(iv) The first paragraph of the introduction of the paper seems to suggest that the method developed by the authors will fill the gap between laboratory catalysts and technical catalysts. I am sure that the authors are aware of the fact that the latter are multicomponent formulations whose behavior in industrial units cannot be understood only from chemical kinetics on powders. Therefore, I suggest that the authors take this into account for modifying the paragraph.
+
+Reviewer #3 (Remarks to the Author):
+
+Authors report the synthesis of Pt/SiO2 catalyst using polymer stabilized polyol method. This catalyst contains ca.2nm Pt nanoparticles and these materials have been tested for CO oxidation. Fundamental studies on the kinetics of this reaction have been done in a TAP reactor. The authors have done an excellent study on the site dependency of the kinetics of CO oxidation using two different Pt nanoparticles sites (well coordinated and under coordinated sites) on a practical catalyst. The results are interesting and are of fundamental importance. It is a very well written article. Typically support materials play an important role in CO oxidation, however here the whole discussion is on Pt sites. I appreciate it is a SiO2 support. Authors can comment on the versatility of this methodology for other catalytic systems where support play an active role in the catalysis.
+
+Reviewer #4 (Remarks to the Author):
+
+The manuscript reports an interesting and well-constructed kinetic and spectroscopic investigation of the
+oxidation of CO on Pt supported over silica. The conclusions of the study propose that at least two parallel reaction pathways are taking place on Pt, related to sites with different coordinations. Although Pt/SiO2 is effectively a purely academic catalyst with activity far lower than that of redox oxide-supported materials, the results underlines new methodologies to investigate this reaction and will appeal to the community.
+
+The main shortcoming of the paper resides in the data analysis that does not take into account the potential bulk oxidation of Pt at low CO coverages or O2 excess pulses. This could explain the third irreversible adsorption pathway for O2 (line 214), rather than mere surface adsorption. To this respect, the work of van Bohhoven 's group on the oxidic nature of the Pt phase at low CO coverage/high temperature should be cited and discussed in the present paper (Angew. Chem. Int. Ed. 2008, 47, 9260–9264). The simultaneous presence of reduced and oxidised Pt phases during low temperature CO oxidation has also been reported and emphasises the complex evolution of Pt phases that may occur when reaction conditions are changed (e.g. Meunier et al, Angew. Chem. Int. Ed. 2021, 60, 3799 – 3805). This may thus relate to the potential changes of Pt structure as hypothesised by the authors on line 418. I therefore suggest that Pt bulk oxidation should be considered and discussed in the data analysis and model.
+
+Minor point: line 98: CO reaction order is -1, not +1, please correct.
+We would like to thank the reviewers for their feedback on the manuscript. Outside of a few clarifying questions on the oxidation state of the catalyst, we feel that the primary concern was related to the broad applicability of the kinetic site deconvolution method. In response to this we have included a new section in our manuscript discussing the applicability of this method to commonly used site-titration experiments in heterogeneous catalysis. Although this was not mentioned by the reviewers, we have also decided to rename the “bridge” CO in our DRIFTS spectra to “multi-bound” CO as the three-fold hollow site also sits within that adsorption band.
+
+Our responses to reviewers’ specific comments are included below. The reviewers’ comments are in black, and our responses are in red. All line numbers are based on the unmarked edited manuscript.
+
+Reviewer #1
+
+The manuscript of Kim et al. presents the study of the site-dependent kinetics of CO oxidation over SiO2-supported Pt nanoparticles. The experimental results are solid, novel, and clearly described. The used methods are insightful and quantitative. I have some doubts, however, if the paper is of broad interest… maybe it can be improved by showing more concrete perspectives. Based on it, I recommend major revision. The detailed comments are listed below:
+
+We thank reviewer #1 for their interest in our paper and constructive comments. As this is a new method of quantifying active sites, we can understand their concerns with respect to applicability. We have included a new section of the paper (see below) where we further discuss the future perspectives of this method and also provide candidates for future applications.
+
+I am not sure that the perspectives on the use of this methodology for other catalytic systems, beyond CO oxidation, are sufficiently presented. I think it would be interesting to know what are the limitations of the methods, and for which other catalytic systems and processes they can be applied. Somehow, I do not see a direct link to operando catalysis, due to the pressure gap, but see perspectives in bridging the gap between the single crystal model catalysts and realistic powder catalysts and comparing the structure of powder catalysts (not necessarily operando) prepared by different methods and different supports.
+
+We agree with reviewer #1 that the term operando was misused. With regards to the pressure gap, the peak pressure during a pulse in the TAP reactor reaches approximately 1 mbar, meaning it is near ambient pressure. Further, pre-treatments of the catalyst are performed using large pulsing where the peak pressure in the microreactor reaches \( \geq 1 \) bar. We agree that the experiment is not within the specific subclass of operando measurements, but we feel that it can be considered analogous to in situ methods and have reworded the paper as such.
+
+In response to the broad applicability of the method, we have included a new section in the paper outlining future perspectives on the use of this methodology. We would like to emphasise that use of probe molecules for characterising heterogeneous catalysts has been commonplace for many years. We acknowledge that CO oxidation is not a catalytically relevant process, but it is an excellent tool for probing catalytic activity and for determining the number of active sites. Probe molecules such as CO for metal sites, ammonia/pyridine for acid sites in zeolites, or oxidants (e.g., O2, NO2) to probe reducible oxides/catalytic centres in zeolites can be readily utilized in this method. The reactions of these species occur via (relatively) simple first-order relationships meaning that the active-site deconvolution method we have developed is directly applicable. In fact, we aim to broadly apply this method to new materials in the future. We acknowledge that this methodology is still in the early stages of application, but it is our hope that many others will utilise it in the further for more complex systems.
+
+Lines 456 – 472 now read:
+
+“The use of probe molecules to titrate catalytically active sites is commonplace in heterogeneous catalysis research\(^1\). Using molecules such as CO, H\(_2\), or N\(_2\)O for metal sites, NH\(_3\) or
+pyridine for zeolites, and O2 for oxygen vacancies it becomes possible to count the number of active centres on a catalyst. By performing these experiments in a TAP reactor and coupling them with Multi-Zone TAP Reactor Theory it becomes possible to not only quantify the number of sites, but simultaneously measure their catalytic activity for simple probe reactions (e.g., the oxidation of CO). As the activity for a given probe reaction is directly related to the environment in which that probe molecule is adsorbed, the intrinsic rate constant for the rate of transformation of that species provides a fingerprint of that specific site. Using the kinetic site deconvolution method outlined in this work it then becomes possible to not only count the total number of sites, but to also count the number and distribution of different sites on the catalyst. This allows the structural characterization of catalysts allowing insight regarding size-effects (from a single atom to bulk catalyst) and support-effects, but it also opens up the possibility of rationalising how catalysts dynamically restructure by seeing how the number of sites and the intrinsic rate constants of the probe reactions are modified based on the catalyst state. While this methodology is still in its infancy, we believe that this new approach is general enough to apply to other catalytic systems and can serve as a new toolkit in the characterisation of heterogeneous catalysts.”
+
+Only one Pt/SiO2 catalyst is studied. The conclusions could become more significant if the Pt particle size were varied or different supports could be compared. Currently, there is a curious result but I do not see the impact of the obtained knowledge on the catalytic science.
+
+Ideally, it would be great to study different size Pt nanoparticles, but I’m sure the reviewer can sympathise that generating well-defined Pt nanoparticles with a narrow size distribution at different sizes that also don’t sinter/restructure under reaction conditions is very difficult. The narrow size distribution is mandatory otherwise it is not feasible to prescribe catalytic activity to specific sites. As developing the kinetic deconvolution method is already a significant body of work that could be directly applicable to other catalytic systems, we feel that even with the one case study the work warrants publication. However, we would like to mention that future work studying the effect of Pt nanoparticle size is currently underway.
+
+Considering the previous literature, were different pathways of CO oxidation on platinum nanoparticles ever considered or observed? What do the authors think about this paper claiming room temperature CO oxidation on Pt particles (https://www.nature.com/articles/ncomms9675) or maybe other literature?
+
+The paper mentioned claims that room temperature CO oxidation on Pt/Al2O3 occurs on isolated “oxidic” Pt centres through formation of a Pt carbonate intermediate. While the paper is interesting, we do not feel that it is relevant to our work as the formation of these centres seem specific to Al2O3 supported Pt catalysts whereas we used SiO2 as a support material. Further, we see no evidence of Pt single atoms or the formation of Pt(CO3) species in the DRIFTS spectra on our catalyst, but we also cannot completely rule out this mechanism.
+
+We would also like to emphasise that our methodology doesn’t suggest a specific pathway, and it is just simply a measurement of an intrinsic rate constant for a given elementary reaction step. While those intrinsic rate constants can provide insight into the nature of that active site (the rate, coverage dependence, temperature dependence) we cannot suggest a specific reaction mechanism without further characterisation methods / experiments / theory. Our rationale for the site-specificity is due to the strong correlation between the estimated distribution of under-coordinated and well-coordinated sites and the distribution of distinct CO oxidation sites on the surface, but how that reaction proceeds on that site is somewhat ambiguous. We recognise that this required further clarification and so have expanded upon our discussion of the oxidation of CO over the undercoordinated sites.
+
+Lines 388 – 390 now read:
+
+“While it is now possible to identify where the reaction is occurring, the intrinsic rate constants alone cannot provide specifics on how the reaction is occurring without further characterisation methods.”
+Lines 400 – 403 now read:
+
+“Other experiments have reported that the barrierless (or near barrierless) oxidation of CO can occur via a Pt(CO_3) intermediates^2, or through an Eley-Rideal type mechanism^3. While we do not find any direct evidence of those pathways, it is also not possible to entirely rule them out.”
+
+I do not understand why the term “operando” is used in this paper. This term is typically reserved for the methods providing direct information about the structure of a catalyst. I believe, TAP with all its uniqueness still provides indirect information, as it analyses the gas phase composition, and DRIFTS is done in situ.
+
+We agree with reviewer #1 that this is a valid comment. We have removed the term *operando* / changed it to *in situ* where applicable. We believe that the presented *kinetic site deconvolution* as an *in situ* characterisation method, but we recognise that is contentious and so have refrained from it’s use in this paper.
+
+Minor comment: On page 3, it is mentioned that the reaction order in CO is 1.02. I believe it should be negative.
+
+We thank reviewer #1 for pointing out this mistake. We have corrected the reaction order in CO to −1.02.
+Reviewer #2
+
+This is a very interesting paper that claims “Herein, we can bypass the pressure, materials, and temperature gaps, resolving and quantifying two distinct pathways for CO oxidation over SiO2-supported 2 nm Pt nanoparticles under operando conditions.” Therefore, new venues for kinetic analysis may be open if this study is further corroborated independently. However, there are several aspects of the work that need careful consideration to properly sustain such a claim. Please find them below:
+
+We thank reviewer #2 for their positive feedback on the manuscript.
+
+My main concern with the presented results is the possible influence of transport artifacts on the measurement of reaction rates and further modelling of the kinetic data. On the one hand, the authors do not provide any information whatsoever on the porosity of their catalyst. Ideally, if the authors are ascribing all catalysis to the metal, the latter should be fully exposed at the external surface of the SiO2 support. For this, the support should either be macroporous or non-porous. Which of these instances apply here?
+
+We understand reviewer #2’s concerns. We have included BET results that confirm that our support material is nonporous/macroporous and included it in Supplementary Fig. 13.
+
+Lines 484 – 486 now read:
+
+“the 0.3 g of nonporous (Supplementary Fig. 13) SiO2 powder (pretreated at 700 °C for 1 hr; 10–20 nm, Sigma-Aldrich, Product No. 637238) with vigorous stirring (400 rpm).
+
+![N2 adsorption isotherm plot for SiO2 support material demonstrating nonporous/macroporous behaviour.](page_579_1012_484_388.png)
+
+Supplementary Figure 13. N2 adsorption isotherm plot for SiO2 support material demonstrating nonporous/macroporous behaviour.
+
+On the other hand, CO oxidation is a highly exothermic reaction thus eliminating temperature gradients during catalytic tests is hard to accomplish. Therefore, in my opinion, the authors must present a rigorous evaluation of the possible influence of mass and heat transport limitations in the paper to validate the claims that they are making.
+
+We understand why reviewer #2 may have concerns regarding temperature gradients and mass/heat transport limitations as these are very important in steady-state flow experiments. However, one benefit of the TAP experiment is that these factors are significantly minimised.
+In the TAP experiment the primary transport mechanism is Knudsen diffusion which is well-defined and independent of composition of the gas mixture and its pressure. This has been discussed extensively in previous publications, most notably in the seminal work of Gleave (https://doi.org/10.1016/S0926-860X(97)00124-5)⁴ but also by Constales in their derivations of Multi-Zone TAP Reactor Theory (https://doi.org/10.1016/S0009-2509(00)00216-5)⁵. Further, even though CO oxidation is highly exothermic, the total amount of reactive gas in a single pulse is very small (~1nmol) which means even in the extreme case of every CO molecule instantaneously reacting, the total amount of heat imparted into the system is multiple orders of magnitude than the specific heat capacity of our catalyst. We have added an extra statement clarifying that we are not heat/mass transfer limited under these conditions.
+
+Lines 520 – 522 now read:
+
+“As the primary transport mechanism is Knudsen diffusion any mass transfer effects can be minimised. Further, the small pulse size means that the amount of heat imparted into the system due to the exothermic reaction is negligible.”
+
+I am also concerned about the possible influence of impurities from the SiO₂ support on the catalytic activity. Particularly, commercial SiO₂ samples tend to be contaminated with traces of Na. Furthermore, the authors used NaOH for the preparation of the catalyst. The authors must then present a full chemical analysis (both bulk and surface) of the composition of the catalyst to discard undesired effects on the measured kinetics. In this sense, I couldn’t find results of blank tests that serve to discard effects from the diluent of the catalyst and from the SiO₂ support. These results must be included in the Supplementary information of the paper.
+
+Reviewer #2 raises a good point. While we have performed extensive blank tests over the SiO₂ sand used as the inert packing in the TAP reactor, we did not report them as part of the paper. To ensure that no catalytic activity was coming from the SiO₂ support material (and the inert SiO₂ sand), we have synthesised a blank sample using same synthetic procedure (including the addition of NaOH) as that of the Pt/SiO₂ catalyst but without including the Pt nanoparticles which we call SiO₂ (blank). We investigated the chemical states of the SiO₂ (blank) sample and Pt/SiO₂ catalyst using XPS. We consider the XPS measurement to be a bulk chemical analysis for the 2 nm Pt nanoparticles because the XPS probing depth is ~3 nm using an Al Kα X-ray source. For the both samples, there is no peak for Na compounds in the Na 1s core-level spectrum (Supplementary Fig. 14).
+
+![XPS measurements for Na 1s core-level spectrum of (a) SiO₂ (blank) sample and Pt/SiO₂ catalyst.](page_1012_1042_388_246.png)
+
+Supplementary Figure 14. a,b, XPS measurements for Na 1s core-level spectrum of (a) SiO₂ (blank) sample and Pt/SiO₂ catalyst.
+
+However, to further confirm that the catalytic activity is primarily from the Pt nanoparticles, the SiO₂ (blank) sample is packed in the exact same configuration as used during the experiments and the CO oxidation and TPO pulsed experiments were repeated (Supplementary Fig. 17). Little-to-no activity for CO oxidation is recorded on the blank sample.
+Supplementary Figure 17. a, Temperature-dependent integrated exit flux of m/z = 44 (CO₂) normalised via Ar on CO*−covered Pt/SiO₂ catalyst and SiO₂ (blank) for CO oxidation (6.6% CO 13.4% O₂ gas mixture in an inert Ar tracer) while heating from RT−350 °C at a heating rate of 8 °C/min. b, Integrated Ar normalised exit flux of m/z = 44 (CO₂) during TPO experiments on the CO*−covered Pt/SiO₂ catalyst and SiO₂ (blank) where CO* was preadsorbed at RT. Then O₂ was repeatedly pulsed over the catalyst while being linearly heated to 350 °C at 8 °C/min.
+
+Lines 494 – 497 now read:
+
+“A SiO₂ (blank) sample, was also synthesised using the exact same procedure without the addition of the Pt nanoparticles. We find that no Na contamination can be observed on both the Pt/SiO₂ and the SiO₂ (blank) samples (Supplementary Fig. 14) using XPS.”
+
+Lines 539 – 541 now read:
+
+“Minimal activity was recorded over the SiO₂ (blank) sample (Supplementary Fig. 17) meaning the catalytic activity recorded during the TAP experiments is solely prescribed to the Pt nanoparticles.”
+
+Quantification by mass spectrometry is complex. According to the manuscript, the authors normalized the signals from the mass spectrometer with the Ar signal. However, when MS analysis is made, the amount of substance of the analyte may strongly influence quantification; particularly when the sum of the stoichiometric numbers of the reaction is not zero; which is the case for CO oxidation. This causes an increase in the pressure which combined with the fact that tests are being performed at ramped temperatures may strongly affect quantification. Therefore, the authors must discuss the latter in the experimental section of the paper and should discuss how this can affect their data analysis.
+
+It is important to note that in TAP experiment we are not measuring concentration of a gas stream, but instead we are measuring the flux of gas at the reactor exit during a vacuum pressure pulse experiment. Therefore, the non-zero stoichiometry for the reaction is not relevant and does not affect the data analysis. Further, the quantity of reactive gas in each pulse is known by normalising the signal to the inert Ar tracer (which remains at a fixed amount). By comparing the Ar normalised integrated exit flux for the reactive species (O₂, CO, CO₂) to standards measured by pulsing known mixtures of gas over a bed packed with inert sand, it becomes possible to quantify how much reactant/product gas is produced in each pulse. This is outlined in section V of the supplementary information. We realised that the term concentration is misused in the section: Modelling of Temporal Analysis of Products Pulse Responses and have changed line 571 to: “Then, the curves were further normalised to the amount of reactant gas...”.
+In the flow reactor experiments, the total concentration of reactants in the gas stream is 7.5% (balanced in Ar) the maximum conversion is 13% giving <1% maximum error in the total relative concentration due to the non-stoichiometric reaction. This is well within the noise of the mass spectrometer signal and so does not affect our results.
+
+We have included the following statement in the caption of Supplementary Fig. 2.
+
+“The total conversion of reactants relative to the entire gas stream is sufficiently low that any change in relative concentration due to the non-stoichiometric reaction is within the noise of the mass spectrometer signal.”
+
+Although the authors made a reduction treatment of their catalyst, no evidence of the full reduction of the metal is presented.
+
+We understand reviewer #2’s concern regarding the oxidation state of the Pt sample. The combination of an oxidative and reductive treatment at elevated temperatures should be sufficient enough to ensure the Pt is metallic based on previous surface science literature6,7. Further, our CO-DRIFTS spectra match that of metallic Pt, and we record no PtO2-CO binding modes. However, we recognise that perhaps more direct evidence is required. We would also like to emphasise that the H2 treatment is repeated before each experiment to ensure that catalyst is returned to its original state.
+
+We have performed supplemental XPS to identify the oxidation state of the 2 nm Pt/SiO2 catalyst after O2 treatment and after a subsequent H2 treatment at 350 °C in Supplementary Fig. 15. The H2-treated 2 nm Pt/SiO2 catalyst shows the dominant metallic state of Pt (Pt0), according to the previous literature regarding oxidation states of ultra-small sized metallic Pt nanoparticles via XPS analysis8. Lastly, we have investigated additional TAP experiments over the oxidised Pt catalyst which is prepared via O2 treatment at 350 °C. It shows a higher portion of cationic Pt2+ species than that of the H2-pretreated catalyst as shown in Supplementary Fig. 15. Interestingly, the oxidised Pt catalyst shows completely different catalytic behaviour in Supplementary Fig. 18, indicative of higher catalytic activity at low temperatures (i.e., a lower onset temperature of CO* conversion) and less amount of total CO* intake. Thus, we conclude that the H2-treated Pt/SiO2 catalyst has a metallic Pt surface.
+
+![XPS measurements for Pt 4f core-level spectrum of the Pt/SiO2 catalyst after O2 treatment and after a subsequent H2 treatment at 350 °C.](page_393_1042_668_482.png)
+
+Supplementary Figure 15. XPS measurements for Pt 4f/core-level spectrum of the Pt/SiO2 catalyst after O2 treatment and after a subsequent H2 treatment at 350 °C.
+Supplementary Figure 18. a, Flow chart about the description of four catalysts; the Pt/SiO₂ catalysts prepared by (1) H₂, (2) O₂ pretreatment, CO oxidation (RT–350°C–RT), and CO oxidation (RT–200 °C–RT) are regards to metallic Pt, bulk oxidised Pt, spent Pt, and partially spent Pt catalysts, respectively. b, Temperature-dependent integrated exit flux of m/z = 44 (CO₂) normalised via Ar on the CO⁺-covered Pt/SiO₂ catalysts (the metallic Pt, bulk oxidised Pt, spent Pt, and partially spent Pt) for CO oxidation (6.6% CO 13.4% O₂ gas mixture in an inert Ar tracer); CO⁺ was preadsorbed at 25 °C while heating from RT–200 °C at a heating rate of 8 °C/min.
+
+Lines 526 – 530 now read:
+
+“After injecting a series of O₂ pulses at 350 °C, the surface of Pt catalyst was oxidised (Supplementary Fig. 15). So, before all pulse/transient response experiments, the Pt/SiO₂ catalyst is reduced at 350 °C by injecting 600 pulse sets of large H₂ pulses (160 μs pulse width) to achieve a metallic Pt surface (Supplementary Fig. 15).”
+
+Lines 541 – 542 now read:
+
+“The effect of the oxidation of the Pt catalyst during the CO oxidation and TPO experiments below 200 °C can be ruled out in this work (See Supplementary VI).”
+
+In addition, literature has presented evidence on the fact that traces of carbonaceous species may remain tightly bound to supported noble metal catalysts even after oxidation treatments. In particular, unpublished results from our lab have shown supported platinum catalysts that undergo oxidation
+treatments followed by reductions treatments produce methane during the latter. This can, of course, be due to impurities in the gas fed to the reactor. The authors should then ensure that such effects are not affecting their analysis.
+
+We agree that it is challenging to completely remove carbonaceous species from the Pt catalyst, particularly when only using an oxidative treatment. As predicted, we see a trace amount of CH$_4$ produced when pulsing H$_2$ over the O$_2$ treated catalyst (Supplementary Fig. 16a), but after our H$_2$ pretreatment we see that the CH$_4$ signal is completely removed (Supplementary Fig. 16b). As we always perform a H$_2$ treatment after the oxidative treatments, this is a very strong indication that any carbonaceous species on the catalyst are not affecting our analysis.
+
+![Argon normalised exit flux curves for CH4 before and after H2 treatment at 350 °C](page_370_563_1002_388.png)
+
+Supplementary Figure 16. a,b. Argon normalised exit flux curves of m/z = 16 (CH$_4$) for a pulse set of 20% of H$_2$ gas in an inert Ar tracer at 350 °C over oxidised Pt/SiO$_2$ catalyst (underwent O$_2$-treatment at 350 °C) (a) before and (b) after H$_2$ treatment. The lack of CH$_4$ production indicates that no carbonaceous species can be detected on the catalyst after the combined O$_2$ and H$_2$ treatments.
+
+Lines 530 – 531 now read:
+
+“After the combination of the O$_2$ and the H$_2$ treatments we find that no carbonaceous species can be detected on the Pt catalyst (Supplementary Fig. 16).”
+
+According to the paper, catalytic tests were made with an O$_2$ to CO ratio ~ 2 which is four times higher than the stoichiometric ratio for the reaction. Why did you make this choice? What would be effect of changing this ratio on the presented conclusions? Would the two claimed mechanisms exist under both the stoichiometric and an under-stoichiometric reaction ratio?
+
+We chose an O$_2$ to CO ratio ~2 to investigate the catalytic behaviour of pre-adsorbed CO* during reaction. The excess O$_2$ in the reactant can be used to act as a titrant for pre-adsorbed CO* and minimises CO re-adsorption to effectively probe the catalytic reactivity as a function of CO* coverage. In short, this is a TPO experiment while under reaction conditions. Additional isotope experiments were performed using a stoichiometric 2:1 CO:O$_2$ ratio and CO rich 3:1 CO:O$_2$ ratio (Fig. R1), but under these conditions the adsorption of $^{13}$CO inhibits the conversion of preadsorbed $^{13}$CO* by maintaining a high coverage during the reaction. Further, we find that the $^{13}$CO can place exchange with the adsorbed $^{13}$CO* (Fig. R2). As we were interested in probing the reactivity as a function of CO* coverage, the CO:O$_2$ ratio of 1:2 was chosen. Further analysis on this dataset is being performed as it is very interesting, but it is outside the scope of this work which is focused on identifying the active sites for the reaction between CO* and O*.
+Figure R1. a,b, Temperature-dependent integrated exit flux of m/z = 44 (CO₂) and m/z = 45 (¹³CO₂) normalised via Ar from the TAP experiment where (a) stoichiometric (2:1 molar ratio, 13.3% CO 6.6% O₂), and (b) carbon monoxide rich (CO/O₂ = 3:1 molar ratio, 15.0% CO 5.0% O₂) were pulsed over a ¹³CO*-covered Pt/SiO₂ catalyst while heating from RT–350 °C at a heating rate of 8 °C/min.
+
+Figure R2. a, Integrated Ar normalised exit flux of m/z = 29 (¹³CO) during the ¹³CO adsorption via consecutive ¹³CO pulses at 100 °C. b, Integrated Ar normalised exit flux of m/z = 29 (¹³CO) and m/z = 28 (¹²CO) during the consecutive ¹²CO pulsing over the ¹³CO*-covered Pt/SiO₂ catalyst at 100 °C.
+
+The data for the apparent activation energy presented in Figure 2a suggests an alternative interpretation from the one provided by the authors. Indeed, the authors claim that all their data is fitted by a linear curve, but the dispersion of the data is strong starting around 1/RT ~ 0.282 mol/KJ. On the one hand, this suggests that the statistics of the data after such a value require very careful checking of influence of the correlation effects over the data. On the other hand, this indicates that reaction regime is modified after some temperature. This does not necessarily imply a new mechanism because heat transport artifacts may strongly influence the measured kinetics. And, in the case of the observed effect in Figure 2a, the existence of two different mechanisms when changing the temperature of the catalytic tests seems to contradict the claim of the authors.
+
+The spread in the data at 0.298 mol/KJ (130 °C) to 0.282 mol/KJ (153 °C) is an artifact of the noise present in the mass spec signal at low CO conversions (Supplementary Fig. 2a). The appearance of any poor fit to the linear curve over this temperature range cannot be confidently attributed as a change reaction mechanism as suggested. We have included the temperature programmed reaction spectra in
+Supplementary Fig. 2a to demonstrate the large noise in the QMS data compared to the low CO conversion for the corresponding temperature range as the apparent activation energy data.
+
+![Temperature programmed reaction spectra for CO oxidation over 2 nm Pt/SiO2 from the rate of CO consumption using a heating rate of 5 °C/min (100 ml/min total flow; 2.5%CO, 5%O2) from 100 to 170 °C. Determination of the apparent activation energy from 130 to 160 °C of data in (a). Determination of the reaction order in (c) CO (1.5–3.5%CO, 5 %O2) and (d) O2 (2.5%CO, 3–7%O2) from the rate of CO2 production at 160 °C. The rate of CO2 production was used for determining the reaction orders because of the higher sensitivity to CO2 production than CO consumption at low conversions. The total conversion of reactants relative to the entire gas stream is sufficiently low that any change in relative concentration due to the non-stoichiometric reaction is within the noise of the mass spectrometer signal.](page_184_312_1080_1012.png)
+
+Supplementary Figure 2. a, Temperature programmed reaction spectra for CO oxidation over 2 nm Pt/SiO2 from the rate of CO consumption using a heating rate of 5 °C/min (100 ml/min total flow; 2.5%CO, 5%O2) from 100 to 170 °C. b, Determination of the apparent activation energy from 130 to 160 °C of data in (a). c,d, Determination of the reaction order in (c) CO (1.5–3.5%CO, 5 %O2) and (d) O2 (2.5%CO, 3–7%O2) from the rate of CO2 production at 160 °C. The rate of CO2 production was used for determining the reaction orders because of the higher sensitivity to CO2 production than CO consumption at low conversions. The total conversion of reactants relative to the entire gas stream is sufficiently low that any change in relative concentration due to the non-stoichiometric reaction is within the noise of the mass spectrometer signal.
+
+Other minor concerns are:
+
+(i) The description of the experiments is often times incomplete so one may have problems trying to reproduce the work of the authors. First, although the techniques used for the characterization of the catalyst are kind of rutinary for catalysis researchers, every laboratory uses some slight modifications when performing them and this hinders reproducibility. Therefore, I recommend including full details of the presented experiments in the Supplementary Information of the paper. Please, do not make the reader read other papers to understand and reproduce your experiments.
+
+We have expanded upon our description of the experiments and provided more specificities as requested. We have also included a new section in the supplemental (IV) which outlines the specific way we pack our flow reactor system to assist with reproducibility. While we recognise it is frustrating to have to read papers to understand experimental methods, we hope the reviewer can sympathise that this paper
+is already significant in length and as such a full description of every component used in our systems is far outside the scope of this work.
+
+(ii) The “error” bars presented for the data in Supplementary Figures does not allow understanding the data. Please, make these plots clearer. Also, you may include a Table for reporting the statistics of the measurements.
+
+We would like to specify that the bars represent the 95% confidence intervals from the regression of the rate constants as mentioned in “Modelling of Temporal Analysis of Products Experiments” lines 582 – 584. We do recognise that they are difficult to see due to the transparency (particularly after being compressed) and so we have made them less transparent and clearer.
+
+(iii) How did you measure the flux of the products of the reactor? Typically, flux refers to a quantity per area of flow. What was the area of flow?
+
+The flux of the gas at the reactor exit is measured by a mass spectrometer mounted directly beneath the microreactor. The area of flow is the surface area of the exit of the microreactor.
+
+(iv) The first paragraph of the introduction of the paper seems to suggest that the method developed by the authors will fill the gap between laboratory catalysts and technical catalysts. I am sure that the authors are aware of the fact that the latter are multicomponent formulations whose behavior in industrial units cannot be understood only from chemical kinetics on powders. Therefore, I suggest that the authors take this into account for modifying the paragraph.
+
+Industrial catalysts are indeed far more complicated than laboratory catalysts. However, if the sample can be pelletised and crushed into a powder, then there is no practical reason why it cannot be placed into the TAP reactor. While the analysis would be complex, it is not impossible.
+
+While catalytic behaviour cannot be purely understood from chemical kinetics on powders, it is the chemical kinetics itself that is the foundation of any complex modelling of an industrial reactor as it is the chemistry that largely drives the heat and mass transfer limitations. However, we recognise that the entire process is more complex than simply kinetics and on line 26 have reworded industrial processes to industrial reactions.
+Reviewer #3
+
+Authors report the synthesis of Pt/SiO2 catalyst using polymer stabilized polyol method. This catalyst contains ca.2nm Pt nanoparticles and these materials have been tested for CO oxidation. Fundamental studies on the kinetics of this reaction have been done in a TAP reactor. The authors have done an excellent study on the site dependency of the kinetics of CO oxidation using two different Pt nanoparticles sites (well coordinated and under coordinated sites) on a practical catalyst. The results are interesting and are of fundamental importance. It is a very well written article. Typically support materials play an important role in CO oxidation, however here the whole discussion is on Pt sites. I appreciate it is a SiO2 support. Authors can comment on the versatility of this methodology for other catalytic systems where support play an active role in the catalysis.
+
+We thank the reviewer for their positive feedback on the manuscript. We agree that a broader perspective on the application of the method is required, and we have expanded the manuscript to include one.
+
+Lines 456 – 472 now read:
+
+“The use of probe molecules to titrate catalytically active sites is commonplace in heterogeneous catalysis research1. Using molecules such as CO, H2, or N2O for metal sites, NH3 or pyridine for zeolites, and O2 for oxygen vacancies it becomes possible to count the number of active centres on a catalyst. By performing these experiments in a TAP reactor and coupling them with Multi-Zone TAP Reactor Theory it becomes possible to not only quantify the number of sites, but simultaneously measure their catalytic activity for simple probe reactions (e.g., the oxidation of CO). As the activity for a given probe reaction is directly related to the environment in which that probe molecule is adsorbed, the intrinsic rate constant for the rate of transformation of that species provides a fingerprint of that specific site. Using the kinetic site deconvolution method outlined in this work it then becomes possible to not only count the total number of sites, but to also count the number and distribution of different sites on the catalyst. This allows the structural characterization of catalysts allowing insight regarding size-effects (from a single atom to bulk catalyst) and support-effects, but it also opens up the possibility of rationalising how catalysts dynamically restructure by seeing how the number of sites and the intrinsic rate constants of the probe reactions are modified based on the catalyst state. While this methodology is still in its infancy, we believe that this new approach is general enough to apply to other catalytic systems and can serve as a new toolkit in the characterisation of heterogeneous catalysts.”
+Reviewer #4
+
+The manuscript reports an interesting and well-constructed kinetic and spectroscopic investigation of the oxidation of CO on Pt supported over silica. The conclusions of the study propose that at least two parallel reaction pathways are taking place on Pt, related to sites with different coordinations. Although Pt/SiO2 is effectively a purely academic catalyst with activity far lower than that of redox oxide-supported materials, the results underlines new methodologies to investigate this reaction and will appeal to the community.
+
+We thank the reviewer for their positive feedback on the manuscript. Pt/SiO2 is certainly an academic catalyst, and (perhaps ironically) we chose the catalyst to develop our kinetic site deconvolution technique due to it’s supposed “simplicity”!
+
+The main shortcoming of the paper resides in the data analysis that does not take into account the potential bulk oxidation of Pt at low CO coverages or O2 excess pulses. This could explain the third irreversible adsorption pathway for O2 (line 214), rather than mere surface adsorption. To this respect, the work of van Bokhoven’s group on the oxidic nature of the Pt phase at low CO coverage/high temperature should be cited and discussed in the present paper (Angew. Chem. Int. Ed. 2008, 47, 9260–9264). The simultaneous presence of reduced and oxidised Pt phases during low temperature CO oxidation has also been reported and emphasises the complex evolution of Pt phases that may occur when reaction conditions are changed (e.g. Meunier et al, Angew. Chem. Int. Ed. 2021, 60, 3799 – 3805). This may thus relate to the potential changes of Pt structure as hypothesised by the authors on line 418.
+
+I therefore suggest that Pt bulk oxidation should be considered and discussed in the data analysis and model.
+
+We agree with reviewer #4 that the bulk oxidation of Pt is of extreme importance and thank them for their very insightful feedback. As described in both papers (Angew. Chem. Int. Ed. 2008, 47, 9260–9264 and Angew. Chem. Int. Ed. 2021, 60, 3799–3805), the reactivity for CO oxidation over the Pt/SiO2 is quite different on the oxidised and metallic Pt surface. The O2-rich reaction gas mixture (O2/CO = 2) in this work has a similar ratio to the condition that the reviewer mentioned (low CO coverages and excess O2 molecules), which potentially makes the bulk oxidation of Pt relevant under steady-state conditions.
+
+We have performed additional TAP experiments over the oxidised Pt catalyst which is prepared via O2 treatment at 350 °C. It shows a higher portion of cationic Pt2+ species than that of the H2-treated catalyst (see Supplementary Fig. 15). As we expected, the oxidised Pt catalyst shows completely different catalytic behaviour compared to metallic Pt (see Supplementary Fig. 18), demonstrating higher catalytic activity at low temperatures (i.e., a lower onset temperature of CO* conversion). Notably, based on their distinguishable catalytic activity on the oxidised and metallic Pt surface, we can use this to approximate the oxidation state of Pt (e.g., bulk oxidised, partially oxidized, and metallic). To determine when oxidation begins during the CO reaction, we measured the catalytic performance for CO oxidation over the CO*-covered Pt/SiO2 for the spent Pt (25–350 °C) and partially spent Pt (25–200 °C). The spent Pt shows similar results to that of the bulk oxidised Pt and the partially spent Pt exhibits similar results to that of the metallic Pt. Therefore, we conclude that Pt nanoparticles are metallic until at least 200 °C. Although this is not a direct spectroscopic measurement, it can serve as an indicator to define surface states via their distinguishable reactivities. Thus, we can justify our methodology is effective up to at least 200 °C without oxidation effect. In the original paper draft in the caption of Figure 7 we mention that “When the production of CO2 is sufficiently low in the TPO experiment (> 200 °C) the signal/noise ratio of the CO2 exit flux curves significantly decreases, which in turn decreases the confidence in the model fitting, particularly for pathway 2, as shown in Supplementary Fig. 12.” in the caption of Fig. 7. We now think the oxidation of Pt most likely also plays a role in the decreased confidence of the model fitting and have adjusted the caption for Figure 7, so it now reads:
+“When the production of CO₂ is sufficiently low in the TPO experiment (> 200 °C) the signal/noise ratio of the CO₂ exit flux curves significantly decreases, and the oxidation state of Pt is uncertain (see Supplementary VI), which in turn decreases the confidence in the model fitting, particularly for pathway 2, as shown in Supplementary Fig. 12.”
+
+The Pt catalyst almost certainly gets oxidised at high temperature (> 200 °C) in the TPO experiment, but as H₂ treatments were preformed between every experiment we rule out the oxidation effect in this work.
+
+Regarding line 418, as we see now have evidence of no direct oxidation of the Pt below 200 °C we do not believe that this is facilitating the change in rate constant that we observe at 100 °C.
+
+![XPS measurements for Pt 4f core-level spectrum of the Pt/SiO₂ catalyst treated in H₂ and O₂ at 350 °C.](page_370_629_1002_496.png)
+
+Supplementary Figure 15. XPS measurements for Pt 4f core-level spectrum of the Pt/SiO₂ catalyst treated in H₂ and O₂ at 350 °C.
+
+Lines 540 – 541 now read:
+
+“The effect of the oxidation of the Pt catalyst during the CO oxidation and TPO experiments below 200 °C can be ruled out in this work (See Supplementary VI).”
+Supplementary Figure 18. a, Flow chart about the description of four catalysts; the Pt/SiO2 catalysts prepared by (1) H2, (2) O2 pretreatment, CO oxidation (RT–350°C–RT), and CO oxidation (RT–200 °C–RT) are regards to metallic Pt, bulk oxidized Pt, spent Pt, and partially spent Pt catalysts, respectively. b, Temperature-dependent integrated exit flux of m/z = 44 (CO2) normalised via Ar on the CO*-covered Pt/SiO2 catalysts (the metallic Pt, bulk oxidised Pt, spent Pt, and partially spent Pt) for CO oxidation (6.6% CO 13.4% O2 gas mixture in an inert Ar tracer); CO* was preadsorbed at 25 °C while heating from RT–200 °C at a heating rate of 8 °C/min.
+
+Minor point: line 98: CO reaction order is -1, not +1, please correct.
+
+We thank reviewer #4 for pointing out this mistake. We have corrected the reaction order in CO to –1.02.
+1. Vogt, C. & Weckhuysen, B. M. The concept of active site in heterogeneous catalysis. Nat. Rev. Chem. **6**, 89–111 (2022).
+
+2. Newton, M. A., Ferri, D., Smolentsev, G., Marchionni, V. & Nachtegaal, M. Room-temperature carbon monoxide oxidation by oxygen over Pt/Al$_2$O$_3$ mediated by reactive platinum carbonates. Nat. Commun. **6**, 8675 (2015).
+
+3. Allian, A. D. *et al.* Chemisorption of CO and mechanism of CO oxidation on supported platinum nanoclusters. *J. Am. Chem. Soc.* **133**, 4498–4517 (2011).
+
+4. Gleaves, J. T., Yablonskii, G. S., Phanawadee, P. & Schuurman, Y. TAP-2: An interrogative kinetics approach. *Appl. Catal. A-Gen.* **160**, 55–88 (1997).
+
+5. Constales, D., Yablonsky, G. S., Marin, G. B. & Gleaves, J. T. Multi-zone TAP-reactors theory and application: I. The global transfer matrix equation. *Chem. Eng. Sci.* **56**, 133–149 (2001).
+
+6. Miller, D. J. *et al.* Oxidation of Pt(111) under near-ambient conditions. *Phys. Rev. Lett.* **107**, 195502 (2011).
+
+7. Porsgaard, S. *et al.* Stability of platinum nanoparticles supported on SiO$_2$/Si(111): a high-pressure X-ray photoelectron spectroscopy study. *ACS Nano* **6**, 10743–10749 (2012).
+
+8. Wang, H. *et al.* Influence of size-induced oxidation state of platinum nanoparticles on selectivity and activity in catalytic methanol oxidation in the gas phase. *Nano Lett.* **13**, 2976–2979 (2013).
+
+9. Meunier, F. C. *et al.* Synergy between metallic and oxidized Pt sites unravelled during room temperature CO oxidation on Pt/Ceria. *Angew. Chem. Int. Ed.* **60**, 3799–3805 (2021).
+REVIEWER COMMENTS
+
+Reviewer #1 (Remarks to the Author):
+
+I agree with publication of this work in the present state
+
+Reviewer #2 (Remarks to the Author):
+
+I have well received the authors' rebuttal to my queries. I appreciate their efforts and value their consideration. I keep my initial view that the paper is very interesting and I add that it'd be very useful in future catalytic endeavors. However, risking being perceived as the now (in)famous reviewer#2 -which, according to my luck with the editorial system, I actually am!!!, I have to insist on the following issues:
+1. Please, describe experimental techniques with sufficient detail. I agree that the manuscript is already a bit extensive, but experimental details can be placed in the SI where the interested reader can find them. The need for such detail in describing experiments cannot be further insisted upon when reproducibility issues are hotly debated in the literature (and even in the media!), please read: https://nap.nationalacademies.org/catalog/25303/reproducibility-and-replicability-in-science, https://onlinelibrary.wiley.com/doi/full/10.1002/anie.201606591,
+https://www.annualreviews.org/doi/abs/10.1146/annurev-chembioeng-060718-030323.
+2. The following guidelines on reporting XPS measurements should be followed:
+https://avs.scitation.org/doi/10.1116/1.5065501, https://avs.scitation.org/doi/10.1116/1.5140747,
+https://avs.scitation.org/doi/10.1116/6.0000661, https://avs.scitation.org/doi/10.1116/6.0000685,
+https://avs.scitation.org/doi/10.1116/6.0000377.
+3. The following guidelines on reporting physisorption experiments should be followed:
+https://www.degruyter.com/document/doi/10.1515/pac-2014-1117/html?lang=en. The experimental part should at least tell the following: (1) range of P/P0 used for tests, (2) number of data points recorded during the tests, (3) equilibration time, (4) procedure adopted for BET fitting -include CBET values in the report-, (5) Standard deviation of measurements. (6) Amounts of material for tests. (7) Outgassing procedure.
+4. Concerning BET surface area, please include its value in the paper. According to the paper by Gleaves (App Catal A: Gen 160 (1997) 55) -that the authors cited in their rebuttal-: "Assuming a catalyst sample has a surface area of 10 m'/g, a single pulse would be equivalent to l/l 000 000 of the total surface area of a 0.1 g sample. If the active surface area of the catalyst comprises a reasonable fraction (e.g., 20.1%) of the total surface area of the catalyst, then a single pulse will have a negligible effect on the active surface." Accordingly, I consider important to inform the reader whether the above assumption is fulfilled by the catalyst studied in the paper. I have to say that the reader needs to be informed of such details. By the way, formally, the SiO2 support featured in the paper is non-nanoporous rather than "non-porous".
+5. I thank the authors for suggesting the excellent papers by Gleaves & Constales et al. It was a very interesting and instructive read. However, after reading them, I don't know if I misread these papers, but
+the statement: "As the primary transport mechanism is Knudsen diffusion any mass transfer effects can be minimised." made by the authors seems contradictory since the modelling of the TAP reactor considered by Gleaves actually includes mass transport effects. What the method claims is that diffusion constants can be discerned from apparent reaction constants after modelling. This then needs clarification.
+6. Although TAP modelling was beautifully done by previous authors, it seems that some well established facts of mass transfer have not been considered so far. Particularly, the fact that "Bulk and Knudsen diffusion mechanisms occur together and it is prudent to take both mechanisms into account rather than assume that one or other mechanism is 'controlling'." -Krishna & Wesselingh, Chem Eng Sci 52 (1997) 861. Therefore, I recommend the authors being more prudence when making categorical statements about mass transport in the TAP reactor.
+7. Concerning heat transport, the argument posed by the authors makes sense. But making sense does not constitute scientific proof. This particular issue is sensitive to the analysis of the TAP data because, once again according to Gleaves et al, the following assumptions are made when modelling the reactor: "The basis of the one-zone-model is the following [...] assumptions: [...] 2. There is no radial gradient of concentration in the catalyst bed. [...] 3. There is no axial or radial temperature gradient in the catalyst bed. [...]." Therefore, from the start, no heat transfer limitations are assumed -not proved!- for the experiments. Therefore, once again, I recommend being more prudent with the pen in the manuscript.
+8. Concerning the analysis of XPS data, it is important to recall that 3 nm is considered to be the average depth for XPS made on a homogeneous sample. For multicomponent samples however, the depth of analysis depends on the particular elements of the sample and on the power at which the X-ray source is operated. Therefore, one may not directly conclude that the XPS data for a Pt/SiO2 sample is "bulk". For prudence sake, one may rather say that XPS analysis is near-surface.
+9. Concerning the results obtained with the SiO2 support, "Minimal activity" is not the same as "zero activity". Therefore, again, prudence is advised. The conclusion should be toned down to say that most of the activity of the Pt/SiO2 can be attributed to Pt neglecting its possible synergistic interactions with the SiO2 support. There is plenty of evidence of the latter in the literature (e.g. https://www.sciencedirect.com/science/article/pii/S0021951722004675; https://www.sciencedirect.com/science/article/pii/S0920586118310344 + others).
+10. Concerning flux and concentration, I guess that flux is either the quantity of mass (or moles) per unit transport area which is (in a more general sense) the concentration of a given compound -or element- per unit area. Isn't it? Therefore, saying that "we are not measuring concentration of a gas stream, but instead measuring the flux of gas..." appears confusing. Therefore, I ask the authors to be a bit clearer about their definitions. Also, what is the "transport area" to which their flux is referred to?
+11. Concerning the quantification via MS data, the problem is not with the noise but with the changes in baseline of the MS spectra. One may check this in the literature: e.g., J. Vac. Sci. Technol. A 5, 134–139 (1987), J. Am. Soc. Mass Spectrom. 2021, 32, 8, 2135–2143, etc. Therefore, once again a more careful language should be used in the paper.
+12. Concerning the chemical state of Pt after reduction, XPS data dictates prudence, once again, because what one sees is that after H2 treatment some fraction of Pt maybe remain oxidized. However, the low intensity of the presented Pt 4f (?) hinders interpretation. Also, I guess that authors meant "Partially spent Pt" in Figure SI-18.a
+13. The justification for using the selected O2-CO ratio of the work should be mentioned in the revised paper.
+14. Concerning data fitting for estimating apparent activation energies, the response provided by the authors reaffirms the need to make covariance analysis of the data. This is due to the fact that conventional regression models are inherently based on normal distribution of data. It is suggested that the authors make a covariance analysis of the data:
+https://en.wikipedia.org/wiki/Analysis_of_covariance
+Design and analysis: A researcher’s handbook (3rd ed.). Prentice-Hall, Inc.
+
+I hope that the authors receive the above suggestions in a positive sense since I only do them in the spirit of helping improving the quality of the paper.
+
+Reviewer #3 (Remarks to the Author):
+
+Authors have revised the manuscript satisfactorily and all the points raised by the reviewer have been addressed. Now this manuscript can be accepted for publication.
+
+Reviewer #4 (Remarks to the Author):
+
+The authors have answered adequately to my earlier concerns and I believe that the present manuscript is sound and brings about a very interesting study and method to discriminate parallel reaction pathways on catalysts.
+REVIEWER COMMENTS
+
+Reviewer #1:
+
+I agree with publication of this work in the present state.
+
+Reviewer #3:
+
+Authors have revised the manuscript satisfactorily and all the points raised by the reviewer have been addressed. Now this manuscript can be accepted for publication.
+
+Reviewer #4:
+
+The authors have answered adequately to my earlier concerns, and I believe that the present manuscript is sound and brings about a very interesting study and method to discriminate parallel reaction pathways on catalysts.
+
+We would like to thank reviewers #1, #3, and #4 for their time and are glad that our changes to the manuscript were sufficient.
+
+Reviewer #2:
+
+I have well received the authors' rebuttal to my queries. I appreciate their efforts and value their consideration. I keep my initial view that the paper is very interesting and I add that it’d be very useful in future catalytic endeavors. However, risking being perceived as the now (in)famous reviewer#2 -which, according to my luck with the editorial system, I actually am!!!, I have to insist on the following issues:
+
+1. Please, describe experimental techniques with sufficient detail. I agree that the manuscript is already a bit extensive, but experimental details can be placed in the SI where the interested reader can find them. The need for such detail in describing experiments cannot be further insisted upon when reproducibility issues are hotly debated in the literature (and even in the media!), please read: https://nap.nationalacademies.org/catalog/25303/reproducibility-and-replicability-in-science, https://onlinelibrary.wiley.com/doi/full/10.1002/anie.201606591, https://www.annualreviews.org/doi/abs/10.1146/annurev-chembioeng-060718-030323.
+
+We completely agree that reproducibility is important in catalysis. However, in lieu of any specific suggestions from reviewer #2 we are confident that the methods and analysis are described sufficiently that a researcher in heterogeneous catalysis could reproduce the results.
+
+2. The following guidelines on reporting XPS measurements should be followed: https://avs.scitation.org/doi/10.1116/1.5065501, https://avs.scitation.org/doi/10.1116/1.5140747, https://avs.scitation.org/doi/10.1116/6.0000661, https://avs.scitation.org/doi/10.1116/6.0000685, https://avs.scitation.org/doi/10.1116/6.0000377.
+
+We have added the following statement to clarify the XPS sample preparation which missing in the revised manuscript:
+The XPS sample pretreatments were performed in the DRIFTS reactor and resultant catalyst powder was pressed onto a carbon tape mounted on a Si wafer for each XPS measurement.”
+
+All other reporting of the XPS data falls within the community guidelines.
+
+3. The following guidelines on reporting physisorption experiments should be followed: https://www.degruyter.com/document/doi/10.1515/pac-2014-1117/html?lang=en. The experimental part should at least tell the following: (1) range of P/P0 used for tests, (2) number of data points recorded during the tests, (3) equilibration time, (4) procedure adopted for BET fitting -include CBET values in the report-, (5) Standard deviation of measurements. (6) Amounts of material for tests. (7) Outgassing procedure.
+
+We have included the P/P0 range, the number of data points, equilibration time, standard deviation of measurements, amount of material for tests, model used for BET fitting, and the outgassing procedure in the figure caption so that it now reads:
+
+“Supplementary Figure 13. N2 adsorption isotherm plot for SiO2 support material demonstrating non-nanoporous/macroporous behaviour. BET Measurements were performed using a micrometrics 3flex adsorption analyser. Pressure range: 0 – 1000 mbar, number of data points recorded: 62, equilibration interval: 10 to 45s, standard deviation of fit: 1.735 mmol/g. sample mass: 40 mg. BET Surface area: 514 m²/g. model: N2 - Tarazona NLDFT, Esf = 30.0K. The sample was degassed at 160 °C under vacuum (10⁻³ torr) for 600 min.”
+
+4. Concerning BET surface area, please include its value in the paper. According to the paper by Gleaves (App Catal A: Gen 160 (1997) 55) -that the authors cited in their rebuttal-: "Assuming a catalyst sample has a surface area of 10 m²/g, a single pulse would be equivalent to 1/1 000 000 of the total surface area of a 0.1 g sample. If the active surface area of the catalyst comprises a reasonable fraction (e.g., 20.1%) of the total surface area of the catalyst, then a single pulse will have a negligible effect on the active surface." Accordingly, I consider important to inform the reader whether the above assumption is fulfilled by the catalyst studied in the paper. I have to say that the reader needs to be informed of such details.
+
+The TAP experiment is considered to be state defining if a single pulse has negligible impact on the active surface. We direct the reviewer to Supplementary Figure 7a which demonstrates it takes ~400 pulses of reactant gas to saturate the surface in CO, and Figures 3a and 3b where it takes 200 pulse sets (600 pulses) to remove the adsorbed CO. While there is no specific definition of what constitutes as “state defining” we are confident this experiment fulfils that requirement and have added the line:
+
+“Given the large number of pulses required to saturate/titrate the catalyst surface, the experiments fall well-within the “state defining” regime as required by the MZTRT model.”
+
+We would like to state that the BET surface area is not relevant to the total number of active sites and therefore can be misleading and as such we made a conscious choice to not include the data. Further, we do not report any site-normalised activity data (e.g., turnover frequencies). However, the BET surface area of our support material is reported in the caption to Supplementary Figure 13.
+
+By the way, formally, the SiO2 support featured in the paper is non-nanoporous rather than "non-porous".
+Reviewer #2 is correct, and we have re-worded non-porous to non-nanoporous
+
+5. I thank the authors for suggesting the excellent papers by Gleaves & Constales et al. It was a very interesting and instructive read. However, after reading them, I don't know if I misread these papers, but the statement: "As the primary transport mechanism is Knudsen diffusion any mass transfer effects can be minimised." made by the authors seems contradictory since the modelling of the TAP reactor considered by Gleaves actually includes mass transport effects. What the method claims is that diffusion constants can be discerned from apparent reaction constants after modelling. This then needs clarification.
+
+The primary mass transfer mechanism is Knudsen diffusion, which is precisely described by the 1D diffusion model. Differing from a conventional flow experiment at elevated conversions where the mass transfer is not precisely described and can adversely affect the calculation of kinetics, in the TAP 1D model the transport (mass transfer) is precisely described and the kinetics we calculate are not correlated to the mass transfer mechanism. As it seems that this line has caused some confusion, we have decided to remove it instead.
+
+6. Although TAP modelling was beautifully done by previous authors, it seems that some well established facts of mass transfer have not been considered so far. Particularly, the fact that "Bulk and Knudsen diffusion mechanisms occur together and it is prudent to take both mechanisms into account rather than assume that one or other mechanism is 'controlling!'" - Krishna & Wesselingh, Chem Eng Sci 52 (1997) 861. Therefore, I recommend the authors being more prudence when making categorical statements about mass transport in the TAP reactor.
+
+While increasingly complex models may model the physics of a TAP reactor under a wider range of boundary conditions, the model currently employed captures all the physics relevant to the TAP experiment as we apply it as we precisely recreate the transient behaviour of our inert tracer (see Figure 4b). It is not the purview of this paper to precisely describe the physics (and the limitations) of the TAP experiment which has been described extensively in the previous literature that is cited in this work. As such, we feel a reference to the many papers where this has been discussed is more than sufficient. If the author would like a full description of how non-ideal conditions effect TAP reactor systems, we direct them to the fantastic work of Constales (https://doi.org/10.1016/j.ces.2005.10.022), where they empirically demonstrate that the 1D model is valid for a wide range of conditions, which our experiment falls well within, please see our previous publication on the TAP reactor design utilised in this work where we demonstrate that the 1D model is indeed fulfilled (https://doi.org/10.1016/j.cej.2023.147489).
+
+7. Concerning heat transport, the argument posed by the authors makes sense. But making sense does not constitute scientific proof. This particular issue is sensitive to the analysis of the TAP data because, once again according to Gleaves et al, the following assumptions are made when modelling the reactor: "The basis of the one-zone-model is the following [...] assumptions: [...]2. There is no radial gradient of concentration in the catalyst bed. [...] 3. There is no axial or radial temperature gradient in the catalyst bed. [...]" Therefore, from the start, no heat transfer limitations are assumed -not proved!- for the experiments. Therefore, once again, I recommend being more prudent with the pen in the manuscript.
+
+We measure the temperature of our catalyst using a thermocouple inserted into the catalyst bed, which is very thin, meaning that we are confident in the accuracy of our temperature measurement of our catalyst. Given the highly complex nature of the TAP reactor, and small size of the microreactor housing the catalyst, it is not physically possible to insert multiple
+thermocouples and/or a calorimeter inside our catalyst bed to confirm that there are no heat thermal gradients. However, we would like to direct reviewer #2 to Figure 4b. Our transport curves are reproduced precisely by the thin-zone (an extension of the one-zone) model. If there were any significant temperature gradients observed in the experiment, by definition the model would not apply, which is not the case here. It is not feasible to remove all temperature gradients in an experiment but given that we are able to precisely describe the transport using the 1D model, and that we measure the temperature of our catalyst directly, we are confident in its validity. While making sense does not constitute a scientific proof, in the absence of idealised system, it is more than sufficient.
+
+8. Concerning the analysis of XPS data, it is important to recall that 3 nm is considered to be the average depth for XPS made on a homogeneous sample. For multicomponent samples however, the depth of analysis depends on the particular elements of the sample and on the power at which the X-ray source is operated. Therefore, one may not directly conclude that the XPS data for a Pt/SiO2 sample is "bulk". For prudence sake, one may rather say that XPS analysis is near-surface.
+
+We would like to clarify that we do not mention that the XPS measurement is a “bulk” measurement in the manuscript but state in the revision comments:
+
+“We consider the XPS measurement to be a bulk chemical analysis for the 2 nm Pt nanoparticles because the XPS probing depth is ~3 nm using an Al Kα X-ray source.”
+
+We want to clarify in the statement that a probing depth of ~3nm does indeed probe the bulk region of 2 nm Pt nanoparticles (~1 nm depth). It is well established that the mean free path of electrons slightly changes through different elemental samples (https://doi.org/10.1002/sia.740010103) but this does not affect our original assessment (https://doi.org/10.1002/sia.5789).
+
+9. Concerning the results obtained with the SiO2 support, "Minimal activity" is not the same as "zero activity". Therefore, again, prudence is advised. The conclusion should be toned down to say that most of the activity of the Pt/SiO2 can be attributed to Pt neglecting its possible synergistic interactions with the SiO2 support. There is plenty of evidence of the latter in the literature (e.g. https://www.sciencedirect.com/science/article/pii/S0021951722004675; https://www.sciencedirect.com/science/article/pii/S0920586118310344 + others).
+
+The first paper is discussing the role that SiO2 plays in hydrogen spillover, which is not relevant to CO oxidation. The second paper talks about the role of synergistic physical mixtures of catalytically active materials – not catalysts and inert supports. We are very confident in the inert nature of our SiO2 support material, particularly for the TPO experiments which constitute the core part of this work, we have however reworded the sentence so that it is clearer now reads:
+
+“Minimal activity was recorded over the SiO2 (blank) sample (Supplementary Fig. 17) during co-pulsed experiments, with zero activity recorded during a TPO experiment, meaning the catalytic activity recorded during the TPO experiments is to a solely prescribed to the Pt nanoparticles.”
+
+10. Concerning flux and concentration, I guess that flux is either the quantity of mass (or moles) per unit transport area which is (in a more general sense) the concentration of a given compound -or element- per unit area. Isn't it? Therefore, saying that "we are not measuring concentration of a gas stream, but instead measuring the flux of gas..." appears confusing. Therefore, I ask the
+authors to be a bit clearer about their definitions. Also, what is the "transport area" to which their flux is referred to?
+
+The exit flux is the number of molecules leaving the TAP reactor per unit area per second of the microreactor exit, which is 0.2 cm.
+
+11. Concerning the quantification via MS data, the problem is not with the noise but with the changes in baseline of the MS spectra. One may check this in the literature: e.g., J. Vac. Sci. Technol. A 5, 134-139 (1987), J. Am. Soc. Mass Spectrom. 2021, 32, 8, 2135-2143, etc. Therefore, once again a more careful language should be used in the paper.
+
+We are well aware that mass spectrometry is not a 1:1 relationship between concentration and explicitly describe how we perform our quantification in the supplementary information. In lieu of any specific language being pinpointed by the reviewer, we are happy with our discussion on how we perform our quantitative mass spec.
+
+12. Concerning the chemical state of Pt after reduction, XPS data dictates prudence, once again, because what one sees is that after H2 treatment some fraction of Pt maybe remain oxidized. However, the low intensity of the presented Pt 4f (?) hinders interpretation.
+
+There is no conclusive evidence of a partially oxidized Pt species in our XPS data after a H2 reduction treatment considering the signal to noise ratio (SNR) and peak full width at half maxima (FWHM). We would like to clarify that the relatively high SNR is due to a Pt weight loading of 0.72% which is close to the detection limit of conventional XPS lab-based systems. The implication of this is that an appropriate pass energy (which controls the FWHM) must be set on the detector which allows for sufficient intensity to detect species. Further adjustment of the pass energy to decrease the FWHM in order to be able to determine if this is a minor contribution of partially optimized Pt species is not feasible with our Pt/SiO2 sample on conventional lab based XPS systems. we cannot definitively rule out the presence of partially oxidized Pt by XPS but refer the reviewer to our previous DRIFTS evidence for solely metallic Pt identified in our previous response. We would caution reviewer #2 to not overanalyse noise, which is inherent in every measurement.
+
+With regards to: “the presented Pt 4f (?)”. The caption states that the XPS spectra is of the Pt 4f region.
+
+Also, I guess that authors meant "Partially spent Pt" in Figure SI-18.
+
+We can see no errors with Figure SI-18.
+
+13. The justification for using the selected O2-CO ratio of the work should be mentioned in the revised paper.
+
+We have added the sentence:
+
+“The 1:2 ratio of CO:O2 was chosen to allow excess O2 in the reactant stream to act as a titrant to sequentially remove the preadsorbed CO* to probe the catalytically activity as a function of CO* coverage.”
+
+14. Concerning data fitting for estimating apparent activation energies, the response provided by the authors reaffirms the need to make covariance analysis of the data. This is due to the fact that
+conventional regression models are inherently based on normal distribution of data. It is suggested that the authors make a covariance analysis of the data: https://en.wikipedia.org/wiki/Analysis_of_covariance  Design and analysis: A researcher's handbook (3rd ed.). Prentice-Hall, Inc.
+
+This level of analysis is unnecessary. The linear regression of apparent activation energies is a well-established protocol and is not specific enough to require this level of analysis. Standard line-fitting programs as present in Origin, Excel, MATLAB, or LabVIEW is more than sufficient for this dataset.
+
+We reference the reviewer to recent publications in Nature Communications which demonstrate our analysis is consistent with standard procedures in heterogeneous catalysis research:
+
+https://doi.org/10.1038/s41467-022-28366-w
+https://doi.org/10.1038/s41467-023-36339-w
+https://doi.org/10.1038/s41467-021-22946-y
+
+I hope that the authors receive the above suggestions in a positive sense since I only do them in the spirit of helping improving the quality of the paper.
+REVIEWERS’ COMMENTS
+
+Reviewer #2 (Remarks to the Author):
+
+Dear authors,
+Provided the nature and tone of your responses, I have nothing further to comment about the paper.
+REVIEWER COMMENTS
+
+Reviewer #2:
+
+Dear authors,
+
+Provided the nature and tone of your responses, I have nothing further to comment about the paper.
+
+We recognise that it is not easy to perform a robust and rigorous peer review. The feedback has significantly helped with readership and providing the required information for others to reproduce this work. As such, we would like to thank reviewer #2 for their extensive effort in reviewing this paper.

0eccaef55dcb59ca1b81c7f04d09c150ba54c7571b656e22e7118c670e4141a7/preprint/preprint.md

@@ -0,0 +1,335 @@
+Interrogating Site Dependent Kinetics over SiO2-Supported Pt Nanoparticles
+
+Christian Reece
+christianreece@fas.harvard.edu
+
+Harvard University    https://orcid.org/0000-0002-3626-7546
+Taek-Seung Kim
+Harvard University    https://orcid.org/0000-0001-8137-0326
+Christopher O'Connor
+Harvard University    https://orcid.org/0000-0002-9224-9342
+
+Article
+
+Keywords:
+
+Posted Date: September 6th, 2023
+
+DOI: https://doi.org/10.21203/rs.3.rs-3235489/v1
+
+License: This work is licensed under a Creative Commons Attribution 4.0 International License.
+Read Full License
+
+Additional Declarations: There is NO Competing Interest.
+
+Version of Record: A version of this preprint was published at Nature Communications on March 7th, 2024. See the published version at https://doi.org/10.1038/s41467-024-46496-1.
+Interrogating Site Dependent Kinetics over SiO₂-Supported Pt Nanoparticles
+Taek-Seung Kim, Christopher R. O’Connor and Christian Reece*
+Rowland Institute at Harvard, Harvard University, Cambridge, MA 02142
+*Corresponding author: christianreece@fas.harvard.edu
+
+Abstract
+A detailed knowledge of reaction kinetics is key to the development of new more efficient heterogeneous catalytic processes. However, the ability to resolve site dependent kinetics has been largely limited to surface science experiments on model systems. Herein, we can bypass the pressure, materials, and temperature gaps, resolving and quantifying two distinct pathways for CO oxidation over SiO₂-supported 2 nm Pt nanoparticles under operando conditions. We find that the pathway distribution directly correlates with the distribution of well-coordinated (e.g., terrace) and under-coordinated (e.g., edge, vertex) CO adsorption sites on the 2 nm Pt nanoparticles as measured by in situ DRIFTS. We conclude that well-coordinated sites follow classic Langmuir-Hinshelwood kinetics, but under-coordinated sites follow non-standard kinetics with CO oxidation being barrierless but conversely also slow. This fundamental method of kinetic site deconvolution is broadly applicable to other catalytic systems, affording bridging of the complexity gap in heterogeneous catalysis.
+Introduction
+
+Heterogeneous catalytic processes are the foundation of the chemical industry. However, our ability to rationalise and predict the behaviour of these complex industrial processes has been largely limited due to the significant complexity gap\(^1\) that exists between our fundamental understanding of catalytic systems and their application. Surface science experiments over planar model catalysts have been able to precisely resolve intrinsic catalytic kinetics and dynamic catalytic behaviour\(^2-6\); however, their application to “real-world” catalytic systems is often limited due to perceived pressure, material and temperature gaps\(^7\). These gaps are even more apparent in small (\( \lesssim 5 \) nm) supported nanoparticle systems where the metals no longer retain their bulk-like properties and notable support-metal interactions can exist\(^8,9\). Therefore, a method of directly measuring intrinsic kinetics over complex multi-faceted supported nanoparticle catalysts is highly desirable.
+
+As the rate of a reaction is defined by the specific geometric and electronic characteristics of an “active site”, we propose that measurement of an intrinsic rate constant (directly related to the free energy of the reaction) would be specific to a given active site. Therefore, a precisely resolved kinetic coefficient (or set of kinetic coefficients) can act as a parameterised representation of a given active site. CO oxidation has been utilised as a fundamental model reaction for understanding surface catalytic processes for decades\(^{4,10-13}\). In particular, CO oxidation over Pt catalysts has attracted significant attention due to its complex and dynamic surface chemistry, with the reaction generally understood to proceed *via* a Langmuir-Hinshelwood mechanism\(^{14,15}\). More recently, CO oxidation was used as a probe to study atom utilisation from nanoparticles to the single-site limit\(^{13,16}\). Due to the variations in physical structure with changing nanoparticle size\(^{17}\) and reaction environment\(^{18,19}\) understanding the catalytic role of geometric surface sites (*i.e.*, structural-sensitivity) has been\(^{20,21}\), and still is\(^{22}\) of great interest. For example, the activity of Pt catalysts has been considered size-dependent for C–H bond activation in the methane reforming reaction\(^{23,24}\), but conversely their activity for CO oxidation has typically been regarded as size-independent\(^{15,25}\). However, the possibility of site-dependence for CO oxidation on non-reducible oxide-supported Pt catalysts was recently reported\(^{26,27}\) where through a combination of *operando* DRIFTS and steady-state kinetic measurements it was thought that different reaction kinetics for under-coordinated (UC) and well-coordinated (WC) sites exists on the metallic Pt surface. However, as the study was performed under steady state conditions their analysis was limited to simple reaction orders and apparent activation energies.
+
+Non-steady state techniques such as Temporal Analysis of Products (TAP, see section: The Temporal Analysis of Products Experiment) are an effective way of measuring intrinsic kinetics as they can provide information about each sequential elementary step for the overall reaction. The TAP experiment serves to bridge the perceived pressure, material, and temperature gaps with the peak pressure during a pulse over the catalyst being on the order of 1 mbar\(^{28}\) (similar to other *operando* methods) and by using a packed bed microreactor (allowing powdered samples) which can be heated to the reaction temperature. As the pulse of reactant gas contains significantly fewer molecules than the number of reactive sites on the catalyst, a single pulse is not considered to change the surface significantly. However, by repeatedly pulsing it becomes
+possible to dynamically evolve the catalyst state using a technique known as chemical calculus\(^{29}\) making titration-like experiments extremely powerful\(^{30-34}\).
+
+In this work we demonstrate that with the combination of TAP experiments, kinetic modelling, and DRIFTS measurements it is possible to precisely resolve site-dependent kinetics on working catalysts under *operando* conditions. We provide a detailed insight into the site-dependent intrinsic kinetics for CO oxidation over a well-defined 2 nm-sized Pt/SiO\(_2\) catalyst. Using isotopic labelling, we deconvolute the production of CO\(_2\) that arises from the reaction with preadsorbed \(^{13}\)CO* and from the adsorption/reaction of reactant \(^{12}\)CO in the gas phase under CO oxidation conditions. We identify two distinct kinetic features in the adsorbed \(^{13}\)CO*-driven CO\(_2\) production, which when combined with isothermal titration experiments are identified as two distinct pathways for CO oxidation. Regression of a kinetic model to the TAP exit flux curves was used to quantify the distribution of each pathway and calculate the intrinsic kinetics for the surface reaction of adsorbed oxygen with preadsorbed CO* as a function of temperature and coverage. Finally, by combining this data with comparable DRIFTS measurements, we are able to deduce site-specific kinetics as a direct relationship between the distribution of kinetic pathways and the distribution of well-coordinated (*e.g.*, terrace like) and under-coordinated (*e.g.*, edge, vertex) sites.
+
+Results
+
+**Initial characterisation of pristine and CO*-covered 2 nm-sized Pt/SiO\(_2\) catalysts.**
+Uniform and well-dispersed Pt nanoparticles were synthesized *via* a conventional polyol method (Supplementary Fig. 1) and were deposited on a SiO\(_2\) support with a concentration of 0.72 wt%. The average size and distribution of the nanoparticles was measured to be 1.82 ± 0.51 nm (Fig. 1a) on the fresh catalyst, and 1.94 ± 0.37 nm (Fig. 1b) over the spent catalyst. As no sintering of the nanoparticles occurred throughout the duration of the TAP experiments, we can directly correlate the catalytic behaviour to this narrow distribution of particles approximately 2 nm in diameter. The catalytic activity of the 2 nm Pt/SiO\(_2\) catalyst was tested under steady-state CO oxidation conditions (2.5% CO, 5% O\(_2\)) with an apparent activation energy of 89 ± 3 kJ/mol measured between 130 and 160 °C, and reaction orders of 1.02 ± 0.06 in CO and 1.22 ± 0.1 in O\(_2\) (Supplementary Fig. 2). These values match well with previous results over Pt catalysts with similar average particle sizes\(^{15,26,35-37}\), demonstrating that the Pt/SiO\(_2\) catalyst used in this work is comparable with ones reported previously, albeit with a narrower size distribution. Finally, we see excellent reproducibility for all TAP experiments performed in this work (Supplementary Fig. 3).
+Fig. 1. Characterisation of Pt/SiO2 catalyst and TAP CO oxidation experiments. a,b, Representative TEM images with particle size distribution (inset) of (a) fresh and (b) spent Pt/SiO2 catalyst after all of the TAP experiments. c, Argon normalised exit flux curves of m/z = 28 (CO), 32 (O2), and 44 (CO2) at (i) 25 and (ii) 350 °C for a pulse set of 6.6% CO 13.4% O2 gas mixture in an inert Ar tracer over CO*-covered Pt/SiO2 catalyst. d, Temperature-dependent integrated exit flux of m/z = 44 (CO2) normalised via Ar on (i) pristine and (ii) CO-covered Pt/SiO2 catalyst for CO oxidation while heating from 25–350–25 °C at a heating rate of 8 °C/min.
+
+The fresh 2 nm Pt/SiO2 catalyst was loaded into a home-built TAP reactor38 and the catalytic activity for CO oxidation was measured by pulsing an oxygen rich CO/O2 mixture (1:2 molar ratio, 6.6% CO 13.4% O2) over a pristine and CO*-covered catalyst while heating from 25 to 350 °C at a heating rate of 8 °C/min. At 25 °C no conversion of CO or O2 and no production of CO2 was measured (Fig. 1c-(i)), whereas at 350 °C near 100% conversion of the CO to CO2 is recorded (Fig. 1c-(ii)). To simplify the comparison between the experiments, the exit flux curves for every pulse set in the experiment were integrated and normalised to the inert Ar tracer (Fig. 1d). The pristine Pt/SiO2 catalyst (Fig. 1d-(i)) shows a gradual increase in activity from 0% CO conversion at room temperature to almost 100% CO conversion above 100 °C. Similar reactivity for CO2 production between the heating and cooling steps was found indicating the catalyst state remains consistent during the experiment. However, the CO*-covered catalyst (Fig. 1d-(ii)) shows increased production of CO2 compared with the pristine catalyst. The excess O2 in the reactant gas mixture is able to react with the preadsorbed CO* and act as a titrant, sequentially removing the preadsorbed reactive sites with increasing temperatures. By 350 °C it is assumed
+that almost all of the preadsorbed CO* has either been reacted or desorbed off the catalyst surface as the activity during cooling was the same as that measured over the pristine catalyst. Interestingly, during the heating ramp the CO*-covered 2 nm Pt/SiO2 catalyst showed two catalytic features, with peaks in CO2 production around 100 and 200 °C. However, further experiments were required to precisely understand the cause for these two kinetic features.
+
+Identifying pathways for oxidation of preadsorbed CO*. In an attempt to further rationalise the two kinetic features of observed in Fig. 1d-(ii), isotopically labelled 13CO was used to prepare a 13CO*-covered catalyst. This allows a precise deconvolution of the CO2 produced from the reaction of the 6.6% CO 13.4% O2 gas mixture over the catalyst (m/z = 44) and the CO2 produced from the reaction of O2 with preadsorbed 13CO* (m/z = 45). The heating rate experiment was repeated on the 13CO-covered Pt/SiO2 catalyst under the exact same conditions as used in Fig. 1d-(ii). Interestingly, the reaction of gas phase CO and O2 with the catalyst (Fig. 2, red triangles) was similar to that measured over the pristine catalyst whereas the preadsorbed 13CO*-driven CO2 production (Fig. 2, orange circles) shows two well-defined kinetic features around 100 and 200 °C. The total CO2 production (12CO2 + 13CO2, Fig. 2, black circles) also matched well with the CO2 measured in Fig. 1d-(ii). As in other temperature programmed techniques such as Temporal Programmed Oxidation (TPO), the two peaks in the measured signal would indicate two different kinetic pathways (often prescribed to different sites) for the oxidation of preadsorbed CO with gas phase O2.
+
+![Isotopic labelling TAP experiment. Temperature-dependent integrated exit flux of m/z = 44 (CO2) and m/z = 45 (13CO2) normalised via Ar from the TAP experiment where an oxygen rich CO/O2 mixture (1:2 molar ratio, 6.6% CO 13.4% O2) was pulsed over a 13CO*-covered Pt/SiO2 catalyst while heating from 25–350 °C at a heating rate of 8 °C/min.](page_728_1012_627_393.png)
+
+Fig. 2. Isotopic labelling TAP experiment. Temperature-dependent integrated exit flux of m/z = 44 (CO2) and m/z = 45 (13CO2) normalised via Ar from the TAP experiment where an oxygen rich CO/O2 mixture (1:2 molar ratio, 6.6% CO 13.4% O2) was pulsed over a 13CO*-covered Pt/SiO2 catalyst while heating from 25–350 °C at a heating rate of 8 °C/min.
+Fig. 3. Isothermal O2 titration experiments at 100 and 200 °C over the CO*-covered Pt/SiO2 catalyst. a,b, Integrated Ar normalised exit flux of O2 and CO2 during the O2 titration experiments over the CO*-covered Pt/SiO2 catalyst (left), and the apparent rate constant (\( k'_{app} \)) as a function of cumulative CO2 produced (right) at (a) 100 and (b) 200 °C. Yellow lines are provided to guide the eye to the two kinetic regimes.
+
+To directly probe the kinetic features at 100 and 200 °C, isothermal O2 titration experiments were carried out. First, CO was pulsed over the catalyst at the reaction temperature until it was saturated with adsorbed CO*. Then, the preadsorbed CO* was titrated off sequentially with a series of O2 pulses. This affords calculation of the apparent rate constant for the oxidation of CO* as a function of CO coverage\(^{31,34}\). In the first few pulses ~100% conversion of O2 is observed at both temperatures (Fig. 3-left). Then, as O2 is repeatedly pulsed, the CO2 production decreases, and the exit flux of O2 increases up to the saturation state on the Pt surface, confirming that complete removal of the reactive CO* occurs. To estimate the kinetics of the preadsorbed CO* consumption, we plot the temperature corrected apparent rate constant as a function of cumulative CO2 produced (indicative of CO* coverage) in Fig. 3a,b-right, which is calculated using\(^{31}\):
+
+\[
+k'_{app} = \frac{X}{1-X} \sqrt{T} \approx k_{app} \approx k_a \theta_{CO^*}
+\]
+
+Where \( k'_{app} \) is the temperature corrected apparent rate constant, X is the fractional O2 conversion, T is the temperature (K), \( k_{app} \) is the apparent rate constant (s\(^{-1}\)), \( k_a \) is the intrinsic rate constant for the reaction of O2 with preadsorbed CO*, and \( \theta_{CO^*} \) is the coverage of
+preadsorbed CO*. On account of the usage of the same catalyst bed throughout all the pulse experiments, variations in \( k_{app} \) show a direct correlation to the intrinsic rate constant for the O$_2$ titration experiment$^{39,40}$. Specifically, a linearly decrease in \( k_{app} \) with \( \theta_{CO^*} \) (or CO$_2$ produced) indicates the presence of a unique intrinsic rate constants (\( k_a \)) for the reaction of O$_2$ with CO* through the following relationship$^{31,41}$:
+
+\[
+\frac{\Delta k_{app}}{\Delta \theta_{co^*}} = \frac{(1-\varepsilon)}{\varepsilon V} k_a
+\]
+
+Where \( \varepsilon \) is the void fraction of the packed bed, and V is volume of the catalyst zone. We identify two linear regimes for the reaction of O$_2$ with preadsorbed CO* in both isothermal titration experiments (Fig. 3, yellow line), indicating that two intrinsic rate constants, and as such two pathways exist simultaneously at both temperatures. We identify a slow and fast intrinsic reaction rate for CO$_2$ production, as shown by the gradients in Fig. 3-right. At high relative coverage of CO* the “fast” pathway dominates, at lower CO* coverages the “slow” pathway dominates during the titration experiment. Coupling this insight with the two kinetic regimes seen in the temperature programmed experiments, we feel confident in claiming that at least two different pathways for the oxidation of CO* by O$_2$ exist on the 2 nm Pt/SiO$_2$ catalyst.
+
+Quantifying active species using MZTRT and DRIFTS. Due to its well-defined nature, it is possible to precisely resolve the intrinsic kinetics of catalytic processes using the TAP experiment$^{40,42}$. For linear (first order or *pseudo* first order) reactions Multi-Zone TAP Reactor Theory$^{43,44}$ (MZTRT) is a powerful and efficient tool for simulating TAP exit flux responses. The model of the experiment was built using the generalised form of MZTRT (see Supplementary I) with the Symmetric Thin-Zone assumption applied to the catalyst zone$^{40}$. For the reaction of oxygen with preadsorbed CO*, a three-pathway model was identified as the most likely candidate (see Supplementary II; Fig. 4a and Supplementary Fig. 4). The experimental results for two catalytic features (CO$_2$ production around 100 and 200 °C in Fig. 2) and two kinetic regimes (two pathways for the reaction of O$_2$ in Fig. 3) would indicate two separate pathways for oxidation of CO*. As the oxygen balance (*i.e.*, oxygen released as CO$_2$ / oxygen consumed) is not always 1 throughout the experiment a third pathway of irreversible oxygen adsorption is necessary in the model. It is very important to note that the model regression is performed on each set of exit flux curves *individually* (Fig. 4b) with the model fit to both the shape and magnitude of Ar, O$_2$, and CO$_2$ exit flux curves. The kinetic model can be broken down into two parts. First, the apparent adsorption rate constants \( k'_{a,1} \) and \( k'_{a,2} \) represent the irreversible adsorption and subsequent reaction of gaseous O$_2$ with preabsorbed CO*, and the adsorption rate constant \( k'_{a,3} \) represents the irreversible adsorption of O$_2$ to sites where no further reaction with CO* takes place. Second, the intrinsic rate constants \( k_{r,1} \) and \( k_{r,2} \) represent the rate at which the surface reaction between adsorbed oxygen and CO* occurs for pathways 1 and 2, respectively. In short, the adsorption constants \( k'_a \) control the magnitude of the O$_2$ and CO$_2$ exit flux curves, whereas the surface reaction constants \( k_r \) control the shape. As each pulse set is regressed individually during the isothermal O$_2$ titration experiment (Fig. 4c), a set of rate constants for the reaction of oxygen with preadsorbed CO* can be calculated at each point (Fig. 4d). Models of varying complexity were tested, but only the three-pathway model was able to precisely recreate the experimental data without being overparameterised (see Supplementary II;
+Supplementary Fig. 5). The model fitting exhibits a high degree of confidence and consistency with all TAP experiments in this work, although decreased confidence in the intrinsic surface reaction constants is observed at the limit of very low CO$_2$ production.
+
+![Schematic of three-pathway model and experimental results for O2 titration](page_184_370_1207_693.png)
+
+Fig. 4. Model fitting of isothermal O$_2$ titration experiment using MZTRT. a, Schematic of the three-pathway model. b, Experimentally measured and model exit flux curves for pulse set 40 of O$_2$/Ar during O$_2$ titration experiment at 100 °C. c, Experimentally measured and model fitted integrated exit flux curves for the whole O$_2$ titration experiment at 100 °C (corresponding to Fig. 3a). d, Rate constants calculated from model fitting with 95% confidence intervals included. Inset shows small but non-zero value for $k_{r,1}$.
+Fig. 5. Characterisation of CO* covered catalyst via DRIFTS, TAP, and kinetic modelling.
+a, DRIFT spectra for CO adsorption on the CO*-covered 2 nm Pt/SiO2 catalyst where CO* was preadsorbed at 35, 100, 200, and 350 °C. The spectra were obtained after cooling the catalyst to 35 °C. All DRIFTS measurements were acquired at 35 °C which avoids the influence of temperature on vibrational features45. b, Illustration for adsorbed CO* sites (well-coordinated and under-coordinated) on the surface of a model Pt nanoparticle (regular, truncated octahedron; 586 atoms; ~2.17 nm-size). c, Integrated Ar normalised exit flux of m/z = 44 (CO2) during TPO experiments on the CO*-covered Pt/SiO2 catalyst where CO* was preadsorbed at 25, 100, 200, and 350 °C. For TPO experiments, the CO* was preadsorbed at 25–350 °C on the catalyst and the catalyst was cooled to 25 °C. Then O2 was repeatedly pulsed over the catalyst while being linearly heated to 350 °C at 8 °C/min. d–g, Deconvoluted CO2 production pathways and CO2 production pathway ratios calculated using the regressed kinetic model (MZTRT) for the TPO experiments where CO* was preadsorbed at (d) 25, (e) 100, (f) 200, (g) 350 °C.
+
+To rationalise if the two pathways for oxidation of the preadsorbed CO* were correlated to the geometric structure of metallic Pt sites (e.g., terrace, edge, vertex sites) on the 2 nm nanoparticles, a series of DRIFTS and TPO experiments were performed where CO was preadsorbed at 25–350 °C (Fig. 5). In general, it is known that the binding energy for adsorbed CO on the under-coordinated (UC) sites (e.g., edge, vertex sites) is higher than that on the well-coordinated (WC) sites (e.g., terrace sites). This implies that when CO is adsorbed at higher temperatures, an increase in populated UC sites relative to the populated WC sites would be expected46.
+From the DRIFTS investigation in Fig. 5a, it is shown that the pre-adsorption of CO at 35, 100, 200, and 350 °C (35CO, 100CO, 200CO, 350CO, respectively) populates linear bound CO to WC sites, UC sites, and bridge bound CO as evidenced by three ν(C–O) bands (Fig. 5a,b features 1-3). The 35CO yields ν(C–O) bands centred at 2075 cm⁻¹ with a small high frequency shoulder (feature 1), a small band near 2042 cm⁻¹ (feature 2), and a broad band at 1805 cm⁻¹ (feature 3). Increasing the adsorption temperature to 100 °C causes a slight decrease in the intensity of feature 1 and a shift in features 2 and 3 to lower frequency. For the 200CO and 350CO, there is a dramatic decrease in the intensity and slight shift to lower frequency of feature 1. The decrease in the intensity is attributed to the reduction of the total number of adsorbed CO* with increasing temperature. In turn the surface is predominantly relatively strongly bound CO on UC sites. A larger shift to lower frequency of features 2 and 3 is observed, which clarifies feature 2 as a distinct peak from feature 1. The position of the ν(C–O) frequencies as a function of CO adsorption temperature are reported in Supplementary Table 1. Feature 1 with a peak maximum from 2075 to 2052 cm⁻¹ is assigned to the collective oscillation of linear bound CO to WC sites (linear WC) where the high frequency shoulder is attributed to a dense CO phase for high CO coverages. Feature 2 with a peak maximum from 2042 to 1970 cm⁻¹ is assigned to the collective oscillation of linear CO to UC sites (linear UC). The frequency of the ν(C–O) for linear CO on the 2 nm Pt nanoparticles catalyst is in agreement with previous investigations when considering the frequency is dependent on the CO coverage²⁶,⁴⁷–⁵⁷, Pt coordination environment²⁶,³⁵,⁵¹–⁶³, and nanoparticle size²⁶,⁵⁷–⁶¹. Feature 3 with a peak maximum from 1805 to 1701 cm⁻¹ is assigned to the collective oscillation of bridge bound CO to Pt sites and is also in reasonable agreement with previous work⁴⁹–⁵⁴,⁶⁴–⁶⁷. In contrast to the linear CO vibrational features, the identification of unique bridge CO features for different Pt coordination environments was not possible. The CO* adsorption site information from the DRIFTS analysis is graphically summarised in Fig. 5b.
+
+Alongside the DRIFTS investigation, comparable TPO experiments were performed where CO* was preadsorbed at temperatures from 25–350 °C and was titrated using O₂ pulses while heating from 25–350 °C at 8 °C/min (Fig. 5c). Interestingly, the 25CO TPO shows an onset temperature for CO₂ production at around 40 °C, whereas the TPO results of both 100CO and 200CO show 10-20 times higher CO₂ production at 40 °C. It is believed that when CO is preadsorbed at 25 °C the surface is fully covered in CO* meaning there are no vacant sites for adsorption/dissociation of O₂ (i.e., CO poisoning). We prescribe the increased activity for CO₂ production in the 100CO and 200CO TPO experiments to the increased number of vacant sites on the partially CO*-covered surface. This is supported by an additional TPO experiment where CO is pulsed to saturation over the 100CO catalyst at 25 °C. The 100CO + 25CO TPO experiment shows similar tendency to that of 25CO (Supplementary Fig. 6), which implies that the low temperature CO₂ production at 25 °C is vacancy driven. Further, isothermal titration experiments performed at 25 °C show no CO₂ production (Supplementary Fig. 7). When combined, this would indicate that CO₂ production by oxidation of preadsorbed CO* is driven by a Langmuir-Hinshelwood type reaction (as is expected for CO oxidation over Pt)¹⁴,¹⁵. However, we cannot rule out other methods such as CO* assisted O₂ dissociation¹⁵. Interestingly, the low-temperature oxidation of preadsorbed CO* would indicate that the Langmuir-Hinshelwood surface reaction between oxygen and CO* over 2 nm Pt nanoparticles has a very low activation barrier, which is counter to previous work on single crystals and supported Pt catalysts with activation energies ranging from 37 to 85 kJ/mol¹⁵,³⁶,⁶⁸,⁶⁹.
+Similar to the isotopically labelled experiments, two kinetic features are observed: a spike around 80 °C (first feature) and a long shoulder from 100–350 °C (second feature) appear in the 25CO TPO. The first kinetic feature appears at low temperatures (< 50 °C) in both the 100CO and 200CO which we ascribe to the low-temperature CO* conversion mentioned above. Due to decreasing CO* coverage throughout the titration experiment, the CO₂ production would be expected to decrease. However, in the 100CO experiment a distinct second catalytic feature appears around 125 °C, which suggests the presence of temperature-dependent kinetics. Further, the second catalytic feature disappears as the adsorption temperature increases from 100 to 200 °C, which corresponds to the large decrease in WC sites from the DRIFTS results in Fig. 5a. This strongly suggests that site dependent kinetics does exist for the oxidation of CO* over SiO₂-supported 2 nm Pt nanoparticles.
+
+To calculate the intrinsic kinetics at each point in the TPO experiments, the rate constants for the model in Fig. 4a were calculated by regressing the MZTRT Symmetric Thin-Zone model to every pulse set in the experiments. All rate constants for the 25CO, 100CO, 200CO, and 350CO TPO experiments are shown in Supplementary Fig. 8. Also, the MATLAB script used to process the 25CO TPO experiment is included alongside the Supplementary Information. As during the TAP experiment the pulse size is sufficiently small that coverage of CO* species is not changed by any appreciable amount during a pulse, the first order irreversible adsorption rate constants \( k'_{a,1} \) and \( k'_{a,2} \) are *pseudo* first order and are proportional to the concentration of the adsorbed CO* species involved in each pathway (\( k'_{a,3} \) would be proportional to the number of empty sites). This means that it becomes possible to deconvolute the amount of CO₂ produced from each pathway as shown in in Fig. 5d–g. From the MZTRT Symmetric Thin-Zone model, the conversion of O₂ in each pulse set can be calculated using⁴⁰,⁷⁰.
+
+\[
+X_{O_2} = \frac{(k'_{a,1} + k'_{a,2} + k'_{a,3})(L/2D_e)}{1 + (k'_{a,1} + k'_{a,2} + k'_{a,3})(L/2D_e)}
+\]
+
+Where \( X_{O_2} \) conversion of the reactant, \( D_e^R \) is the diffusivity of the reactant (cm²/cm³), \( L \) is the length of the catalyst bed (cm), and \( k'_{a,n} \) represents the apparent pseudo-first order adsorption/reaction constant for each individual site included in the model (cm s⁻¹) and is the parameter that is calculated during the model fitting. The apparent pseudo-first order adsorption/reaction constant is linearly related to the intrinsic adsorption/reaction rate constant through the following relationship⁴¹,⁴³:
+
+\[
+k'_{a,n} = k_{a,n} \theta_n L_{cat} \frac{S_v (1 - \varepsilon_b)}{\varepsilon_b}
+\]
+
+Where \( k_{a,n} \) is the intrinsic adsorption/reaction constant (cm³ mols⁻¹ s⁻¹) and \( \theta_n \) is the concentration of CO* in the case of sites 1 and 2, and the coverage of empty irreversible adsorption sites in the case of site 3 (mol cm⁻³), \( L_{cat} \) is the length of the catalyst zone (cm) \( S_v \) is the surface area of the catalyst per volume of catalyst (cm²/cm³). This is a slight modification to
+forms of the equation previously published\(^{40}\), as the MZTRT Symmetric Thin-Zone model does not explicitly include a value for \(L_{cat}\) and so it is lumped into the apparent pseudo-first order adsorption/reaction constant \(k'_{a,n}\). For each pathway included in the model, the conversion of oxygen specific to each pathway can be deconvoluted using the following:
+
+\[
+X_{O_2,n} = \frac{k'_{a,n}(L/2D_e)}{1 + (k'_{a,1} + k'_{a,2} + k'_{a,3})(L/2D_e)}
+\]
+
+The amount of CO\(_2\) produced through can be calculated from the conversion of oxygen specific to pathways 1 and 2 by considering the reaction stoichiometry using the following:
+
+\[
+M^{CO_2,n}_{0, norm} = 2X_{O_2,n}
+\]
+
+From the pathway deconvolution in Fig. 5d–g, we find that pathway 1 is dominant for CO\(_2\) production at low-temperatures, whereas at elevated temperatures pathway 2 becomes the dominant pathway. The CO\(_2\) yield from each pathway can be easily calculated by summing the deconvoluted CO\(_2\) production throughout the TPO experiment (Supplementary Fig. 9). We find that the CO\(_2\) yield of pathway 1 stays relatively constant up to a CO adsorption temperature of 200 °C, whereas the CO\(_2\) yield of pathway 2 rapidly decreases. Further, when CO is preadsorbed at 350 °C, the amount of CO species related to pathways 1 and 2 becomes approximately equal on the surface.
+
+To identify if any correlation between the two pathways and geometric surface sites exists, we summarised the ratio of the CO\(_2\) yield of pathway 1 to pathway 2 calculated from the kinetic model with the quantitative DRIFTS analysis for the population of linear UC and WC CO* sites in Fig. 6. The fraction of pathway 1 from the kinetic model (Fig. 6, black) increases with increasing CO adsorption temperature. From the quantitative deconvolution of the DRIFTS spectra for the population of UC and WC CO* sites (see Supplementary III for details on quantification), the fraction of populated linear CO at UC sites is also increasing with CO adsorption temperature. Deconvolution of the bridge CO to WC and UC sites is not possible, but there is a shift to lower frequency of the bridge peak maximum with temperature that is consistent with increasing the relative population of UC Pt sites. Most notably, we find a straightforward relationship between the amount of each pathway as calculated from the kinetic model, and the total amount of UC and WC sites calculated using DRIFTS. Due to this direct relationship, we claim that pathway 1 mainly occurs on UC sites, and pathway 2 occurs mainly at WC sites.
+Fig. 6. Comparison between pathway ratio (TPO experiment) and area ratio of CO* sites (DRIFTS investigation). A direct correlation between the total amount of pathway 1 and pathway 2 calculated from the kinetic model, and the total amount of UC and WC sites from the DRIFTS investigation is found.
+
+Measuring the Intrinsic Kinetics of CO oxidation on UC and WC sites. Along with the reactive site information, the intrinsic surface reaction constants \( k_{r,1} \) and \( k_{r,2} \) (related to the reaction of adsorbed oxygen with adsorbed CO for pathways 1 and 2) from the isothermal titration and TPO experiments were calculated and are shown in Fig. 7. As mentioned previously, the reaction over UC sites is ascribed to pathway 1, whereas the reaction over WC sites is ascribed to pathway 2. It can be seen that the rate constant for pathway 1 (\( k_{r,1} \)) is significantly lower than pathway 2 (\( k_{r,2} \)) under all conditions probed, with pathway 1 being a slow reaction between adsorbed oxygen and CO and pathway 2 being fast. Interestingly, pathway 1 shows no dependence on temperature or the coverage of CO in both the isothermal O$_2$ titration (Fig. 7a,b) and the TPO (Fig. 7c,d) experiments but is unintuitively a slow reaction. One such rationalisation for this behaviour based on transition state theory would be that the reaction results in a significant loss in entropy in the transition state$^{71}$. As adsorbed oxygen is considered to be immobile under these conditions, it could be hypothesized that a CO molecule strongly bound to a vertex of a nanoparticle has a large number of degrees of freedom, but during the transition state to make CO$_2$ the species would become immobile due to the strongly bound oxygen, losing a large number of degrees of freedom. However, as CO adsorption on Pt is not well described by DFT$^{72,73}$, this would be difficult to confirm, so this idea remains conceptual. Experiments using molecular beam scattering$^{14,68}$ or velocity resolved kinetics$^{74}$ do not observe this barrierless reaction, but it should be noted that these were performed on Pt single crystals, whereas this work is performed on 2 nm Pt supported nanoparticles, and as such the nanoparticle size effect must also be considered. Further, due to the slow nature of the reaction, this pathway would be difficult to isolate as it would certainly be limited by CO desorption under steady-state conditions at any appreciable CO pressure.
+We find that pathway 2 shows more classic kinetic behaviour. Under isothermal conditions we find a linear dependence on the coverage of CO* (Fig. 7b) indicating lateral interactions between adsorbed CO* molecules and/or adsorbed O*, which is expected based on previous work36. Under non-isothermal conditions an exponential increase in rate with increasing temperature (Fig. 7d) is observed above 80 °C. It should be noted that as the surface coverage is also changing during the TPO experiment, a classic Arrhenius style analysis to calculate activation energies and pre-exponential factors is non-trivial and will be attempted in future publications. Further, we observed complex kinetic behaviour in pathway 2 below 80 °C (which was not recreated in the isothermal O2 titration experiments) which cannot be described by classical Arrhenius kinetics. It could be hypothesized that some restructuring of the Pt nanoparticles is occurring around 100 °C, but this will be evaluated in future work combining these methods with techniques such as X-ray Absorption Spectroscopy.
+
+![Rate constants for isothermal O2 titration experiments and TPO experiments](page_420_563_1092_1012.png)
+
+Fig. 7. Calculated rate constants (\( k_{r,1} \) and \( k_{r,2} \)) for the surface reaction between adsorbed oxygen and CO from the three-pathway kinetic model with 95% confidence intervals overlaid. a,b, Isothermal titration experiments where CO was adsorbed at 100 and 200 °C. Increasing total CO2 produced is correlated with decreasing CO coverage. c,d, TPO experiments where CO was adsorbed at temperature ranging from 25–200 °C. When the production of CO2 is sufficiently low in the TPO experiment (> 200 °C) the signal/noise ratio of the CO2 exit flux curves significantly decreases, which in turn decreases the confidence in the model fitting, particularly for pathway 2, as shown in Supplementary Fig. 12.
+Conclusion
+
+Pathway 1        Pathway 2        Pathway 3
+
+Slow Kinetics    Fast Kinetics    No reaction
+Coverage-Independent    Coverage-Dependent    No reaction
+Temperature-Independent    Temperature-Dependent    Well-Coordinated Sites
+Under-Coordinated Sites    Well-Coordinated Sites    Under-Coordinated Sites
+
+Well-Coordinated Sites   Under-Coordinated Sites
+
+Fig. 8. Summary of the three-pathway model for the reaction of O_2 with preabsorbed CO^* over SiO_2-supported 2 nm Pt nanoparticles.
+
+The combination of TAP, kinetic modelling, and DRIFTS measurements provides unparalleled levels of kinetic insight into the dynamic site dependent activity for CO oxidation over 2 nm-sized Pt/SiO_2 catalysts. The precisely defined nature of the TAP experiment means that fine kinetic features are resolvable by modelling the exit flux curves using efficient analytical functions. By coupling this insight with DRIFTS measurements, we have been able to identify that site-specific kinetics exists for CO oxidation over 2 nm Pt nanoparticles with the three pathways for the interaction of oxygen with CO^* summarised in Fig. 8. We find two pathways for the oxidation of CO^* and one pathway for the irreversible adsorption of oxygen (no reaction). Pathway 1 mainly occurs at the UC sites and has slow kinetics, is coverage independent, and is temperature independent. On the contrary, pathway 2 mainly occurs at WC sites with fast kinetics, is highly dependent on the CO^* or O^* coverage and shows an exponential increase with temperature. These results serve as a significant insight into understanding the kinetics of various reactive sites in heterogeneous catalysis. Typically, it has been widely accepted that increasing the number of UC sites is advantageous for CO conversion^{22,27}. However, even though the reaction at the UC sites is found to be barrierless, it has slow kinetics which may not be optimal for CO conversion.
+
+Once the reaction pathways have been assigned to specific sites, this method of kinetic site deconvolution can be applied generally, allowing features such as restructuring, sintering, and even potentially metal-support interactions to be understood. The quantitative nature of the TAP experiment means simultaneous calculation of the number of active sites, their distribution on the surface, and the intrinsic kinetics of the surface reactions is now possible. We believe that our approach is general enough to apply to other catalytic systems and can serve as a new toolkit in the characterisation of heterogeneous catalysts.
+
+Methods
+Preparation of Pt/SiO2 catalyst. In a typical synthesis of 2 nm-sized Pt nanoparticles,75 100 mg of chloroplatinic acid hydrate (H2PtCl6·xH2O, 99.9%, Sigma–Aldrich), 20 mg of poly(vinylpyrrolidone) (PVP, Mw=40000, Sigma-Aldrich), 2.5 mL of sodium hydroxide (NaOH, 1 N) were dissolved in 10 mL of ethylene glycol (Sigma-Aldrich) in a 50 mL three-neck round-bottom flask. The flask was heated to 80 °C and evacuated for 30 min with vigorous stirring, then heated to 200 °C. The solution was kept at 200 °C for 2 hr with Ar gas purging. After the reaction, the solution cooled down to RT. The colloidal suspension was diluted to 50 mL of acetone and centrifuged at 6500 rpm for 10 min twice, repeatedly. Then, the as-synthesized Pt nanoparticles were re-dispersed in 40 mL of ethanol. Then, 10 mL of the Pt-dispersed solution was dropped onto the 0.3 g of SiO2 powder (pretreated at 700 °C for 1 hr; 10–20 nm, Sigma-Aldrich) with vigorous stirring. The suspension was sonicated for 20 min, subsequently evaporating the solvent in a vacuum at 50 °C overnight. The microstructure of the Pt/SiO2 catalyst was investigated via XRD measurement (Supplementary Fig. 1b) and shows diffraction peaks at 39.5 and 46°, corresponding to the (111) and (200) planes of reference Pt (JCPDS #04-0802). For characterisation and TAP experiments, the Pt/SiO2 catalyst was calcined at 500 °C for 1 hr in air condition to remove majority of carbonaceous capping agent with a ramp up rate of 1 °C/min. To prepare the metallic Pt nanoparticles, the Pt/SiO2 catalyst was reduced at 300 °C for 1 hr with a ramp up rate of 1 °C/min under 10% H2 in Ar flow.
+
+Characterisations. The morphology and size distribution of Pt/SiO2 catalyst were investigated by transmission electron microscopy (TEM; ARM 200F, JEOL) at 200 kV. The concentration of catalyst was determined using inductively coupled plasma optical emission spectroscopy (ICP-OES; 5110 ICP-OES; Agilent). The catalyst microstructure was measured by X-ray diffractometer (XRD; D2 Phaser, Bruker). The steady-state flow catalytic activity was measured in a home-built ambient pressure flow reactor that has been previously described76 with all gas mixtures reported balanced in Ar.
+
+Temporal Analysis of Products experiments. The TAP technique has been described extensively in the literature41,42,77, but it is summarised here. During the TAP experiment a nanomole pulse of gas (~10^{15} molecules, 108 μs pulse width) is sent into a packed bed microreactor that is held at ultra-high vacuum (< 10^{-9} torr). During the experiment, the pulsed gas diffuses through the packed bed via Knudsen Diffusion where it can interact with the catalyst surface. Eventually the gas diffuses out the exit of the microreactor and the exit flux of is measured via mass spectrometry. Due to the precisely defined nature of Knudsen Diffusion, the shape (and magnitude) of the exit flux curves provides highly resolved kinetic insight, in particular when coupled with kinetic modelling of the exit flux curves (see section: Modelling of Temporal Analysis of Products Pulse Responses).
+
+For the TAP experiments, the Pt/SiO2 catalyst is first calcined at 350 °C by injecting 1000 pulse sets of large O2 pulses (160 μs pulse width) until the CO2 signal (m/z = 44) becomes near-zero to minimise the decomposition of the remaining carbonaceous capping. Before all pulse/transient response experiments, the Pt/SiO2 catalyst is reduced at 350 °C by injecting 600 pulse sets of large H2 pulses (160 μs pulse width) to achieve a metallic Pt surface. We utilise a home-built TAP reactor38 where the microreactor contains a layer of commercial sand (29.7 mm; 50–70 mesh SiO2; Sigma-Aldrich) followed by a layer of Pt/SiO2 catalyst (5.4 mg) followed by a final layer of commercial sand (34.4 mm) for a total reactor length of 64.1 mm. The exit flux of
+CO, O₂, Ar, and CO₂ is monitored via mass spectrometry. The integrated exit flux of the Ar tracer is used for normalisation of all pulse experiments (see Supplementary IV). As the mass spectrometer can only investigate one m/z value per pulse, multiple pulses are used to scan the whole range of m/z values and are combined to one pulse set³⁸. All gas mixtures reported are balanced in Ar.
+
+Diffused Reflectance Infrared Fourier Transform Spectroscopy experiments. DRIFTS experiments were carried out in a low-temperature reaction chamber (Harrick Scientific) equipped with ZnSe windows, mounted inside the sample compartment of a Bruker Invenio FT-IR spectrometer using a Praying Mantis diffuse reflectance accessory (Harrick Scientific). The catalyst sample was prepared by pressing approximately 2 mg of 2 nm Pt/SiO₂ onto a 304 stainless-steel mesh (150 × 150 mesh). The DRIFTS reactor was loaded by placing the catalyst-containing mesh on top of approximately 110 mg of 120 grit SiC, an inert support with high thermal conductivity. There can exist large temperature gradients between the thermocouple contact in a DRIFTS reactor cell and the catalyst surface temperature exposed to the infrared beam.⁷⁸ Therefore, a thermocouple was mounted in physical contact with the bottom of the stainless-steel mesh and the temperature gradient to the catalyst surface at 350 °C was less than 20 °C as calibrated by an optical pyrometer. All DRIFTS experiments used a total volumetric flow rate of 100 sccm. Each absorbance spectrum was obtained by averaging 200 background and sample scans at a resolution of 4 cm⁻¹ using a liquid-nitrogen-cooled HgCdTe (MCT) detector, while the Praying Mantis diffuse reflectance accessory and FT-IR spectrometer was purged with dry N₂. The background measurement was acquired after the catalyst sample was annealed at 350°C for 30 mins in 5% H₂ in Ar and cooled to 35 °C in Ar. The sample measurements were acquired after the catalyst sample was annealed at 30 °C/min in Ar to the CO adsorption temperature, the temperature was maintained for 10 mins in 0.1% CO in Ar until saturation was achieved, and the sample was cooled to 35 °C in Ar. A description of the quantitative analysis of the DRIFTS spectra is provided in the Supplementary (see Supplementary III).
+
+Modelling of Temporal Analysis of Products Pulse Responses. To simulate the TAP exit flux response curves, Multi-Zone TAP Reactor Theory⁴³,⁴⁴ (MZTRT) was utilised with the catalyst zone being approximated as a Thin Zone⁴⁰ in the centre of the microreactor between two layers of inert packing. To perform the curve fitting first, the experimentally measured signals were normalised to the inert Ar tracer and corrected using their corresponding calibration factors (see Supplementary IV). Then, the curves were further normalised to the concentration of reactant gas in the pulsed mixture such that the integrated area under the reactant curve is 0 at 100% conversion and 1 at 0% conversion. Next, the diffusivity of Argon in the packed bed reactor was calculated by fitting a one-zone TAP model to the Ar exit flux curve. As the Knudsen diffusivity is proportional to \( \sqrt{1/M} \) where \( M \) is the molecular weight of the gas, it becomes possible to calculate the diffusivity of the reactant (\( O_2, M = 32 \)) and product (\( CO_2, M = 44 \)) gases by scaling the diffusivity relative to the inert gas (\( Ar, M = 40 \)). When performing the fitting of the reactant and product curves, the diffusivities of the gases, the reactor length, and the void fraction of the reactor were all fixed, with the only variables being the rate constants for the corresponding model. It is very important to note the regression is performed on each set of exit flux response curves (i.e., exit flux plotted as a function of time) individually. Therefore, the rate constants are calculated separately at each pulse set (and catalyst state) during the experiment. All curve fitting
+was performed in the MATLAB environment using the lsqcurvefit function, with the 95% confidence intervals for the fitted variables evaluated using the nlpaci function. A full description of the MZTRT model used in this work and how the model fitting is performed is available in Supplementary Information I, II, IV, and an example of the MATLAB script used to simulate the TAP experiments is included alongside this paper.
+
+Data availability
+
+The authors declare that the data supporting the findings of this study are available within the article and its Supplementary Information files. An example MATLAB script for the modelling of the TAP response curves is also included alongside the data for the 2STPO experiment. All other relevant data is available from the authors upon reasonable request.
+
+Acknowledgements
+
+C.R. gratefully acknowledges the Rowland Fellowship through the Rowland Institute at Harvard.
+
+Author contributions
+
+Taek-Seung Kim: Conceptualization, Investigation, Formal analysis, Writing – original draft
+Christopher R. O’Connor: Investigation, Writing – original draft
+Christian Reece: Conceptualization, Formal analysis, Supervision, Writing – original draft, Writing – review & editing
+
+T.S.K performed the synthesis, characterisation and TAP experiments. C.R.O. performed the DRIFTS experiments. C.R. performed the TAP modelling and supervised the project. All authors in frequent discussions and contributed significantly to writing the manuscript.
+
+Additional information
+
+Supplementary information accompanies this paper. The MATLAB script accompanying this paper requires the Curve Fitting Toolbox and the Statistics and Machine Learning Toolbox.
+
+Competing financial interests
+
+The authors declare no competing financial interests.
+
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+Supplementary Files
+
+This is a list of supplementary files associated with this preprint. Click to download.
+
+• SiteDependentKineticsSI.pdf
+• 23InterrogatingSites3PathwayModel.zip

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+Retro-MTGR: Molecule Retrosynthesis Prediction via Multi-Task Graph Representation Learning
+
+Jian-Yu Shi
+jianyushi@nwpu.edu.cn
+
+Northwestern Polytechnical University
+Pengcheng Zhao
+School of Life Sciences, Northwestern Polytechnical University
+Xue-Xin Wei
+School of Life Sciences, Northwestern Polytechnical University
+Qiong Wang
+School of Life Sciences, Northwestern Polytechnical University
+Qi-Hao Wang
+School of Chemistry and Chemical Engineering, Northwestern Polytechnical University
+Jia-Ning Li
+School of Life Sciences, Northwestern Polytechnical University
+Jie Shang
+School of Life Sciences, Northwestern Polytechnical University
+Cheng Lu
+Institute of Basic Research in Clinical Medicine China Academy of Chinese Medical Sciences
+
+Article
+
+Keywords:
+
+Posted Date: September 6th, 2023
+
+DOI: https://doi.org/10.21203/rs.3.rs-3205328/v1
+
+License: This work is licensed under a Creative Commons Attribution 4.0 International License.
+Read Full License
+
+Additional Declarations: There is NO Competing Interest.
+Version of Record: A version of this preprint was published at Nature Communications on January 18th, 2025. See the published version at https://doi.org/10.1038/s41467-025-56062-y.
+Retro-MTGR: Molecule Retrosynthesis Prediction via Multi-Task Graph Representation Learning
+
+Peng-Cheng Zhao¹, Xue-Xin Wei¹, Qiong Wang¹, Qi-Hao Wang², Jia-Ning Li¹, Jie Shang¹*, Cheng Lu³*, Jian-Yu Shi¹*
+
+¹School of Life Sciences, Northwestern Polytechnical University, Xi’an 710072, China
+²School of Chemistry and Chemical Engineering, Northwestern Polytechnical University, Xi’an 710072, China
+³Institute of Basic Research in Clinical Medicine China Academy of Chinese Medical Sciences, Beijing 100700, China
+Corresponding author: jianyushi@nwpu.edu.cn; lv_cheng0816@163.com; shangjie03@nwpu.edu.cn
+
+Abstract
+It is a vital bridging step to infer appropriate synthesis reaction routes (i.e., retrosynthesis) of newly-designed molecules. Unlike classical experience-based retrosynthesis approaches, artificial intelligence enables a cheap and fast retrosynthesis approach. Template-based models, limited in known synthesis templates, leverage substructure searching to infer candidate reaction centers (i.e., bonds). In contrast, both translation-based models (TransMs) and discriminative methods (DiscMs) are free to synthesis templates. TransM regards retrosynthesis as a translation from the target molecule to its reactants by generative algorithms. DiscM, directly inspired by chemical synthesis, performs reaction center recognition and leaving group identification in turn. Nevertheless, TransMs are redundant and weakly interpretable, while existing DiscMs neglect the associations between reaction centers and leaving groups. To address these issues, this paper elaborates a novel discriminative Multi-Task Graph Representation learning model of Retrosynthesis prediction (Retro-MTGR). It solves two major supervised discriminative tasks (i.e., the reaction center recognition and the leaving group identification respectively), and an auxiliary self-supervised task (i.e., atom embedding enhancer) simultaneously. The comparison with various state-of-the-art methods first demonstrates the superiority of Retro-MTGR. Then, the ablation studies reveal how its crucial components contribute to the prediction respectively, including the atom embedding enhancer, bond energies, and the leaving group co-occurrence graph. More importantly, comprehensive investigations validate its chemical interpretability by answering two questions: why a bond can be the reaction center or not, and what leaving groups are appropriate to given synthons. The answers demonstrate that Retro-MTGR can reflect five underlying chemical synthesis rules by characterizing molecule structures
+alone. Finally, two case studies demonstrate that the inferred retrosynthesis routes by Retro-MTGR are significantly consistent with those achieved by performed chemical synthesis assays. It’s anticipated that our Retro-MTGR can provide prior guidance for real retrosynthesis route planning. The code and data underlying this article are freely available at https://github.com/zpczaizheli/Retro-MTGR.
+
+1 Introduction
+
+By integrating artificial intelligence (AI) technologies¹, modern drug design has exhibited marvelous achievements on diverse tasks (e.g., target screening², molecule generation³, ADMET prediction⁴, etc.) with a significant reduction in cost and time ⁵,⁶. Once the chemical structure of a small molecule is determined in silico, there is an important task, retrosynthesis, which finds available reactants to be synthesized into the drug-like molecule in reality⁷. Such a retrosynthesis process works as a bridge from in silico to in reality. Compared to the ordinary synthesis reaction, the retrosynthesis is its inverse inference process⁸,⁹. A complete route of retrosynthesis is composed of multiple steps of synthesis reactions. However, even inferring a single step of synthesis heavily relies on individual domain experiences of chemists under costly trial-and-error assays ¹⁰.
+
+In recent years, both the accumulation of chemical synthesis data and the blooming of deep learning methods boost the rapid development of computer-assisted synthesis processes (CASP) in retrosynthesis, which are roughly grouped into template-based, translation-based and discriminative methods.
+
+Upon summarizing empirical rules of existing chemical syntheses (by usually RDKit¹¹), template-based methods infer the single-step retrosynthesis of a newly given molecule by local structure similarity-based searching. For example, after determining possible reaction types of a target molecule, DHN, derived from gating neural networks, searches candidate templates among reaction type-specific templates¹². GLN, a conditional graphical model upon graph neural networks, acquires candidate templates of the target molecule by subgraph pattern matching¹³. However, template-based methods cannot predict the retrosynthesis for target molecules having novel synthesis patterns outside the synthesis rules in the template library. In addition, it is tedious to update template libraries as new synthesis knowledge is discovered¹⁴.
+
+In contrast, both translation-based and discriminative methods are template-free and can predict the retrosynthesis reaction without a pre-built template library. Translation-based methods generally regard the retrosynthesis process as a case of machine translation¹⁵, which learns a translation model from the target molecule to its reactants by generative algorithms (e.g., LSTM¹⁶ and Transformer¹⁷). Existing
+translation-based methods can be further categorized into sequence-to-sequence translation models (Seq2Seq) and graph-to-seq translation models (Graph2Seq).
+
+(1) Seq2Seq models treat a target molecule as one string (e.g., SMILES) and its two reactants as another string (the concatenation of two reactant SMILES). The first Seq2Seq model retrosynthesis method utilizes attention-enhanced LSTMs to convert the target molecule to its reactants under an encoder-decoder architecture\(^{16}\). As the new super-star in natural language processing, Transformer is also applied to retrosynthesis prediction by treating each character in SMILE as a word in recent years\(^{18}\). However, these methods arise a new issue that generated reactants are probably invalid in terms of chemistry. To meet the chemical validity of generated reactants, SCROP designs an extra syntax post-checker (derived from RDKit) based on Transformer\(^{15}\). RetroTRAЕ treats molecule substructures (capturing local atomic environment) as words in the Transformer to guarantee the validity of generated reactants\(^{19}\). Although these Seq2Seq models have achieved inspiring retrosynthesis predictions, they ignore rich information hidden in molecule chemical structures (i.e., the topology between atoms and bonds)\(^{20}\).
+
+(2) Graph2Seq models, representing target molecules as graphs, enriches the molecule representation and then map them into their reactant sequences under the auto-regressive generation framework\(^{8}\). Since the decoders of Graph2Seq models are similar, their contributions mainly focus on the design of encoders by graph neural networks (GNNs). For example, to encode target molecular graphs, G2GT designs a self-attention module enhanced by degrees of atoms and pairwise shortest distances between atoms\(^{21}\). Graph2SMILES utilizes a directed message-passing neural network (MPNN) to capture atom representations with the extra enhancement of global attention encoding\(^{22}\). By treating a chemical reaction as a queue of graph edits, MEGAN adopts a GNN-based encoder–decoder architecture and outputs reactants by a queue of leaned graph edits on the input molecule graph step by step\(^{23}\). Usually, these Graph2Seq models achieve better retrosynthesis prediction since they capture richer topology of molecule structures than Seq2Seq models.
+
+However, both Seq2Seq and Graph2Seq models are still derived from generative models, which cannot provide well-interpretable results to chemists or pharmacologists in terms of chemical synthesis mechanisms. Moreover, dissimilar to the translation from one language to another language, translation-based retrosynthesis prediction has a redundant learning process due to highly overlapping structures between target molecules and their reactants.
+
+Different from translation-based models, discriminative models are inspired by real
+chemical synthesis. In brief, their prime step is to find the reaction center (e.g., the bond broken in retrosynthesis inference) where the molecule is split into two synthons (i.e., incomplete reactants) \(^{24}\). Then, two synthons are attached to appropriate functional groups (i.e., leaving groups, LGs) to form reactants respectively. For example, Hasic et al. characterize local substructures of two bonding atoms as the bond representation by extended-connectivity fingerprints, and query candidate reactants by similarity search in a pre-built compound library\(^{25}\). The G2Gs model encodes bonds by atom local topology and molecule global topology to find the reaction center by relational graph convolutional networks, and then builds a variational graph model to infer functional groups to be attached to synthons\(^{26}\). However, current discriminative models treat the reaction center recognition and the LG identification as two separate steps, such that the association between the target molecule and its reactants is neglected.
+
+In summary, existing translation-based generative models have weak interpretability and a redundant translation from target molecules and their reactants, while current discriminative models neglect the association between the reaction center recognition and the LG identification.
+
+To address these issues, this paper elaborates a novel Multi-Task Graph Representation learning framework of Retrosynthesis prediction (Retro-MTGR), which is a discriminative model in essence. It solves three related tasks, including two major supervised discriminative tasks (i.e., the reaction center recognition and the LG identification respectively) and an auxiliary self-supervised task (i.e., atom embedding enhancer).
+
+Overall, the main contributions of this work are as follows.
+
+(1) **This work proposes a novel retrosynthesis prediction model (Retro-MTGR)**, which consists of a reaction-center perceptron (RCP), a leaving group predictor (LGP), and an atom embedding enhancer (AEE). RCP characterizes the molecule topology to recognize the retrosynthesis reaction center, while AEE utilizes the redundancy between the product molecule and its synthons to boost atom embeddings for RCP. By leveraging the co-occurrence between LGs, LGP identifies appropriate LGs of synthons to provide complete reactants.
+
+(2) **Aiming to better chemical interpretability of retrosynthesis prediction, Retro-MTGR answers why a bond can be the reaction center or not from three aspects**. First, a bond having high-breaking energy (\(>=360\) kJ/mol) is usually an ordinary bond. Secondly, aromatic bonds (c~c) between carbon atoms are always ordinary bonds, while other types of bonds can be either reaction
+centers or ordinary bonds. Last, a bond is the reaction center in a molecule if its member atoms tend to have opposite electrical properties (reflected by local substructures), otherwise an ordinary bond.
+
+(3) **Furthermore, Retro-MTGR answers what leaving groups are appropriate to given synthons as follows.** First, LG pairs in reaction centers usually have opposite electrical properties, and occurrence-dominant LG pairs always consist of two simple groups (e.g., H, OH, or halogens). Secondly, individual LGs can be categorized into reaction-common and reaction-specific LGs. The former group is usually of simple LG and occurs in multiple types of synthesis reactions. The latter is of usually chemical substructure groups and occurs only in specific types of reactions. Also, either similar chemical properties or structures between LGs imply their potential substitution in synthesis reactions.
+
+2. Methods
+
+2.1 Problem formulation and model construction
+
+Given a set of \( n \) chemical reactions \( R = \{r_1^i + r_2^i = c_i|i = 1,...,n\} \), where the reactants \( r_1^i \) and \( r_2^i \) are two reactant molecules for the synthesis of target molecule \( c_i \). The task is to find the retrosynthetic strategy for a newly-designed target molecule \( c \) (i.e., to recommend reactants \( (r_1, r_2) \) for \( c \)).
+
+To perform a chemist-like retrosynthesis, we elaborate a Multi-Task Graph Representation learning framework of Retrosynthesis prediction (Retro-MTGR), which contains a Reaction-Center Perceptron (RCP) module, an Atom Embedding Enhancer (AEE) module and a Leaving Group Predictor (LGP). They account for two major tasks and one auxiliary task respectively. The first major task, implemented by RCP, is modeled as a binary discriminative problem, which recognizes the reaction center \( b_{u^*,v^*} \) among all the bonds \( \{b_{u,v}\} \) of the target molecule. Also, it breaks down \( b_{u^*,v^*} \) to obtain two synthons \( s_{u^*} \) and \( s_{v^*} \), where \( u,v \) are two bonding atoms in \( c \). To support the first major task in terms of atom embeddings, the auxiliary task (implemented by AEE) is modeled as a self-supervised contrast learning problem, which characterizes the structural commonality and difference between \( c \) and its synthons \( (s_{u^*}, s_{v^*}) \). The second major task is modeled as a multi-class discriminative problem, which assigns appropriate leaving groups \( (k_{u^*}, k_{v^*}) \) to the synthons \( (s_{u^*}, s_{v^*}) \) to form complete reactants \( (r_{u^*}, r_{v^*}) \) under the enhancement of leaving group dependence.
+Figure 1. The framework of Retro-MTGR. Molecules in the form of graphs first are represented by an MPNN-based atom encoder to learn initial atom embeddings. The atom embedding enhancer (AEE) further boosts the atom embeddings by contrastive learning on molecules and their synthons w.r.t. molecule embeddings. The Reaction-Center Perceptron (RCP) leverages a bond-level readout on enhanced atom embeddings to learn bond embeddings, which are sequentially augmented by extra bond energies and then recognize reaction centers among bonds. After that, the leaving group predictor (LGP) learns LG embeddings based on a leaving group co-occurrence graph and measures the proximity between them and synthon embeddings (involving atoms and bonds in reaction centers) to predict appropriate LGs for given synthons.
+
+2.2 Reaction-Center Perceptron
+
+Identifying the reaction center is the first step in the inference of retrosynthesis. Inspired by this chemical empirical approach, we primarily attempt to recognize the reaction center among all the bonds of a given target molecule. The reaction center is the bond broken in terms of retrosynthesis. Thus, the task of reaction center recognition can be naturally
+modeled as a binary discriminative problem, which recognizes the reaction center \( b_{u^*,v^*} \) among all the bonds \( \{b_{u,v}\} \) of the target molecule.
+
+For this task, we design a reaction-center perceptron (RCP) module, which includes an atom encoder, a bond-level readout layer, and a multi-layer perceptron (MLP). The atom encoder is implemented by a two-layer message passing neural network (MPNN) to turn molecule graphs \( \mathcal{G} = (\mathcal{A}, \mathcal{B}) \) into atom embeddings \( \{\mathbf{a}_i\} \), which are further refined by an Atom Embedding Enhancer (AEE). The bond-level readout layer generates bond embeddings \( \{\mathbf{b}_{u,v}\} \), which are further boosted by concatenating with bond energy \( b_e \). The MLP accounts for the discrimination of bonds by \( y = \mathcal{F}(\mathbf{b}_{u,v}) \), where \( y = 1 \) if \( b_{u,v} \) is the reaction center, \( y = 0 \) otherwise.
+
+Atom Encoder
+
+According to chemical structure, each compound \( m \) is represented as a molecule graph \( \mathcal{G} = (\mathcal{A}, \mathcal{B}) \), where \( \mathcal{A} \) is the set of its atoms \( \{a_i\} \), \( \mathcal{B} \) is the set of its chemical bonds \( \{b_{ij}\} \), and \( i,j = 1,2,...,|\mathcal{A}| \). Let \( \mathbf{E} \in R^{N \times N}(N = |\mathcal{A}|) \) be its adjacency matrix, in which \( e_{ij} = 1 \), indicates the occurring bond \( (b_{ij} \in \mathcal{B}) \) between two atoms (i.e., \( a_i \) and \( a_j \)) and \( e_{ij} = 0 \) indicates no bond. Suppose that \( \mathbf{x}_l \in R^n \) is the initial feature vector of atom \( a_l \), which is usually coded into a vector containing one-hot-shaped atom types, number of hydrogen atoms, and other attributes\(^{27}\). Since \( \mathbf{x} \) is sparse, an extra multi-layer MLP maps it into its dense form (\( \mathbf{x}_l \in R^p \)) to avoid the vanishing gradient problem\(^{28}\).
+
+Both \( \mathbf{E} \) and \( \mathbf{x} \) are input into a two-layer MPNN to generate atom embeddings \( \{\mathbf{a}_i\} \) for molecule \( c \). The MPNN updates the embedding \( \mathbf{a}_i \) of each atom \( a_i \) by aggregating those of its neighboring atoms in a layer as follows,
+
+\[
+\mathbf{a}_i^{t+1} = \sigma \left( \mathbf{w}_i^t \left( \sum_{j \in \mathcal{N}(a_i)} (\mathbf{w}_j^t \mathbf{a}_j^t) + \mathbf{b}_i^t \right) + \mathbf{w}_i^t \mathbf{a}_i^t \right), \quad t = \{1,2\},
+\]
+
+where \( \mathbf{a}_i^t \) denotes the embedding of atom \( i \) in the t-th layer of MPNN, \( \mathbf{a}_i^1 = \mathbf{x} \), \( \mathcal{N}(a_i) \) denotes the neighbors of atom \( a_i \) in the molecule graph \( \mathcal{G} \), \( \sigma(\cdot) \) is a non-linear activation function (e.g., *ReLU*), all \( \{\mathbf{w}^t\} \) are layer-wise learnable weight matrices accounting for a linear transformation, and \( \mathbf{b}^t \) denotes a learnable bias.
+
+Perceptron
+
+After passing through the MPNN, the initial atom feature \( \mathbf{x} \in R^n \) is turned to the updated atom embedding \( \mathbf{a}_i \in R^q \). It is further refined by the AEE module, which characterizes the structural commonality and difference between the molecule and its synthons. Meanwhile, the refined atom embeddings are utilized by the LGP module to help find appropriate leaving groups for the synthons. All three tasks are associated together by shared atom embeddings. See Sections 2.3 and 2.4 for details.
+
+Sequentially, the refined atom embeddings \( \{\mathbf{a}_i\} \) are then used to generate bond
+embedding by the bond-level readout. Let \( b_{ij} \) be the bond connecting atoms \( a_i \) and \( a_j \). Unlike the ordinary molecule-level readout (e.g., the combination of all atoms), the RCP model defines a bond-level readout function \( \mathcal{R}_B(a_i, a_j) \), which is augmented by bond energy, to obtain the bond embedding \( \mathbf{b}_{ij} \) as follows,
+
+\[
+\mathbf{b}_{ij} = \mathcal{R}_B(a_i, a_j) = [(a_i + a_j); \; g_{ij}],
+\]
+
+where \( g_{ij} \) is the theoretical bond energy, and ‘;’ indicates the concatenation of \( g_{ij} \) and the atom embedding summation. As we observed, bond energy contributes to screen out the ordinary bonds having high bond energies. See also Section 3.4.1.
+
+Last, RCP identifies the reaction center among all the bonds of \( m \). Define \( \mathcal{C} \) as the set of bond flags \( \{c_{ij}\} \) w.r.t. molecule \( m \), where \( c_{ij} = 1 \) if \( b_{ij} \) is the reaction center (a positive sample), \( c_{ij} = 0 \) otherwise (a negative sample). Based on the abovementioned bond embeddings \( \{\mathbf{b}_{ij}\} \), it is naïve to construct a two-layer MLP (denoted as \( \mathcal{F}_b \)) as the classifier to achieve such a bond identification (i.e., \( c_{ij}^* = \mathcal{F}_b(\mathbf{b}_{ij}) \)). To train the model, the cross-entropy loss function over all the training molecules is defined as follows:
+
+\[
+l_{bond} = -\frac{1}{|\mathcal{M}|} \sum_{m=1}^{|\mathcal{M}|} \left( \frac{1}{|B_m|} \sum_{b_{ij} \in B_m} (c_{ij} \log c_{ij}^* + (1 - c_{ij}) \log (1 - c_{ij}^*)) \right),
+\]
+
+where \( \mathcal{M} \) is the set of all the training molecules, and \( B_m \) is the bond set of \( m \).
+
+2.3 Atom Embedding Enhancer
+
+As we observed, there is an amazing analog between the edge perturbation in graph contrast learning \( ^{29} \) and the breaking of the reaction center in the retrosynthesis. Inspired by this observation, we designed an atom embedding enhancer (AEE) module based on graph contrastive learning.
+
+For a target molecule \( m \), we treat its two synthons (\( s_1 \) and \( s_2 \)) as a new perturbed molecule \( s \), which is generated by removing the reaction center from \( m \). We also collect another different molecule \( \bar{s} \), which is randomly selected from other molecules or their perturbed molecules. Let \( \mathbf{h}_m \), \( \mathbf{h}_s \), and \( \mathbf{h}_{\bar{s}} \) be their embeddings respectively. These molecule embeddings are generated by an atom encoder and a molecule-level readout function \( \mathcal{R}_M(\cdot) \). The former has the shared parameters with the atom encoder used in the RCP module. For a given molecule, \( \mathcal{R}_M(\cdot) \) aggregates the embeddings of its all atoms to generate the molecular-level embedding by an ordinary average pooling \( \mathbf{h} = \frac{1}{|A|} \sum_{i=1}^{|A|} \mathbf{a}_i \).
+
+In terms of contrastive learning, the molecule embedding pair of \( \mathbf{h}_m \) and \( \mathbf{h}_s \) is regarded as a positive sample while the pair of \( \mathbf{h}_m \) and \( \mathbf{h}_{\bar{s}} \) is taken as a negative sample. Our goal is to train a contrastive learning model, which pushes \( \mathbf{h}_m \) and \( \mathbf{h}_s \) as near as possible (similar) while pushing \( \mathbf{h}_m \) and \( \mathbf{h}_{\bar{s}} \) as far as possible (different). For this
+purpose, we design a contrastive loss function as follows:
+
+\[
+l_{contrast} = - \frac{1}{|\mathcal{M}|} \sum_{m=1}^{|\mathcal{M}|} \log \left( \frac{\exp(\mathbf{h}_m, \mathbf{h}_i^T)}{\exp(\mathbf{h}_m, \mathbf{h}_i^T) + \exp(\mathbf{h}_m, \mathbf{h}_j^T)} \right).
+\]
+
+Thus, the AEE module enables an ingenious utility of chemical structural commonness and differences between a molecule and its synthons to enhance atom embeddings for other tasks.
+
+2.4 Leaving Group Predictor
+
+Once synthons are decided based on the reaction center, chemists can obtain corresponding reactants by attaching appropriate leaving groups (LGs) to them. Thus, the task of LG recognition can be modeled as a multi-class classification. Inspired by chemists, we hold the idea that both the reaction center and the local substructures around reaction sites are crucial factors to determine LGs. Meanwhile, we consider the fact that LGs are not independent but are associated in the chemical synthesis sense (See also Section 3.4.2). Based on these considerations, we propose an elaborate leaving group predictor (LGP) based on multi-class classification to identify leaving groups.
+
+Let \( \mathcal{K} \) be the list of all possible LGs, \( b_{u,v} \) be the reaction center of molecule \( m \), \( a_u, a_v \) be the reaction sites (i.e., atoms forming \( b_{u,v} \)), \( s_u, s_v \) be its synthons. Formally, \( s_u \) can be assigned with one or more LGs (i.e., \( \mathcal{K}_u = \mathcal{F}(s_u) \subseteq \mathcal{K} \)) to form its corresponding reactants \( r_u \) (i.e., \( r_u(i) = \mathcal{K}_u(i) + s_u \)), \( i = 1, ..., |\mathcal{K}_u| \).
+
+To implement our first idea, the reaction center \( b_{u,v} \) is represented by its bond embedding \( \mathbf{b}_{u,v} \) in RCP, while the local substructure around reaction site \( a_u \) is just represented by the atom embedding \( \mathbf{a}_u \), which already aggregates its neighbors due to the MPNN in RCP. Thus, the embedding of the synthon \( s_u \) containing \( a_u \) can be defined as their concatenation \( s_u = [\mathbf{a}_u; \mathbf{b}_{u,v}] \). Similarly, we can define the embedding of \( s_v \) by \( s_v = [\mathbf{a}_v; \mathbf{b}_{u,v}] \).
+
+To implement our second idea, we construct the leaving group co-occurrence graph (LGCoG) \( G_k = (\mathcal{K}, \mathcal{E}) \), where \( \mathcal{K} = \{k_i|i = 1, ..., |\mathcal{K}|\} \) denotes the set of nodes (leaving groups), and \( \mathcal{E} = \{e_{ij}\} \) denotes the set of weighted edges (normalized co-occurrences between leaving groups). Each LG is a small-size chemical substructure (e.g., -OH, -B(OH)2) or an atom/ion individual (e.g., -Cl, -Br, -H). The popular one-hot coding is used as initial node features \( \{k_i^1\} \). The edge building contains two steps as follows. First, the LG co-occurrence is calculated based on the training dataset, where the co-occurrence of two LGs is counted if they are involved in the same reaction. Define \( \mathbf{U} = \{u_{ij}\} \in \mathbb{R}^{|\mathcal{K}| \times |\mathcal{K}|} \) as the LG co-occurrence matrix, where \( u_{ij} \) denotes the pairwise co-occurrence counts between \( k_i \) and \( k_j \). Then, a probability matrix \( \mathbf{P} \) can be calculated by \( \mathbf{U} \). Therefore, \( p_{ij} \) is calculated as follows:
+\[
+p_{ij} = \frac{u_{ij}}{\sum_{j=1}^k \sum_{i=1}^k u_{ij}} .
+\]
+(5)
+
+We set it as the weight of the edge from \( k_j \) to \( k_i \) (i.e., \( e_{ij} = p_{ij} \)). Thus, the embedding (\( \mathbf{k}_i \)) of LG \( k_i \) can be represented by performing an MPNN on \( G_k \) as follows:
+\[
+\mathbf{k}_i^{t+1} = \sigma \left( w_1^t \left( \sum_{j \in N(k_i)} (e_{ij} w_2^t \mathbf{k}_j^t) + b^t \right) + w_2^t \mathbf{k}_i^t \right), \quad t = \{1,2\},
+\]
+(6)
+where \( j \in N(k_i) \) is the neighborhood of \( k_i \), \( \mathbf{w} \) is the learnable transformation matrix, and \( \sigma(\cdot) \) is a non-linear activation function (i.e., ReLU).
+
+After obtaining the synthon embeddings and the LG embeddings, we can directly perform discriminate the candidate LG to be attached to a synthon. As suggested by MLGL-MP (2022)\(^{30}\), we measure the proximities between a given synthon \( s_u \) and a given LG \( k_i \) as follows:
+\[
+\hat{y}_{ui} = \mathbf{s}_u \ (\mathbf{k}_i)^T .
+\]
+(7)
+The proximity \( \hat{y}_{ui} \) is the predicting score of the given synthon attaching the \( i \)-th LG among the LG set \( \mathcal{K} \), and reflects how possibly \( s_u \) is attached to \( k_i \).
+
+However, such a direct proximity measure would be senseless since the synthon embedding space and the LG embedding space are of different vector spaces. To tackle this issue, we design an adapter to map \( \{s_u\} \) into \( \{k_i\} \). The adapter can be implemented by an MLP containing an input layer, a hidden layer, and an output layer. Thus, the final compound representation feature is defined as \( \mathbf{s}_i^* = \text{MLP}(\mathbf{s}_u) \in \mathbb{R}^s \), where \( s \) is the dimension of \( \mathbf{k}_i \).
+
+Last, the mean square error (MSE) loss function is used when training LGP as follows:
+\[
+l_{group} = \frac{1}{2M|\mathcal{K}|} \sum_{u=1}^{2M} \sum_{i=1}^{|\mathcal{K}|} (\hat{y}_{ui} - y_{ui})^2 ,
+\]
+(8)
+where \( y_{ui} \in \{0,1\} \) is the true label indicating whether or not a synthon \( s_j \) is attached by an LG \( k_i \), \( \hat{y}_{ji} \) is the corresponding score output by LGP, \( M \) is the number of all the training molecules, and \( 2M \) represents the number of their synthons.
+
+2.4 Training Loss and Testing
+
+To train the whole Retro-MTGR model, we combine the three abovementioned loss functions w.r.t. tasks into a linear joint as follows
+\[
+Loss = w_1 * l_{bond} + w_2 * l_{contrast} + w_3 * l_{group},
+\]
+(9)
+where \( \sum_{i=1}^3 w_i = 1 \) are normalized hyperparameters to adjust task weights.
+
+Note that Retro-MTGR in the testing should remove the AEE module since it cannot be available in the scenario.
+
+3. Result and discussion
+
+3.1 Dataset and parameter settings
+
+As popularly used in existing methods\(^{31}\), we collected the benchmark dataset from the USPTO-50K dataset, which was derived from an open-source patent database
+containing 50,016 atom-mapped reactions\(^{32}\). In this work, by discarding modification-like chemical reactions, we only extracted the chemical reactions where one target molecule is synthesized from two reactants. As a result, our dataset contains 30,565 reaction entries, which are divided into 7 categories according to reaction type (Table 1).
+
+In the Atom Encoder, as suggested in existing methods\(^4\), each atom was initially represented by a 28-dimensional (28-d) atom feature vector (\( \mathbf{x}_i \in R^{28} \)), including Atom Type (23-d), the number of Hydrogens (1-d), the number of linking neighbors of atom (Degree, 1-d), Is Aromatic (1-d), Formal Charge (1-d), as Atomic Mass (1-d). See also Table 2 for details. Due to the one-hot coding of Atom Type, the initial atom representation \( \mathbf{x}_k \) is sparse. To avoid the vanishing gradient problem\(^{28}\), an extra three-layer MLP maps it into its dense form (\( \mathbf{x}_k \in R^{32} \)). We empirically set 64 and 32 neurons in its hidden layer and output layer respectively. Moreover, bonds are represented as a binary adjacent matrix \( \mathbf{E} \), of which \( e_{ij} = 1 \) indicates the occurring bond between two atoms (\( a_i \) and \( a_j \)), and no bond otherwise. Both \( \{ \mathbf{x}_k \} \) and \( \mathbf{E} \) are input into a two-layer MPNN to obtain atom embeddings having the same dimensions as those of \( \{ \mathbf{x}_k \} \).
+
+In the RCP module, the MLP accounting for reaction center identification contains also an input layer, a hidden layer, and an output layer. There are 33 neurons in the input layer, where 32 neurons are responsible for the resulting embeddings from the bond-level readout and the last one takes charge of the bond energy. The number of neurons is empirically set to 16. The unique neuron in the output layer accounts for the confidence score of being a reaction center.
+
+In the LGP module, the nodes in the leaving group co-occurrence graph (LGCoG) are initially represented as \( n \)-dimensional one-hot coding vectors \( \{ \mathbf{k}_i^0 \in \mathbb{R}^{|\mathcal{K}|} \} \), where \( n = |\mathcal{K}| \) is the cardinality of the LG set. Then, they are mapped into LG embeddings \( \{ \mathbf{k}_i \in \mathbb{R}^{|\mathcal{K}|} \} \) by another two-layer MPNN without dimensional change. On the other side, the adapter maps the synthon embedding space (the concatenation of 32-d atom embeddings and 33-d bond embeddings) into the LG embedding space. It is implemented by a three-layer MLP, which contains an input layer accounting for synthon embeddings (\( \mathbf{s}_u \in \mathbb{R}^{65} \)), a hidden layer having empirically 128 neurons, and an output layer having \( n \) neurons respectively. Thus, \( \mathbf{s}_u^* = \mathrm{MLP}(\mathbf{s}_u) \in \mathbb{R}^n \), where \( n \) (i.e., \( |\mathcal{K}| \)) is scenario-specific since the type-known scenario and the type-unknown scenario have different types of LGs.
+Table 1. Dataset overview
+
+<table>
+  <tr>
+    <th>Reaction type</th>
+    <th>Reaction name</th>
+    <th>No. of examples</th>
+  </tr>
+  <tr>
+    <td>1</td>
+    <td>heteroatom alkylation and arylation</td>
+    <td>14188</td>
+  </tr>
+  <tr>
+    <td>2</td>
+    <td>acylation and related processes</td>
+    <td>10509</td>
+  </tr>
+  <tr>
+    <td>3</td>
+    <td>C–C bond formation</td>
+    <td>4378</td>
+  </tr>
+  <tr>
+    <td>4</td>
+    <td>protections</td>
+    <td>144</td>
+  </tr>
+  <tr>
+    <td>5</td>
+    <td>oxidations</td>
+    <td>142</td>
+  </tr>
+  <tr>
+    <td>6</td>
+    <td>functional group interconversion (FGI)</td>
+    <td>986</td>
+  </tr>
+  <tr>
+    <td>7</td>
+    <td>functional group addition (FGA)</td>
+    <td>218</td>
+  </tr>
+  <tr>
+    <td>Total</td>
+    <td>/</td>
+    <td>30565</td>
+  </tr>
+</table>
+
+Table 2. Atom attributes
+
+<table>
+  <tr>
+    <th>Feature</th>
+    <th>Description</th>
+    <th>Dimension</th>
+  </tr>
+  <tr>
+    <td>Atom type</td>
+    <td>Cl, N, P, Br, B, S, I, F, C, O, ... (one-hot)</td>
+    <td>23</td>
+  </tr>
+  <tr>
+    <td>Number of H</td>
+    <td>Integer</td>
+    <td>1</td>
+  </tr>
+  <tr>
+    <td>Degree</td>
+    <td>Integer</td>
+    <td>1</td>
+  </tr>
+  <tr>
+    <td>Is Aromatic</td>
+    <td>True or False (binary)</td>
+    <td>1</td>
+  </tr>
+  <tr>
+    <td>Formal charge</td>
+    <td>Integer</td>
+    <td>1</td>
+  </tr>
+  <tr>
+    <td>Atomic Mass</td>
+    <td>Integer</td>
+    <td>1</td>
+  </tr>
+</table>
+
+3.2 Comparison with state-of-the-art methods
+
+To evaluate the effectiveness of Retro-MTGR, we compared it with five state-of-the-art single-step retrosynthesis methods, including two sequence-to-sequence translation methods (including seq2seq\(^{16}\) and SCPOP\(^{15}\)), two graph-to-seq translation methods (including MEGAN\(^{23}\) and Graph2SMILES\(^{22}\)), and one discriminative method (i.e., G2Gs\(^{26}\)). They are briefly summarized below.
+
+• Seq2seq: It is the first sequence-2-sequence translation method, which utilizes attention-enhanced LSTMs to convert the target molecule to its reactants in the form of SMILES under an encoder-decoder architecture\(^{16}\).
+• SCROP: It is a transformer-based method with the aid of an extra syntax post-checker to guarantee the chemical validity of generated reactants\(^{15}\).
+• MEGAN: Its outputs reactants by a queue of leaned graph edits (chemical structure modification) on the input molecule graph step by step under a GNN-based auto-regressive architecture\(^{23}\).
+• Graph2SMILES: It is also an auto-regressive model, which utilizes a directed MPNN to capture atom representations with the extra enhancement of global
+attention encoding\(^{22}\).
+• G2Gs: It is a two-step GNN-based discriminative model, which first encodes bonds to find the reaction center by relational GCNs, and then builds a variational graph model to infer leaving groups to be attached on synthons\(^{26}\).
+
+For a fair comparison, we run ten-fold cross-validation (10-CV) as suggested by these methods\(^{33}\). In detail, the dataset was randomly and equally split into 10 subsets, of which each subset (10% samples) was taken as the testing set and the remaining subsets (90% samples) were taken as the training set. Such a 10-CV was repeated 50 times under different random seeds. The average performance over 50 rounds of cross-validations was reported to measure the retrosynthesis prediction of Retro-MTGR. Moreover, the top-k accuracy (e.g., Top-1, Top-3, and Top-5) was adopted as the measuring metric in 10-CV. It is defined as the ratio of the number of correctly predicted target molecules to the total number of target molecules, where a target molecule is correctly predicted if its correct reactants are found among the top-k predicted candidates.
+
+In addition, two retrosynthesis scenarios, Reaction Type Known (RTK) and Reaction Type Unknown (RTU), were considered, as these methods performed. In the first scenario RTK, we are required to perform a retrosynthesis for a molecule while being given its possible reaction type. In the second one RTU, we have no information about its potential reaction type. Usually, RTU is more practical but difficult than RTK. Besides, since the prediction in RTK is specific to reaction types, we reported only the average performance over those reaction types in Table 3 and listed the detailed results in Supplementary (Section 1).
+
+The comparison results demonstrate that our Retro-MTGR achieves the best prediction and is significantly superior to other state-of-the-art methods over two testing scenarios. The results also validate that RTU is more difficult than RTK since extra type information in RTK helps the prediction. In detail, it achieves 69.1%, 89.2%, and 91.0% accuracies in the case of RTK while achieving 57.3%, 81.0%, and 86.5% respectively in the case of RTU in terms of Top-1, Top -3, and Top-5. Remarkably, Retro-MTGR achieves 5–7% improvements in the case of RTK while achieving 4–12% improvements in RTU over Top-1, Top -3, and Top-5 accuracies respectively.
+Table3. Top-k accuracy for retrosynthesis prediction on USPTO.
+
+<table>
+  <tr>
+    <th rowspan="2">Methods</th>
+    <th colspan="4">Reaction Type Unknown</th>
+    <th colspan="4">Reaction Type Known</th>
+  </tr>
+  <tr>
+    <th>1</th>
+    <th>3</th>
+    <th>5</th>
+    <th>1</th>
+    <th>3</th>
+    <th>5</th>
+  </tr>
+  <tr>
+    <td rowspan="2">Sequence-to-Sequence</td>
+    <td>Seq2seq</td>
+    <td>35.0±2.5</td>
+    <td>41.7±2.1</td>
+    <td>56.5±3.5</td>
+    <td>43.4±2.7</td>
+    <td>60.2±2.8</td>
+    <td>69.2±2.7</td>
+  </tr>
+  <tr>
+    <td>SCROP</td>
+    <td>44.6±3.5</td>
+    <td>63.3±2.2</td>
+    <td>66.8±3.2</td>
+    <td>58.1±2.5</td>
+    <td>75.6±3.1</td>
+    <td>79.8±3.0</td>
+  </tr>
+  <tr>
+    <td rowspan="2">Graph-to-Seq</td>
+    <td>MEGAN</td>
+    <td>46.8±5.9</td>
+    <td>72.7±5.1</td>
+    <td>75.4±5.0</td>
+    <td>57.7±6.0</td>
+    <td>83.1±5.6</td>
+    <td>85.8±5.7</td>
+  </tr>
+  <tr>
+    <td>Graph2Smiles</td>
+    <td>51.7±3.5</td>
+    <td>65.9±1.7</td>
+    <td>72.8±2.4</td>
+    <td>61.7±3.2</td>
+    <td>80.3±2.5</td>
+    <td>86.7±2.9</td>
+  </tr>
+  <tr>
+    <td rowspan="2">Discriminative</td>
+    <td>G2Gs</td>
+    <td>53.0±1.2</td>
+    <td>70.5±1.2</td>
+    <td>74.2±0.9</td>
+    <td>59.0±0.9</td>
+    <td>83.4±1.0</td>
+    <td>86.5±1.3</td>
+  </tr>
+  <tr>
+    <td>Retro-MTGR</td>
+    <td><b>57.3±1.4</b></td>
+    <td><b>81.0±0.8</b></td>
+    <td><b>86.5±0.7</b></td>
+    <td><b>69.1±0.6</b></td>
+    <td><b>89.2±1.1</b></td>
+    <td><b>91.0±1.5</b></td>
+  </tr>
+</table>
+
+3.3 Ablation studies
+
+In this section, we investigated how crucial components of our Retro-MTGR contribute to the retrosynthesis prediction by ablation studies. We made three variants of our original model by masking one block of Retro-MTGR in turn. First, we removed the AEE module (denoted as w/o AEE). Secondly, we discarded bond energies in bond embeddings (denoted as w/o BE). Last, we deleted the leaving group co-occurrence graph (LGCoG) in the LGP module and used one-hot coding as the initial representations of leaving groups (denoted as w/o LGCoG).
+
+As the ablation comparison illustrates, the superiority of Retro-MTGR to all its variants demonstrates that all of the AEE module, the bond energy, and the leaving group graph play significant roles in the retro-synthesis prediction in the case of both unknown and known reaction types (Figure 2). Specifically, the AEE module plays the most important role. For example, Retro-MTGR with the AEE module improves the Top-1, Top-3, and Top-5 accuracies by 5.9%, 8.2%, and 3.1% respectively in the case of unknown reaction type. The result indicates that the AEE module can enhance bond embeddings in finding the reaction centers because it utilizes chemical structural commonness and differences between a molecule and its synthons.
+
+The bond energy block also provides an untrivial contribution to bond embeddings. For example, Retro-MTGR with bond energies improves the Top-1, Top-3, and Top-5 accuracies by 1.6%, 4.9%, and 3.0% respectively when reaction types are unknown. The underlying reason is that bonds having high bond energies are usually ordinary bonds but not reaction centers. See also Section 3.4.1 for details.
+
+The LGCoG provides a significant contribution to leaving group identification. For instance, Retro-MTGR with the LGCoG improves the Top-1, Top-3, and Top-5 accuracies by 3.3%, 3.7%, and 1.8% respectively when reaction types are unknown. The essential
+reason for such improvements is that the captured LG dependences enrich LG representations when identifying LGs for synthons. Details can be found in Section 3.4.2.
+
+In general, all of the AEE module, the bond energy, and the leaving group co-occurrence graph play indispensable roles in retrosynthesis prediction. More detailed investigations in the next section indicate why they work.
+
+![Bar chart comparing Top-k Accuracy (%) for different models and reaction types](page_370_613_1002_388.png)
+
+Figure 2. Ablation comparison. Compared with the three variants (red, green and purple bars), Retro-MTGR (blue bars) achieves the best retrosynthesis prediction in terms of top-1, top3, and top-5 in the case of both unknown and known reaction types.
+
+3.4 Retrosynthesis rule discovery
+
+In this section, we shall attempt to uncover retrosynthesis rules by Retro-MTGR in two interpretable views, bond view and leaving group view. First, we shall investigate three questions to reveal why a bond can be the reaction center. Furthermore, we shall explore two questions to indicate what leaving groups are appropriate to given synthons.
+
+3.4.1 Bond view
+
+To interpret why a bond can be the reaction center, we considered three bond-derived questions as follows.
+
+(1) Can bond energies determine the reaction center in a molecule alone?
+
+For a chemical bond, its bond energy (i.e., the minimum energy to break it down) measures its stableness\(^{34}\). The larger, the stabler, the more difficult to be synthesized from the point of view of chemical retrosynthesis. Thus, we assume that the reaction center is of low bond-energy bond.
+
+To validate it, we made a statistical distribution of bond energies across all the bonds of molecules in a histogram (Figure 3). Note that we considered only the theoretical breaking energy of each chemical bond, but not considering the influence of its neighboring bonds or near atoms. The bonds were sorted into 20 equally spaced bins along the axis of bond energy between the
+minimum and maximum energy values (kJ/mol). Due to the number difference between reaction centers and ordinary bonds, the heights of bins (i.e., the number of bonds falling in the bins) were normalized by the total number of bonds for convenient comparison.
+
+As illustrated, the majority of bonds fall into four bins, [270,315], [315, 360], [450-495], and [495-540]. Specifically, the bond energies of reaction centers are usually located in the lower range of bond energy (i.e., 95.26% having bond energy <360 kJ/mol). In contrast, 45.33% of ordinary bonds have bond energy <360 kJ/mol and 54.65% have bond energy >=360 kJ/mol. Thus, a naïve decision can be made that bonds having bond energy >360 kJ/mol are usually ordinary bonds. Such a finding can be used to filter out the ordinary bonds having large breaking energies in the process of reaction center identification. This is why bond energies have a significant contribution to finding the reaction center. However, bond energies can NOT determine the reaction center in a molecule alone, since there are still a large number of ordinary bonds (45.33 %) overlapping with reaction centers in the case of having low breaking energies < 360 kJ/mol. This issue can be further investigated by the answer to the second question.
+
+![Bar chart showing the distribution of chemical bonds by breaking energy, with two bars per bin: one for ordinary bonds and one for reaction centers.](page_384_1012_1012_384.png)
+
+Figure 3. Breaking energy distribution of chemical bonds. The X-axis shows the bond energy (0-900) divided into 20 intervals. The Y-axis shows the frequency of chemical bonds falling in different bins. As illustrated, bonds having bond energy >360 kJ/mol are usually ordinary bonds. However, 45.33 % of ordinary bonds overlap with reaction centers in the case of breaking energies < 360 kJ/mol.
+
+(2) What is the underlying chemical rule captured by bond embeddings such that reaction centers can be distinguished from ordinary bonds?
+
+One of the core contributions of our model (Retro-MTGR) is just the discrimination of reaction centers from ordinary bonds in the case of low bond energy. Since bond embedding representations (Formula 2) characterize bond features based on molecule graph topology, we
+utilized them to exhibit the difference between reaction centers and ordinary bonds. Principal component analysis (PCA) was used to visualize bonds in 2-dimensional space, where each point represents a bond.
+
+Such a bond space was rendered in three maps (Figure 4).
+• The first map shows a clear separation between reaction centers (red points) and ordinary bonds (blue points), except for a small overlapping (Figure 4-a). Such a separation demonstrates that our model can characterize the difference between reaction centers and ordinary bonds well. More importantly, both reaction centers and ordinary can be split into communities, which are strongly specific to bond types.
+• The second map indicates that bond communities are consistence with bond types (Figure 4-b). Some bonds are always ordinary bonds, such as c~c (an aromatic bond linking two carbon atoms). More importantly, it is remarkable that some bonds having the same types (e.g., C-C, C-O, and C-N.) may occur in different communities, which belong to reaction centers and ordinary bonds respectively. The underlying reason is investigated in the answer to the third question.
+• The last map illustrates the distribution of bond energies in terms of energy bins (Figure 4-c). As observed, bonds with large breaking energies (two bins) are almost of ordinary bonds. More importantly, reaction centers and ordinary bonds having low breaking energies can be clearly distinguished. With the consideration of bond types, the bonds in the energy bin [270-315] mainly include C-N (a bond linking a carbon atom to a nitrogen atom) and C-Br (a bond linking a carbon atom to a bromine atom), while those in the energy bin [315-360] mainly include C-C (a bond linking two carbon atoms) and C-O (a bond linking a carbon atom to an oxygen atom).
+Figure 4. Bond space. (A). Reaction centers and ordinary bonds. Red dots indicate reaction centers while blue dots indicate ordinary bonds. (B). Bond types. Different colors represent different bonds. (C). Bond energies. Different colors indicate different bond energy bins (kJ/mol). In terms of chemical symbols, C stands for carbon atoms, c is for carbon atoms in aromatic bonds, and C' is for carbon atoms in general rings.
+Moreover, N stands for nitrogen atoms, n is for nitrogen atoms in aromatic bonds, and N' represents nitrogen atoms in general rings. In addition, O is for oxygen atoms, O' represents oxygen atoms in general rings, and S is for sulfur atoms. Four specific symbols, including '∼', '·', '─', and '#', denotes aromatic, single, double, and triple bonds respectively.
+
+(3) Why can a bond be the reaction center in a molecule but cannot be in another one?
+
+Considering that bond energy can NOT determine the reaction center in a molecule alone, our model (Retro-MTGR) leverages molecule graph topologies to capture the differences between reaction centers and ordinary bonds, even having the same bond types. We investigated what chemical rule hidden is captured by atom/bond embeddings. It is anticipated that the inherent law helps identify reaction centers and ordinary bonds, especially in the case of both common bond type and similar bond energy.
+
+Our investigation was inspired by the chemical knowledge that the electrical property (denoted as \( p \)) of an atom in a molecule is determined by the conjugation effect of the motion of its electrons as well as the union of its spatial neighboring atoms. When showing an attractive effect on electrons, the atom is considered an electron-withdrawing atom. On the contrary, it is called an electron-donating atom. Since it is difficult to quantify atom electrical properties due to complicated inter-atom influences, we first proposed a qualitative manner to label their strength and weakness. Then, by enumerating atom-centered substructures, we found 356 substructures (Section 2 in Supplementary), which are categorized into four groups in terms of electrical property strength. In detail, the atoms showing strong electron-withdrawing/donating properties are labeled as \( p^{++}|p-- \) respectively. Meanwhile, those atoms exhibiting weak electron-withdrawing/donating properties are marked as \( p+/p- \) respectively. As a result, the atom pairs forming bonds show ten possible pairs of electrical properties (e.g., \( (p^{++} | p--), (p+ | p-) \)) in total. Last, we counted the percentages of all types of electrical property pairs in the case of both reaction centers and ordinary bonds (Figure 5). The result illustrates that the atom pairs forming reaction centers have dominant opposite electrical properties (97.0% with 'p+ | p-', 'p+ |p--', 'p++ | p-', and 'p++ |p--' pairs) while those pairs forming ordinary bonds have same or similar electrical properties (80.1%). In fact, some ordinary bonds having opposite electrical properties are also reaction centers in the deeper steps of retrosynthesis. See also Section 3.5 Case Study. Thus, we conclude that the pair of an electron-withdrawing atom and an electron-donating atom tends to form a reaction center.
+
+In summary, our answers to these questions demonstrate that our Retro-MTGR can capture the underlying matching rule of why a bond can be the reaction center by embedding molecule topologies.
+Figure 5. Electrical property distribution of chemical bonds. The X-axis denotes pairwise electrical property patterns of atom pairs forming bonds. Its left zone lists six patterns of same/similar electrical properties while its right zone lists four patterns of opposite electrical properties. The Y-axis indicates the frequencies of electrical property patterns. The member atoms of ordinary bonds usually have same or similar electrical properties (80.1%), whereas those in reaction centers tend to have opposite electrical properties (97.0%).
+
+3.4.2 Leaving Group view
+
+To dig out what leaving groups are appropriate to given synthons, we leveraged the leaving group co-occurrence graph (LGCoG) to answer two LG-derived questions as follows.
+
+(1) Whether are two leaving groups associated when accounting for a pair of synthons derived from the same molecule?
+
+We sought its answer in two aspects. First, we followed the answer to the third question in the previous section that retrosynthesis site atoms in synthons always have opposite electrical properties. Analogously, when two leaving groups account for a pair of synthons derived from the same molecule, they are also supposed to have opposite electrical properties based on the electrical matching rule between a synthon and its LG. We validated this assumption by labeling the electrical properties of LGs (Figure 6-A) in a similar manner as that in Section 3.4.1. As counted, 94.3% of LG pairs (28823/30565) have opposite electrical properties.
+
+Then, we considered the occurrence of LG pairs. The co-occurrence is indicated by the edge thickness in the graph (Figure 6-A). As calculated, we found that the LG pairs consisting of two simple groups (e.g., H, OH, or halogens) usually occur frequently. Especially, the pairs ‘H, OH’ (27.8%), ‘H, Cl’(27.4%), ‘H, Br’(12.9%), and ‘H, I’ (8.1%) are the most frequent LG pairs. Moreover, the LG pairs including a simple group and a chemical substructure occur in a low frequency, such as ‘Br, CC1(C)OBOC1(C)C’ (1.8%). Few LG pairs (0.386%) are composed of chemical substructures only, such as ‘O=S(=O)(O)C(F)(F)F-B(OH)2, O=S(=O)(O)C(F)(F)-CC1(C)OBOC1(C)C’. More details can be found in Supplementary
+(Section 3).
+Thus, two leaving groups accounting for a pair of synthons are associated.
+
+(2) Whether is a leaving group specific to a reaction type?
+After taking a close look at the topology of the graph, we found a few LGs having many partner LGs and many LGs having only one partner. The former is always of simple groups (e.g., H, OH, or halogens), while the latter is usually chemical substructures. In addition, the remaining LGs have a small number of partners. To dig out the underlying reason, we made an investigation by counting LG occurrences according to reaction types (Section 4 in Supplementary).
+
+The investigation reveals interesting knowledge that LGs can be split into two categories according to the number of reaction types they attending in.
+
+The first category, named ‘reaction-common’ LGs, contains the LGs appearing in equal to or more than the half number of reaction types (i.e., \( \geq 4 \)). They are usually of simple LGs, and occur frequently and have many matching partner LGs. In details, ‘H’, ‘OH’, ‘Cl’, and ‘Br’ appear in 7, 7, 6 and 5 categories, respectively. Especially, ‘H’ attends in almost all the reactions while occurring 27623 times and having 37 kinds of matching partner LGs (denoted by the node degree in the graph). Moreover, halogens including ‘Cl’, ‘Br’, and ‘I’, have many common partner LGs. The possible reason is that they have similar chemical properties, which suggests a potential replacement between them.
+
+The second category, named ‘reaction-specific’ LGs, includes the LGs occurring only in specific types of reactions. They are of usually chemical substructure groups, such as ‘-CC’, ‘-OCC(Cl)(Cl)Cl’, and ‘-OCC(F)(F)F’. We found that reaction-specific LGs are surrounding reaction-common LGs or clustered together (Figure 6-B). In addition, some LGs involving in the same type of reaction have similar chemical structures, such as the pair of ‘CCOC(=O)O’ and ‘CC(C)(C)OC(=O)O’ in Type 2 reaction (0.783) and the pair of ‘B1OCCO1’ and ‘B1OCCCO1’ (0.754) in Type 3 reaction, where the similarity is calculated by MACCS fingerprints in terms of Jaccard similarity. Again, the chemical structure similarity of LGs implies their possible substitution, which is determined by the cost or the reaction condition available in synthesis reaction routes.
+
+In general, the co-occurrence graph of leaving groups contains rich retrosynthesis information, including the inter-associations between LGs and their reaction specificity. Our Retro-MTGR can capture such rich information to enhance the retrosynthesis prediction. The answers in this section dig out why the graph contributes to the prediction.
+Figure 6. Leaving Group view. (A) Electrical property map. LGs having positive and negative electrical properties are rendered by red and blue. In total, 94.3% of LG pairs have opposite electrical properties. (B) Reaction type map. LGs occurring in single reaction types, multiple reaction types (<=3) and many types (>=4, reaction-common) are highlighted in different colors.
+
+3.5 Case Study
+To evaluate the ability of our Retro-MTGR in the real scenario of retrosynthesis prediction, we collected two drugs (i.e., Sonidegib\(^{35}\) and Acotiamide\(^{36}\)), not included in our dataset, as the studying cases. We inferred their retrosynthesis routes by our Retro-MTGR and then validated
+them by chemical assays respectively.
+
+The two drugs we selected are briefly summarized as follows. The first drug, Sonidegib, is a Hedgehog signaling pathway inhibitor (via smoothened antagonism), which was developed as an anticancer agent by Novartis and approved by the FDA in 2015 for the treatment of basal cell carcinoma. Now it is commonly used for the treatment of locally advanced recurrent basal cell carcinoma (BCC) following surgery and radiation therapy, or in cases where surgery or radiation therapy are not appropriate (DrugBank ID: DB09143) \(^{35}\). The second drug, Acotiamide, being an investigational drug, was designed and developed for the treatment of functional dyspepsia (FD)\(^{36}\) (DrugBank ID: DB12482). It works as a novel upper gastrointestinal (GI) motility modulator and stress regulator by improving upper gastrointestinal functions in both the stomach and esophagus.
+
+Since Retro-MTG is a single-step retrosynthesis prediction model, we iteratively applied it to infer a complete retrosynthesis route for a given drug molecule. In the first iteration, Retro-MTG split the complete molecule into two synthons under the top-1 criterion (the first candidate reaction center), which were further turned into smaller intermediate molecules by appending appropriate leave groups. Intermediate molecules were then split into smaller ones by Retro-MTG in a similar way unless the intermediate molecules are reactants, which can be easily bought in the market.
+
+As shown in Figure 7, the predicted retrosynthesis route of Sonidegib illustrates that it (marked as ‘1’) can be split into two intermediate molecules (marked as ‘2’ and ‘3’). Further, they are split into two pairs of reactants respectively, where one pair is (marked as ‘4’ and ‘5’) while another is (marked as ‘6’ and ‘7’). In each retrosynthesis step, the attention scores of bonds are labeled and the highest one (top-1) is considered as the reaction center. During predicting the retrosynthesis route, both reaction centers and leaving groups are corrected predicted (Figure 7-A). Furthermore, according to the prediction, a series of chemical synthesis reactions starting from reactants (‘4’, ‘5’, ‘6’, and ‘7’) were performed (Figure 7-B) to validate the predicted retrosynthesis route. Remarkably, due to the potential intra-reaction among ‘6’ molecules triggered by their own Chlorine (-Cl) and amino group (-NH2), the expected reaction between ‘6’ and ‘7’ would generate less amount of ‘3’ molecules. To guarantee a high production of ‘3’ in the real synthesis, we converted ‘6’ to ‘8’ by a nitration reaction, which alters the amino group to a nitro group (-NO2). Then, the reaction of ‘8’ and ‘7’ produced ‘9’, of which the nitro group was further converted back into the amino group in a reduction reaction to obtain ‘3’ with the desired production. Meanwhile, the reaction of ‘4’ and ‘5’ generated ‘2’. Finally, we performed an amidation reaction by combining ‘2’ and ‘3’ to form the product molecule Sonidegib (‘1’).
+
+Similarly, the retrosynthesis route of Acotiamide (marked as ‘10’) is correctly predicted in terms of both reaction centers and leaving groups, and validated by chemical synthesis reactions
+as well. Specifically, the first retrosynthesis step generates an intermediate molecule (‘11’) and a reactant (‘12’). Then, the former is split into two reactants (‘13’ and ‘14’) in the second step (Figure 7-C). Since there is also an intra-reaction issue in ‘14’, a similar strategy was adopted to guarantee the final production of ‘10’. In brief, the carboxylic acid group (-OH) of ‘14’ was altered to a methoxy group (-OCH3) so as to generate ‘15’ by an esterification reaction. As the substitution of ‘14’, ‘15’ was put together with ‘13’ to generate a new intermediate molecule ‘16’, which was sequentially hydrolyzed to intermediate molecule 11 by both NaOH and HCl. Finally, a similar amidation reaction combining ‘11’ and ‘12’ was performed to form Acotiamide (‘10’) (Figure 7-D).
+
+To summarize, Retro-MTGR shows that its inspiring retrosynthesis prediction is significantly consistent with chemical assays. Thus, it can provide clear guidance for retrosynthesis route planning with extra reaction conditions.
+
+![Predicted retrosynthetic routes and real chemical synthetic routes. A. Retrosynthesis prediction of Sonidegib. B. Synthetic route of Sonidegib. C. Retrosynthesis prediction of Acotiamide. D. Synthetic route of Acotiamide.](page_384_693_1080_1012.png)
+
+Figure 7. Predicted retrosynthetic routes and real chemical synthetic routes. A. Retrosynthesis prediction of Sonidegib. Sonidegib (‘1’) is split at the reaction center into intermediate molecules ‘2’ and ‘3’, where the highest
+attention score generated by our Retro-MTGR is highlighted. Then, ‘2’ and ‘3’ are further decomposed into four reactants (‘4’, ‘5’, ‘6’ and ‘7’) respectively according to their reaction centers. **B. Chemical synthesis of Sonidegib**. First, the Suzuki cross-coupling reaction between ‘4’ and ‘5’ was performed to obtain intermediate molecule ‘2’. Meanwhile, ‘6’ is converted to ‘8’ with the help of m-CPBA (m-Chloroperbenzoic Acid) for preventing its intra-reaction. Then, ‘8’ is combined with ‘7’ in the presence of DIEA (N, N-diisopropylethylamine) to form another intermediate molecule ‘9’, which is further reduced by H2 in the presence of Pd/C to generate ‘3’. In the last step, the coupling of compound ‘2’ with ‘3’ in the presence of HATU (2-(7-Azabenzotriazol-1-yl)-N, N, N', N'-tetramethyluronium hexafluorophosphate) and DIEA (N,N-Diisopropylethylamine) in DMF (N,N-Dimethylformamide) generates Sonidegib (‘1’). **C. Retrosynthesis prediction of Acotiamide**: Acotiamide (‘10’) is split at the reaction center into intermediate molecules ‘11’ and reactant ‘12’, where the highest attention score generated by our Retro-MTGR is highlighted as well. Then, ‘11’ is further decomposed into two reactants (‘13’ and ‘14’) respectively according to their reaction centers. **D. Chemical synthesis of Acotiamide**. First, reactant ‘14’ is esterified with methanol to form ‘15’. Then, the coupling compound 13 with 15 in the presence of HATU and DIEA obtains the intermediate molecule ‘16’, which is sequentially hydrolyzed to another intermediate molecule ‘11’ by NaOH and HCl. Finally, the coupling between the intermediate molecule ‘11’ and the reactant ‘12’ in the presence of HATU and DIEA in DMF generates the molecule of Acotiamide (‘10’). More details (e.g., reaction conditions and instruments) about the chemical synthesis reactions of these two drugs can be found in Supplementary (Section 5). Note: DIEA works as a catalyzer in the reduction reaction or a promoter in the aromatic nucleophilic substitution of N-hydrophosphoramidate. HATU works as a popular condensation reagent in promoting amide bond formation by activating carboxyl groups. m-CPBA is a strong oxidizing agent widely used in organic synthesis. Pd/C is also a kind of popular catalyst in hydrogenation reduction.
+
+**4 Conclusions**
+
+Aiming at a well-interpretable discriminative model in terms of chemical synthesis mechanism, this paper elaborates a novel multi-task graph representation learning framework of retrosynthesis prediction (Retro-MTGR). Based on molecule graphs, three related tasks are considered in Retro-MTGR simultaneously, where two major supervised discriminative tasks account for recognizing reaction centers and identifying leaving groups respectively, and an auxiliary self-supervised task accounts for generating better atom embeddings.
+
+The comparison with various state-of-the-art methods demonstrates the overall superiority of Retro-MTGR in terms of cross-validation prediction performance in both reaction-type unknown and reaction-type known scenarios. Furthermore, the ablation study demonstrates its contributions as follows. First, it significantly enhances atom embedding by leveraging chemical structural redundancy and differences between a molecule and its synthons. Then, it uncovers that bond energies can partially boost bond
+embeddings due to the difference between ordinary bonds and reaction centers in the case of high bond energy. Last, it utilizes LG co-occurrences to enrich LG representations.
+
+Furthermore, multiple comprehensive investigations validate the chemical synthesis interpretability of Retro-MTGR by answering two questions: why a bond can be the reaction center or not, and what leaving groups are appropriate to given synthons. The answers demonstrate that Retro-MTGR can capture and illustrate the underlying chemical synthesis rules as follows: (1) a bond having high-breaking energy (>=360 kJ/mol) is usually an ordinary bond; (2) aromatic bonds (c~c) between carbon atoms are always ordinary bonds, while other types of bonds can be either reaction centers or ordinary bonds; (3) a bond is the reaction center in a molecule if its member atoms tend to have opposite electrical properties, otherwise an ordinary bond;(4) accordingly, leaving group (LG) pairs in reaction centers usually have opposite electrical properties and occurrence-dominant LG pairs always consisting of two simple groups (e.g., H, OH, or halogens); (5) individual LGs can be categorized into reaction-common LGs (simple groups) and reaction-specific LGs (chemical substructures).
+
+Finally, the practical ability of Retro-MTGR is evaluated by two novel drugs. The results reveal that the inferred retrosynthesis routes by Retro-MTGR are significantly consistent with those achieved by chemical synthesis assays.
+
+In summary, our Retro-MTGR can provide prior guidance for retrosynthesis route planning. We believe that its extension with the integration of extra synthetic factors (e.g., reaction yield, conditions, and reagents) can be a complete retrosynthesis route planning in the coming future.
+
+Acknowledgements:
+The authors would like to thank anonymous reviewers for suggestions that improved the paper.
+
+Funding
+This work was supported by the National Nature Science Foundation of China [61872297], the Shaanxi Province Key R&D Program [2023-YBSF-114], and the CAAI-Huawei Mind Spore Open Fund [CAAIXSJLJJ-2022-035A].
+
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+Supplementary Files
+
+This is a list of supplementary files associated with this preprint. Click to download.
+
+• Data1.xlsx
+• Data2.xlsx
+• Data3.xlsx
+• Supplementary.pdf

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+Peer Review File
+
+Trichalcogenasupersumanenes and its concave-convex supramolecular assembly with fullerenes
+
+Open Access This file is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. In the cases where the authors are anonymous, such as is the case for the reports of anonymous peer reviewers, author attribution should be to 'Anonymous Referee' followed by a clear attribution to the source work. The images or other third party material in this file are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.
+Reviewers' Comments:
+
+Reviewer #1:
+Remarks to the Author:
+This manuscript reports the synthesis of new large buckybowl molecules based on a hexabenzo-coronene core. In general, giant buckybowls are very difficult to synthesize due to their instability caused by ring strain. However, the elegant synthetic strategy in this manuscript solved this problem to successfully make the superbuckybowl molecules. The synthesis itself is worth of reporting in a prestigious journal. The authors also investigated many properties of the obtained molecules, albeit very conventional ones. I recommend this manuscript to be published in Nature Communications. However, the following issues should be addressed and resolved prior to publication.
+
+1) Title: "Trichalcogenohexaindenocoronene" is not appropriate because one indene structure is fused to adjacent indene rings. In this case, it cannot be called "hexaindeno". This should be changed.
+
+2) Page 4, left column: "This is the first time that such a supersized buckybowl was achieved" is wrong. The carbon nanocone reported in J. Am. Chem. Soc. 2019, 141, 13008 is much larger because it has 26 fused pentagon/hexagons.
+
+3) Page 5, right column: I could not understand the sentence, "As shown in Figs 4(c) and 4(f), there are 4 circles, totally 36 different pyramidal trigonal carbon atoms existed in these coronene-based superbowls, except for 18 atoms at the peripheral vertexes."
+What does "4 circles" mean? Why is the number of trigonal carbon atoms 36? If I am correct, this molecular core has forty two(42) sp2-carbon and three(3) sp3-carbon atoms. What does "18 atoms at the peripheral vertexes" mean?
+
+4) The stability of the super buckybowl compounds should be mentioned. For example, are they stable in oxygen or water?
+
+5) Reference [15-29] are too roughly organized. In my opinion, "buckybowls with only carbon and hydrogen atoms" and "heteroatoms-embedded buckybowls" should be mentioned separately.
+
+6) Some important references are missing. The following papers on pi-extended buckybowls should be cited.
+6-1) The Würthner group reported a carbon nanocone: J. Am. Chem. Soc. 2019, 141, 13008–13012.
+6-2) The Ito group reported some pi-extended azacorannulenes: Angew. Chem. Int. Ed. 2018, 57, 9818; Angew. Chem. Int. Ed. 2022, 61, e202112638; Nat. Commun. 2022, 13, 1498.
+6-3) The Hatakeyama group reported a B2N2-embeddee corannulene: J. Am. Chem. Soc. 2018, 140, 13562.
+
+7) The references cited are a bit old (mostly before 2020). As this field is advancing quickly, please update the references to cite recent papers as well.
+
+8) There are many grammatical errors and expressions that do not make sense. English should be polished by a native professional proofreader.
+
+Reviewer #2:
+Remarks to the Author:
+This is an interesting manuscript which describes the synthesis of two novel bowl-shaped poly-cyclic aromatics endowed with three chalcogen (S or Se) atoms and three substituted methylene groups at the bay regions of well-known hexa-peri-hexabenzocoronene. The synthetic approach is original, involving only three-steps, namely an aldol cyclotrimerization, a Scholl reaction, and a Stille
+dehydration. The resulting compounds have an interesting C3v symmetry which has been confirmed by X-ray crystallography. Furthermore, a full spectroscopic characterization has been performed and also some relevant properties which have been underpinned by theoretical calculations, thus provided a nice description of the new nanographene.
+The work has been competently carried out and the results are sound, based in a new controlled synthetic approach. Therefore, I feel that the manuscript meets the criteria of novelty and quality to be accepted for publication after addressing the following points:
+1) The authors should mention the essays carried out in order to improve the Scholl reaction yield as mentioned. This could be of interest for the specialized community working on this topic.
+2) In Figure 8 the axes cannot be visualized in (a) and (b). This makes difficult to follow the CV discussion. In this regard, the wave of the first oxidation potential seems to be reversible but, the second one, should be considered as quasireversible. Furthermore, the oxidation potential values for pristine HBC (or alkyl substituted) as a reference, would provide the real effect of the heteroatoms on the electrochemical properties.
+3) The HOMO-LUMO gap for both compounds (1a and 1b) are basically the same. A small difference is, however, noted in the CV data. However, I do not see the explanation given by the authors to the slightly better oxidation potential value for the S compared to Se. Furthermore, the HOMO value is slightly higher for the Se compound, which means a better donor character.
+4) Perhaps this review could be of interest for ref. 11-13: Angew. Chem. Int. Ed., 2012, 51, 7094-7101.
+
+Reviewer #3:
+Remarks to the Author:
+This manuscript by Li, Wei, and co-workers describes the synthesis and properties of trichalcogenohexaindenocoronenes. The titled compound represents a curved hexabenzocoronene (HBC) derivative having six bridging units at the bay area. Incorporation of these bridging units affords fused five-membered rings, resulting in a significantly curved structure. The synthesis of a similar compound was examined by a different group in 2015 by subjecting dodecachlorinated HBC to the nucleophilic aromatic substitution reaction with sulfide. This precedented synthesis afforded a tri-bridged compound instead of the desired bowl-shaped compound. The authors have overcome this issue in this manuscript by connecting three fluorene units by palladium-catalyzed C-S coupling reactions. The fact that the authors succeeded in synthesizing such a big and beautiful bowl-shaped hydrocarbon is worthy of praise. The authors explored the fundamental properties of 1a and 1b, including X-ray diffraction analysis, spectroscopic measurements, cyclic voltammetry, and DFT calculations. The discussions are solid, and this reviewer agrees for the most part.
+However, this reviewer thinks that this manuscript lacks the novelty which deserves publication in Nature Communications. First, although the synthetic strategy shown in this manuscript is elegant, all the reactions have been developed previously. Especially the fact that a palladium-catalyzed C–S coupling reaction, which is a key step in the current strategy, is a powerful tool to create distortion has been demonstrated for the synthesis of distorted perylene bisimide derivatives (ref. 35). Second, the fundamental properties of trichalcogenohexaindenocoronenes including their structural distortion, photophysical properties, redox responses, and aromaticity are within expectations. In conclusion, this reviewer will support the acceptance if the authors describe other outstanding properties of the trichalcogenohexaindenocoronenes (i.e. unique reactivity, ferroelectricity in the solid state, and efficient fullerene-binding). The last two topics may require synthesizing other trichalcogenohexaindenocoronene derivatives with smaller alkyl chains.
+
+Comments to authors
+1. How about comparing the structural factors (bond lengths and bond alternation) of trichalcogenohexaindenocoronenes with those of HBC, which will give fruitful insight into the effect of distortion.
+2. The authors note that hexagons (b) present a feeble antiaromatic character. However, this reviewer
+thinks this argument is overstated because the NICS(1)zz values are close to zero.
+3. On page 8, "Eying" should be "Eyring".
+4. On page 12, "1,3,5-Tris" should be "1,3,5-tris".
+5. For the 13C NMR spectrum of 3, two signals are missing. Please comment.
+6. On page S28 in SI, "Erying" should be "Eyring".
+7. The 1H NMR spectrum of 1b exhibits some undefined signals in the up-fielded region (i.e. triplet at 2.4 ppm and weak signals in the range of 1.3–0.6 ppm). Furthermore, the 13C NMR signals of 1b are weak. These two points should be improved.
+Point-by-point response
+
+Reviewer comments:
+
+Reviewer #1 (Remarks to the Author):
+
+This manuscript reports the synthesis of new large buckybowl molecules based on a hexabenzo[coronene] core. In general, giant buckybowls are very difficult to synthesize due to their instability caused by ring strain. However, the elegant synthetic strategy in this manuscript solved this problem to successfully make the superbuckybowl molecules. The synthesis itself is worth of reporting in a prestigious journal. The authors also investigated many properties of the obtained molecules, albeit very conventional ones. I recommend this manuscript to be published in Nature Communications. However, the following issues should be addressed and resolved prior to publication.
+
+Response:
+
+We express our sincere thanks to this reviewer for his/her extensive reading and we are so delighted to see these supportive comments.
+
+1) Title: "Trichalcogenohexaindenocoronene" is not appropriate because one indene structure is fused to adjacent indene rings. In this case, it cannot be called "hexaindeno". This should be changed.
+
+Response:
+
+Thank you very much for your comments and suggestions. Because the IUPAC name for **1a** and **1b** are rather onerous, it is appropriate to introduce a more convenient trivial name. As it happens, the all-carbon version of **1a** and **1b** belongs to a family of large polycyclic aromatic hydrocarbons (PAHs) in which pentagonal and hexagonal rings alternately encircle a coronene (superbenzene) core, we prefer to call it "supersumanene" based on the similar structural characteristic and larger size compared with sumanene. In this way, **1a** and **1b** can be called trichalcogenasupersumanenes due to the heteroatoms doping. We have modified the title and added a description in the revised manuscript as follows.
+
+Title: "Trichalcogenasupersumanenes and its concave-convex supramolecular assembly with fullerenes"
+
+Such bowl molecules feature a coronene core successively circumscribed by alternate hexagonal and pentagonal rings, we prefer to call it "(hetero)supersumanene" as a convenient trivial name based on similar structural characteristics and larger size compared with sumanene.
+sumanene (X = CH₂)
+heterosumanene (X = heteroatom)
+
+supersumanene (X = CH₂)
+heterosupersumanene (X = heteroatom)
+
+2) Page 4, left column: "This is the first time that such a supersized buckybowl was achieved" is wrong. The carbon nanocone reported in J. Am. Chem. Soc. 2019, 141, 13008 is much larger because it has 26 fused pentagon/hexagons.
+
+Response:
+
+Thank you very much for your comments and suggestions. We have deleted it in the revised manuscript.
+
+3) Page 5, right column: I could not understand the sentence, "As shown in Figs 4(c) and 4(f), there are 4 circles, totally 36 different pyramidalized trigonal carbon atoms existed in these coronene-based superbowls, except for 18 atoms at the peripheral vertexes." What does "4 circules" mean? Why is the number of torigonal carbon atoms 36? If I am correct, this molecular core has fourty two(42) sp²-carbon and three(3) sp³-carbon atoms. What does "18 atoms at the peripheral vertexes" mean?
+
+Response:
+
+Thank you very much for your comments and suggestions. We apologize for the lack of sufficient explanation. As shown in the following figure, "4 circles" represents the range of torigonal carbon atoms with POAV angles from the central hub ring to the periphery of bowl molecule. Because 12 (not 18) atoms at the peripheral vertexes including the torigonal carbon atoms of peripheral vertexes and 3 sp³-carbon atoms as well as heteroatoms have no POAV angles. There are errors and vagueness in previous expressions, we have corrected them in the revised manuscript as follows.
+
+6 species of 36 pyramidalized carbon atoms (X ≠ Y)
+4 species of 36 pyramidalized carbon atoms (X = Y)
+12 atoms at the peripheral vertexes (X, Y, ○)
+As shown in Figs 4(c) and 4(f), there are six categories in a total of 36 different pyramidalized trigonal carbon atoms that existed in these trichalcogenasupersumanenes, except for 6 negligible pyramidalized sp^2 carbon atoms at the peripheral vertexes.
+
+4) The stability of the super buckybowl compounds should be mentioned. For example, are they stable in oxygen or water?
+
+Response:
+
+Thank you very much for your comments and suggestions. We have modified it in the revised manuscript as follows.
+
+Meanwhile, these trichalcogenasupersumanenes are stable enough and can be stored in solution and solid under air atmosphere for weeks without any change.
+
+5) Reference [15-29] are too roughly organized. In my opinion, "buckybowls with only carbon and hydrogen atoms" and "heteroatoms-embedded buckybowl" should be mentioned separately.
+
+Response:
+
+Thank you very much for your comments and suggestions. We have modified it in the revised manuscript as follows.
+
+Owing to the huge inner strain of bowl-shaped hydrocarbons makes their synthesis a major challenge, the number of buckybowl is still relatively rare compared with flat PAHs. Hitherto the most literature-known hydrocarbon buckybowl were related to C_{60}[11–19] or C_{70}[20–26] fullerene fragments and their π-extended derivatives[27–30]. In addition, some heteroatoms-embedded buckybowl involving B[31], N[32–38], P[39], S[40], Se[41–43], etc. have also been synthesized and sought as model compounds and partial structures for higher heterofullerenes.
+
+New added references in the manuscript:
+
+[14] Reisch, H. A., Bratcher, M. S. & Scott, L. T. Imposing curvature on a polyarene by intramolecular palladium-catalyzed arylation reactions: A simple synthesis of dibenzo[a,g]corannulene. Org. Lett. 2, 1427–1430 (2000).
+
+[17] Sygula, A., Marcinow, Z., Guzei, I. & Rabideau, P. W. The first crystal structure characterization of a semibuckminster fullerene, and a novel synthetic route. Chem. Commun. 24, 2439–2440 (2000).
+
+[18] Dickinson, C. F., Yang, J. K., Yap, G. P. A. & Tius, M. A. Modular synthesis of a semibuckminsterfullerene. Org. Lett. 24, 5095–5098 (2022).
+
+[21] Hishikawa, S. et al. Synthesis of a C_{70} fragment buckybowl C_{28}H_{14} from a C_{60} fragment sumanene. Chem. Lett. 46, 1556–159 (2017).
+[22] Nishimoto, M. et al. Synthesis of the C_{70} fragment buckybowl, homosumanene, and heterahomosumanenes via ring-expansion reactions from sumanenone. J. Org. Chem. **87**, 2508–2519 (2022).
+
+[24] Gao, G. P. et al. Rational functionalization of a C_{70} buckybowl to enable a C_{70}: buckybowl cocrystal for organic semiconductor applications. J. Am. Chem. Soc. **142**, 2460–2470 (2020).
+
+[26] Tanaka, Y., Fukui, N. & Shinokubo, H. as-Indaceno[3,2,1,8,7,6-ghijklm]terrylene as a near-infrared absorbing C_{70}-fragment. Nat. Commun. **11**, 3873 (2020).
+
+[27] Shoyama, K. & Würthner, F. Synthesis of a Carbon nanocone by cascade annulation. J. Am. Chem. Soc. **141**, 13008–13012 (2019).
+
+[28] Zhu, Z. Z. et al. Rational synthesis of an atomically precise carboncone under mild conditions. Sci. Adv. **5**, eaaw0982 (2019).
+
+[29] Amaya, T., Nakata, T. & Hirao, T. Synthesis of highly strained π-bowls from sumanene. J. Am. Chem. Soc. **131**, 10810–10811 (2009).
+
+[30] Amaya, T., Nakata, T. & Hirao, T. Construction of a hemifullerene skeleton: A regioselective intramolecular oxidative cyclization. Angew. Chem. Int. Ed. **54**, 5483–5487 (2015).
+
+[31] Nakatsuka, S., Yasuda, N. & Hatakeyama, T. Four-step synthesis of B_2N_2-embedded corannulene. J. Am. Chem. Soc. **140**, 13562–13565 (2018).
+
+[34] Tokimaru, Y., Ito, S. & Nozaki, K. A hybrid of corannulene and azacorannulene: synthesis of a highly curved nitrogen-containing buckybowl. Angew. Chem. Int. Ed. **57**, 9818–9822 (2018).
+
+[35] Li, Q. Q. et al. Diazapentabenzoazacorannulenium: a hydrophilic/biophilic cationic buckybowl. Angew. Chem. Int. Ed. **61**, e202112638 (2022).
+
+[36] Wang, W., Hanindita, F., Hamamoto, Y., Li, Y. & Ito, S. Fully conjugated azacorannulene dimer as large diaza[80]fullerene fragment. Nat. Commun. **13**, 1498 (2022).
+
+[37] Krzeszewski, T., Dobrzycki, Ł., Sobolewski, A. L., Cyrański, M. K. & Gryko, D. T. Bowl-shaped pentagon and heptagon embedded nanographene containing a central pyrrolo[3,2-b]pyrrole core. Angew. Chem. Int. Ed. **60**, 14998–15005 (2021).
+
+[39] Furukawa, S. et al. Triphosphasumanene trisulfide: high out-of-plane anisotropy and Janus-type π-surfaces. J. Am. Chem. Soc. **139**, 5787–5792 (2017).
+
+[40] Imamura, K., Takimiya, K., Otsubo, T. & Aso, Y. Triphenylene[1,12-bcd:4,5-b'c'd':8,9-b"c'd"]trithiophene: the first bowl-shaped heteroaromatic. Chem. Commun. **1859–1860** (1999).
+[43] Qiu, Z. L. et al. Synthesis and interlayer assembly of a graphenic bowl with peripheral selenium annulation. J. Am. Chem. Soc. **145**, 3289–3293 (2023).
+
+6) *Some important references are missing. The following papers on pi-extended buckybowls should be cited. 6-1) The Würthner group reported a carbon nanocone: J. Am. Chem. Soc. 2019, 141, 13008–13012. 6-2) The Ito group reported some pi-extended azacorannulenes: Angew. Chem. Int. Ed. 2018, 57, 9818; Angew. Chem. Int. Ed. 2022, 61, e202112638; Nat. Commun. 2022, 13, 1498. 6-3) The Hatakeyama group reported a B2N2-embeddee corannulene: J. Am. Chem. Soc. 2018, 140, 13562.*
+
+**Response:**
+
+Thank you very much for your comments and suggestions. We have added these important references in the revised manuscript.
+
+7) *The references cited are a bit old (mostly before 2020). As this field is advancing quickly, please update the references to cite recent papers as well.*
+
+**Response:**
+
+Thank you very much for your comments and suggestions. We have updated the references [11-43] to cite recent papers as references.
+
+8) *There are many grammatical errors and expressions that do not make sense. English should be polished by a native professional proofreader.*
+
+**Response:**
+
+Thank you very much for your comments and suggestions. Lastly, we revised the whole manuscript carefully to avoid language errors. In addition, we consulted a professional editing service and asked several colleagues who are native English speakers to check the English. We believe that the language is now acceptable for the review process.
+
+Reviewer #2 (Remarks to the Author):
+
+*This is an interesting manuscript which describes the synthesis of two novel bowl-shaped poly-cyclic aromatics endowed with three chalcogen (S or Se) atoms and three substituted methylene groups at the bay regions of well-known hexa-peri-hexabenzocoronene. The synthetic approach is original, involving only three-steps, namely an aldol cyclotrimerization, a Scholl reaction, and a Stille dehydrogenation. The resulting compounds have an interesting C3v symmetry which has been confirmed by X-ray crystallography. Furthermore, a full spectroscopic characterization has been performed and also some relevant properties which have been underpinned by theoretical calculations, thus provided a nice description of the new nanographene. The work has been competently carried out and the results are sound, based in a
+new controlled synthetic approach. Therefore, I feel that the manuscript meets the criteria of novelty and quality to be accepted for publication after addressing the following points:
+
+Response:
+
+We express our sincere thanks to this reviewer for his/her extensive reading and we are so delighted to see these supportive comments.
+
+1) The authors should mention the essays carried out in order to improve the Scholl reaction yield as mentioned. This could be of interest for the specialized community working on this topic.
+
+Response:
+
+We feel great thanks for your nice suggestions and made the following changes in the revised manuscript.
+
+We also briefly explored the improvement of Scholl reaction of 3 including temperature, reaction time, and stoichiometry of acid and finally found relatively satisfactory conditions, as denoted in Fig. 2. It is noteworthy that the presence of chlorine atoms is also critical to the success of the Scholl reaction, replacing the chlorine atoms with the hydrogen atoms will lead to complex products. Moreover, the hexfluorinated and hexabrominated versions of key intermediate TFC 4 could not be obtained via oxidative cyclization.
+
+2) In Figure 8 the axes cannot be visualized in (a) and (b). This makes difficult to follow the CV discussion. In this regard, the wave of the first oxidation potential seems to be reversible but, the second one, should be considered as quasi-reversible. Furthermore, the oxidation potential values for pristine HBC (or alkyl substituted) as a reference, would provide the real effect of the heteroatoms on the electrochemical properties.
+
+Response:
+
+Thanks for your nice suggestions. We have remeasured the cyclic voltammetry curve to display the reversibility of each oxidation wave. Furthermore, we have synthesized hexa-tert-butyl substituted HBC derivate (‘Bu-HBC) as a reference and added some discussions in the revised manuscript as follows.
+
+Cyclic and differential pulse voltammetric experiments (Fig. 8b) were conducted to demonstrate the electrochemical properties of 1a and 1b with ‘Bu-HBC as a reference. The cyclic voltammetry of 1a gave the first reversible and second quasi-reversible as well as the third irreversible oxidation wave. In comparison, 1b displayed the first quasi-reversible and subsequent multi-irreversible oxidation waves. The low reversibility of the oxidation waves for 1b compared with 1a may be ascribed to a stronger electron-rich characteristic of selenium atoms. The first half-wave potentials \( E_{ox}^{1/2} \) of 1a and 1b locate at 0.87 V and 0.92 V against SCE respectively, both of them are lower than ‘Bu-HBC (\( E_{ox}^{1/2}=1.06 \) V) due to the heteroatoms doping. In addition, 1a displayed negatively shifted first oxidation potentials compared to 1b, which can be attributed to the better p-\(\pi\) conjugation and electron-donating effect of sulfur compared with selenium. All of the HOMO/LUMO energy levels were estimated from the onsets of oxidation from CV and approximate onsets of reduction from the DPV data, which displayed -5.23/-2.35 eV for 1a and -5.30/-2.38 eV for 1b, corresponding to the electrochemical energy gaps of 2.88 eV and 2.92 eV
+respectively (Table S4), following their optical gaps and HOMO-LUMO gaps of DFT calculations.
+
+![Cyclic voltammetry and DPV curves for compounds 1a, 1b, and Bu-HBC, showing oxidation potentials and energy levels.](page_370_328_695_393.png)
+
+3) *The HOMO-LUMO gap for both compounds (1a and 1b) are basically the same. A small difference is, however, noted in the CV data. However, I do not see the explanation given by the authors to the slightly better oxidation potential value for the S compared to Se. Furthermore, the HOMO value is slightly higher for the Se compound, which means a better donor character.*
+
+**Response:**
+
+We feel great thanks for your nice suggestions, we have remeasured the cyclic voltammetry curve and corrected the discussion as follows.
+
+In addition, **1a** displayed negatively shifted first oxidation potentials compared to **1b**, which can be attributed to the better p-π conjugation and electron-donating effect of sulfur compared with selenium. All of the HOMO/LUMO energy levels were estimated from the onsets of oxidation from CV and approximate onsets of reduction from the DPV data, which displayed -5.23/-2.35 eV for **1a** and -5.30/-2.38 eV for **1b**, corresponding to the electrochemical energy gaps of 2.88 eV and 2.92 eV respectively (Table S4), following their optical gaps and HOMO-LUMO gaps of DFT calculations.
+4) Perhaps this review could be of interest for ref. 11-13: Angew. Chem. Int. Ed., 2012, 51, 7094-7101.
+
+Response:
+
+Thank you very much for your comments and suggestions. We have added this important reference.
+
+[9] Bunz, U. H. F., Menning, S. & Martin N. para-Connected cyclophenylenes and hemispherical polyarenes: building blocks for single-walled carbon nanotubes? Angew. Chem. Int. Ed. 51, 7094–7101 (2012)
+
+Reviewer #3 (Remarks to the Author):
+
+This manuscript by Li, Wei, and co-workers describes the synthesis and properties of trichalcogenohexaindenocoronenes. The titled compound represents a curved hexabenzocoronene (HBC) derivative having six bridging units at the bay area. Incorporation of these bridging units affords fused five-membered rings, resulting in a significantly curved structure. The synthesis of a similar compound was examined by a different group in 2015 by subjecting dodecachlorinated HBC to the nucleophilic aromatic substitution reaction with sulfide. This preceded synthesis afforded a tri-bridged compound instead of the desired bowl-shaped compound. The authors have overcome this issue in this manuscript by connecting three fluorene units by palladium-catalyzed C–S coupling reactions. The fact that the authors succeeded in synthesizing such a big and beautiful bowl-shaped hydrocarbon is worthy of praise. The authors explored the fundamental properties of 1a and 1b, including X-ray diffraction analysis, spectroscopic measurements, cyclic
+voltammetry, and DFT calculations. The discussions are solid, and this reviewer agrees for the most part. However, this reviewer thinks that this manuscript lacks the novelty which deserves publication in Nature Communications. First, although the synthetic strategy shown in this manuscript is elegant, all the reactions have been developed previously. Especially the fact that a palladium-catalyzed C–S coupling reaction, which is a key step in the current strategy, is a powerful tool to create distortion has been demonstrated for the synthesis of distorted perylene bisimide derivatives (ref. 35). Second, the fundamental properties of trichalcogenohexaindenocoronenes including their structural distortion, photophysical properties, redox responses, and aromaticity are within expectations. In conclusion, this reviewer will support the acceptance if the authors describe other outstanding properties of the trichalcogenohexaindenocoronenes (i.e. unique reactivity, ferroelectricity in the solid state, and efficient fullerene-binding). The last two topics may require synthesizing other trichalcogenohexaindenocoronene derivatives with smaller alkyl chains.
+
+Response:
+
+Thank you very much for your comments and suggestions. We are sorry for the innovation of the synthesis strategy is not fully reflected in the manuscript. Here we want to emphasize the most notable merits more clearly. We must acknowledge that the reactions of three key steps make use of existing synthetic conditions (although with a little modification), but the work is by no means a simple stitching of existing methods. The window for success at each step is small, and finding the right conditions and breaking through the synthetic route is our painstaking effort.
+
+Firstly, the aldol cyclotrimerization reaction to build a carbon skeleton is a great innovation, because the potential intramolecular cyclization of the acetyl group may fail the reaction.[1] This reaction was found to result in a reduced yield upon scaling up, perhaps influenced by the undesired intramolecular cyclization. Meanwhile, as described in the literature, "this method for assembling substituted benzene rings with 3-fold symmetry works well for some ketones, but fails for others, and the factors responsible for the success or failure of the reaction have never been firmly established."[2] So, the success of the aldol cyclotrimerization reaction for this substrate provides a unique case for this strategy.
+
+![Reaction scheme showing the synthesis of TFB 3 from complex substances, involving intramolecular cyclization and aldol cyclotrimerization](page_184_1017_1082_186.png)
+
+[1] Cho, Y. J. & Lee, J. Y. Thermally stable aromatic amine derivative with symmetrically substituted double spirobifluorene core as a hole transport material for green phosphorescent organic light-emitting diodes. Thin Solid Films 522 415–419 (2012).
+[2] Ansems, R. B. M. & Scott, L. T. Circumtrindene: a geodesic dome of moleculardimensions. rational synthesis of 60% of C60. J. Am. Chem. Soc. 122, 2719–2724 (2000).
+
+Secondly, the situation for the Scholl reaction of intermediate **TFB 3** is completely different from what has been reported in 1,3,5-tris(2-biphenyl)ylbenzene,[3] the contraction of
+the five-membered ring elongates the distance to form the six-membered ring, meanwhile, the inactivation and steric hindrance of the chlorine atoms both make oxidation cyclization more difficult and make the success of the reaction less certain before the design route. The presence of chlorine atoms is also critical to the success of the Scholl reaction. Replacing the chlorine atoms with the hydrogen atoms will fail the Scholl reaction and lead to complex products. Moreover, the hexfluorinated and hexabrominated versions of key intermediates could not be obtained via oxidative cyclization. So, the success of this reaction is a matter of luck and miracle. Nowadays, the introduction of multi-chlorine atoms into the bay region of \( p \)-HBC was only realized by electrophilic substitution strategy,[4] so the success of this reaction provides an appealing strategy towards the controlled edge chlorination of \( p \)-HBC. The success of key intermediate **TFC 4** also opens the chance for other heteroatom doping and further functionalization.
+
+![Reaction scheme showing the synthesis of p-HBC from 1,3,5-tris(2-biphenyl)ylbenzene through Scholl Reaction and electrophilic substitution](page_246_682_957_180.png)
+
+1,3,5-tris(2-biphenyl)ylbenzene   Scholl Reaction ref. 3   p-HBC   electrophilic substitution ref. 4
+
+![Reaction scheme showing the synthesis of TFC 4 from TFB 3 through Scholl Reaction](page_246_1012_957_180.png)
+
+TFB, 3   Scholl Reaction   TFC, 4
+
+[3] Feng, X. L., Wu, J. S., Enkelmann, V. & Müllen, K. Hexa-peri-hexabenzo-coronenes by efficient oxidative cyclodehydrogenation: the role of the oligophenylene precursors. *Org. Lett.* **8**, 1145–1148 (2006).
+
+[4] Tan, Y.-Z. *et al.* Atomically precise edge chlorination of nanographenes and its application in graphene nanoribbons. *Nat. Commun.* **4**, 3646 (2013).
+
+Thirdly, although the introduction of sulfur is based on the existing methods,[5] However, in the case of di-sulfur annulated perylene bisimide derivatives, the aromatic core frameworks have almost perfectly flat structures with ignorable mean plane deviations (MPDs) of 0.018 Å, from the least-squares plane defined by peripheral 20 atoms of the aromatic core. Therefore, the structure strain is so small for the introduction of sulfur atoms. In striking contrast, the incorporation of sulfur into our curved system faces more difficulties due to the high strain involved, so this method is not guaranteed to work before the experiment. The incorporation of sulfur into the curved system, such as trithiasumanene, usually involves the initial formation of six-membered 1,2-dithiin rings followed by copper-mediated desulfurization,[6]
+so it is the first demonstration that this method can be applied to the synthesis of bowl molecules and introduce curvature.
+
+![X-ray crystallographic structure of S-heterocyclic annelated perylene bisimide](page_246_183_957_120.png)
+
+mean plane deviations (MPDs) of 0.018 Å
+X-ray crystallographic structure of S-heterocyclic annelated perylene bisimide
+
+[5] Qian, H. L., Liu, C. M., Wang, Z. H. & Zhu, D. B. S-heterocyclic annulated perylene bisimide: synthesis and co-crystal with pyrene. Chem. Commun. 4587–4589 (2006).
+[6] Li, X. X. et al. Non-pyrolytic, large-scale synthesis of trichalcogenasumanene: a two-step approach. Angew. Chem. Int. Ed. 53, 535–538 (2014).
+
+Finally, thank you very much for your valuable suggestions to remind us to synthesize other trichalcogenasupersumanene derivatives with smaller alkyl chains for other outstanding properties. According to your nice suggestions, we have synthesized trithiasupersumanene derivative with methyl chains (1a-Me) and demonstrated moderate binding ability towards C_{60} and C_{70}. The crystal structures are shown below, meanwhile, the host-guest chemistry with fullerenes section has been added in the manuscript and Supplementary Information respectively.
+
+![X-ray crystal structures of host-guest complex 1a-Me@C_{60} (a) and 1a-Me@C_{70} (b, c).](page_246_1012_957_120.png)
+
+Fig. 10 X-ray crystal structures of host-guest complex 1a-Me@C_{60} (a) and 1a-Me@C_{70} (b, c).
+
+1) How about comparing the structural factors (bond lengths and bond alternation) of trichalcogenohexaindenocoronenes with those of HBC, which will give fruitful insight into the effect of distortion.
+
+Response:
+
+We feel great thanks for your nice suggestions, we have added some discussions in the revised manuscript as follows.
+
+The peripheral and hub benzene rings of **1a** and **1b** possess the smallest BLA values, which are similar to the parent HBC (Supplementary Fig. S19). In addition, both **1a** and **1b** display elongated bond lengths for the hub and periphery but shortened bond lengths for the rim of
+coronene core in comparison with parent HBC (Supplementary Fig. S20) due to the high inner strain of their bowl geometries.
+
+![Three molecular diagrams showing BLA in 1a, 1b and p-HBC with labeled atoms and bond distances](page_184_153_1079_246.png)
+
+The comparison of BLA in **1a**, **1b** and *p*-HBC based on the result of X-ray crystal structure analysis (Figs S8, S17 and S19).
+
+![Three molecular diagrams showing average bond lengths (Å) in 1a, 1b and p-HBC](page_184_420_1079_246.png)
+
+Figure S20. The comparison of average bond lengths (\(\text{\AA}\)) in **1a**, **1b** and *p*-HBC based on the result of X-ray crystal structure analysis.
+
+*2) The authors note that hexagons (b) present a feeble antiaromatic character. However, this reviewer thinks this argument is overstated because the NICS(1)*zz* values are close to zero.*
+
+Response:
+
+We feel great thanks for your nice suggestions, we have corrected them in the revised manuscript.
+
+The calculated NICS(1)*zz* values, as denoted in the corresponding rings (Figs 5(a) and 5(b)), suggest that the hub hexagons (ring a) and the six outer (e) hold a pronounced aromatic character, as shown by the blue shaded benzene rings, while the hetero pentagons (d) and the hexagons (c) are faintly aromatic. *The hexagons (b) possess small positive average NICS(1)*zz* values, thus indicating a nearly non-aromatic character.* Note that the hexagons (c) in *p*-HBC become non-aromatic, thus indicating the aromaticity distribution in each bowl system is nearly, yet not completely similar to that in *p*-HBC[55].
+
+*3) On page 8, "Eying" should be "Eyring".*
+Response:
+
+We thank this reviewer for his/her careful checking. We have corrected it in the revised manuscript.
+
+4) On page 12, "1,3,5-Tris" should be "1,3,5-tris"
+
+Response:
+
+We thank this reviewer for his/her careful checking. We have corrected it in the revised manuscript.
+
+5) For the \(^{13}\mathrm{C}\) NMR spectrum of 3, two signals are missing. Please comment.
+
+Response:
+
+We thank this reviewer for his/her careful checking, we have recollected the \(^{13}\mathrm{C}\) NMR spectrum of 3 as follows.
+
+![NMR spectrum and structure of compound 3](page_370_682_1002_496.png)
+
+Figure S66. \(^{13}\mathrm{C}\) NMR spectrum of 3 (151 MHz, CDCl\(_3\), 298K).
+
+6) On page S28 in SI, "Erying" should be "Eyring".
+
+Response:
+
+We thank this reviewer for his/her careful checking. We have corrected it in the Supplementary Information.
+
+7) The \(^1\mathrm{H}\) NMR spectrum of 1b exhibits some undefined signals in the up-fielded region (i.e. triplet at 2.4 ppm and weak signals in the range of 1.3–0.6 ppm). Furthermore, the \(^{13}\mathrm{C}\) NMR signals of
+1b are weak. These two points should be improved.
+
+Response:
+
+We thank this reviewer for his/her careful checking, we have purified carefully and recollected the 1H NMR and 13C NMR spectrum of 1b as follows.
+
+![NMR spectrum and structure of compound 1b](page_246_256_957_384.png)
+
+Figure S72. 1H NMR spectrum of 1b (600 MHz, CDCl3, 298K).
+
+![NMR spectrum and structure of compound 1b](page_246_768_957_384.png)
+
+Figure S73. 13C NMR spectrum of 1b (151 MHz, CDCl3, 298K).
+Reviewers’ Comments:
+
+Reviewer #2:
+Remarks to the Author:
+The authors have nicely addressed the previous suggestions/concerns of this reviewer and, therefore, I feel that the manuscript in its present form meets the criterria of novelty and quality to be accepted for publication in Nature Communications.
+
+Reviewer #3:
+Remarks to the Author:
+The authors have provided compelling arguments in response to my inquiries. Additionally, they have satisfactorily addressed the concerns of the other reviewers who posed insightful questions, providing clear and concise answers.
+
+Therefore, I am confident that the manuscript in its current form meets the necessary criteria to be accepted for publication in Nat. Commun. without further revisions.
+Reviewer comments:
+
+Reviewer #2 (Remarks to the Author):
+
+The authors have nicely addressed the previous suggestions/concerns of this reviewer and, therefore, I feel that the manuscript in its present form meets the criterria of novelty and quality tobe accepted for publication in Nature Communications.
+
+Response:
+
+    We express our gratitude to this reviewer for his/her extensive reading and we are delighted to see the recommendation for acceptance.
+
+Reviewer #3 (Remarks to the Author):
+
+    The authors have provided compelling arguments in response to my inquiries. Additionally, they have satisfactorily addressed the concerns of the other reviewers who posed insightful questions, providing clear and concise answers. Therefore, I am confident that the manuscript in its current form meets the necessary criteria to be accepted for publication in Nat. Commun. without further revisions.
+
+Response:
+
+    We express our gratitude to this reviewer for his/her extensive reading and we are delightedto see the recommendation for acceptance.

0ef88a3d250cc02e121a31263f7d3eb45880dc07208a92e0c8644d22f4cb03f6/preprint/preprint.md

@@ -0,0 +1,270 @@
+Trichalcogenohexaindenocoronenes: Super Buckylbowls Based on Coronene Core
+
+Yixun Sun
+Shaanxi Normal University
+Xin Wang
+Shaanxi Normal University
+Muhua Chen
+Shaanxi Normal University
+Bo Yang
+Shaanxi Normal University
+Ziyi Guo
+Shaanxi Normal University
+Mingyu Xu
+Shaanxi Normal University
+Yunjie Zhang
+Shaanxi Normal University
+Huaming Sun
+Shaanxi Normal University
+Jingshuang Dang
+Shaanxi Normal University
+Juan Fan
+Shaanxi Normal University
+Jing Li
+Shaanxi Normal University
+Junfa Wei (weijf@snnu.edu.cn)
+Shaanxi Normal University
+
+Article
+
+Keywords:
+
+Posted Date: September 29th, 2022
+
+DOI: https://doi.org/10.21203/rs.3.rs-2095883/v1
+License: This work is licensed under a Creative Commons Attribution 4.0 International License.
+Read Full License
+Trichalcogenohexaindenocoronenes: Super Buckybowls Based on Coronene Core
+
+Yixun Sun1†, Xin Wang1†, Muhua Chen1†, Bo Yang1, Ziyi Guo1, Mingyu Xu1, Yunjie Zhang1, Huaming Sun1, Jingshuang Dang1, Juan Fan1, Jing Li1* and Junfa Wei1*
+
+1School of Chemistry and Chemical Engineering, Shaanxi Normal University, Xi’an, 710119, China.
+
+*Corresponding author(s). E-mail(s): li_jing@snnu.edu.cn; weijf@snnu.edu.cn;
+†These authors contributed equally to this work.
+
+Abstract
+Synthesis of buckybowls, especially, the large sized ones, have remained a huge challenge yet due to the inherent high strain induced by curvature. Herein, we report two novel bowl-shaped polycyclic aromatics with three chalcogen (sulfur or selenium) atoms and three methylene groups embedded at the bay regions of hexa-peri-hexabenzocoronene and an expeditious three-step synthetic strategy for these superbows, including an aldol cyclotrimerization, a Scholl reaction, and a Stille reaction. The superbows of this type feature a nanosized, compact, and \( C_{3v} \)-symmetric architecture, composing of 19 fused rings, 48 constituent atoms. NMR spectroscopic and X-ray crystallographic studies confirmed their bowl-shaped geometries. The crystal structures revealed that they encompass 36 pyramidalized trigonal carbon atoms and have the bowl depths of 2.29 Å and 2.16 Å and diameters of 11.06 Å and 11.35 Å for the sulfur and selenium isologs. The curvature mainly distribute at the carbon atoms of the coronene frame and edge-to-convex packing predominates due to intermolecular C–H···π and chalcogen···π interactions in two instances. Variable temperature \( ^1\mathrm{H} \) NMR experiments and theoretical calculations demonstrated the bowls have considerably high inversion barriers. The optical and electrochemical properties were elucidated by UV/vis and fluorescence spectroscopy and cyclic voltammetry. Moreover, the aromaticity distribution and electrostatic potential characteristics as well as perpendicularly aligned convex-to-concave dipolemoments were investigated by density functional theory calculations.
+
+Bowl-shaped polycyclic aromatic hydrocarbons (PAHs), often referred as buckybowls or \( \pi \)-bowls, have emerged as attractive targets that captivate scientists from chemistry to materials science in light of their intriguing characteristics as well as potential applications in a diverse of scientific fields [1–10]. More significantly, some of the buckybowls could also serve as templates or seeds for the growth of single walled carbon nanotubes [11–13] having a controlled chirality and diameter and
+thus having uniform electronic properties useful in molecular electronic devices [14]. Owing to the huge inner strain of bowl-shaped hydrocarbons makes their synthesis a major challenge. Hitherto the most literature-known buckybowls were related to C_{60} or C_{70} fullerene fragments and their \( \pi \)-extended or heteroatoms doping derivatives [15–29]. The syntheses of large-sized heteroatom-doped buckybowls derivatives remain limited.
+
+In the past decades, our group has been involved in design and synthesis of new PAHs and, naturally, bowl shaped polyarenes have never escaped from our consideration. It is of course interesting to imagine that if each of all six bay regions of hexa-peri-hexabenzocoronene (\( p \)-HBC, also known as “superbenzene”) were bridged by one divalent group, it should formally constitute a large, compact, highly symmetric, zigzag rimed, and bowl-shaped architecture composed of 48 atoms and 19 rings in its bowl system (Fig. 1). Such unprecedented molecules feature a coronene core successively circumscribed by alternate hexagonal and pentagonal rings. Simple Chem3D simulation and normative density functional theory (DFT) calculation indicates a beautiful bowl-shaped geometry for these coronene-based polyarenes (i.e., X, Y = C, S, Se etc.). However, experimentally bringing these imagined molecules into existence by chemical synthesis represents a gigantic challenge. No precedent has been known for bridging all six bay regions of \( p \)-HBCs to form decorated pentagonal rings, albeit methodologies for bridging the bays of triphenylene [27, 28] and perylene [24, 29, 30] has been established. Very recently, Mülle and Feng et al. disclosed an elegant synthesis of trisulfur annulated \( p \)-HBC derivatives in which only three five-membered rings form in bay regions, emphasizing the difficulty to construct such a curved structure with strain [31].
+
+![Our synthetic concept of bowls from p-HBC.](page_1012_1012_377_181.png)
+
+Fig. 1 Our synthetic concept of bowls from \( p \)-HBC.
+
+To address this daunting challenge, we proposed a new synthetic concept based on the following philosophy: three of all six five-membered rings for these coronene-based bowls are provided by fluorene moieties; while the remaining three pentagonal rings should be constructed by inserting three chalcogen atoms in the bay positions pre-existing chlorine atoms as closable functionalities with the concomitant introduction of curvature. Fig. 2 depicts our three-step synthetic route for constructing these highly strained geodesic polyarenes based on this strategy.
+
+Our synthetic campaign was commenced with a aldol cyclotrimerization of 1-(9,9-dibutyl-2,7-dichloro-9\( H \)-fluoren-4-yl)ethan-1-one (2), which
+Fig. 2 The synthetic route for the superbowls. Reagents and conditions: (i) 6.6 equiv. TiCl4, o-dichlorobenzene, (microwave), 180 °C, 3 h; (ii) 8 equiv. DDQ, 5% TiOH, 1,2-dichloroethane, 50 °C, 6 h; (iii) 4 equiv. (Bu3Sn)2S or (Bu3Sn)2Se, 1 equiv. Pd(PPh3)4, toluene, 150 °C, Ar, 48 h.
+
+was prepared from commercially available 2,7-dichloro-9H-fluorene in three steps (see the Supplementary Information for details). The initial attempts towards the cyclotrimerization of **2** using SiCl4 [32] as catalyst in ethanol failed; only a trace amount of the desired product, 1,3,5-tris(9,9-dibutyl-2,7-dichloro-9H-fluoren-4-yl)benzene (TFB, **3**), was detected in the reaction mixture by MS spectroscopy. Fortunately, several explorations rewarded us with finding proper conditions to access the cyclotrimer **3** by performing the reaction in *o*-dichlorobenzene (*o*-DCB) at 180 °C under microwave irradiation using TiCl4 as catalyst [33, 34]. This venerable method, albeit under slightly harsh conditions, delivered the product **3** in 52% isolated yield after chromatographical purification. Noticeably, TFB has the carbon structure that constitutes the entire carbon scaffold of final bowls and the functionalities necessary for the formation of the five-membered rings.
+
+Also fortunately and delightfully, the consequent Scholl reaction of **3** with DDQ/triflic acid in DCE at 50 °C, which is the crucial step toward the total synthesis of the designed bowls, afforded the hunted trifluorenoncoronene (**TFC**, **4**) in an isolated yield of 37%. Although not high, the achieved yield is quite reasonable if considering the high ring strain from three five-membered rings and steric hindrance of two chlorine atoms at each bay region in the product **4**. The preinstalled *n*-butyl groups endow TFC with adequate solubility amenable to isolation and full spectroscopic characterization. All analytical data are consistent with the expected structure of TFC **4** (Supplementary Figs 52 and 53). We also briefly explored the improvement of Scholl reaction of **3** and found relatively satisfactory conditions, as denoted in Fig. 2.
+
+With the requisite TFC (**4**) in hand, we then accomplished the total synthesis of the designed buckybowls via threefold heteroatom annulation at its dichlorinated bay positions using Stille type reaction, which has been established by Wang group in their synthesis of sulfur heterocyclic annulated perylene bisimide derivatives [35] with
+some modifications. To our delight, we obtained successfully the hunted buckybowl, trithiahexaindenocoronene **1a**, as a yellowish powder in 58% isolated yield using (Bu$_3$Sn)$_2$S as the sulfur donor and Pd(PPh$_3$)$_4$ as the catalyst at 150 °C in a sealed tube under Ar atmosphere. This is the first time that such a supersized buckybowl was achieved. The HR-MS spectrum showed the molecular peak at *m/e* 985.3936 consistent with the desired product (C$_{69}$H$_{60}$S$_3$+H$^+$, 985.3930) and also, the measured isotopic distribution was well coincident with that stimulated (Supplementary Fig. 56). The $^1$H NMR spectrum (Fig. 3) presented only one sharp low field singlet at 8.06 ppm for the six equivalent aromatic protons; while the high field signals, which are well resolved, implied two inequivalent sets of *n*-butyl groups. These observations strongly suggest its 3-fold symmetry and the bowl-shaped conformation in solution since only if access was gained to the bowl structure, the aliphatic chains can be differentiated by their location at regions demarcated by the convex and concave faces of the bowl. The chemical shifts of butyl chains inside the concave follow an order of H$_a$>H$_c$>H$_d$>H$_b$, similar to 9,9-dibutyl-9*H*-fluorene [36]. While butyl chains outward the bowl follow a different order of H$_a$'>H$_b$'>H$_c$'>H$_d$'. Interestingly, two distinctive signals, H$_b$ and H$_d$, assignable to methylene and methyl protons in the butyl moieties inward bowl orientations manifest negative chemical shifts (���1.04 to −0.02 ppm), which can be ascribed to the stronger shielding effect caused by the ring current of the bowl system. The $^{13}$C NMR data further support the bowl topological character of **1a** (Supplementary Fig. 55).
+
+![NMR spectrum and geometry of compound 1a](page_728_682_627_246.png)
+
+Fig. 3 $^1$H NMR characterization of **1a** (CDCl$_3$) and geometry predicted by DFT calculations.
+
+The selenium version was also synthesized by bridging the bays with selenium atoms under the same conditions, but switching (Bu$_3$Sn)$_2$S to (Bu$_3$Sn)$_2$Se [37], as a yellowish powder in 39% isolated yield. Similarly, all spectroscopic data (Supplementary Figs 57 to 59) are well consistent with the expected structure of triselenohexaindenocoronene **1b**. It should be pointed out that its $^1$H NMR and $^{13}$C NMR spectra show virtually the same pattern to the sulfur analog. Furthermore, the corresponding CH$_2$(b) and CH$_3$(d) signals at higher field (−0.96 to 0.01 ppm) due to the weaker shielding effect, reflecting that the bowl is flatter than its sulfur analog.
+Fig. 4 a,d, X-ray crystal structures of **1a** (a) and **1b** (d). b,e, The side view of **1a** (b) and **1b** (e) with diameters and depths. c,f. The top view of **1a** (c) and **1b** (f) together with POAV angles (blue) and mean bond lengths (red). Butyl groups in the side and top views are omitted for clarity. Thermal ellipsoids are shown at 30% probability.
+
+Single crystals of **1a** and **1b** suitable for X-ray diffraction studies were grown by slow vapor diffusion of methanol into solution of chloroform at room temperature. The X-ray structural analyses unambiguously confirm the anticipated bowl-shaped architecture (Figs 4(a) and 4(d)), with an approximate \( C_{3v} \)-like symmetry in both crystals; the deviations from ideal symmetry should be blamed to the crystal packing forces in crystalline state [38]. The maximum bowl depths and diameters are 2.29 Å and 11.06 Å for **1a** while 2.16 Å and 11.35 Å for **1b**, defined by the perpendicular distance between the plane of three peripheral heteroatoms and the centroid of the hub and by the horizontal distance between saturated carbons and heteroatoms at opposite vertexes, respectively (Figs 4(b) and 4(e)). Deservedly, the selenium bowl is slightly shallower than its sulfur isolog due to its bigger atomic radius. It is worth mentioning that the depths and widths as well as other structural parameters of the bowls are closely aligned with those of DFT calculations (Supplementary Figs 25 and 31).
+
+Both **1a** and **1b** crystallize in P2$_1$/c space group with a disordered chloroform molecule filling over each hub ring of concave side by C–H···π
+or Cl···π interactions with the formation of chloroform in bowl supermolecular complex isologs (Supplementary Figs 1 and 11). Normal concave-convex stacking fashion is restricted due to the presence of three pairs of \( n \)-butyl groups. Note that edge-to-convex predominant stacking manner stabilized with C–H···π and chalcogen···π interactions was observed (Supplementary Figs 3 and 13). Both bowls exhibit concave to concave packing motifs along \( a \) axis via six C–H···chalcogen hydrogen bonds between chalcogen atoms and hydrogen atoms (\( H_d \)) of methyl groups inward bowls (Supplementary Figs 4, 5, 14 and 15). Notably, **1a** contains three crystallographically independent molecules while the selenium isolog **1b** contains two crystallographically independent molecules in unit cell.
+
+As shown in Figs 4(c) and 4(f), there are 4 circles, totally 36 different pyramidalized trigonal carbon atoms existed in these coronene-based superbowls, except for 18 atoms at the peripheral vertexes. The \( \pi \)-orbital axis vector (POAV) angle analyses [39, 40] show that the carbon atoms of the hub ring of two bowls are moderately curved with a mean POAV angle of 5.40° (**1a**) and of 4.79° (**1b**); the most curvature occurs at the carbon atoms making up the coronene rim, of which the mean POAV angles are 6.26° (**1a**) and 5.85° (**1b**) for carbon atoms fusion with cyclopentadiene rings. The carbon atoms linked to each hub ring are pyramidalized significantly with a mean POAV angle of 6.14° (**1a**) and of 5.61° (**1b**), the secondary maximum value of those of the carbons in respective molecule. The curvature is even distributed among the peripheral carbons attached to heteroatom and to the saturated carbon atom of cyclopentadiene ring, of which POAV angles are 3.91° (**1a**) and 3.55° (**1b**) and 3.73° (**1a**) and 3.60° (**1b**), respectively (see the Supplementary Information for details).
+
+The bond lengths, as denoted in Figs 4(c) and 4(f) (red colored data), are the symmetry-averaged values of all equivalent bonds around their respective \( C_3 \) symmetric axis disregard deviations from perfect geometry. The hub ring in both molecules remains an almost regular hexagon with a negligible bond length alternation (BLA) of 0.002 Å (**1a**) and 0.001 Å (**1b**) and equalized yet elongated bond lengths of 1.422 and 1.424 Å (**1a**) or 1.421 and 1.422 Å (**1b**) in comparison with that in benzene (1.40 Å), indicating their reduced aromatic bond character. The radial bonds joining the hub to the rim hexagons are elongated to 1.450 Å (**1a**) and 1.447 Å (**1b**), considerably longer than the others in the same ring and thus indicative of quasi-single bond character. These bonds are not components of aromatic rings and function only as geometric connections between the hub and outer rings. Accordingly, the six-membered rings containing the radial bonds deviate markedly from regular hexagon. Six rim benzene rings in both compounds are non-negligibly
+irregular hexagons with the bond lengths spanning from 1.386 to 1.420 Å (\(\mathbf{1a}\)) and from 1.389 to 1.420 Å (\(\mathbf{1b}\)), falling within the scope of aromatic bond character. The C–S bond (1.779 Å) in \(\mathbf{1a}\) and C–Se bond (1.923 Å) in \(\mathbf{1b}\) are fairly longer than that in dibenzothiophene (1.744 Å) [41] and in dibenzoselenophene (1.895 Å) [42], indicating also declined aromatic bond character at the corresponding positions. These results lend support to that the peripheral and hub benzene rings possess more benzenoid character, consistent with the deductions from BLA analysis [43] based on the X-ray determined (Supplementary Fig. 9 and 19) and DFT calculated structural data (Supplementary Figs 26 and 32). In addition, the fluorene moieties show a C–C\(_{sat.}\) bond length of 1.559 Å (\(\mathbf{1a}\)) and 1.560 Å (\(\mathbf{1b}\)), longer than that in 9,9-dioctyl-9\(H\)-fluorene (1.523 Å) [44], might due to the high inner strain of their bowl geometries.
+
+The aromaticity distribution characteristics in the bowl systems were further evaluated by nucleus independent chemical shift (NICS) [45–47] and anisotropy of the induced current density (ACID) [48] calculations on their unsubstituted analogs \(\mathbf{1a'}\) and \(\mathbf{1b'}\). The calculated NICS(1)\(_{zz}\) values, as denoted in the corresponding rings (Figs 5(a) and 5(b)), suggest that the hub hexagons (ring a) and the six outer hexagons (e) hold a pronounced aromatic character while the hetero pentagons (d) and the hexagons (c) are faintly aromatic. The hexagons (b), which possess positive average NICS(1)\(_{zz}\) value values, present a feeble antiaromatic character. Therefore, the aromaticity distribution in each bowl system is are nearly, yet not completely similar to that in \(p\)-HBC [49], as shown by the blue shaded benzene rings (Figs 5(a) and 5(b)). Such aromaticity distribution characteristics is also consistent with Clar sextet rule [50] because the largest number of aromatic sextets can be found in the resonance hybrid when aromatic sextets locate at rings (a and e) overwhelm rings (d and c)((Supplementary Figs 30 and 36)). ACID plots of \(\mathbf{1a'}\) and \(\mathbf{1b'}\) revealed that clockwise 6\(\pi\)-electron local current pathways are presented in the hub (a) and rim (e) benzene rings. On the contrary, no significant local currents were observed in rings (c and d) of neither bowl (Figs 5(c) and 5(d)). Rings (b) showed unnoticeable anticlockwise ring currents, reflecting their weak antiaromatic character. Remarkably, a clockwise global current was observed along 30\(\pi\)-electron pathway consisting of the lone pair electrons on S or Se atoms, which are caused by the superposition of these local currents in each molecule. Taken together, these outcomes lend further supports to the aromaticity distribution characteristics obtained by NICS calculations.
+
+The electrostatic potential (ESP) [51, 52] of \(\mathbf{1a'}\) and \(\mathbf{1b'}\) were also calculated (Figs 6(a) and 6(b) for \(\mathbf{1a'}\), Figs 6(d) and 6(e) for \(\mathbf{1b'}\)). Unlike planar PAHs containing two identical faces, the
+Fig. 5 a,b, NICS(1)_{zz} values (ppm) of **1a'** (a) and **1b'** (b) calculated at the GIAO B3LYP/6-311G(d,p) level of theory. c,d, Calculated AICD plots (isovalue = 0.03) of **1a'** (c) and **1b'** (d). Only contributions from π-electrons of the aromatic cores are considered. Red arrows indicate directions of induced ring current.
+
+ESP maps of these bowl-shaped compounds illustrate that the convex faces display more negative values compared with their concave faces, corresponding to the directions of the intrinsic dipole moment from the convex surface to the concave surface (Figs 6(c) and 6(f)). The calculated dipole moments are 3.59 Debye (**1a'**) and 3.45 Debye (**1b'**), much higher than those of corannulene (2.19 Debye) [53] and surmarnene (2.7 Debye) [54], likely due to the enlarged π-surface and depth of these supersized bowls. In addition, the incorporation of thiophene or selenophene subunits enhances their concave-convex polarization effect.
+
+Bowl to bowl inversion of two bowls were investigated by variable temperature \(^1\)H NMR measurements in 1,2-dichlorobenzene-\(d_4\) from 30–180 °C (Supplementary Figs 38 and 39) and no alteration on chemical shifts was observed, reflecting their inability to undergo bowl-inversion at the temperatures screened and thus their high inversion barriers. The DFT calculations for inversion barriers of the unsubstituted **1a'** and **1b'** at the M062x/6-31g(d) level of theory (Fig. 7) revealed that the inversion would proceed via a planar transition state like corannulene [55–58] and sumanene [59, 60], with inversion barriers (\(\Delta G^\ddagger\)) of 70.2 kcal/mol and 51.0 kcal/mol for **1a'** and **1b'**, respectively (see the Supplementary Information for details). Such high energy barriers suggest that the bowl-to-bowl inversion process might be impossible at ordinary temperatures according to Eying equation [61] (Supplementary Fig. 41). So, their bowl-shaped π-systems are conformationally locked at mild temperature.
+
+To elucidate the optophysical properties of both sulfur and selenium isologs, their UV-vis absorption and fluorescence spectra were recorded in dichloromethane (Fig. 8(a)). Both absorption spectra displayed a similar pattern with the maximum absorbance at around 400 nm and a faint hump extending up 510 nm. These observations implied that the displacement of sulfur by selenium only changes the relative absorptive intensity rather than the positions of bands. The spectroscopic similarity of two isologs stems from their similar structures in terms of geometrical and
+Fig. 6 a,d, Calculated electrostatic potentials of bowl concave for 1a' (a) and 1b' (d). b,e, Calculated electrostatic potentials of bowl convex for 1a' (b) and 1b' (e). c,f, Dipole moments of 1a' (c) and 1b' (f). Electrostatic potentials calculated on the 0.001 au. isodensity surface together with surface maxima (blue) and minima points (red) at the B3LYP/6-311G(d,p) level of theory.
+
+Fig. 7 a,b, Inversion barriers of 1a' (a) and 1b' (b) calculated at M062x/6-31G(d) level of theory.
+
+electronic aspects, as revealed by X-ray structural analysis and DFT calculations described above. TD-DFT calculations at the PBE/def2tzvp level for models 1a' and 1b' (Figs 8(c) and Figs 8(d), see the Supplementary Information for details) revealed that the maximum absorbance of 1a is caused by the S_0→S_3 and S_0→S_4 transitions of 1a' which contain those from frontier MOs to nondegenerate LOMO+2 (\( f = 0.4286 \)) while the lowest energy absorption band can be attribute to the S_0→S_1 transition (\( f = 0.0005 \)). The low intensity of S_0→S_1 transition is related to the degeneracy of frontier molecular orbitals involved in the transition. The same rationale could be applied to explain the UV-vis spectrum of 1b
+Fig. 8 a. UV-Vis absorption (solid curves) and emission spectra (dotted curves) of **1a** (black) and **1b** (red) in CH$_2$Cl$_2$ at a concentration of 1.0 × 10$^{-5}$ M. b. Cyclic voltamogram and differential pulse voltamogram of **1a** and **1b** in CH$_2$Cl$_2$ (0.1 mol/L *n*-Bu$_4$NPF$_6$) at a scan rate of 0.1 V/s. All potentials were calibrated versus an aqueous SCE by the addition of ferrocene as an internal standard taking E$_{1/2}$ (Fc/Fc$^+$) = 0.424 V vs. SCE [62]. c,d. Orbital correlation diagram and transition composition of the S$_0$→(S$_1$, S$_3$, S$_4$) excited states for **1a**' (c) and **1b**' (d) calculated at PBE/def2tzvp level of theory.
+
+with similar molecular orbital energy level distribution in **1b**'. The optical energy gaps were estimated to be 2.43 eV (**1a**) and 2.39 eV (**1b**) from the onset wavelength of lowest energy absorption edge (Table S7). The fluorescence spectra of both isologs featured distinctive vibronic structures with multiple maxima at 503, 515, 523, and 543 nm. The sulfur isolog **1a** displayed a weak fluorescence while and selenium isolog **1b** was found to be almost non-emissive due to stronger heavy atom effect of selenium than sulfur. These results are explicable to that the degeneration from S$_1$ are symmetry forbidden, thus leading to the excited state relaxation via different vibronic levels of S$_0$. The absolute quantum yield and fluorescence lifetime of **1a** were measured to be 4% and 1.9 ns and the radiative ($k_f$) and nonradiative ($k_{nr}$) decay rate constants were calculated from the singlet excited state to be $2.3 \times 10^7$ s$^{-1}$ and $5.0 \times 10^8$ s$^{-1}$, respectively.
+
+Cyclic and differential pulse voltametric studies (Fig. 8(b)) revealed that both compounds
+underwent two reversible oxidation waves and an irreversible oxidation wave corresponding to the three sequential one-electron oxidation processes of three heteroatoms, indicating that the generation of the cation radical during the first two oxidation processes are stable to repeated cycles, the third oxidation process is unstable under the selected electrochemical conditions. The half-wave potentials \( E_{ox}^{1/2} \) of two reversible oxidation processes locate at 0.90 V and 1.35 V (\(\mathbf{1a}\)) and 0.93 V and 1.38 V (\(\mathbf{1b}\)) against SCE. Note that the oxidation potential of selenium isolog \(\mathbf{1b}\) is lower than that of sulfur isolog \(\mathbf{1a}\) due to the smaller electronegativity of selenium atoms. Their HOMO/LUMO energy levels were estimated from the onsets of oxidation and reduction to be -5.25/-2.50 (\(\mathbf{1a}\)) and -5.24/-2.50 eV (\(\mathbf{1b}\)), corresponding to the electrochemical energy gaps of 2.75 eV and 2.74 eV, respectively (Table S8).
+
+Thermogravimetric analysis (TGA) experiments were conducted to determine the thermal stability of both compounds. The results showed that the onset decomposition temperatures of both \(\mathbf{1a}\) and \(\mathbf{1b}\) are above 400 \(^\circ\)C (Supplementary Fig. 24), reflecting their thermal robustness.
+
+In conclusion, we have paved a new synthetic strategy and, based on which, a concise 3-step approach for expeditiously access to large, compact, and symmetric buckybowls that underscore the following features: 1) a bowl-like architecture nanosized, 19 rings, 48 atoms, and 36 pyramidalized trigonal carbon atoms; 2) a coronene core fully circumscribed by alternate hexagonal and pentagonal rings. Single-crystal X-ray crystallography and NMR spectroscopy clearly confirmed their bowl-shaped geometry in crystal and in solution. DFT calculations and variable temperature \(^1\)H NMR experiments suggest their much high inversion barriers. Quantum chemical calculations also reveal their aromaticity distribution and electrostatic potential characteristics. Distinguishing from most known buckybowls, we present the first instance containing coronene core as the bowl bottom with complete edge topological structure. The success on the synthesis of these previously unknown superbows delivered a new family of \(\pi\)-bowls and a new synthetic strategy and the most important of all, verified accessibility of bridging all bays of \(p\)-HBCs. We believed that it will promote more synthetic efforts towards their all-carbon parent, other hetero versions as well as the analogs based on other PAHs with bay regions.
+
+Data availability
+
+X-ray crystallographic data for compounds \(\mathbf{1a}\) and \(\mathbf{1b}\) are freely available from the Cambridge Crystallographic Data Centre (CCDC 2205194 and 2205195, respectively).
+Methods
+
+Preparation of 3. In a glove box, 1-(9,9-dibutyl-2,7-dichloro-9H-fluoren-4-yl)ethan-1-one 2 (390 mg, 1.0 mmol, 1.0 equiv.), TiCl4 (0.7 mL, 6.6 mmol, 6.6 equiv.) and 5 mL dry o-dichlorobenzene were added to a 10 mL microwave vial and the vial was capped. The vessel was removed from the glove box and placed into a microwave reactor where it was heated at 180 °C for 3 h. After cooling down, the mixture was poured over concentrated hydrochloric acid/ice to quench the reaction and then extracted with CH2Cl2. The combined organic phase was washed with saturated aqueous NaHCO3 and dried over Na2SO4. The organic solvent was removed at reduced pressure to give a yellow-brown solid. The above procedure was repeated 4 times and the crude material from each reaction was combined. The combined crude material was purified by column chromatography over silica gel (eluent: petroleum ether) to afford 1,3,5-Tris(9,9-dibutyl-2,7-dichloro-9H-fluoren-4-yl)benzene 3 (970 mg, 52%) as an off-white powder; melting point (m.p.), 147–148 °C; 1H NMR (600 MHz, CDCl3): δ 7.67 (d, \( J = 14.9 \) Hz, 3H), 7.32 (s, 6H), 7.29 (d, \( J = 1.9 \) Hz, 3H), 7.12 (d, \( J = 8.2 \) Hz, 3H), 6.89 (d, \( J = 8.0 \) Hz, 3H), 1.98–1.91 (m, 12H), 1.13–1.07 (m, 12H), 0.69 (t, \( J = 7.4 \) Hz, 18H), 0.60 (d, \( J = 7.5 \) Hz, 12H); 13C NMR (150 MHz, CDCl3): δ 153.6, 153.2, 138.3, 137.3, 133.3, 132.9, 129.2, 128.9, 126.7, 123.3, 123.1, 122.6, 55.0, 40.3, 25.8, 22.9, 13.7; HRMS (APCI): \( m/z \) calcd for C69H73Cl6 (M+H)+: 1111.3838, found: 1111.3836.
+
+Preparation of 4. To a mixture of 3 (220 mg, 0.2 mmol, 1.0 equiv.) and DDQ (360 mg, 1.6 mmol, 8.0 equiv.) in 1,2-dichloroethane (20 mL) was added trifluoromethanesulfonic acid (1 mL) under argon atmosphere, and the mixture was stirred at 50 °C for 6 h. After cooling to room temperature, the reaction mixture was quenched by adding saturated aqueous NaHCO3, and then the mixture was extracted with CH2Cl2. The combined organic layer was dried over Na2SO4, and the solvent was removed under reduced pressure. The crude product was purified by silica gel column chromatography (eluent: petroleum ether) to give the trifluorenocoronene 4 (80 mg, 37%) as a yellow powder; m.p.>300 °C; 1H NMR (600 MHz, Tol-d8): δ 8.28 (s, 6H), 2.26 (dd, \( J = 9.8, 6.6 \) Hz, 12H), 1.16 (dd, \( J = 14.6, 7.3 \) Hz, 12H), 1.08–1.02 (m, 12H), 0.66 (t, \( J = 7.3 \) Hz, 18H); 13C NMR (150 MHz, Tol-d8): δ 151.7, 135.0, 133.9, 127.3, 126.9, 126.1, 122.0, 63.1, 38.8, 27.9, 23.9, 14.4; HRMS (APCI): \( m/z \) calcd for C69H61Cl6 (M+H)+: 1099.2908, found: 1099.2898.
+
+Preparation of 1a and 1b. Inside the glovebox, to an oven-dried pressure vessel with a Teflon screw cap was added compound 4 (110 mg,
+0.1 mmol, 1.0 equiv.), Bu3SnSSnBu3 (245 mg, 0.4 mmol, 4.0 equiv.) and Pd(PPh3)4 (115 mg, 0.1 mmol, 1.0 equiv.) and 5 mL dry and degassed toluene. After the vessel was resealed and moved out from the glovebox, the mixture was heated and stirred at 150 °C for 48 h. On cooling to room temperature, the reaction mixture was quenched with saturated aqueous KF solution and extracted with CH2Cl2. The combined organic phase was dried over Na2SO4 before being filtered and concentrated down to a solid under reduced pressure. The crude solid was adsorbed onto silica gel and subjected to silica gel column chromatography (eluent, petroleum ether) to afford trithiahexaindenocoronene 1a (57 mg, 58% yield) as a yellowish powder;m.p.>300 °C; Triselenohexaindenocoronene 1b was obtained under the similar procedure by using Bu3SnSeSnBu3 which was prepared according to literature procedure [39]. Characterization data of 1a: 1H NMR (600 MHz, CDCl3): δ 8.06 (s, 6H), 2.70–2.66 (m, 6H), 2.13–2.09 (m, 6H), 2.05–2.00 (m, 6H), 1.58–1.56 (m, 6H), 1.05 (t, \( J = 7.4 \) Hz, 9H), 0.59 (dd, \( J = 14.7, 7.4 \) Hz, 6H), −0.02 (t, \( J = 7.3 \) Hz, 9H), −1.01–1.07 (m, 6H). 13C NMR (150 MHz, CDCl3): δ 153.0, 142.9, 139.8, 134.8, 130.8, 128.6, 119.6, 64.4, 42.1, 35.8, 28.7, 26.1, 23.6, 22.5, 14.3, 13.2; HRMS (APCI): m/z calcd for C69H61S3 (M+H)+: 985.3930, found: 985.3936. Characterization data of 1b. 1H NMR (600 MHz, CDCl3): δ 8.21 (s, 6H), 2.71–2.66 (m, 6H), 2.17–2.12 (m, 6H), 2.02–1.98 (m, 6H), 1.57–1.54 (m, 6H), 1.04 (t, \( J = 7.4 \) Hz, 9H), 0.59 (dd, \( J = 14.7, 7.4 \) Hz, 6H), 0.01 (t, \( J = 7.3 \) Hz, 9H), −0.93–0.98 (m, 6H). 13C NMR (150 MHz, CDCl3): δ 151.8, 141.9, 139.0, 136.0, 129.3, 128.2, 121.6, 64.4, 41.5, 36.5, 28.5, 25.8, 23.6, 22.4, 14.3, 13.2; MS (MALDI-TOF): m/z calcd for C69H60Se3 (M)+: 1126.1, found: 1126.4.
+
+Acknowledgments
+
+J. W. thanks the National Science Foundation of China (NSFC) (Grant Nos. 21871169); J. L. thanks the National Science Foundation of China (NSFC) (Grant Nos. 21702131); Y. S. thanks the Fundamental Research Funds for the Central Universities (SNNU 2019TS040).
+
+Author contributions
+
+Y. S., X. W. and M. C. conducted the experiments with help from B. Y., M. X. and Y. Z., Y. S. performed the most DFT calculations. Z. G. and J. D. performed the inversion barrier calculations. H. S. collected and processed X-ray diffraction data. J. F. collected high-resolution mass spectrometry. J. W. conceived the original idea, designed and supervised the whole studies. J. W., Y. S. and J. L. performed the data analysis and wrote the manuscript with feedback from others. All authors discussed the results and commented on the manuscript.
+Additional information
+
+Supplementary information and chemical compound information are available in the online version of the paper. Reprints and permissions information is available online at www.nature.com/reprints. Correspondence and requests for materials should be addressed to J. L. and J. W.
+
+Competing financial interests
+
+The authors declare no competing financial interests.
+
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+Supplementary Files
+
+This is a list of supplementary files associated with this preprint. Click to download.
+
+• SupplementaryInformation.pdf

118e48f8906d9884fe96b830f39986096147254471f7b700649dc45674684d7f/peer_review/peer_review.md

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+Reviewers' Comments:
+
+Reviewer #1:
+Remarks to the Author:
+This paper considers the problem of hierarchical or multiscale community detection in a complex network.
+
+The authors combine Ollivier Ricci curvature with a diffusion process. Consider a network and define a standard diffusion process at each node, then calculate the Ollivier Ricci curvature between two nodes i, j, which involves two distributions, taken as the distribution of the diffusion starting from i and j respectively, at time t.
+
+Prior work has used Ollivier Ricci curvature for identifying bottleneck edges (vulnerable edges) and have used both Ollivier Ricci curvature itself and Ollivier Ricci curvature flow for community detection. The difference in this paper is to combine Ollivier Ricci curvature with a diffusion process.
+
+This is an interesting idea. As a diffusion process would first propagate within a cluster, at different time t, one could observe clustering structures at multiple scales. The paper presented simulation results and some theoretical results with asymptotic behaviors in stochastic block models.
+
+I find the idea to be interesting and of value. Finding hierarchical clusters is also an important problem. The paper is also generally well written.
+
+There are places that the paper could be improved, in particular, in terms of comparison with prior community detection methods. The paper reported comparison with Markov stability and demonstrated superior performance. But given the vast amount of prior work on community detection, comparison with only one seems to fall short.
+
+The previous method of using Ollivier Ricci flow can also detect hierarchical clusters. It would be very interesting to compare with that, to see what is the real benefit from using the distribution with diffusion for Ollivier Ricci curvature.
+
+There are also many other methods for multi-scale community detection. For example:
+
+Hierarchical Community Detection via Rank-2 Symmetric Nonnegative Matrix Factorization
+https://www.cc.gatech.edu/~hpark/papers/HierCommunity2017.pdf
+
+Graph Wavelets for Multiscale Community Mining
+Nicolas Tremblay; Pierre Borgnat
+
+I would encourage the authors to do a full literature search and compare with prior methods as well.
+
+Minor issue:
+
+Page 2, page 64, A_ij=max_ij w_ij-w_ij. I am not sure I understand what this means.
+
+Reviewer #2:
+Remarks to the Author:
+In this manuscript, the authors define a time varying edge curvature in order to study arbitrary networks, where the weights measure the similarity between pairs of dynamical network processes. Similar to some of the prior works, the authors show that the edge curvature distribution exhibits gaps at some time scales. The paper is in general well written, but there are few issues that require clarification or improvement:
+1) One important question is whether the proposed Ollivier-Ricci curvature based edge clustering method is able to detect and distinguish community structure of nodes as spectral and node
+clustering methods? For example, in the SBM network experiments, the in-cluster linking probability p_in are identical over different blocks/communities, therefore all in-community edges are equivalent (as in figure 2b, orange curves include all in-community edges even though there can be multiple communities; in figure 1f, there are three groups of edge curvatures and each represents an edge probability 0.8/0.1/0.02, but there can be more edge probabilities with nodes in different combination of the communities). However, what if the linking probability p_in varies with different communities (e.g., p_out=0.05, p_in=0.5 for cluster A and p_in=0.4 for cluster B)? Is it possible to differentiate the edges within cluster A and cluster B by examining the dynamic Ollivier-Ricci curvature of the edges?
+2) Regarding lines [#64-69, Eq. 1], the definition of the probability measure of diffusion starting from unit mass \( \delta_{t_i} \) is defined in Eq. 1 closely resembles the diffusion equation of a network. Trying to understand this conceptually, this is a distribution of the starting mass \( \delta_{t_i} \) diffused across the (entire?) network structure (as encapsulated by the graph Laplacian) at different time scales \( \tau \) but at a fixed rate of diffusion. Is this correct? Also, how different diffusion rates can be captured?
+3) Following up my above comment, the inclusion of this rate of diffusion parameter could also provide some interesting addition to the proposed dynamical ORC formulation similar to the idleness parameter in the classical ORC. Can the authors provide additional clarifications?
+4) The authors state “Here, instead of structural neighbourhoods we consider distributions generated by diffusion processes across scales $\\tau$.” My understanding is that instead of the fixed mass distribution on the adjacent neighbors assumed in the classical ORC formulation (Eq. 12), the dynamical ORC instead applies the probability measure of diffusion as defined in Eq. 1. Tying this with the previous question 2) and the analogy with the classical ORC, is the computation of the optimal transport distance (via the Wasserstein distance) now spread throughout the entire network or still limited to the immediate neighbors of the two end nodes? If it is the former, I can foresee time complexity issues for larger network sizes. The complexity analysis should be discussed similar to prior works cited in this work like [17].
+5) The following statement “…the classical OR curvature measures the change of one-step neighbourhoods between nodes…” is not entirely clear to me. I believe this statement is trying to relate the analogy of the mass transport (via the optimal transport theory) in a Riemannian manifold to a coarse geometry such as a network. Please provide additional explanations in the manuscript.
+6) Understanding the extension of the classical ORC to the dynamic ORC intuitively as defined and described in Eqs. 1 & 2 is critical. Redefinition of the $p_i(\tau)$ generated by diffusion processes wrt the mass distributions $p_j$s is not straight-forward. I would suggest to the authors to provide additional explanations of this analogy/extension between the classical and dynamic ORCs will give the paper more conceptual clarity.
+7) Regarding the lines [#86-88] and Fig. 1a,b, it is not obvious to me how the scale organization is clearly seen from these subfigures. Please provide additional explanations and analysis.
+8) I think in line [#95] “If i,j lie within the same subnetwork...” a subnetwork refers to a cluster, right? Please clarify.
+9) In line [#113], “Fig. 1f shows three groups of edges, those with most positive curvature are found within clusters, while the other two groups of edges are found between pairs of clusters.” I’m not clear which part of the figure is being referred. To me two groups of edges (those containing the colored lines) have positive dynamic ORCs across all time scales. Annotating the groups of edges in the figure could help.
+10) Regarding line [#173] and Eq.5, I believe that the \( \delta(C_i, C_j) \) here is the Kronecker delta. Please define. As the \( \delta \) notation is also used to indicate the gap.
+11) In lines [#226-229], the geometric modularity function definition is shown in Eq. 10. I believe the C_i and C_j are the cluster assignments. However, earlier in the text the C_i’s are defined as the ground truth in line #127. This could cause some confusion. In addition, main difference from the classical modularity maximization procedure is that the proposed geometric modularity is also a function of the time scale $\\tau$. Thus, the optimization procedure has to iterate across the time scales. Please clarify if a specific time scale is used for clusterization.
+12) The authors mention in the introduction that the “…curvature provides a natural parametrization of complex networks to unveil their self-similar clusters across scales”, yet the discussion does not refer to existing works that quantify the self-similarity of complex networks and determine their embedding dimensions. There have been several efforts concerning the embedding dimension such as Origins of fractality in the growth of complex networks. Nature Phys
+(2006), Reliable Multi-Fractal Characterization of Weighted Complex Networks: Algorithms and Implications. Sci Rep (2017), Chimera states in complex networks: interplay of fractal topology and delay. Eur. Phys. J. Spec. Top. 226, 1883–1892 (2017), Chimera states in brain networks: Empirical neural vs. modular fractal connectivity Chaos 28, 045112 (2018). In general the complex network literature on self-similarity, embedding dimensions, etc. should be better discussed.
+13) The authors mention in the abstract and discussion that the curvature and embedding dimension can be used to “tune the geometry of the graph to control the flux or interaction of network-driven dynamical processes”. This is indeed an important problem and several efforts are underway like Controlling the Multifractal Generating Measures of Complex Networks (2020).
+14) The two case studies on the power grid and the gene expression are very interesting, but to me it seems that the authors missed to capitalize on the advantages of the method. How does the dynamic ORC compare to other community detection methods like modularity-based, eigenvalue based, previous time independent ORC methods? I can see a decrease in error from Fig 4.i but one can wonder if this is the best it can be achieved.
+15) Lastly, the manuscript requires a careful reading to avoid hard to comprehend or grammar issues like “regime where when there is no...”. There are not many such issues, but a careful pass would eliminate even the ones I missed.
+Overall, I think this is an interesting idea and hopefully my comments will help to improve the manuscript.
+
+Reviewer #3:
+Remarks to the Author:
+This is the latex version of the review. I attached the pdf file below.
+
+\documentclass[12pt]{article}
+
+\begin{document}
+
+\begin{center}
+{\Large \bf Review of `` Unfolding the multiscale structure of networks with dynamical Ollivier-Ricci curvature''}\end{center}
+
+\bigskip\noindent
+This paper is built around a multiscale extension of the Olliver-Ricci (OR) curvature on weighted graphs.
+In general, given a measure metric space $X$ equipped with metric $d_X$ and probability measures $\mu_x$ at each point $x\in X$, one defines the OR curvature $\kappa(x,y)$ as
+$$\kappa(x,y)=1-\frac{W_1(\mu_x,\mu_y)}{d(x,y)}.$$ In the case of an (undirected) weighted graph $(G,V,W)$ ($V$ denotes the set of vertices and $W$ denotes the set of positive weights $w_{ij}$), with distance $d_{ij}$ between nodes $i$ and $j$ (e.g., the hop distance) one sets,
+$$\kappa_{ij} = 1 - \frac{W_1(\mu_i,\mu_j)}{d_{ij}},$$ where
+$$\mu_i(j) = \frac{w_{ij}}{\sum_k w_{ik}}.$$
+Now the authors propose the following twist. Defining the normalized graph Laplacian $L$, they diffuse the measures $\mu_i$ via
+\begin{equation}\label{eq:2} \bf{\mu}_i(\tau) = \delta_i e^{-\tau L},\end{equation}
+and accordingly define a {\em dynamic} version of OR via
+\begin{equation}\label{eq:1} \kappa_{ij}(\tau)=1- \frac{W_1(\bf{\mu}_i(\tau),\bf{\mu}_j(\tau))}{w_{ij}}.\end{equation}
+Here $\delta_i(j)=1$ for $i=j$ and 0 otherwise.
+
+The intuition is to make OR multiscale. Note that at $\tau=0$, $\kappa_{ij}(0)$ will be $0$, then when the measures diffuse to steady state $\pi$, one gets that $\kappa_{ij}(\tau)=1$. (There is a small typo on lines 102 and 103 where $d_{ij}$ should be replaced by $w_{ij}$.) The bottom line, as the authors argue, is that the characteristic scales should be related to the overlap of pairs of diffused measures. This is used as a measure of information propagation on the various subnetworks. Indeed, they derive an upper bound on the mixing time of the diffusion pair. Finally,
+the method is tested to derive some interesting results on several test cases, such as the European power grid and the {\em C. elegans} gene regulatory network.
+
+The experiments look nice, and the paper seems technically correct. The authors do an excellent job analyzing their approach. My problem is ``impact.' There have been other diffusion based methods applied to such problems, e.g., in references [8] and [23]. In fact, even in the original paper of Ollivier [9] and in Bauer-Jost [14], diffused versions of the Ollivier-Ricci curvature are considered. So we have another proposed algorithm with a diffusion-based version of OR, which gives some intriguing and sensible results on some well-chosen examples.
+
+This being said, I like the paper, it is very well-written, and I enjoyed reading it. Every method has its strengths and weaknesses, and it is not fair to demand an endless series of comparisons with other approaches. Nevertheless, I am curious about a comparison with another related methodology in which one uses a ``diffusion' type equation to evolve the metric via OR and detect hubs, subnetworks, communities, etc. Namely, one could use a Ricci flow. There have been several papers on this, but a well-explained one is ``Community Detection on Networks with Ricci Flow,' by Chien-Chun Ni, Yu-Yao Lin, Feng Luo and Jie Gao, {\em Scientific Reports} volume 9, 2019. The code is available and easy to run (my group has done it). I think it would be very interesting to see how the discrete Ricci flow compares with the method proposed here. Some of the results seem similar. So in the present paper, one is diffusing the node based measures, and in discrete Ricci flow, via the OR curvature one is changing the metric.
+
+A couple of other minor remarks: The OR curvature seems to be unnecessary and can be replaced by the ratio of the $W_{1}$ distance of the diffused measures (\ref{eq:2}) and the weightings $w_{ij}$. On very large networks, the computation of $e^{-tL}$ could be challenging even though there is a body of work treating this issue, e.g., due to the Andrea Bertozzi group. Have the authors thought of applying their method to partition (segmenting) images, in which one gets very dense large graphs?
+RESPONSE TO REVIEWERS (NCOMMS-21-05303)
+
+Summary of revision actions
+
+We thank the Reviewers for their insightful comments and the careful reading of our manuscript. Before addressing the Referee’s comments point-by-point, here we list the major changes to the revised manuscript. We have also included a diff file to mark all changes.
+
+Our additions have centred around the main criticisms of all Reviewers about the need for improved comparisons with other methods, particularly relating to the performance of our geometric clustering algorithm.
+
+1) Performance comparison on generative graphs
+
+We now perform a detailed accuracy comparison of our geometric modularity clustering algorithm against other methods on two widely-used benchmark graphs: the Stochastic Block Model (SBM) and the Lancichinetti-Fortunato-Radicchi (LFR). See Supplementary Note 3 and Supplementary Figure 2.
+
+Since our paper focuses on the limits of detectability of clusters, we performed the SBM benchmark in the sparse regime (the average degree (3) was much less than the number of nodes (1000)). Clustering in this regime is particularly challenging because the clusters do not contain a ‘core’, which could be captured by density-based algorithms. Geometric modularity performed close to the theoretical (Kesten-Stigum) limit given by the belief propagation method (see Decelle et al., PRE, 2011 and Massoulié, STOC, 2014). As expected, geometric clustering outperformed classical node clustering methods including spectral clustering and Girvan-Newman edge betweenness (Supplementary Fig. 2a). Remarkably, geometric modularity also significantly outperformed classical modularity, which reiterates that it is the edge curvature distribution that encapsulates the cluster structure and not density differences, which could otherwise be captured by modularity alone.
+
+As requested by all Reviewers, we also attempted to compare geometric modularity with the Ricci-flow method (Ni et al. Sci Rep, 2019), but found that it could not detect clusters in sparse graphs. Although Ni et al. did perform tests using the SBM benchmark, they did so in the dense regime (they fixed p_in=0.15 and varied p_out/p_in between 0.1 and 1, so the edge density they considered was at least (0.1+0.15)500 = 125, which is two orders of magnitude higher than 3 used in our study). This is in line with theoretical results showing that Ollivier-Ricci curvature is sensitive to local degree fluctuations (Proposition 2, Jost, Liu, Discrete Comput Geom, 2013). This reinforces our theoretical insight that combining diffusion processes (constructed from the graph Laplacian) and OR curvature is what allows suppressing fluctuations in the Laplacian spectrum (Fig. 3) thus bypassing the inherent limitations of previous methods.
+
+We also performed a benchmarking on the LFR generative network, where community sizes and edge densities are heterogeneous (see comment 1 of Reviewer 2). We show that our method remains robust performing comparably to the state-of-the-art spinglass and modularity
+methods (Supplementary Fig. 2b). In this uniscale benchmark, the fact that geometric modularity performs as well as standard modularity is a statement that information is not lost by reweighting the edges by the curvatures and that we indeed identify the correct clustering scae. Here we could also compare to the Ricci flow method of Ni et al., showing that our method performs substantially better.
+
+2) Performance comparison on the C. elegans homeobox gene network
+
+The Reviewers also requested a better comparison with multiscale methods and diffusion-based methods. To emphasize that our method is not specifically designed to perform on generative networks, we decided to use the C. elegans homeobox gene network (Figure 4) as a real-world graph example, which has the added benefit that the ground truth is known (see Supplementary Node 4 and Supplementary Fig. 3). We compared against a range of well-known methods, including several based on diffusions, modularity, Laplacian spectrum and matrix-factorisation. An important feature of any good multiscale methods is to robustly detect clusters at meaningful scales, while rejecting other scales. We found that most methods did not have this feature and either over-partition the graph or fail to resolve clusters at the small resolution. In contrast, we found that geometric modularity performed better than the wide range of multiscale and uniscale methods we studied. Our method returned a large plateau of meaningful scales, which are all very close to the ground truth and vary only by aggregating neighbouring small clusters (Fig. 4g), demonstrating a high degree of robustness to noise. The method of Tremblay and Borgnat, IEEE, 2014 (suggested by Reviewer 1) also performed remarkably well and the best returned cluster (of lowest VI) was close to the ground truth.
+
+3) Clarifying conceptual differences
+
+We clarified conceptual differences of the multiscale geometric notion developed in our work with other diffusion-based approaches and with other Ollivier-Ricci curvature-based approaches with particular focus on the recent Ricci-flow method of Ni et al, 2019, as requested by all Reviewers. We also extended the Introduction and Discussion to present a more comprehensive literature review of the relevant methods as suggested by the Referees.
+
+Overall, we thank the Referees for their thoughtful critiques and feel that these revisions have significantly clarified and strengthened our contributions.
+Reviewer 1
+
+This paper considers the problem of hierarchical or multiscale community detection in a complex network.
+
+The authors combine Ollivier Ricci curvature with a diffusion process. Consider a network and define a standard diffusion process at each node, then calculate the Ollivier Ricci curvature between two nodes i, j, which involves two distributions, taken as the distribution of the diffusion starting from i and j respectively, at time t.
+
+Prior work has used Ollivier Ricci curvature for identifying bottleneck edges (vulnerable edges) and have used both Ollivier Ricci curvature itself and Ollivier Ricci curvature flow for community detection. The difference in this paper is to combine Ollivier Ricci curvature with a diffusion process.
+
+This is an interesting idea. As a diffusion process would first propagate within a cluster, at different times t, one could observe clustering structures at multiple scales. The paper presented simulation results and some theoretical results with asymptotic behaviors in stochastic block models.
+
+I find the idea to be interesting and of value. Finding hierarchical clusters is also an important problem. The paper is also generally well written.
+
+We thank the Reviewer for the enthusiastic evaluation of our manuscript.
+
+There are places that the paper could be improved, in particular, in terms of comparison with prior community detection methods. The paper reported comparison with Markov stability and demonstrated superior performance. But given the vast amount of prior work on community detection, comparison with only one seems to fall short.
+
+In response to this comment, we performed detailed comparisons on two benchmark graphs (SBM and LFR) with the state-of-the-art methods on these benchmarks as well as further comparisons on the C. elegans homeobox gene network. Please see points 1-2 on the introductory page for details and see Supplementary Notes 3,4 and Supplementary Figs. 2,3 for the results.
+
+In addition, we extended our literature review and more explicitly clarified the connection to related classes of methods.
+The previous method of using Ollivier Ricci flow can also detect hierarchical clusters. It would be very interesting to compare with that, to see what is the real benefit from using the distribution with diffusion for Ollivier Ricci curvature.
+
+We believe that the Reviewer refers to the work of Ni et al. Sci Rep, 2019, which we cited in the original manuscript (Ref. 18). This method detects communities in a two-step heuristic. In step 1, it uses Ricci flow to evolve the edge weights until convergence, i.e., the curvature (in the classical Ollivier-Ricci sense) is as flat as possible. During this process, densely connected nodes will get closer (their edge weight decreases) while sparsely connected nodes move farther. In the second step, they use thresholding to cut edges that are further than a predefined length.
+
+We now show that our method substantially outperforms the Ricci flow method on the LFR benchmark and, unlike the Ricci flow method, it can detect clusters in sparse graphs where the detection problem is particularly hard. See summary point 2 on the introductory page above along with Supplementary Note 3 and Supplementary Figure 2.
+
+We have not performed further comparisons on our multiscale examples because of fundamental differences and limitations of the Ricci flow method.
+
+Ricci flow method (Ni et al.) – Not a true multiscale method because they evolve the Ricci flow until convergence. Thus the multiscale nature is discarded as the algorithm is asked to output only one geometric representation (edge weight distribution after converged Ricci flow).
+
+>> Our method – Diffusions provide different geometric representations at certain characteristic time scales (see next point on how we define these scales).
+
+Ricci flow method (Ni et al.) – In one of their use cases (Figure 7 in Ni et al., 2019) they claim to detect hierarchical clusters by choosing different cutoff thresholds. However, their chosen cutoff points are selected by hand and they provide no comparison to a ground truth or justification that they in fact find meaningful communities.
+
+>> Our method – We found conditions when to stop the diffusions to obtain informative curvature distributions: based on maximal curvature gap (Fig. 2e,f) and based on minima of variation of information (Fig. 4). Both of these conditions are theoretically justified: maximising curvature gap optimally detects communities in SBMs (Fig. 2h, i), whereas minimising VI is motivated by the fact that we search for equilibrium solutions of the Boltzmann distribution induced by the edge curvatures (Eq. (5)).
+We rewrote the paper at several points to highlight the benefits for using diffusion processes in the construction of the edge curvature.
+
+There are also many other methods for multi-scale community detection. For example:
+
+Hierarchical Community Detection via Rank-2 Symmetric Nonnegative Matrix Factorization
+https://www.cc.gatech.edu/~hpark/papers/HierCommunity2017.pdf
+
+Graph Wavelets for Multiscale Community Mining
+Nicolas Tremblay; Pierre Borgnat
+
+We thank the Reviewer for the suggestion. To address this point, we re-analyzed the C. elegans example against a host of other methods including the wavelet method by Tremblay and Borgnat (see points 2 in the summary above along with Supplementary Note 3 and Supplementary Fig. 3). We found that most methods underfit or overfit the cluster structure. Our method and the wavelet method were among the few methods that captured the correct clustering scale.
+
+We could not test our method against the hiernmf2 method recommended by the Reviewer. The code corresponding to the paper is designed to cluster data points with feature vectors and not graphs. So although it could apply to our C. elegans dataset, this would be not a fair comparison with graph clustering methods.
+
+I would encourage the authors to do a full literature search and compare with prior methods as well.
+
+Thank you for this feedback. We have now extended our literature review in the Introduction.
+
+Minor issue:
+
+Page 2, page 64, A_ij=max_ij w_ij-w_ij. I am not sure I understand what this means.
+
+We apologise for the confusion on this subtle but important point.
+
+Perhaps the confusion is caused by our inaccurate use of subscripts. We have changed the expression to \( A_{ij} = \max_{kl} w_{kl} - w_{ij} \).
+Let us also clarify that to construct the diffusion process on the graph (Eq. 1) we need to interpret the entries in the adjacency matrix A_ij as node-to-node similarities (or affinities). Then the transition probabilities for the diffusion process are obtained by normalising these similarities by the node degree. However, when we compute the geodesic distance matrix (used in the computation of the optional transport distance W in Eq. 2) we need to define distances. Therefore, we decided to define edge weights as distances w_ij and construct the adjacency matrix as A_ij = e^{-{w_ij}} or A_ij = \max_{kl} w_{kl} - w_{ij}. The latter is just a first order expansion of the former, while keeping all edge similarities positive.
+
+We have further clarified this in the revised manuscript.
+Reviewer 2
+
+In this manuscript, the authors define a time varying edge curvature in order to study arbitrary networks, where the weights measure the similarity between pairs of dynamical network processes. Similar to some of the prior works, the authors show that the edge curvature distribution exhibits gaps at some time scales.
+
+We thank the Reviewer for the summary of our work. Let us, however, emphasise that our *time-dependent edge curvature* (Eq. (1)-(2)), and the resulting ‘curvature gap’ (Eq. (4)) are both important novel concepts of our paper. We agree that other (time-indepenent) edge curvature notions may also heuristically lead to curvature gaps when strong communities are present. However, *we go well beyond heuristic methods by providing solid theoretical support to the concept of curvature gap*.
+
+1. The curvature gap encodes the presence of edges in the graph with limited information flow. Edges constituting the curvature gap are bottleneck edges across which mixing is incomplete relative to the clusters to which the endpoints of these edges belong (Fig. 1, Eq. (3)).
+2. The curvature gap is a robust extension of the ‘spectral gap’ that exists until the fundamental limit of detecting communities (Fig. 2h, i).
+3. Since curvatures optimally encode communities we could derive the geometric modularity algorithm, which therefore does not require additional parameters or a statistical null model.
+
+As also requested by Reviewer 1, we expand the literature background of our work and take this opportunity to emphasise the important advances 1-3 in our work.
+
+The paper is in general well written, but there are few issues that require clarification or improvement:
+
+1) One important question is whether the proposed Ollivier-Ricci curvature based edge clustering method is able to detect and distinguish community structure of nodes as spectral and node clustering methods?
+
+This is an important question. In our paper, we put particular emphasis on clustering sparse graphs. This is partly because sparse SBM graphs are particularly hard to cluster as they do not enjoy community properties such as small world or preferential attachment and are locally tree-like with long cycles meaning that many density-based algorithms will fail.
+We have now performed benchmarking against common clustering methods in two well-known graph classes (see point 2 on the introductory page, as well as Supplementary Note 3 and Supplementary Figure 2). We also compared deometric modularity to other methods on the C. elegans dataset (Supplementary Note 4, Supplementary Fig. 3).
+
+For example, in the SBM network experiments, the in-cluster linking probability p_in are identical over different blocks/communities, therefore all in-community edges are equivalent (as in figure 2b, orange curves include all in-community edges even though there can be multiple communities; in figure 1f, there are three groups of edge curvatures and each represents an edge probability 0.8/0.1/0.02, but there can be more edge probabilities with nodes in different combination of the communities). However, what if the linking probability p_in varies with different communities (e.g., p_out=0.05, p_in=0.5 for cluster A and p_in=0.4 for cluster B)? Is it possible to differentiate the edges within cluster A and cluster B by examining the dynamic Ollivier-Ricci curvature of the edges?
+
+We thank the Reviewer for this question. Indeed, in all stochastic block model examples in our paper we used equal cluster sizes and equal within-cluster edge probabilities (p_in). In Fig. 1 this serves no particular purpose beyond simply being the simplest example to illustrate how to geometrically reveal characteristic scales in a multiscale graph.
+
+In the revised manuscript, we changed Fig. 1 to having asymmetric communities of sizes (30,40,35,50) and corresponding p_in of (0.7,0.8,0.9,0.5). We kept the between community probabilities the same, 0.1 or 0.02. For illustration purposes, these need to be around an order of magnitude apart, otherwise the curvature gaps start to be visually harder to distinguish. However, small differences are still picked up by our curvature gap metric (see Fig. 2f as an example). This is the basis of our geometric modularity clustering algorithm demonstrated in Fig. 4.
+
+To show that the algorithm works for asymmetric clusters we have performed a comparison with the LFR benchmark, in which both the within cluster probabilities and cluster sizes are drawn from exponential distributions and the number of clusters is also unknown (Supplementary Note 3 and Supplementary Fig. 2b). This benchmark is uni-scale because the between-cluster edge probabilities are set by the same mixing parameter \mu_t. Our method performs at an accuracy similar to the state-of-the-art spinglass and modularity optimisation methods, yet still having the possibility to adjust the scale parameter in other multiscale scenarios (see also point 2 in the introductory page).
+It is also important to note, in the SBM example (Fig. 2, 3), having equal community sizes and p_in is an important symmetry requirement, which is necessary to compare to known theoretical results. The algorithm does not assume equal cluster sizes and p_ins, however, currently, the theoretical results we refer to (in particular Refs [19-21,34]) are only proved for this case.
+
+2) Regarding lines [#64-69, Eq. 1], the definition of the probability measure of diffusion starting from unit mass \( \delta_i \) is defined in Eq. 1 closely resembles the diffusion equation of a network. Trying to understand this conceptually, this is a distribution of the starting mass \( \delta_i \) diffused across the (entire?) network structure (as encapsulated by the graph Laplacian) at different time scales \( \tau \) but at a fixed rate of diffusion. Is this correct?
+
+This is correct. Eq. 1 is the solution of a diffusion equation
+
+\[
+dp_i/d\tau = - Lp_i
+\]
+
+started from unit point mass \( \delta_i \). The masses, in theory, are supported on all nodes on the network and are preserved across \( \tau \) (however, we explain in point 4 below how we ‘trim’ these distributions to reduce the complexity of our algorithm).
+
+Also, how different diffusion rates can be captured?
+
+In our current framework, we use diffusions to capture the features of the graph. Therefore, we consider the diffusion rates are proportional to the edge similarities and are fully captured in the normalised Laplacian. In effect, diffusion is the continuous-time analogue of an unbiased random walker moving from node to node on the graph with probability of moving from note i to j given by \( A_{ij} / K_i \), where \( A_{ij} \) is the corresponding entry in the adjacency matrix and \( K_i \) is the degree of node i.
+
+Varying diffusion rates could be captured by reweighting graph edges, i.e., considering biased diffusions on the graph. While varying the diffusion rates is an interesting extension of our framework, the systematic exploration of this direction is not within the scope of this work.
+
+3) Following up my above comment, the inclusion of this rate of diffusion parameter could also provide some interesting addition to the proposed dynamical ORC formulation similar to the idleness parameter in the classical ORC. Can the authors provide additional clarifications?
+The idleness parameter is important only for the classical ORC because of how the measures are defined: one-step random walk applied on a delta measure. In this discrete random walk, at t=0 all mass is on nodes i and j, whereas at time t=1 all mass is on the neighbours. The idleness parameter interpolates between these two extremes adjusting how much weight is given to the direct connection between adjacent nodes relative to the (transport) distance between their neighbours.
+
+In our framework, the role of the idleness parameter is fully accounted for in the time (\( \tau \)) parameter in the diffusion processes. Moreover, as mentioned in the response of the previous question, there is no rate of diffusion parameter in our formulation; the diffusion rates are fully encoded in the network weights. In this context, laziness corresponds to having a graph with self-loops, which, for us, corresponds to a choice of network, not a parameter in our notion of curvature.
+
+We clarified this in the revised manuscript.
+
+4) The authors state “Here, instead of structural neighbourhoods we consider distributions generated by diffusion processes across scales \( \tau \)." My understanding is that instead of the fixed mass distribution on the adjacent neighbors assumed in the classical ORC formulation (Eq. 12), the dynamical ORC instead applies the probability measure of diffusion as defined in Eq. 1. Tying this with the previous question 2) and the analogy with the classical ORC, is the computation of the optimal transport distance (via the Wasserstein distance) now spread throughout the entire network or still limited to the immediate neighbors of the two end nodes? If it is the former, I can foresee time complexity issues for larger network sizes. The complexity analysis should be discussed similar to prior works cited in this work like [17].
+
+We thank the Reviewer for this question which was also raised by Reviewer 3. The computation of the dynamic OR curvature is moderately expensive and scales similarly to several other algorithms (random walk based algorithms, Girvan-Newman, belief propagation). We could practically use it to cluster graphs up to 10^4 nodes on a desktop computer. However, it is highly parallelizable and several approximative algorithms exist to increase the applicability of our method
+
+In the revised work, we have expanded our discussion about the computational complexity and implemented several techniques for speed-up including see Supplementary Note 5 and Supplementary Fig. 4)
+1. a cutoff to trim the measures, setting very small node values to zero, to speed up the computation of the optimal transport distance,
+2. the Sinkhorn algorithm, based on entropy regularised optimal transport distance, to estimate the optimal transport distance,
+3. GPU implementation of the Sinkhorn algorithm to parallelise the computation of the curvatures on the whole graph.
+
+In addition, we expect complexity to dramatically reduce in the future with machine learning techniques to approximate optimal transport distances (c.f. Arjovski et al., arXiv, 2017).
+
+5) The following statement “… the classical OR curvature measures the change of one-step neighbourhoods between nodes.” is not entirely clear to me. I believe this statement is trying to relate the analogy of the mass transport (via the optimal transport theory) in a Riemannian manifold to a coarse geometry such as a network. Please provide additional explanations in the manuscript.
+
+We apologise for the lack of clarity here. We have improved this sentence in the text, which was meant to only be a brief, intuitive description of the original OR curvature.
+
+6) Understanding the extension of the classical ORC to the dynamic ORC intuitively as defined and described in Eqs. 1 & 2 is critical. Redefinition of the \( p_i(\tau) \) generated by diffusion processes wrt the mass distributions \( p_i \) is not straight-forward. I would suggest to the authors to provide additional explanations of this analogy/extension between the classical and dynamic ORCs will give the paper more conceptual clarity.
+
+As mentioned in point 3) above, the measures defined in the original ORC can be viewed as a one step lazy (or with self-loops) discrete time random walk. Our dynamic ORC is a natural extension to more than one step, or to continuous time random, which provides an intrinsic timescale to the curvature.
+
+We have elaborated on this analogy in the revised manuscript.
+
+7) Regarding the lines [#86-88] and Fig. 1a,b, it is not obvious to me how the scale organization is clearly seen from these subfigures. Please provide additional explanations and analysis.
+
+We apologise for the confusion. Multi-scale structure in undirected graphs can emerge either due to large differences in edge densities or cluster sizes between different pairs of clusters. In Fig. 1, for illustration we fixed the cluster sizes (we relaxed this in the
+revised manuscript) and introduced between-cluster edge densities that are approximately an order of magnitude different (0.02 and 0.1 in the original manuscript). Note that in the revised manuscript we introduced variations in the cluster sizes and between cluster probabilities in response to remark 1).
+
+We have more carefully explained the construction of this graph in the paper.
+
+8) I think in line [#95] “If i,j lie within the same subnetwork…” a subnetwork refers to a cluster, right? Please clarify.
+
+Yes, we meant cluster. We clarified this.
+
+9) In line [#113], “Fig. 1f shows three groups of edges, those with most positive curvature are found within clusters, while the other two groups of edges are found between pairs of clusters.” I’m not clear which part of the figure is being referred. To me two groups of edges (those containing the colored lines) have positive dynamic ORCs across all time scales. Annotating the groups of edges in the figure could help.
+
+We thank the Reviewer for pointing this out. First, we would like to note that the relevant feature of the curvature evolution is the relative magnitude of edge curvatures at a given snapshot in time and not the sign of the curvature. In Fig. 1f we aimed to distinguish the three edge curvature ‘bundles’, which correspond to edges connecting regions with similar degree of connectivity. Specifically, one of the bundles (with the highest curvature) corresponds to within-cluster edges and the two other bundles correspond to between-cluster edges at the two scales.
+
+We have now added insets to Fig. 1f to illustrate the position of the edges in the corresponding bundles.
+
+10) Regarding line [#173] and Eq.5, I believe that the \( \delta(C_i, C_j) \) here is the Kronecker delta. Please define. As the \( \delta \) notation is also used to indicate the gap.
+
+We have defined the Kronecker delta after Eq. (5) and changed the notation of the curvature gap to \( \Delta \kappa(\tau) \).
+
+11) In lines [#226-229], the geometric modularity function definition is shown in Eq. 10. I believe the \( C_i \) and \( C_j \) are the cluster assignments. However, earlier in the text the \( C_i \)'s are defined as the ground truth in line #127. This could cause some confusion.
+Thank you for pointing out this inconsistency. We have updated the notation in the text to clarify the cluster assignments (C) vs the ground truth (C**).
+
+In addition, main difference from the classical modularity maximization procedure is that the proposed geometric modularity is also a function of the time scale \( \tau \). Thus, the optimization procedure has to iterate across the time scales. Please clarify if a specific time scale is used for clusterization.
+
+To find the clustering scale, we run, at each scale, the Louvain algorithm on the curvature-weighted graph many (100) times with random initializations, and from the robustness of Louvain partitions via the variation of information we can assess candidate scales. In addition, similar clusters found across a large range of scales is another indication of a meaningful community structure.
+
+12) The authors mention in the introduction that the “…curvature provides a natural parametrization of complex networks to unveil their self-similar clusters across scales”, yet the discussion does not refer to existing works that quantify the self-similarity of complex networks and determine their embedding dimensions. There have been several efforts concerning the embedding dimension such as Origins of fractality in the growth of complex networks. Nature Phys (2006), Reliable Multi-Fractal Characterization of Weighted Complex Networks: Algorithms and Implications. Sci Rep (2017), Chimera states in complex networks: interplay of fractal topology and delay. Eur. Phys. J. Spec. Top. 226, 1883–1892 (2017), Chimera states in brain networks: Empirical neural vs. modular fractal connectivity Chaos 28, 045112 (2018). In general the complex network literature on self-similarity, embedding dimensions, etc. should be better discussed.
+
+Connections to fractal geometry is a very interesting research direction, which we have thought about pursuing. In fact, by stopping the diffusion processes at appropriate times and aggregating nodes one can design various coarse graining schemes based on our diffusive geometry which we think are related to renormalisation groups in fractal geometry. However, this connection is not immediate but one which we will likely pursue in the future. We have mentioned this research direction in the Discussion along with the references suggested by the Reviewer.
+
+We must, however, clarify that we use Refs [3-4] as examples when latent space embeddings have provided insight into the multiscale organisation of an important class of networks (complex networks). However, this is in contrast to our formalism, which departs from the (often limiting) network_embedding_viewpoint_and_develops_a_geometric_notion_that_applies_to_a_general_class_of_networks. As we write, “thus, there is
+a need for a geometric notion that does not require embedding, yet allows studying the multiscale structure of a general class of networks". Specifically, rather than focusing on characterising the embedding space, we focused on constructing a geometric object that has the expected behaviour in various limits (Supplementary Figure 1), and provides insight to limits of clustering on SBM graphs and multiscale clustering of real-world graphs. Therefore, we also focused the text in the Introduction to better distinguish our contribution from approaches that rely on embeddings.
+
+13) The authors mention in the abstract and discussion that the curvature and embedding dimension can be used to “tune the geometry of the graph to control the flux or interaction of network-driven dynamical processes”. This is indeed an important problem and several efforts are underway like Controlling the Multifractal Generating Measures of Complex Networks (2020).
+
+We agree that this is a research direction that our work will likely have the largest impact on. Motivated by this comment we elaborated in the Discussion on possible research directions concerning the study of synchronisation problems and chimera states by identifying information limiting edges.
+
+14) The two case studies on the power grid and the gene expression are very interesting, but to me it seems that the authors missed to capitalize on the advantages of the method. How does the dynamic ORC compare to other community detection methods like modularity-based, eigenvalue based, previous time independent ORC methods? I can see a decrease in error from Fig 4.i but one can wonder if this is the best it can be achieved.
+
+We thank the Reviewer for pointing out this shortcoming. We now include a detailed benchmarking of our method against other classical methods (including modularity-based, eigenvalues, based, and the time-independent ORC method of Ni et al, 2019) on generative graphs (SBM and LFR). See point 2 in the introductory page as well as Supplementary Notes 3,4 and Supplementary Figures 2,3. We find that our method performs close to the theoretical limit in both cases matching or outperforming state-of-the-art methods. Notably, our method does substantially better than the classical (time-independent) ORC method of Ni et al. We also performed comparison of our methods to a broad selection of other methods on the C. elegans network. We find that while most other methods either overfit or underfit the clusters, our method was among the few methods that could identify the correct clustering scale.
+15) Lastly, the manuscript requires a careful reading to avoid hard to comprehend or grammar issues like “regime where when there is no...”. There are not many such issues, but a careful pass would eliminate even the ones I missed.
+
+Thank you for this comment. We did a careful pass on the paper to remove these issues.
+
+Overall, I think this is an interesting idea and hopefully my comments will help to improve the manuscript.
+
+We thank the Reviewer for the enthusiastic evaluation of our work!
+Reviewer 3
+
+This paper is built around a multiscale extension of the Olliver-Ricci (OR) curvature on weighted graphs. In general, given a measure metric space X equipped with metric dX and probability measures \( \mu_x \) at each point \( x \in X \), one defines the OR curvature \( \kappa(x, y) \) as
+
+\[
+\kappa(x, y) = 1 - W1(\mu_x, \mu_y)/d(x, y)
+\]
+
+In the case of an (undirected) weighted graph (G,V,W) (V denotes the set of vertices and W denotes the set of positive weights wij), with distance dij between nodes i and j (e.g., the hop distance) one sets,
+
+\[
+k_{ij} = W1(\mu_i, \mu_j) / dij
+\]
+
+where
+
+\[
+\mu_i(j) = wij/ \sum_{\{k \sim i\}} w_{ik}
+\]
+
+Now the authors propose the following twist. Defining the normalized graph Laplacian L, they diffuse the measures \( \mu_i \) via
+
+\[
+\mu_i(t) = \delta i e^{-tL},
+\]
+
+and accordingly define a dynamic version of OR via
+
+\[
+k_{ij}(t) = 1 - W1(\mu_i(t), \mu_j(t)) / wij
+\]
+
+Here \( \delta i(j) = 1 \) for \( i = j \) and 0 otherwise.
+
+The intuition is to make OR multiscale. Note that at \( t = 0 \), \( k_{ij}(0) \) will be 0, then when the measures diffuse to steady state \( \pi \), one gets that \( k_{ij}(t) = 1 \). (There is a small typo on lines 102 and 103 where dij should be replaced by wij.)
+
+Thank you for pointing out the typo. We have corrected this along with a few other typos we have spotted.
+
+The bottom line, as the authors argue, is that the characteristic scales should be related to the overlap of pairs of diffused measures. This is used as a measure of information propagation on the various subnetworks. Indeed, they derive an upper bound on the mixing time of the diffusion pair. Finally, the method is tested to derive some interesting
+results on several test cases, such as the European power grid and the C. elegans gene regulatory network.
+
+We thank the Reviewer for the summary or our manuscript.
+
+The experiments look nice, and the paper seems technically correct. The authors do an excellent job analyzing their approach. My problem is “impact.” There have been other diffusion based methods applied to such problems, e.g., in references [8] and [23]. In fact, even in the original paper of Ollivier [9] and in Bauer-Jost [14], diffused versions of the Ollivier-Ricci curvature are considered. So we have another proposed algorithm with a diffusion-based version of OR, which gives some intriguing and sensible results on some well-chosen examples.
+
+Indeed, we are not the first (nor the last) to use diffusion to study network structure. Diffusions (heat kernels) are central objects in the graph learning and graph signal processing literatures. However, we believe our work is the first that combines diffusions and discrete geometry to
+
+1) Show that pairs of diffusions used in the construction of the curvature pick up random variation in the graph independently and allow uninformative fluctuations to be ‘averaged out’. In this light, the main difference between Refs. [8, 23] and our approach is that while those approaches (and other approaches relying on single diffusions) rely on the spectrum of the Laplacian being well-behaved (the eigenvalues decay sufficiently quickly), we show that pairs of diffusions can pick up structure in the graph well below what is expected from methods based on spectral properties of the Laplacian (see Figure 3).
+2) As a result of the construction in point 1) our dynamic OR curvature captures the cluster structure near the fundamental limit of detection (Figure 2h, i). In contrast, previous ‘local’ OR curvature constructions are sensitive to degree variations. For example, in the revised work we show that the clustering method of Ni et al. (2019) fails to detect clusters when the graph is sparse (and hence node degree fluctuations are large). See next response for details.
+3) Introduce a scale parameter in the definition of the curvature and show how to set this to obtain meaningful geometric representations and inspire a multiscale clustering algorithm (Figure 4). In contrast, Refs. [9, 14] have a different notion of diffusion OR curvature, which they define as the limit for t->0 of a time derivative term, and have no resulting time scale parameters.
+
+This being said, I like the paper, it is very well-written, and I enjoyed reading it. Every method has its strengths and weaknesses, and it is not fair to demand an endless series of comparisons with other approaches. Nevertheless, I am curious about a comparison with another related methodology in which one uses a “diffusion” type
+equation to evolve the metric via OR and detect hubs, subnetworks, communities, etc. Namely, one could use a Ricci flow. There have been several papers on this, but a well-explained one is “Community Detection on Networks with Ricci Flow,” by Chien-Chun Ni, Yu-Yao Lin, Feng Luo and Jie Gao, Scientific Reports volume 9, 2019. The code is available and easy to run (my group has done it). I think it would be very interesting to see how the discrete Ricci flow compares with the method proposed here. Some of the results seem similar. So in the present paper, one is diffusing the node based measures, and in discrete Ricci flow, via the OR curvature one is changing the metric.
+
+This is a very interesting question that was also raised by other reviewers. As a result, we now discuss the comparison with the Ricci flow method of Ni et al.
+
+In the Ricci flow method the edge weights w_ij are evolved according to
+
+dw_ij/dt = -\kappa_ij w_ij
+
+Where \kappa_ij is the classical Ollivier-Ricci curvature. Importantly, they run this process until they are within an epsilon distance from the converged state and, consequently, the time parameter does not play the role of a resolution parameter. Although it is expected that curvature evolution integrates information from the graph due to the diffusive nature of the Ricci flow, this information is aggregated into one geometric representation in the form of a set of edge weights {w_ij^*} obtained by the converged Ricci flow. Instead, in our dynamical Ollivier-Ricci formulation, we evolve the diffusions, and in turn the edge curvatures, and stop this evolution at certain well-defined timescales. Therefore we decompose the graph into geometric representations containing features of increasing sizes. We use these representations to perform clustering. We kindly refer the Reviewer to our response to Reviewer 1 (on page 4 of this document), where we also outline several fundamental differences from the Ricci flow method of Ni et al.
+
+We also provide performance comparisons with the Ricci flow method on two benchmark graphs (see also point 1 in the revision summary on the first page). Our method significantly outperformed the Ricci flow on the LFR benchmark. On the SBM benchmark, our method approached the theoretical limit of detection, whereas the Ricci flow method altogether failed to detect communities in the sparse regime.
+
+Based on our previous experiments with Ricci flows we think it could be interesting in the future to combine the Ricci flow approach with Ni et al. with our dynamic Ollivier Ricci framework. At its simplest, picking a diffusive scale \tau and running the Ricci flow until convergence could, in principle, enable the algorithm to extract features at different resolutions. However, at present this is very computationally expensive to perform.
+A couple of other minor remarks: The OR curvature seems to be unnecessary and can be replaced by the ratio of the W1 distance of the diffused measures (1) and the weightings wij.
+
+This is correct. However, we prefer to keep the constant part of the expression in order to preserve the intuition in canonical graph topologies such as trees, grids and cliques, yielding negative, zero and positive curvature, respectively (see Supplementary Figure 1).
+
+On very large networks, the computation of e–tL could be challenging even though there is a body of work treating this issue, e.g., due to the Andrea Bertozzi group.
+
+We refer to some replies to Reviewer 2 regarding possible improvements of the numerical complexity, but indeed, the computation of the matrix exponential is always the bottleneck in any continuous diffusion-based method. We use the scaling and squaring algorithm available in Python, as it is fast enough for the size of graphs we considered in this paper, but any other improvements on it are indeed welcome. We are not familiar with Andrea Bertozzi’s work on that topic, nor could find it in her papers, but we will definitely keep it in mind for future improvement of our Python package to extend to larger graphs. Thank you for pointing this out.
+
+Have the authors thought of applying their method to partition (segmenting) images, in which one gets very dense large graphs?
+
+This is an interesting application, which could be a future research direction, but which we did not think about. We think our method will be most valuable to cluster sparse graphs where the limited number of edges conveys very little information about the cluster structure. Thus, learning a geometric representation of the graph as a first step can increase effectiveness of clustering algorithms. In the case of dense graphs, it may be relevant to first apply some sparsification algorithm in order to extract the ‘backbone’ structure of the graph from the ‘noise’ induced by its high density. We used this approach in the C. elegans example (Fig. 4g-j).
+Reviewers' Comments:
+
+Reviewer #1:
+None
+
+Reviewer #2:
+Remarks to the Author:
+I read the revised manuscript and the response letter and the changes made by the authors are substantial and commendable. I summarize below a few minor issues:
+- In this response "In addition, we extended our literature review and more explicitly clarified the connection to related classes of methods.", I would have liked to see how the discussion in the manuscript has been enriched. Similar comment applies for this reviewer's comment "I would encourage the authors to do a full literature search and compare with prior methods as well." and response from the authors "Thank you for this feedback. We have now extended our literature review in the Introduction." where it would have been useful to learn what is the newly added information and how it changed the manuscript. Similarly for this comment of reviewer 2 "13) The authors mention in the abstract and discussion that the curvature and embedding dimension can be used to ..." for which the authors responded "We agree that this is a research direction that our work will likely have the largest impact on. Motivated by this comment we elaborated in the Discussion on possible research directions concerning the study of synchronisation problems and chimera states by identifying information limiting edges." Of note, the control or tuning of the network either by adding or removing links or by adjusting the edge weights goes beyond synchronization and can deal with controllability of complex networks. I believe that their proposed work can be well aligned with recent efforts on controlling multifractality of networks but this needs to be carefully discussed. In general, changes in revisions should have been highlighted. Please note that reference [28] is cited, but it is unclear where the comparison exists.
+- I appreciate the comparison with the graph wavelet and the other method suggested by the reviewer, it would be nice if the codes are made available. Please explain where readers can find the code.
+- Regarding comment 4 of reviewer 2 on computational complexity, the response doesn't shed light on the computational complexity, I assume it is bounded by the computational complexity of the linear program to solve for the ORC right? Please note that the discussion paragraph added on page 10 lines 277-288 should specify what m and n are representing, i.e., number of edges, number of nodes, etc. Also, it would be good to provide intuition to why the particular O(mn^5/2), since the discussion misses the convention or definitions of the notations, I cannot help to provide a correct O complexity result. I appreciate the authors' efforts but this needs a bit more precision in notation.- It is unclear from the response and the manuscript what the authors mean by multiscale. I do agree with the authors that neither of the prior Ollivier-Ricci community detection algorithms (i.e., Sia et al., Sci Rep 2019 and Ni et al Sci Rep 2019) do not address multiscale, but this should be mentioned for both I believe. Of note, some of the references the authors mention like 57 already exploited multiscale and self-similarity for community detection as well.
+- I would have appreciated if in each answer precise explanations on how text / discussion has been changed and what has been added.I consider all of the above minor issues and so I recommend this manuscript for acceptance.
+
+Reviewer #3:
+Remarks to the Author:
+Thank you for your revisions. This is a well-written paper, and I have no further requests. It should be accepted for publication.
+We have addressed the comments of Reviewer 2 as described below. We have also addressed the editorial requests and highlighted the changes in the manuscript and the supplementary material in the attached diff.pdf and diff_si.pdf files, respectively.
+
+We hope that our manuscript is now formally acceptable for publication.
+
+Kind Regards,
+
+Adam Gosztolai and Alexis Arnaudon
+
+--------
+Reviewer #2
+
+I read the revised manuscript and the response letter and the changes made by the authors are substantial and commendable. I summarize below a few minor issues:
+
+- In this response "In addition, we extended our literature review and more explicitly clarified the connection to related classes of methods.", I would have liked to see how the discussion in the manuscript has been enriched.
+
+We have now extended the Discussion in Lines 373-378 to reflect on the performance comparison with other methods.
+
+Similar comment applies for this reviewer's comment "I would encourage the authors to do a full literature search and compare with prior methods as well." and response from the authors "Thank you for this feedback. We have now extended our literature review in the Introduction," where it would have been useful to learn what is the newly added information and how it changed the manuscript.
+
+We have addressed all these points in the previous revision. We noticed that we referenced the wrong Supplementary Note in lines 274-275, which may have caused the confusion. In this revised version, we have corrected the reference to the Supplementary Figures and Notes. We have also sharpened the text in Supplementary Note 4.
+
+To summarise, we have
+    1) Briefly surveyed the multiscale community detection literature in lines 53-58 and 62-64 in the Introduction.
+    2) Compared our ‘geometric clustering’ method with state-of-the-art algorithms from major classes of clustering methods in generative benchmark graphs (see lines 272-277, Supplementary Figure 2 and details in Supplementary Note 3).
+3) Compared against multiscale clustering methods on the C. elegans dataset (see lines 323-327, Supplementary Figure 3 and details in Supplementary Note 4).
+
+Similarly for this comment of reviewer 2 "13) The authors mention in the abstract and discussion that the curvature and embedding dimension can be used to ..." for which the authors responded " We agree that this is a research direction that our work will likely have the largest impact on. Motivated by this comment we elaborated in the Discussion on possible research directions concerning the study of synchronisation problems and chimera states by identifying information limiting edges." Of note, the control or tuning of the network either by adding or removing links or by adjusting the edge weights goes beyond synchronization and can deal with controllability of complex networks. I believe that their proposed work can be well aligned with recent efforts on controlling multifractality of networks but this needs to be carefully discussed. In general, changes in revisions should have been highlighted.
+
+We have briefly mentioned the possibility to use our methods for controlling the multifractal geometry on Line 358-359. However, as we have not explored this direction we kept this discussion to a minimum.
+
+Please note that reference [28] is cited, but it is unclear where the comparison exists.
+
+The comparison with the method of Tremblay and Borgnat (Ref. [28]) on the C. elegans dataset is discussed in Supplementary Note 4. Beyond this numerical comparison we have not analysed the theoretical connection between the methods because apart from the use of diffusions the construction of the two methods is quite different.
+
+- I appreciate the comparison with the graph wavelet and the other method suggested by the reviewer, it would be nice if the codes are made available. Please explain where readers can find the code.
+
+We uploaded all code and data as detailed under the ‘Code availability’ and ‘Data availability’ statements.
+
+- Regarding comment 4 of reviewer 2 on computational complexity, the response doesn't shed light on the computational complexity, I assume it is bounded by the computational complexity of the linear program to solve for the ORC right?
+
+Given a set of diffusion measures, the theoretical complexity of computing the curvatures is at most O(mn^5/2). The Reviewer is correct that, intuitively, one needs to solve m-times a linear program (transportation problem) of complexity O(n^5/2). We also note that the computation also involves obtaining the shortest path distances and the diffusion measures. Although the complexity of the latter is not known, as we show in Supplementary Note 5 and Supplementary Figure 4 the computation of the curvatures is the limiting factor in practice.
+
+We have clarified this intuition in the main text in lines 383-384.
+
+Please note that the discussion paragraph added on page 10 lines 277-288 should specify what m and n are representing, i.e., number of edges, number of nodes, etc.
+
+We have defined n and m in Line 80 during the initial problem setup and, indeed, they refer to the number of nodes and edges, respectively.
+Also, it would be good to provide intuition to why the particular O(mn^5/2), since the discussion misses the convention or definitions of the notations, I cannot help to provide a correct O complexity result. I appreciate the authors' efforts but this needs a bit more precision in notation.
+
+We have explained the intuition in the response above. We have now clarified the O() notation on lines 282-283.
+
+It is unclear from the response and the manuscript what the authors mean by multiscale. I do agree with the authors that neither of the prior Ollivier-Ricci community detection algorithms (i.e., Sia et al., Sci Rep 2019 and Ni et al Sci Rep 2019) do not address multiscale, but this should be mentioned for both I believe. Of note, some of the references the authors mention like 57 already exploited multiscale and self-similarity for community detection as well.
+
+In our work multiscale structure refers to the existence of clusters at different distinguishable resolutions. We clarified this on line 33.
+
+I would have appreciated if in each answer precise explanations on how text / discussion has been changed and what has been added. I consider all of the above minor issues and so I recommend this manuscript for acceptance.

118e48f8906d9884fe96b830f39986096147254471f7b700649dc45674684d7f/preprint/preprint.md

@@ -0,0 +1,514 @@
+Unfolding the multiscale structure of networks with dynamical Ollivier-Ricci curvature
+
+Adam Gosztolai (adam.gosztolai@epfl.ch)
+École Polytechnique Fédérale de Lausanne   https://orcid.org/0000-0002-0699-5825
+Alexis Amaudon
+Imperial College London
+
+Article
+
+Keywords: network structure, learning algorithms, network processes, Ollivier-Ricci curvature
+
+Posted Date: February 16th, 2021
+
+DOI: https://doi.org/10.21203/rs.3.rs-222407/v1
+
+License: This work is licensed under a Creative Commons Attribution 4.0 International License.
+Read Full License
+
+Version of Record: A version of this preprint was published at Nature Communications on July 27th, 2021. See the published version at https://doi.org/10.1038/s41467-021-24884-1.
+Unfolding the multiscale structure of networks with dynamical Ollivier-Ricci curvature
+
+Adam Gosztolai*1 and Alexis Arnaudon†2
+
+1 Neuroengineering Laboratory, Brain Mind Institute & Interfaculty Institute of Bioengineering, EPFL, Lausanne, Switzerland
+2 Department of Mathematics, Imperial College London, London, United Kingdom
+
+Abstract
+
+Defining the geometry of networks is typically associated with embedding in low-dimensional spaces such as manifolds. This approach has helped design efficient learning algorithms, unveil network symmetries and study dynamical network processes. However, the choice of embedding space is network-specific, and incompatible spaces can result in information loss. Here, we define a dynamic edge curvature for the study of arbitrary networks measuring the similarity between pairs of dynamical network processes seeded at nearby nodes. We show that the evolution of the curvature distribution exhibits gaps at characteristic timescales indicating bottleneck-edges that limit information spreading. Importantly, curvature gaps robustly encode communities until the phase transition of detectability, where spectral clustering methods fail. We use this insight to derive geometric modularity optimisation and demonstrate it on the European power grid and the C. elegans homeobox gene regulatory network finding previously unidentified communities on multiple scales. Our work suggests using network geometry for studying and controlling the structure of and information spreading on networks.
+
+Real-world networks are rarely embedded in physical or Euclidean spaces, which complicates their analysis. However, to correctly represent node similarities, it is typical to assume that the network’s nodes lie in a low-dimensional subspace, such as a manifold or linear subspace1. Having this geometric backbone permits the efficient functioning of standard clustering methods, including ones based on Euclidean geometric features such as k-means or expectation maximisation2. A related means of geometrising networks is possible by embedding nodes into a continuous space. For example, the hyperbolic space of constant negative curvature provides a natural parametrisation of complex networks to unveil their self-similar clusters across scales3,4. Likewise, embedding networks into a geometric space based on a suitable distance metric between dynamical network processes has helped reveal their functional organisation5,6. However, in general, there is no guarantee that a network is compatible with a given metric space without suffering significant distortion7. At the same time, a network may have several, not necessarily self-similar, geometric representations arising, for example, from clusters at multiple resolutions8. Thus, there is a need for a geometric notion that does not require embedding, yet allows studying the multiscale structure of a general class of networks.
+
+A promising candidate is the Ollivier-Ricci (OR) curvature9, which measures the change of local connectivity from one node to another, given by the cost of transporting a unit of mass between their respective neighbourhoods. Instead of imposing a geometry on the network through embedding, the OR curvature induces an effective geometry that has precise interpretation in limiting cases. In fact, it is the only one among a number of discrete curvature notions10,11 known to converge rigorously to the traditional Ricci curvature of a Riemannian manifold12. The OR curvature is also related to graph theoretical objects, including the local clustering coefficient and bounds on the spectrum of the graph Laplacian13,14, and has
+lead to advances in applications such as studying the robustness of economic networks\(^{15}\), characterising the human brain structural connectivity\(^{16}\) and designing clustering heuristics\(^{17,18}\).
+
+However, several properties of the OR curvature hinder its widespread applicability to study network clusters. Since it depends on structural neighbourhoods, it lacks a resolution parameter to define a geometry on different resolutions, that is necessary to study the multiscale structure in real-world networks. Further, the OR curvature of an edge is a local quantity, in a sense that it is controlled by the degree of its endpoints\(^{13}\). Thus, it may provide a suboptimal geometric representation of sparse networks - including many real-world networks where each node connects only to a few others - in which node degrees vary widely. This lack of robustness of the OR curvature for sparse networks also precludes its use for studying from a geometric perspective the phase transition occurring as the community structure gets weaker and become abruptly undetectable\(^{19-21}\). In other words, there is a need for a geometric notion that does not rely on embeddings, robustly captures multiscale clusters in real networks, and captures the phase transition at the limit of cluster detection.
+
+Results
+
+Dynamical Ollivier-Ricci curvature from graph diffusion
+
+We address this need by combining two distinct frameworks – network-driven dynamical processes and geometry with OR curvature. The spreading of network-driven dynamical processes is shaped by the heterogeneity of the network. In turn, one may infer the network structure by observing properties of their evolution. We focus on Markov diffusion processes\(^{8,22-24}\), a class of linear dynamical systems which is rich enough to capture several properties of nonlinear processes on networks\(^{25,26}\). On a connected network \(G\) weighted by pairwise distances \(w_{ij}\), the continuous time diffusion is constructed by the standard procedure\(^{27}\) of defining the normalised graph Laplacian matrix \(\mathbf{L} := \mathbf{K}^{-1}(\mathbf{K} - \mathbf{A})\), where \(\mathbf{K}\) is the diagonal matrix of node degrees with \(K_{ii} = \sum_j A_{ij}\) and \(\mathbf{A}\) is the weighted adjacency matrix encoding similarities between nodes. For example, one may simply take \(A_{ij} = \max_{ij} w_{ij} - w_{ij}\), or \(A_{ij} = e^{-w_{ij}}\). Then, the probability measure of the diffusion started from the unit mass \(\delta_i\) on node \(i\) (Fig. 1a, b) evolves according to
+
+\[
+p_i(\tau) = \delta_i e^{-\tau \mathbf{L}} .
+\]
+
+In analogy to the Ricci curvature on a manifold, the classical OR curvature\(^{9,28}\) measures the change of one-step neighbourhoods between nodes (see Methods and Supplementary Fig. 1a for background). Here, instead of structural neighbourhoods we consider distributions generated by diffusion processes across scales \(\tau\). Specifically, we start a diffusion process at each node \(i = 1, \ldots, n\) to obtain a set of measures \(p_i(\tau)\). We then define the *dynamic* Ollivier-Ricci curvature of an edge as the distance of adjacent pairs of measures relative to the distance of their starting points
+
+\[
+\kappa_{ij}(\tau) := 1 - \frac{\mathcal{W}_1(p_i(\tau), p_j(\tau))}{w_{ij}} ,
+\]
+
+whenever \(ij\) is an edge and 0 otherwise. Intuitively, Eq. (2) measures how much 'closer' diffusions get over time when started \(w_{ij}\) distance apart, measured by \(\mathcal{W}_1\), the optimal transport distance\(^{29}\). It is obtained as a solution to a minimisation problem (Eq. (13) in Methods) and encodes the least cost of transporting the measure \(p_i(\tau)\) to \(p_j(\tau)\) via the edges on the graph. The minimiser of this problem is the optimal transport plan represented as a matrix \(\zeta(\tau)\). The entries of this matrix shown on Fig. 1c, d quantify how much mass is moved between each pair of nodes \(u\) and \(v\) along their connecting geodesic of length \(d_{uv}\) (Fig. 1e).
+
+As expected, our definition recovers the classical OR curvature\(^{9}\) as a first-order approximation for small times \(\tau \ll 1\). Indeed, \(p_i(\tau) \simeq \delta_i \mathbf{K}^{-1} \mathbf{A}\) is the one-step measure encoding the local connectivity. Further, the dynamical OR curvature inherits the geometric intuition of the classical definition. Notably, on canonical trees-like and cliques-like networks the \(\kappa_{ij}(\tau)\) is negative and positive, respectively, for all finite scales \(\tau\) analogously to the Ricci curvature on hyperboloids and spheres (Supplementary Fig. 1b, c).
+Figure 1: Dynamical Ollivier-Ricci curvature capturing the spreading of diffusion processes. a Snapshot at time \( \log \tau = 0.15 \) of a pair of diffusion measures \( p_i(\tau) \) and \( p_j(\tau) \) started at nodes \( i, j \) of a stochastic block model network (\( n = 120 \) with four equal clusters with edge probabilities 0.8 within clusters and 0.1 or 0.02 between clusters). When \( i \) and \( j \) are in the same cluster, the measures overlap significantly. The size of half-circles is proportional to the amount of mass on the respective nodes. b For \( i', j' \) in different clusters the measures remain largely disjoint. c Optimal transport plan \( \zeta(\tau) \) superimposed with \( p_i(\tau), p_j(\tau) \). When \( i, j \) (colored dashed lines) lie in the same cluster only diagonal elements \( \zeta_{uu} \) are positive, meaning only geodesics within a cluster transport significant mass. The white dashed lines correspond to the four clusters. d Same as c, but with diffusions started at nodes \( i' \) and \( j' \) in different clusters. Only entries \( \zeta_{uv} \) with \( u \) and \( v \) in different clusters have significant nonzero weight. e Geodesic distance matrix showing the block structure of the network. f The evolution of the edge curvatures (Eq. (2)) against time, with the highlighted lines corresponding to edges in a, b. Here \( \kappa_{ij}(\tau) \simeq 0.75 \) indicates scales when local mixing occurs between diffusion pairs. The dashed vertical lines show two such scales (\( \log \tau = 0.15, 0.43 \)). g, h Graph edges coloured by the curvature reveals the clusters at the two scales.
+
+In the following we are interested in studying the curvature distribution across edges when the network structure deviates from these canonical topologies.
+
+Edge curvature gap differences in rate of information spreading
+
+Most real-world networks exhibit organisation on several scales. As an illustration, the unweighted stochastic block model (SBM) network\(^{30}\) of four equal-size clusters contains two nontrivial scales if the edges are drawn independently with probability 0.8 within clusters and 0.1 or 0.02 between clusters (Fig. 1a, b). We show that multiscale structure can be revealed by scanning through a finite range of scales \( \tau \) and studying snapshots of curvature distribution across edges.
+
+The characteristic scales of a network are related to the overlap between pairs of diffusion measures \( p_i(\tau), p_j(\tau) \). This overlap depends on the starting points \( i, j \) and on network clusters which can confine diffusions on well-connected regions for long times before reaching the stationary state \( \pi^{8,22,23,31} \), with \( \pi_i = K_{ii}/\sum_i K_{ii} \). This transient phenomenon is reflected by the structure of the optimal transport matrix \( \zeta(\tau) \). If \( i, j \) lie within the same subnetwork, the measures quickly overlap (Fig. 1a) and only diagonal entries of \( \zeta(\tau) \) are positive (Fig. 1c), weighing only short, within-cluster geodesics. By contrast, started at different subnetworks, the measures remain almost disjoint (Fig. 1b) and \( \zeta(\tau) \) is forced to select longer
+geodesics (Fig. 1d, e), reflected by the large entries in the off-diagonal block.
+
+The evolution of the edge curvature \( \kappa_{ij}(\tau) \) (Fig. 1f) aggregates the information in \( \zeta(\tau) \) into a single number that is related to the rate of mass exchange between subnetworks at a given scale. We see in Fig. 1f that, initially, when all nodes support disjoint point masses and the diffusions have not yet mixed, \( \lim_{\tau \to 0} \kappa_{ij}(\tau) \to 1 - \mathcal{W}_1(\delta_i, \delta_j)/d_{ij} = 0 \). At the other extreme, as the diffusions reach stationary state, \( \lim_{\tau \to \infty} \kappa_{ij}(\tau) \to 1 - \mathcal{W}_1(\pi, \pi)/d_{ij} = 1 \). At intermediate scales, the curvature can take values between 1 and some finite negative number depending on the graph. We find that, as the curvature of an edge evolves, the scale at which it approaches unity indicates how easy it is to propagate information between the subnetworks. More precisely, in the Methods, we prove that this scale gives an upper bound on the mixing time \( \tau_{ij}^{\text{mix}} \) of the diffusion pair, namely,
+
+\[
+\tau_{ij}^{\text{mix}} := \frac{1}{2} \sum_{uv} |\zeta_{uv}(\tau) - \zeta_{uv}(\infty)| 
+\]
+\[
+\leq \min\{ \tau : \kappa_{ij}(\tau) \geq 0.75 \},
+\]
+
+where \( \zeta(\tau) \) is the optimal transport plan with marginals \( \mathbf{p}_i(\tau) \) and \( \mathbf{p}_j(\tau) \). Note that \( \kappa_{ij}(\tau) \geq 0.75 \) does not imply that the corresponding diffusion processes have approached stationary state independently, but only that they exchange negligible mass at that or larger scales.
+
+Importantly, a gap in the distribution of curvatures appears when the curvature exceeds 0.75 for some edges while remaining less than 0.75 for others indicating a network bottleneck that limits mass flow. To illustrate this, Fig. 1f shows three groups of edges, those with most positive curvature are found within clusters, while the other two groups of edges are found between pairs of clusters. Figs. 1g, h correspond to two scales on Fig. 1f (\( \log \tau = 0.15, 0.43 \)) where the curvature has exceeded 0.75 for some groups of edges, indicating the diffusions are well mixed within these groups, but not across other edges for which the curvature is less than 0.75. The latter mark bottleneck edges which lie between the expected partitions with 4 and 2 clusters, respectively. This simple example shows the importance of the scale parameter \( \tau \) in our curvature definition to capture the network structure at multiple scales. Before applying this to real networks, we take a closer look at the curvature gap in the theoretical context of the stochastic block model.
+
+Curvature gap is a robust indicator of clusters in stochastic block models
+
+Since in our example any pair of diffusions are supported by one (Fig. 1a) or two (Fig. 1b) clusters, we focus on studying the subgraph \( G \) induced by two clusters (Fig. 2a). The subgraph \( G \) is a realisation of \( \mathcal{G} = \mathrm{SSBM}(n/2, p_{in}, p_{out}) \), the symmetric SBM composed of two planted partitions of equal size. Edges are generated independently with probability \( p_{in} \) within-clusters and probability \( p_{out} \) between-clusters. We will denote the ground truth with \( C_i \in \{1, -1\} \) for each node \( i \) and define \( \bar{k} = n(p_{in} + p_{out})/2 \) as the average degree.
+
+Classical spectral clustering methods\(^{27}\) perform well for dense graphs (Fig. 2a), where \( \bar{k} \) is an increasing function of \( n \). This suppresses fluctuations for large \( n \) causing a spectral gap to appear when the eigenvalue \( \lambda_c \) of the Laplacian matrix \( \mathbf{L} \) of \( G \) separates from bulk eigenvalues arising from randomness\(^{27}\) (Fig. 2c). In this dense regime, \( \lambda_c \) is well approximated by \( \langle \lambda_c \rangle_G = 2p_{out}/(p_{in} + p_{out}) \), the second eigenvalue of the ensemble averaged Laplacian \( \langle \mathbf{L} \rangle_G \) (see Supplementary Note 1). Since \( \lambda_c \) can be identified due to the spectral gap, clustering involves simply labelling nodes by the sign of the entries of the corresponding eigenvector, which also approximates the ensemble average eigenvector \( \phi_c(u) = 1/\sqrt{n} \) when \( C_u = 1 \) and \( -1/\sqrt{n} \) when \( C_u = -1 \). However, for sparse graphs (Fig. 2b), where \( k \) is constant (independent of \( n \)), the spectral gap ceases to exist\(^{32}\) (Fig. 2d). Thus, spectral algorithms relying on identifying \( \lambda_c \) perform no better than chance. To perform clustering in this regime, one needs to go beyond spectral clustering using, for example, the belief propagation method in statistical physics or the related non-backtracking operator whose spectrum is better behaved\(^{19,21}\).
+Figure 2: Edge curvature gap indicates the presence of clusters where spectral clustering fails. Two-partition symmetric SBM graph in the a dense regime (\( p_{in} = 0.5,\ p_{out} = 0.1 \)) and b sparse regime (\( p_{in} = 8/n,\ p_{out} = 0.5/n \)). Edges are coloured by the curvature (\( n = 100,\ \log \tau = 0.83 \)). c, d The histogram of eigenvalues obtained from five SBM realisations in dense and sparse regime, respectively. In the dense regime, the eigenvalue \( \lambda_c \) corresponding to the community structure is well separated from the bulk eigenvalues, but overlaps in the sparse regime. e, f The evolution of edge curvatures driven against diffusion time. A gap between the curvatures of within-edges and between-edges is associated with the presence of clusters. When \( \kappa_{ij} > 0.75 \) (horizontal dashed line) the diffusions are well mixed across the respective edges. The curvature gap is maximal at \( \tau_k \approx \lambda_c^{-1} \) (orange and black vertical lines). g There is no curvature gap in the limiting ER graph (inset, \( p_{in} = p_{out} = (8 + 0.5)/(2n) \)). h Maximal curvature gap averaged over 20 SBM realisations for each fixed \( k \) with \( 10^4 \) nodes, against edge density ratio. The horizontal line marks the estimated background noise level. The intersection of this line with the mean curvature gap defines \( r_k^* \), the largest possible edge density ratio to detect clusters. i Phase diagram of critical edge density ratio against average degree. The numerically obtained critical edge density ratios computed from the curvature gap are superimposed with the theoretical Kesten-Stigum detection limit (dashed line) and show excellent agreement. Gray shaded area denotes the regime where detection is possible.
+
+To see how robustly the dynamical OR curvature indicates the presence of clusters in the symmetric SBM, let us construct a measure on the curvature evolution. To this end, we define the curvature gap as the difference between the mean curvatures of within- and between-edges
+
+\[
+\delta \kappa(\tau) := \frac{1}{\sigma} \left| \langle \kappa_{ij}(\tau) \rangle_{C_i = C_j} - \langle \kappa_{ij}(\tau) \rangle_{C_i \neq C_j} \right|
+\]
+
+where the averages are on within and between-edges, normalised by \( \sigma = \sqrt{\frac{1}{2} \left( \sigma_{\text{within}}^2 + \sigma_{\text{between}}^2 \right)} \) in terms of the standard deviations of both sets of curvatures. This measure is adapted from the sensitivity index in signal detection theory, known to be, asymptotically, the most powerful statistical test for discriminating two distributions\(^{33}\). Large curvature gap \( \delta \kappa(\tau) \) indicates that the within and between edges have curvatures different enough for the clusters to be recovered (Fig. 2e, f). Correspondingly, in the limits \( \tau \to 0, \infty \)
+Figure 3: Detecting communities using pairs of diffusions near the weak recovery limit. a Difference in eigenvectors \( \Delta \phi_s \) (Eq. (8)) between diffusion processes started at adjacent nodes for a single sparse SBM network (\( p_{in} = 3/n,\ p_{out} = 0.5/n,\ n = 10^4 \)). Each dot marks \( (\lambda_s, \Delta \phi_s) \) for the 50 smallest eigenvectors, colored by the correlation of the corresponding eigenvector with the ground truth, shown in the inset. b The eigenvector with the highest \( \Delta \phi_s \) encodes the cluster structure (solid line), whereas the second eigenvector \( \phi_2 \), used by spectral clustering methods, are driven by high random fluctuations. c Correlation of eigenvectors with ground truth against distance to KS limit (\( n = 10^5,\ k = 3 \)). The eigenvector identified by the highest \( \Delta \phi_s \) approaches the correlation with the ground truth of the best eigenvector in the spectrum. All eigenvectors become uncorrelated with the ground truth at the KS limit.
+
+where the curvatures are uniform across the graph \( \delta \kappa(\tau) \) vanishes and, likewise, in the absence of structure (\( p_{in} \approx p_{out} \) in the Erdős-Rényi (ER) limit) we have \( \delta \kappa(\tau) = 0 \) for all \( \tau \) (Fig. 2g). At intermediate scales, we find that the scale of maximal curvature gap occurs at \( \tau_k \) at which point the curvatures of within-edges is \( \kappa_{ij}(\tau_k) \approx 0.75 \). In agreement with Eq. (3), this indicates well-mixed diffusions across these edges relative to low-curvature bottleneck edges between clusters, which indicate incomplete mixing. We also find that \( \tau_k \approx \lambda_c^{-1} \) (Fig. 2e, f). These results show that positive curvature gap is associated with the presence of clusters.
+
+What is the minimum curvature gap needed to detect clusters? Previous works on the limits of cluster detection has shown that if the clusters are too weak (high \( r := p_{out}/p_{in} \)) or the graph too sparse (low \( \bar{k} \)), no algorithm can assign the vertices to communities better than chance, or distinguish \( G \) from an Erdős-Rényi graph (\( r = 1 \)). This is known as the limit of weak-recovery or detection and is characterised by the Kesten-Stigum (KS) threshold \( r = r_{KS} = (\bar{k} - \sqrt{\bar{k}})/(\bar{k} + \sqrt{\bar{k}}) \) [19,20,34].
+
+To study this limit, we sampled 20 networks from \( G \) for a range of \( \bar{k} \) and \( r \). For each sample, we computed the maximal curvature gap \( \delta \kappa^* := \max_\tau \delta \kappa(\tau) \) and formed the ensemble average quantity \( \langle \delta \kappa^* \rangle_G \). As \( r \) increases for a given \( \bar{k} \) we observe that \( \langle \delta \kappa^* \rangle_G \) decreases exponentially until a certain noise level (Fig. 2h). The critical edge density ratio \( r_k^* \) can be estimated as the smallest \( r \) where \( \langle \delta \kappa^* \rangle_G \) dropped below a threshold background noise level, estimated here at 0.035 (black horizontal line). This choice of threshold is not absolute, as it is affected by the finite-size effect of the SBM graphs. An analytical derivation of this threshold is out of scope of this work, but our numerical experiment clearly shows that the curvature gap detects a signal from the planted partitions up to the KS limit (Fig. 2i).
+
+Geometric cluster detection in the sparse regime
+
+Given that the curvature gap (Eq. (4)) indicates the presence of clusters until the fundamental KS limit we asked if this information could be used to recover the ground truth partition. The definition of curvature gap (Eq. (4)) suggests looking for equilibrium configurations of the unit-temperature Boltzmann distribution over the cluster assignments \( C \),
+
+\[
+\mathbb{P}(C|\kappa) \propto e^{\sum_{ij} \kappa_{ij}(\tau) \delta(C_i, C_j)},
+\]
+
+where \( \kappa \) is a matrix with entries \( \kappa_{ij} \) and the sum is over all edges \( ij \). The distribution involves only within-edges because finding those is equivalent to finding between-edges, up to a normalisation factor.
+The distribution \( \mathbb{P}(C|\kappa) \) is important because all of its equilibrium states are equivalent and correlate with the ground truth partition of the symmetric SBM \( \mathcal{G} \). To see this, we connect \( \mathbb{P}(C|\kappa) \) to the posterior distribution \( \mathbb{P}(C|G) \) of the cluster assignments obtained given the graph drawn from \( \mathcal{G} \). In the sparse regime, the likelihood of observing \( G \) with a given cluster assignment \( C \) is
+
+\[
+\mathbb{P}(G|C) \propto \prod_{ij} \left( \frac{p_{in}}{p_{out}} \right)^{\delta(C_i, C_j)} \propto \mathbb{P}(C|G)
+\]
+
+(see Eq. (17) in Methods). The second part of Eq. (6) results from Bayes’ theorem using a uniform prior on \( C \), since a priori all configurations are equally likely. It has been previously shown\(^{19}\) that \( P(C|G) \) is equivalent to the Boltzmann distribution of an Ising model with constant interaction strength
+
+\[
+\mathbb{P}(C|G) \propto e^{\beta \sum_{ij} \delta(C_i, C_j)}
+\]
+
+with inverse temperature \( \beta = \log(p_{in}/p_{out}) \approx p_{in} - p_{out} \). Note that one of the equilibrium states is trivial assigning all nodes to one cluster. However, asymptotically (\( n \to \infty \)) the probability of this state vanishes and the Boltzmann distribution is uniform over all other configurations with group sizes \( n/2 \) and \( p_{out}n/2 \) between-edges\(^{19}\). The fact that one of these states is the ground truth partition, and all equilibrium states of Eq. (7) are equivalent up to a permutation of nodes within clusters means they are indistinguishable from the ground truth partition.
+
+Due to the equivalence between Eq. (6) and (7), to prove the equivalence between Eq. (5) and (6) we show that Eq. (5) can also be reduced to Eq. (7). The main insight is that the dynamical OR curvature (Eq. (2)) is constructed using pairs of diffusions, as opposed to single diffusions. Thus, eigenmodes arising from random fluctuations are reflected equally in the spectrum of both diffusions and cancel out upon taking differences over all adjacent node pairs. This allows recovering the community eigenvector \( \phi_c \) even in the sparse regime where when there is no spectral gap and \( \lambda_c \) is no longer identifiable from the spectrum (Fig. 2d). Specifically, using pairs of diffusions, we use the spectral expansion to write
+
+\[
+\sum_{ij} \left( p_i^u(\tau) - p_j^u(\tau) \right) = \sum_s e^{\lambda_s \tau} \phi_s \Delta \phi_s
+\]
+
+where
+
+\[
+\Delta \phi_s := \sum_{ij} (\phi_s(i) - \phi_s(j)) .
+\]
+
+We find that, on a single SBM realisation, \( \Delta \phi_s \) is large for only a few eigenvectors \( \phi_s \) and diminishing for others Fig. 3a). Importantly only those eigenvectors with large \( \Delta \phi_s \) correlate strongly with the ground truth (Fig. 3a inset). As seen in Fig. 3b, the best eigenvector is not \( \phi_2 \), i.e., the one whose eigenvalue is second in the spectrum and is used by spectral clustering methods, but the one whose eigenvalue is inside the bulk in Fig. 2d and thus cannot be identified by looking at the spectrum alone. The correlation with the ground truth for \( \phi_c \) with the highest \( \Delta \phi_s \) averaged over 50 SBM realisations remains close to the highest achievable among all eigenvectors as the KS bound is approached. Meanwhile, \( \phi_2 \) is suboptimal (Fig. 3c). We also found that, close to the KS bound, often a few other eigenvectors with similarly high \( \Delta \phi_s \) appear, suggesting an improved clustering method combining several top eigenvectors, but this is out of scope here.
+
+To express the curvature in the exponent of Eq. (5) we use the dual formulation of the optimal transport distance (Eq. (14) in Methods). The fact that \( \Delta \phi_c \) dominates the contribution from other eigenvectors, allows us to approximate \( \sum_{ij} \left( p_i^u(\tau) - p_j^u(\tau) \right) = e^{\lambda_c \tau} \phi_c \Delta \phi_c + \epsilon_\phi \propto e^{\lambda_c \tau} \phi_c + \epsilon_\phi \), where \( \epsilon_\phi \) is an asymptotically small term. We use this expression, together with the duality formula (Eq. (14)) to express Eq. (5). Finally, in the sparse regime, we may make a tree-like approximation of the neighbourhoods of \( i \) and \( j \) to find that Eq. (5) reduces to
+
+\[
+\mathbb{P}(C|\kappa) \propto e^{|p_{in} - p_{out}| \sum_{ij} \delta(C_i, C_j)} .
+\]
+We refer the reader to the Methods for details. Eq. (9) is the same as Eq. (7) when the communities are assortative (\( p_{in} > p_{out} \)). We then conclude that the curvatures encode the communities of the symmetric SBM and allow it to be recovered until close to the Kesten-Stigum bound.
+
+In the next section, we present a clustering algorithm based on this insight that can find multiscale clusters in real-world networks.
+
+Geometric modularity for the multiscale clustering of networks
+
+To exploit the property of the dynamical OR curvature to give multiple geometric representations, we develop a multiscale graph clustering algorithm for real-world networks. Using Eq. (5), we introduce the geometric modularity function
+
+\[
+Q_\kappa(C, \tau) = \frac{1}{2m_\kappa} \sum_{ij} (\kappa_{ij}(\tau) - \kappa_0) \delta(C_i, C_j),
+\]
+
+where \( 2m_\kappa = \sum_{ij} |\kappa_{ij}| \) is a normalisation factor and \( \kappa_0 = \max_{ij} \kappa_{ij}(\tau_{\min}) \) is a constant ensuring that all edges have small non-positive curvature at the smallest computed scale \( \tau_{\min} \). Hence optimising Eq. (10) at small times yields separate communities for each node whereas at large times, when \( \kappa_{ij}(\tau) \to 1 \) for all \( ij \), all nodes are merged to a single community. At intermediate scales, the curvatures will have negative and positive values on different edges, making the detection of non-trivial clusters possible without a statistical null-model. This is in contrast to classical modularity\(^{35}\), which minimises the expected number of edges between clusters, and requires a statistical null-model (typically the configuration model), which can hinder identifying functional communities based on dynamics\(^{5}\).
+
+To detect robust partitions at several scales, we sample the cluster landscape \( Q_\kappa(C, \tau) \) at a sequence of scales \( \tau \) spanning the entire dynamical range of the curvature and, at each \( \tau \), optimising Eq. (10) using the Louvain algorithm\(^{36,37}\) with 200 random initialisations. At a given \( \tau \), we take the cluster with the highest geometric modularity and deem it robust if it has a low variation of information VI\(_\tau\) against 50 other randomly chosen clusters at this scale, as well as low variation of information VI\(_{\tau\tau'}\) against the best cluster assignments at nearby scales \( \tau' \). As an example, we show in Fig. 4a the result of this computation on our four-partition SBM graph with two hard-coded scales. We clearly see two large plateaus with low VI\(_\tau\) and VI\(_{\tau\tau'}\), corresponding to robust clusters, shown in Fig. 4b,c. At the smallest scales we find no robust communities shown by the sharp increase in the number of communities and the large VI\(_\tau\).
+
+Due to the link between high edge curvature and well-mixed state (Eq. (3)), we expected that at robust scales the clusters will correspond to those regions which have a high amount of redundant information, and thus can be disconnected without affecting the dynamics within them. To see this, we applied this clustering algorithm to the European power grid graph in Fig. 4d,e,f, an unweighted network of major electrical lines, which has been previously analysed for robustness\(^{38}\), multiscale communities\(^{39}\) and centrality\(^{24}\). The multiscale community structure can be clearly seen with the many minima of the VI\(_\tau\) function in Fig. 4d. We displayed two scales in Fig. 4e,f which unfold parts of the power grid which have been historically independently developed. The smaller scale (at around \( \log \tau = -0.95 \)) marks countries or economical and historical alliances (Skandinavia, Benelux, Czechoslovakia, Balkans, etc.). Likewise, the larger scale (at around \( \log \tau = -0.5 \)) divides historical Eastern-Western Europe. Interestingly with the boundary in Germany runs along the iron curtain, which also demarcates the regions between major electricity companies.
+
+Finally, we analysed a recent dataset of homeobox gene expression in single neurons of *C. elegans* in Fig. 4g, h, i and j\(^{40}\). This work found based on a multivariate linear regression that the homeobox gene expression profile in a given anatomical neuron class can explain on average 74% of the expression level of the remaining genes in that neuron class. We therefore asked whether the homeobox gene expression profile has sufficient information to cluster neurons into their known anatomical classes.
+
+The data contains a binary feature vector for each of the 301 neurons, indicating the presence of a protein expressed by any of the 105 homeobox genes in the given neuron. To convert this data into a
+Figure 4: Clustering networks based on multiscale geometric modularity a Clustering statistics computed based on \(10^2\) Louvain realisations for the multiscale stochastic block model graph. Vertical dashed lines show scales at which stable clusters are detected based on low variation of information at a given scale and persistent low variation of information between Louvain realisations across scales. The communities obtained at these scales are shown on b for \(\log \tau = -2.3\) and c for \(\log \tau = -1\). Edges are coloured by the curvatures at the respective scales. d Clustering statistics for the European power grid. Two representative stable scales are shown e for \(\log \tau = -0.95\) and f for \(\log \tau = -0.5\). g Clustering statistics for and the network of C. elegans single-neuron homeobox gene expressions show a plateau of stable scales with very similar partitions. h Clustering statistics obtained with Markov stability shows stable scales only at small times with single-node communities, indicating overfitting, and many non-robust partitions at larger scales with high variation of information. i Distance from ground truth based on structural neuronal types or the predicted clusters. Geometric modularity obtained significantly better performance than Markov stability. j Clustering of the C. elegans homeobox gene expression data obtained from geometric modularity optimisation superimposed with the ground truth.
+graph with nodes being neurons, we first eliminated all homeobox genes co-expressed in none or more than 90% of the neurons to retain 67 homeobox genes. We then constructed an all-to-all graph adjacency matrix weighted by the Jaccard similarity index between expression profiles of neurons. To increase the number of edges with negative curvature, thus improve the detection at the smallest scales, we sparsified this network using a geometric sparsification method\(^{41}\) with parameter \( \gamma = 0.01 \). This method retains at most a fraction \( \gamma \) edges of the original graph as minimum spanning tree augmented by edges relevant for preserving local or global geometry of the graph.
+
+The results of our clustering algorithm on this graph is shown on Fig. 4g and compared with the result of Markov stability\(^8\) (Fig. 4h), a multiscale method based on persistence of diffusions. Geometric modularity obtains a large range of robust scales with highly similar clusters - as shown by the low \( VI_{\tau} \) and \( VI_{\tau'\tau'} \). These scales correlate closely with the known ground truth of 117 anatomical neuron classes (Fig. 4i). In contrast, for Markov stability\(^8\), the scales with low \( VI_{\tau} \) overfit the graph finding too many clusters (Fig. 4h) which correlate less with the ground truth (Fig. 4i). Likewise, hierarchical clustering fails to identify the ground truth communities\(^{40}\). On Fig. 4j we superimpose the best clustering from geometric modularity against the ground-truth. We observe little differences, apart from VA and AS nodes as well as VD and DD often clustered together. Careful look reveals close biological relationship between these classes; all four classes correspond to motor neurons, with pairs expressing the same neurotransmitters – VA, AS expressing acetylcholine and VD, DD expressing gamma-aminobutyric acid (GABA). These novel results give direct quantitative support to the claim that homeobox gene expression patterns encode structural neuron types. We also observe other stable partitions at larger scale, but they did not correlate the ground-truth.
+
+Overall, these results give a strong demonstration that our method is able to find stable clusters in sparse graphs, and provide meaningful insights into distinct types of real-world networks.
+
+Discussion
+
+We introduced the concept of dynamical Ollivier-Ricci (OR) curvature which defines an effective geometry from pairs of diffusion processes on the network. Instead of imposing the requirement of a manifold approximation or embedding, used by previous geometric approaches\(^{4,6,23}\), our approach constructs a geometric object - the weighted and signed edge curvature matrix - capturing progressively coarser features as the diffusion processes evolve.
+
+Real-world networks often exhibit community structure on multiple scales, based on difference between the rates of information propagation in regions the network on various timescales. We showed that the edge curvature matrix carries a precise meaning in this context and bounds the rate of information flow across edges. Consequentially, curvature gaps, differences between edge curvatures within and between regions, indicate network bottlenecks. This result does not rely on the dynamics being linear diffusions, making it suitable to study the interaction of arbitrary dynamical processes. We expect that, in the future, this approach can be used to tune the geometry of the graph to control the flux or interaction of network-driven dynamical processes, for example, leading to better insights to synchronisation problems or metapopulation models\(^{42}\).
+
+Although diffusion processes constructed from the graph Laplacian have been explored for network clustering\(^{8,23}\), our work differs in the use of diffusion pairs to construct the curvature. Two diffusions pick up random variations in the graph independently, which can be exploited to average out non-informative fluctuations. On stochastic block models, this feature allows the curvature gap to robustly indicate clusters in the sparse regime down to the fundamental limit, where clustering methods relying on the spectral gap in the Laplacian fail\(^{32}\). We also found a new measure of eigenvalue quality, able to select the best eigenvector to be used in spectral methods. Interestingly, the edge curvatures are defined on the set of shortest paths which cannot contain the same edge twice, a subset of the set of non-backtracking walks. Our results are therefore consistent with previous works on the limits of cluster detection using statistical physics objects including the spectrum of non-backtracking operator\(^{21}\) or related message passing approaches\(^{19}\). We expect this insight to provide a new avenue to study the fundamental limits of efficient clustering from
+a geometric perspective.
+
+Finally, using geometric modularity we built an easy-to-use algorithm to study the multiscale community structure of real networks. We demonstrated on the European power grid network and a recent dataset of C. elegans single-neuron homeobox gene expressions that our method can find robust and interpretable communities on multiple scales on diverse datasets without the tendency of overfitting.
+
+Overall, we expect our insights connecting dynamical processes, geometry and network clustering to open new avenues to studying and controlling the structural and dynamical properties of networks.
+
+Acknowledgements
+
+AG acknowledges support from an HFSP Cross-disciplinary Postdoctoral Fellowship (LT000669/2020-C). We thank Mauricio Barahona for insightful discussions on this topic, Jonas Braun and István Tomon for their helpful comments on the manuscript and Daniel Morales for inspiring us to analyse the C. elegans dataset.
+
+Author contributions
+
+A.G. and A.A. contributed equally to this work.
+
+Code availability
+
+The code to reproduce the results in our paper and to perform geometric modularity optimisation is available at https://github.com/agosztolai/geometric_clustering.
+
+Data availability
+
+The raw data supporting the results is available from the authors upon request.
+
+Methods
+
+Classical Ollivier-Ricci edge curvature
+
+To contrast the dynamical Ollivier Ricci curvature in Eq. (2), we recap the definition of the classical formulation\textsuperscript{9}, which is a generalisation of the Ricci curvature of manifolds in differential geometry. Briefly, consider two close points x and y on a manifold as well as a vector v on the tangent plane at x and another tangent vector v' in the tangent plane at y that is parallel to v, i.e., obtained by parallel transport along the geodesic connecting x, y (Supplementary Figure 1a). These vectors shift x and y to nearby points x' and y', which will be at a distance \( d_{x'y'} \approx d_{xy}(1 - ||v||^2 K_w / 2) \), where \( K_w \) is the sectional curvature. The Ricci curvature \( Ric_{xy} \) between points x, y is then defined as the average sectional curvature and is proportional to
+
+\[
+Ric_{xy} \propto 1 - \frac{\langle d_{x'y'} \rangle}{d_{xy}},
+\]
+
+where \( \langle \cdot \rangle \) denotes the average over all vectors w, w' running over the unit sphere in the tangent planes at x and y. In other words, it measures how much geodesics expand or contract on average around points x, y. On flat planes the geodesics stay equally separated hence \( Ric_{xy} = 0 \), on spheres the geodesics contract hence \( Ric_{xy} > 0 \), whereas in hyperbolic spaces they expand, hence \( Ric_{xy} < 0 \) (Supplementary Figure 1a).
+
+The classical Ollivier-Ricci curvature\textsuperscript{9} is defined by direct analogy to this. Consider two adjacent nodes i and j and place weights on their immediate neighbours in proportion to the edge weights, namely, \( p_i = \delta_i \mathbf{K}^{-1} \mathbf{A} \). Then the Ollivier Ricci curvature becomes
+
+\[
+\kappa_{ij} = 1 - \frac{\mathcal{W}_1(\mathbf{p}_i, \mathbf{p}_j)}{d_{ij}}.
+\]
+
+Contrast this expression to the dynamical Ollivier Ricci curvature in Eq. (2), which considers diffusion measures which weight progressively larger neighbourhoods as \( \tau \) increases.
+
+We remark that Eq. (12) and the dynamical OR curvature in (2) are valid for any two nodes i, j if the denominator is replaced by the weighted geodesic distance between i and j, but for this work, it suffices to consider adjacent nodes. Indeed, for any non-adjacent nodes uv, \( \kappa_{uv} \geq \kappa_{u'v'} \), where \( u'v' \) is an adjacent pair lying on the geodesic connecting u, v (Proposition 19 in Ref.\textsuperscript{9}), meaning that local curvatures control global curvatures.
+Wasserstein distance
+
+To measure the distance between a pair of measures \( \mathbf{p}_i(\tau) \) and \( \mathbf{p}_j(\tau) \) we use the optimal transport distance\(^{29}\) (also known as 1-Wasserstein or earth-mover distance), defined as
+
+\[
+\mathcal{W}_1(\mathbf{p}_i(\tau), \mathbf{p}_j(\tau)) = \min_{\zeta} \sum_{uv} d_{uv} \zeta_{uv},
+\]
+subject to \( \sum_v \zeta_{uv} = p_i^u(\tau) , \quad \sum_u \zeta_{uv} = p_j^v(\tau) . \)
+
+The constraints in Eq. (13) ensure that the optimal transport plan \( \zeta(\tau) \in \mathbb{R}^{n \times n} \) is a coupling of the measures \( \mathbf{p}_i(\tau), \mathbf{p}_j(\tau) \), i.e., \( \zeta(\tau) \) is a joint distribution that admits \( \mathbf{p}_i(\tau) \) and \( \mathbf{p}_j(\tau) \) as marginals.
+
+An equivalent formulation of this distance can be constructed from the Kantorovich-Rubinstein duality\(^{29}\), given by
+
+\[
+\mathcal{W}_1(\mathbf{p}_i(\tau), \mathbf{p}_j(\tau)) = \sup_f \sum_u f(u)[p_i^u(\tau) - p_j^u(\tau)]
+\]
+
+where the supremum is taken over all 1-Lipschitz functions \( f \) on the graph, that is,
+
+\[
+|f(u) - f(v)| \leq d_{uv}
+\]
+
+for any node pair \( u, v \).
+
+Computational complexity
+
+The computational complexity of our clustering method is determined by three components: the computation of the diffusion measures (Eq. (1)), the computation of the optimal transport distance (Eq. (13)) and the computation of the clustering.
+
+We compute each diffusion measure in Eq. (1) by the scaling and squaring algorithm of Ref.\(^{43}\). To our knowledge, the complexity of this algorithm is not known, but we found it to be better than computing the matrix exponential which runs in time \( \mathcal{O}(n^3) \) and then multiplying by the initial condition. The exact computation of Eq. (13) is performed by interior point methods which have a complexity \( \mathcal{O}(n^3 \log n) \). However, note that in our work the explicit computation of \( \zeta(\tau) \) is not required and, moreover, there is typically a significant overlap between the measures \( \mathbf{p}_i, \mathbf{p}_j \) whenever \( i, j \) lie in the same highly connected region. Based on these observations we use recent approximate algorithms to compute the transport cost permitting near \( \mathcal{O}(nm) \)-time computation of the optimal transport distance\(^{44,45}\). This yields a computational complexity of \( \mathcal{O}(nm) \) for sparse graphs with worst case \( \mathcal{O}(n^3) \). These methods also allow GPU parallelisation, which we recommend using for large (\( n \gg 10^3 \)) and dense graphs.
+
+The third component is the complexity of the Louvain algorithm which is linear \( \mathcal{O}(n) \) for sparse networks\(^{36} \).
+
+Upper bound on the mixing time in terms of curvature
+
+Here we prove inequality (3), which gives an upper bound on the mixing time of the coupled diffusions with measures \( \mathbf{p}_i(\tau) \), \( \mathbf{p}_j(\tau) \) in terms the dynamical OR curvature. The \( \epsilon \)-mixing time is defined as the smallest \( \tau \) where the law of the coupled process, the optimal transport plan \( \zeta(\tau) \), is within an \( \epsilon \) radius of the stationary distribution
+
+\[
+\tau_{ij}(\epsilon) := \min\{\tau : \| \zeta(\tau) - \zeta(\infty) \|_{TV} \leq \epsilon \},
+\]
+
+where the notion of "close to stationarity" is quantified by the total variation distance \( \| \zeta(\tau) - \zeta(\infty) \|_{TV} := \frac{1}{2} \sum_{uv} |\zeta_{uv}(\tau) - \zeta_{uv}(\infty)| \). Since \( \mathbf{p}_i(\tau) \) and \( \mathbf{p}_j(\tau) \) are marginals of \( \zeta(\tau) \) we have that
+
+\[
+\tau_{ij}(\epsilon) = \min\{\tau : \| \mathbf{p}_i(\tau) - \pi \|_{TV} + \| \mathbf{p}_j(\tau) - \pi \|_{TV} \leq \epsilon \}
+= \min\{\tau : \| \mathbf{p}_i(\tau) - \mathbf{p}_j(\tau) \|_{TV} \leq \epsilon \},
+\]
+
+where we used the independence of the diffusion processes. From here, we may follow Ref.\(^{46}\) and use the Csiszár-Kullback-Pinsker inequality for the optimal transport distance
+
+\[
+\| \mathbf{p}_j(\tau) - \mathbf{p}_j(\infty) \|_{TV} \leq (1/d_0) \mathcal{W}_1(\mathbf{p}_j(\tau), \mathbf{p}_j(\tau)),
+\]
+
+where \( d_0 = \min_{ij} d_{ij} \) is a global graph constant, which can therefore be absorbed into \( \epsilon \). This gives an upper bound
+
+\[
+\tau_{ij}(\epsilon') \leq \min\{\tau : \mathcal{W}_1(\mathbf{p}_i(\tau), \mathbf{p}_j(\tau)) \leq \epsilon' \}
+= \min\{\tau : \kappa_{ij}(\tau) \geq 1 - \epsilon' \},
+\]
+
+with \( \epsilon' = d_0 \epsilon \) which is what we set out to show. Note that choosing any \( \epsilon' \in (0, 1/2) \) ensures exponential convergence rate to the stationary measure\(^{47}\) and by convention, we take the middle of this range and define \( \tau_{ij}^{\text{mix}} := \tau_{ij}^{\text{mix}}(1/4) \) to obtain Eq. (3).
+Connection between geometric modularity and the symmetric stochastic block model
+
+In this section, we prove that the Boltzmann distribution of cluster assignments given the edge curvatures \( \mathbb{P}(C|\kappa) \) (Eq. (5)) has equilibrium states which are indistinguishable from the ground truth partition of the SBM. We show this by reducing \( \mathbb{P}(C|\kappa) \) as well as the posterior distribution \( \mathbb{P}(C|G) \), to the same constant interaction Ising model (Eq. (7)). In the remainder of this section we work in the sparse regime, where \( p_{in}, p_{out} = O(1/n) \).
+
+First, we recap the well-known equivalence of the SBM and the Ising model\(^{19}\). Let \( E \) denote the set of edges. The probability distribution of the symmetric SBM for two clusters can be written as\(^{30}\)
+
+\[
+\mathbb{P}(G|C) = p_{out}^e (1 - p_{out})^{n(n-1)/2 - e} \times \\
+\times \prod_{ij \in E} \left( \frac{p_{in}}{p_{out}} \right)^{\delta(C_i, C_j)} \prod_{ij \notin E} \left( \frac{1 - p_{in}}{1 - p_{out}} \right)^{\delta(C_i, C_j)} \\
+\propto \prod_{ij \in E} \left( \frac{p_{in}}{p_{out}} \right)^{\delta(C_i, C_j)}
+\]
+
+where \( e \) is the total number of edges and in the last line we used that the effect of non-edges is weak in the sparse regime. Therefore, by Bayes’ theorem with uniform prior one obtains the posterior distribution \( \mathbb{P}(C|G) \propto \mathbb{P}(G|C) \). As a result, the probability of clusters generated by the SBM is equivalent to the Ising model with uniform interaction with Boltzmann distribution given by Eq. (7)\(^{19}\).
+
+Second, we reduce the Boltzmann distribution of clusters given the edge curvature to same Ising model in Eq. (7). From Eq. (5) we have
+
+\[
+\mathbb{P}(C|\kappa) \propto e^{\sum_{ij} \kappa_{ij}(\tau) \delta(C_i, C_j)} \\
+\propto e^{\sum_{ij} [1 - W_1(p_i(\tau), p_j(\tau))] \delta(C_i, C_j)} ,
+\]
+
+where in the last line we used the definition of the curvature in Eq. (2). Comparing Eq. (18) with Eq. (7) note that \( 1 - W_1(p_i(\tau), p_j(\tau)) \) is non-constant and has a non-linear dependence on the scale \( \tau \). However, it is possible to express it in terms of \( p_{in}, p_{in} \) to make the connection to the Ising model. Let us write the diffusion measures in Eq. (1) in terms of the spectral decomposition of \( \mathbf{L} \) as
+
+\[
+p_i^k(\tau) = \delta_i \sum_{s=1}^n e^{-\lambda_s \tau} \phi_s(k) \phi_s(l) = \sum_{s=1}^n e^{-\lambda_s \tau} \phi_s(k) \phi_s(i) .
+\]
+
+At this point let us remark that in the dense regime where \( p_{in}, p_{out} = O(1) \), the first two eigenmodes (\( \lambda_1, \phi_1 \)) and (\( \lambda_c, \phi_c \)) dominate and the second eigenmode contains the anti-symmetric eigenvector \( \phi_c(u) = 1/\sqrt{n} \) when \( C_u = 1 \) and \( -1/\sqrt{n} \) when \( C_u = 2 \) that is associated with the community structure (Fig. 2c). Thus, one can follow spectral clustering methods\(^{27}\) to find the sparsest cut between clusters using \( \phi_c \). In contrast, in the sparse regime, the dominant eigenmodes will be driven by random fluctuations in the node degrees across the graph\(^{48}\), thus spectral clustering algorithms based on \( \mathbf{L} \) are suboptimal (Fig. 2d).
+
+However, the coupled diffusion pair allows for cancelling out random fluctuations in their spectrum. To see this, consider for a between-edge \( ij \) the difference
+
+\[
+\sum_{ij \in E} p_i^k(\tau) - p_j^k(\tau) = \sum_{ij \in E} \sum_{s=1}^n e^{-\lambda_s \tau} \phi_s(k)[\phi_s(i) - \phi_s(j)] \\
+= \sum_{s=1}^n e^{-\lambda_s \tau} \phi_s(k) \Delta \phi_s ,
+\]
+
+where \( \Delta \phi_s \) is defined in Eq. (8). The first term involves the constant eigenvector \( \phi_1 \) corresponding to the stationary state. Therefore, \( \phi_1(i) = \phi_1(j) \) for all \( ij \) and thus its contributions cancels out when taking differences. Further, for eigenvectors \( \phi_s \) with \( s \neq 1, c \) we have asymptotically (\( n \to \infty \)) that
+
+\[
+\Delta \phi_s \to 0
+\]
+
+(Fig. 3). As a result, the only contribution we are left with is coming from the anti-symmetric eigenmode (\( \lambda_c, \phi_c \)). Thus we have that
+
+\[
+\sum_{ij \in E} (p_i^u(\tau) - p_j^u(\tau)) = \begin{cases}
+\epsilon_\phi, & \text{if } C_i = C_j , \\
+e^{-\lambda_c \tau} \phi_c \Delta \phi_c + \epsilon_\phi , & \text{if } C_i \neq C_j ,
+\end{cases}
+\]
+
+where \( \epsilon_\phi \) represents the contribution from the random eigenvectors which is negligible in the limit \( n \to \infty \).
+
+To compute \( W_1 \) in the exponent of Eq. (18), we use Kantorovich-Rubinstein duality (Eq. (14)). Using Eq. (21) in Eq. (14) and ignoring asymptotically small terms, we consider the quantity
+
+\[
+\sum_{ij \in E} \sum_u f(u) \left[ p_i^u(\tau) - p_j^u(\tau) \right]
+\]
+= e^{-\lambda_c \tau} \sum_u f(u) \phi_c(u)
+= \frac{e^{-\lambda_c \tau}}{n} \left[ \sum_{u: C_u = 1} f(u) - \sum_{u: C_u = 2} f(u) \right]
+= \frac{e^{-\lambda_c \tau}}{n} \left[ \sum_{u: C_u = 1} (f(u) - f(i)) - \sum_{u: C_u = 2} (f(u) - f(j)) \right.
++ \left. \sum_{u: C_u = 1} f(i) - \sum_{u: C_u = 2} f(j) \right].
+\tag{22}
+
+In the sparse regime, we may make a tree-like approximation in the neighbourhood of \( i \). This means that the number of neighbours of \( i \) at distance \( q \) inside the cluster is \( p_{in}^q (n/2)^q \), ignoring terms of order \( O(1/n) \) and beyond. Considering only nodes at unit distance (\( q = 1 \)), we approximate Eq. (22) as
+
+\[
+\frac{e^{-\lambda_c \tau}}{n} \Bigg[ \sum_{u: C_u = 1 \atop u \sim i} (f(u) - f(i)) - \sum_{u: C_u = 2 \atop u \sim i} (f(u) - f(i))
++ \sum_{u: C_u = 1 \atop u \sim j} (f(u) - f(j)) - \sum_{u: C_u = 2 \atop u \sim j} (f(u) - f(j))
++ \sum_{u: C_u = 1} f(i) - \sum_{u: C_u = 2} f(i) + \sum_{u: C_u = 1} f(j) - \sum_{u: C_u = 2} f(j) \Bigg]
+= \frac{e^{-\lambda_c \tau}}{n} \Bigg[ \sum_{u: C_u = 1 \atop u \sim i} (f(u) - f(i)) - \sum_{u: C_u = 2 \atop u \sim i} (f(u) - f(i))
++ \sum_{u: C_u = 1 \atop u \sim j} (f(u) - f(j)) - \sum_{u: C_u = 2 \atop u \sim j} (f(u) - f(j))
++ \frac{n}{2} p_{in} (f(i) - f(j)) - \frac{n}{2} p_{out} (f(i) - f(j)) \Bigg].
+\]
+
+Then, taking the supremum over all 1-Lipschitz functions \( f \), we obtain
+
+\[
+\sum_{ij \in E} \mathcal{W}_1(\mathbf{p}_i(\tau), \mathbf{p}_j(\tau))(1 - \delta(C_i, C_j))
+\approx e^{-\lambda_c \tau} (p_{in} + p_{out}) \left( 1 + \frac{|p_{in} - p_{out}|}{2(p_{in} + p_{out})} \right)
+\tag{23}
+
+Substituting this into Eq. (18) and noting that \( p_{in} + p_{out} \) is constant we obtain at a fixed \( \tau \)
+
+\[
+\mathbb{P}(C|\kappa) \propto \exp \left[ \left( \frac{|p_{in} - p_{out}|}{2(p_{in} + p_{out})} \right) \sum_{ij \in E} \delta(C_i, C_j) \right],
+\]
+
+which up to a constant of proportionality equals the expression in Eq. (9).
+
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+Supplementary Figures
+
+Supplementary Figure 1: Ricci and dynamical Ollivier Ricci curvature on canonical surfaces and graph structures. **a** Ricci curvature on a manifold. The geodesic distance of close points \( x \) and \( y \) on average changes when translated by parallel vectors \( \mathbf{v} \) and \( \mathbf{v}' \) on the unit circle in the tangent planes at \( x \) and \( y \). On planes the points remain equidistant, on spheres the points contract and on hyperbolic surface they expand. **b** Canonical graphs with edges coloured by the dynamical OR curvature (Eq. (2)) for \( \tau = 1 \) show that positively and negatively curved graphs have qualitatively different topologies. Away from the boundaries, tree-like topologies are negatively curved, grid-like topologies are flat (zero curvature), whereas clique-like topologies attain positive curvature. Nodes are coloured by the average edge curvature across the neighbours. **c** Analogously, the differential geometric notion of Ricci curvature is negative on hyperbolic surfaces, zero on planes and positive on spherical surfaces.
+Supplementary Notes
+
+Supplementary Note 1
+
+In this section, we compute the spectrum of the expected normalised Laplacian matrix of the symmetric SBM \( \mathcal{G}(n, k_{in}/n, k_{out}/n) \). Here \( k_{in} \) and \( k_{out} \) are constants representing the expected number of edges within and across clusters, respectively. The expected adjacency matrix of the symmetric stochastic block model is:
+
+\[
+\langle \mathbf{A} \rangle_{\mathcal{G}} = \begin{pmatrix}
+\frac{k_{in}}{n} \mathbf{1}_{n/2 \times n/2} & \frac{k_{out}}{n} \mathbf{1}_{n/2 \times n/2} \\
+\frac{k_{out}}{n} \mathbf{1}_{n/2 \times n/2} & \frac{k_{in}}{n} \mathbf{1}_{n/2 \times n/2}
+\end{pmatrix}.
+\] (1)
+
+Then, the expected normalised Laplacian matrix is given by
+
+\[
+\langle \mathbf{L} \rangle_{\mathcal{G}} = \mathbf{I} - \begin{pmatrix}
+\frac{2k_{in}}{n(k_{in}+k_{out})} \mathbf{1}_{n/2 \times n/2} & \frac{2k_{out}}{n(k_{in}+k_{out})} \mathbf{1}_{n/2 \times n/2} \\
+\frac{2k_{out}}{n(k_{in}+k_{out})} \mathbf{1}_{n/2 \times n/2} & \frac{2k_{in}}{n(k_{in}+k_{out})} \mathbf{1}_{n/2 \times n/2}
+\end{pmatrix}
+\] (2)
+
+The first eigenvector is \( \phi_1 = \mathbf{1}_n/\sqrt{n} \in \mathbb{R}^n \), with the corresponding eigenvalue being \( \lambda_1 = 0 \). The second eigenvector has two values, one on each cluster of the SBM. Taking \( \phi_c(u) = 1/\sqrt{n} \) for \( 1 \leq u \leq n/2 \) and \( -1/\sqrt{n} \) for \( n/2 < u \leq n \) one has asymptotically
+
+\[
+\langle \mathbf{L} \rangle_{\mathcal{G}} \phi_c = \left[ 1 - \frac{k_{in}}{k_{in} + k_{out}} \frac{2}{n} - \frac{k_{in}}{k_{in} + k_{out}} \frac{2}{n} \left( \frac{n}{2} - 1 \right) + \frac{k_{out}}{k_{in} + k_{out}} \frac{2}{n} \frac{n}{2} \right] \phi_c \xrightarrow{n \to \infty} \frac{2k_{out}}{k_{in} + k_{out}} \phi_c.
+\] (3)
+Figures
+
+Figure 1
+
+Please see the manuscript file to view figure caption.
+Figure 2
+
+Please see the manuscript file to view figure caption.
+
+Figure 3
+
+Please see the manuscript file to view figure caption.
+Figure 4
+
+Please see the manuscript file to view figure caption.