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01cfd239b63d0b5b3bd8fba2f46c4523116e4ea7471e771fa2f189c14b26428e/metadata.json

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+{
+    "title": "Scalable production of ultrafine polyaniline fibres for tactile organic electrochemical transistors",
+    "pre_title": "Scalable production of ultrafine polyaniline fibres for tactile organic electrochemical transistors",
+    "journal": "Nature Communications",
+    "published": "19 April 2022",
+    "supplementary_0": [
+        {
+            "label": "Supplementary Information",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-022-29773-9/MediaObjects/41467_2022_29773_MOESM1_ESM.pdf"
+        },
+        {
+            "label": "Peer Review File",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-022-29773-9/MediaObjects/41467_2022_29773_MOESM2_ESM.pdf"
+        }
+    ],
+    "supplementary_1": NaN,
+    "supplementary_2": NaN,
+    "source_data": [],
+    "code": [],
+    "subject": [
+        "Chemical engineering",
+        "Electronic devices"
+    ],
+    "license": "http://creativecommons.org/licenses/by/4.0/",
+    "preprint_pdf": "https://www.researchsquare.com/article/rs-1126903/v1.pdf?c=1650379781000",
+    "research_square_link": "https://www.researchsquare.com//article/rs-1126903/v1",
+    "nature_pdf": "https://www.nature.com/articles/s41467-022-29773-9.pdf",
+    "preprint_posted": "08 Dec, 2021",
+    "research_square_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "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 \u00b5m, 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.",
+            "section_image": []
+        },
+        {
+            "section_name": "Additional Declarations",
+            "section_text": "There is NO Competing Interest.",
+            "section_image": []
+        },
+        {
+            "section_name": "Supplementary Files",
+            "section_text": "Supplementaryinformation1130.pdf",
+            "section_image": []
+        }
+    ],
+    "nature_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "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 surface, microstructural orientation, and mechanical strength. 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. The slow diffusion between good solvents distinctly decreases the viscosity of protofibers, which undergo an impressive drawing ratio. The continuously collected polyaniline fibres have a previously unattained diameter below 5\u2009\u00b5m, 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 operated as a tactile sensor detecting pressure and friction forces at different levels.",
+            "section_image": []
+        },
+        {
+            "section_name": "Introduction",
+            "section_text": "The extended conjugated and easily doped \u03c0-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 conductors1,2,3. 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 fibers (CPFs) have introduced an era of \u201celectronic textiles\u201d4. For instance, highly conductive and electrochemically active poly(3-methylthiophene) fibers have been achieved by in situ electrochemical oxidation of monomers5. Fast ion transport between CPFs and ionic liquids has given birth to long-term operation actuators, electrochromic windows, and numeric displays6. In recent studies, the wet-spun poly (3,4-ethylene dioxythiophene) (PEDOT) fibers have been widely used in various frontier fields, such as flexible energy storage electrodes, implantable bioelectronics, and organic transistors7,8.\n\nUnfortunately, 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 in an insufficient elasticity of conducting polymer solutions, which fails to be solely electrospun into fine fibers9. 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 CPFs10,11. 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\u2009\u00b5m12,13,14. The large diameters largely discount the mechanical properties and electrochemical activities of CPFs4,15. 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) fibers (UFPFs) at a 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 UFPFs own a small diameter below 5\u2009\u00b5m, an unprecedented mechanical strength of 1080\u2009\u00b1\u200971\u2009MPa, a high area capacitance beyond 1008\u2009mF\u2009cm\u22122, and an enormous charge storage capacity of 5.25 \u00d7 104\u2009mC\u2009cm\u22122. Based on the structural and electrochemical merits of UFPFs, we demonstrated an ultrathin all-solid organic electrochemical transistor (OECT) with less than 1\u2009V driving voltage, which substantially amplified drain-source electrical signals with 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.",
+            "section_image": []
+        },
+        {
+            "section_name": "Results",
+            "section_text": "In the modified one-step wet spinning process, we used good solvents as the coagulation bath to realize the mass production of UFPFs (Fig.\u00a01a, b and Supplementary Fig.\u00a01). After doping PAni powder (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 fiber length17. 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\u2009cP. Subsequently, we observed a sharp decrease of diameter from ~0.1\u2009mm to ~4.7\u2009\u00b5m when stretching the gel fibers in the bath (Fig.\u00a01c\u2013f), which, to our knowledge, is a record small value in the achieved wet-spun CPFs4. The ultrafine fiber shows a smooth surface (Fig.\u00a01f and Supplementary Fig.\u00a02), highly crystallized microstructures (Supplementary Fig.\u00a03), and uniform electrical properties (Supplementary Fig.\u00a04). Moreover, such an impressive drawing ratio enables a very high production efficiency of UFPFs beyond 40 m/min. For example, we prepared a 5.4-kilometers-long UFPF in 2 h (Fig.\u00a01g).\n\na 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 fibers. 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 fibers. The close observation of 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-kilometers-long UFPF collected in two hours. Scale bars: c 20\u2009\u00b5m, d 2\u2009\u00b5m, e 10\u2009\u00b5m, g 150\u2009mm.\n\nThe sharp necking behaviors of gel protofibres are highly related to the use of good solvents as coagulation bath. In a good solvent, interactions between PAni chains and solvent molecules are energetically favorable, and will cause PAni chains to expand and disperse well. In a poor solvent, the chain interactions are preferred and suppress the dispersion of PAni molecules. We recorded the evolution of surface morphologies of PAni fibers collected from different solvating species. As shown in Fig.\u00a02a, the obtained fibers in poor solvating species, i.e., water, ethanol, ethyl acetate (EA), and acetone, generally present coarse surfaces and large diameters around 20\u2009\u00b5m. 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 fibers to behave ultrafine morphologies, which assists PAni fibers to behave a higher degree of orientation and crystallization (see the X-ray diffraction analysis in Supplementary Fig.\u00a03). Further, the higher degree of crystallization keeps the doping bonding in PAni chains from the attack of ambientes at the molecular level, and is conducive to a better structure and performance stability. We used Raman spectra to evaluate their structural evolution after placing fibers in air for four weeks. As shown in Fig.\u00a02b, we did not find obvious de-doping signals in Raman spectra of the PAni fibers from good solvents, whereas various de-doping peaks (1223 and 1462\u2009cm\u22121) appeared in the cases of poor solvents, which inflects the dissociation of proton-polymer interactions18,19,20.\n\na SEM images of the PAni fibers produced in different solvating species. Specifically, the upper four panels show the fibers prepared from poor solvents, and the lower two panels show the fibers fabricated from good solvents. b Raman spectra of PAni fibers 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 fibers at different interfacial pressure. Comparing to the blue regions, the elements in blue regions are subject to larger stress. f Typical tensile stress-strain curves of UFPFs. g Ashby plot comparing the mechanical strength of UFPFs to previously reported CPFs. Scale bars in a: Water, Ethanol, EA, Acetone 20\u2009\u00b5m (left) 10\u2009\u00b5m (right); NMP 20\u2009\u00b5m (left) 5\u2009\u00b5m (right), DMF 20\u2009\u00b5m (left) 2\u2009\u00b5m (right).\n\nWe 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 fibers21,22. 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.\u00a01a. In previous reports using poor solvents as coagulation bath, although CPFs with a smooth surface could be collected by enhanced shear flow and strong stretching12,14, 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 interactions23,24.\n\nWe 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}\\) (cm2 s\u22121), is determined by Eq. (1):\n\nwhere \\({\\mu }_{B}\\) (cP) is the solvent viscosity, T (K) is the temperature, and \\({V}_{b}\\) (cm3\u2009g\u22121\u2009mol\u22121) is the molar volume of solvent at its normal boiling temperature25. As displayed in Fig.\u00a02c, the diffusivities from m-cresol to DMF (7.5 \u00d7 10\u22126\u2009cm2\u2009s\u22121) and NMP (7.71 \u00d7 10\u22126\u2009cm2\u2009s\u22121) are generally lower than that of poor solvents. Diffusion in bath further dominates the viscosity of protofibres. To monitor the viscosity of gel fibers in practical conditions, we conducted the viscometer tests at a low revolution (e.g., 10 Rev.). As summarized in Fig.\u00a02d, the formed PAni gels in good solvents show a viscosity below 3000\u2009cP, much lower than that of poor solvents (>4000\u2009cP). The established solvating specie-diffusivity-viscosity formula accords well with our proposed explanations.\n\nInterfacial pressure during the solvent exchange is another major factor relating to the necking behavior of PAni protofibres. In a two-fluid system, the interfacial pressure between two kinds of solvents is inclined to decrease with the improved solvent diffusion26. Based on the slow diffusion from m-cresol to good solvents (Fig.\u00a02c), the interfacial pressure between gel fibers and the coagulation bath is considerable, which further induces the necking of protofibres. To understand this, we conducted a mechanic simulation of the stretching behavior of gel fibers at different interfacial pressures (see the progressive results in Supplementary Fig. 5 and \u201cMethod\u201d section). According to the simulation results in Fig.\u00a02e, the higher interfacial pressure drives gel fibers to occur the sharper necking and thinning effects at a given tensile stress. This probably explains the formation of UFPFs in DMF bath.\n\nUFPFs show impressive mechanical performance. Different from that of conventional polymer fibers, the typical linear strain\u2013stress curves of UFPFs demonstrate a brittle fracture behavior with a small tensile strain of 3.67\u2009\u00b1\u20090.64% (Fig.\u00a02f). 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, fibers\u2019 strength generally improves with the decrease of diameter due to the depressed structural defects27. We compared the mechanical performance of UFPFs with previously reported CPFs.\n\nDerived from the strain-stress curves, we concluded that UFPFs have a modulus of 29.89\u2009\u00b1\u20095.6\u2009GPa, and strength of 1080\u2009\u00b1\u200971\u2009MPa, at least one order of magnitude higher than that of CPFs with larger diameters (Fig.\u00a02g), mainly including PEDOT fibers (<450\u2009MPa)7,28,29,30,31,32 and PAni fibers (<400\u2009MPa)12,33,34,35.\n\nUltrafine 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.\u00a03a). 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 UFPFs36 (Fig.\u00a03b). 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 electrodes37 (Fig.\u00a03c). According to the GCD results, we determined the electrochemical properties of UFPFs. Among them, the area capacitance, CA, is between 1008 and 1666 mF cm\u22122 at the current densities between 0.32 and 3.18\u2009mA\u2009cm\u22122, outperforming previously reported thick CPFs27 and other electrodes, such as carbon nanomaterials34,38, metal oxides39 and conducting polymers40,41,42,43, and approaching to that of PAni nanowires44 (Fig.\u00a03d). The volumetric capacitance, power density, and energy density reached 83.8\u2009F\u2009cm\u22123, 0.96\u2009W\u2009cm\u22123, and 4.19\u2009mWh\u2009cm\u22123, respectively (Supplementary Fig.\u00a06). In lifetime tests of UFPF-based capacitors, both the potential and capacitance continued without a significant decrease for 120 charge/discharge cycles at a low current density of 1.59\u2009mA\u2009cm\u22122, indicating the reliable electrochemical performance stability of UFPFs (Fig.\u00a03e).\n\na 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\u2009mV\u2009s\u22121. c Galvanostatic charge/discharge curves at various current densities increasing from 0.32 to 0.63, 1.59, and 3.18\u2009mA\u2009cm\u22122. d The area capacitance of UFPFs compared to previously reported electrodes. e Cycle galvanostatic charge/discharge curves during 120 cycles between 0 and 0.6\u2009V at 1.59\u2009mA\u2009cm\u22122. f The relationship between current and voltage at a slow rate of 10\u2009mV\u2009s\u22121. g The charge storage capacity of UFPFs comparing to other charge storage materials.\n\nWe 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 \u22120.9\u2009V and 1.0\u2009V (water window, see Supplementary Fig.\u00a07) was calculated by integrating the measured current with respect to the time of period at a low scan rate of 10\u2009mV\u2009s\u22121 (Fig.\u00a03f)6. We determined that the charge storage capacity of UFPF was 5.25 \u00d7 104\u2009mC\u2009cm\u22122, a value at least two orders of magnitude higher than that of noble metals45, carbon bulk46,47,48 and previously reported conducting polymers49 (Fig.\u00a03g). This value decreases slightly to 2.015 \u00d7 104\u2009mC\u2009cm\u22122 at a tenfold scan rate of 100\u2009mV\u2009s\u22121 (Supplementary Fig.\u00a08).\n\nBenefitting 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 polymers50,51. This process is controlled by the gate bias, and, to date, has generally conducted in aqueous electrolytes. To preclude the interference of the 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.\u00a04a, b, our OECT is mainly constructed by three polymer layers. The upper layer is the cured polyurethane (PU) working as the dielectric coating and protecting the device from the invasion of external action52. A fibrous silver gate electrode with a diameter of 7\u2009\u00b5m is fixed in PU. Since UFPFs have demonstrated reliable electrochemical activities in PVA-H3PO4 gel, we used PVA-H3PO4 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. Along the gate bias direction, the gate bias is mainly distributed in the gate/electrolyte interface and electrolyte/channel interface due to the almost insulating gel electrolyte (with a resistance beyond 10\u2009M\u03a9). 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.\u00a04c), and a small thickness below 300\u2009\u00b5m.\n\na 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 fiber 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\u2009\u00b5m.\n\nDespite the long channel length (~0.48\u2009cm), much larger than that of a conventional micrometer-scale device, the all-solid OECT showed favorable amplification performance with a high on-off current ratio (>103, Fig.\u00a04e) at low voltages (<1\u2009V, Fig.\u00a04d). The relatively fair transconductance (gm, < 60 \u00b5S) is probably ascribed to the small cross-sectional area, which dramatically magnifies the resistance of fibrillar channel. The comparison of electrical properties with previously reported fiber-based OECTs is listed in Supplementary Tab.\u00a01. Note that the all-solid OECT is an energy-saving device with extremely low power consumption. For example, at a given drain-source voltage of 0.6\u2009V, the consumed power is below 18\u2009\u00b5W (Fig.\u00a04f).\n\nWe 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.\u00a05a, 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 capacitance53. At a VG of \u22120.1\u2009V and a VD of 0.35\u2009V, we observed a stable increase of drain-source current, IDS, with the increasing pressure, up to a 92% amplification from 0 to 40 kPa (Fig.\u00a05b). The sensitivity is at the level of 0.01\u20130.1 kPa\u22121 in this process (dark cyan dots in Fig.\u00a05b). As shown in Fig.\u00a05c, the average rising time and falling time under instantaneous pressure of 17.8 kPa is ~536\u2009ms and ~698\u2009ms, respectively. Such integrated parameters facilitated the all-solid OECT to respond to different pressure levels from 0.92 to 22.2 kPa (Fig.\u00a05d). In addition to the response to pressure in the vertical direction, the all-solid OECT also reacted to friction in the horizontal direction (Fig.\u00a05e and Supplementary Fig.\u00a09). The forward and backward friction of a load on the surface incurred horizontal movement of the PU layer, which drove the displacement of the Ag gate. Further, the real-time distance between the silver gate and the UFPF channel was changed repeatedly, thus producing a bimodal response curve (Fig.\u00a05g). Note that, to enable the enlargement of IDS with the increasing gate-channel distance under the repeated friction, we applied a positive VG of 0.1\u2009V at a VD of 0.55\u2009V. The all-solid OECT responded stably to friction at different magnitudes (Fig.\u00a05f, from 1.84 to 5.55 kPa) and different speeds (Fig.\u00a05h, from 4 to 20\u2009mm\u2009s\u22121) during our cyclic tests. For example, IDS increased ~86% at 5.55 kPa.\n\na Schematic of the mechanism explaining the response to the action of external pressure. b Relative drain-source change (\u0394IDS/IDS0) 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\u2009mm\u2009s\u22121.",
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+            ]
+        },
+        {
+            "section_name": "Discussion",
+            "section_text": "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 a large scale. We proposed a good solvents strategy in modified wet spinning technology. With a principle of diffusion-controlled slow gelation of protofibres, the system successfully downsized the diameter of PAni fibers to below 5\u2009\u00b5m, 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.\n\nIt 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 fibers 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.",
+            "section_image": []
+        },
+        {
+            "section_name": "Methods",
+            "section_text": "All the SEM images were collected on a tungsten thermionic emission SEM system (the Tescan VEGA3). XRD spectra were obtained from the XRD system (Rigaku SmartLab) equipped with a 9\u2009kW rotating anode X-ray source (\u03bb\u2009~\u20091.54\u2009\u00c5) coupling with a 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 a confocal microscope spectrometer and a 785\u2009nm 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 a probe station (Micromanipulator) with Keithley 4200A-SCS parameter analyzer. The test of viscosity was conducted by the viscometer (NDJ-5S/9\u2009S/8\u2009S). The probe of viscometer inserted into PAni gels after soaking in solvents, and the viscosity was measured at an increasing shear speed from 10 to 60 Rev.\n\nPAni powder (emeraldine base, purchased from Aladdin, 25233-30-1) was mixed with CSA at a molar ratio of 2:1. After being milled for 15\u2009min, the uniform doped PAni was dispersed in m-cresol (after degassing) at a concentration of 0.05\u2009g\u2009mL\u22121. The dispersions were used as spinning dopes after blending in air for 4\u201324\u2009h, and extruded through a PEEK microtube with an inner diameter of 100\u2009\u00b5m at a rate of 1\u2009mL\u2009min\u22121. A coagulation bath was chosen according to the experimental requirements. PAni fibers were directly drawn out from the bath and collected on a graphite roller continuously.\n\nThe experimental result is verified by a 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\u2019s modulus, and Poisson\u2019s ratio are selected as 300\u2009kg\u2009m\u22123, 1000\u2009Pa and 0.01, respectively. For the boundary conditions, one end of the gel model set as fixed support, and another end applies extended 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 fibers. 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 is adopted finally.\n\nMicro 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\u2009hours at 85\u2009\u00b0C. Then phosphoric acid was added at a mass ratio of 1:10 with deionized water. The mixture cooled at room temperature and was ready for use. Two UFPFs were placed in parallel on the glass slide. The transparent PVA-H3PO4 gel was dropped between UFPFs. Two copper wires connected to the UPPFs with silver paste worked as the conductor lines. After condensing for 10\u2009\u2009min at 40\u2009\u00b0C, the whole device was subject to electrochemical tests.\n\nThe OECT was built from three layers: two PU layers and one ion gel layer. PU dispersion in DMF was cast on a PVDF substrate. After being treated in the oven at 60\u2009\u00b0C, a thin and transparent layer of pure PU was obtained. One drop of PVA-H3PO4 gel electrolyte was added to the surface of solidified PU. A UFPF was immersed in gel. After being dried at 45\u2009\u00b0C for 15\u2009\u2009min, a UFPF channel locked in PVA-H3PO4 gel was obtained. Afterward, another drop of PU was added and a silver wire operation as the gate electrode was put in PU at the liquid state. After being dried at 60\u2009\u00b0C, an all-solid OECT was prepared. Note that all three electrodes were connected to cooper electrodes for the following measurements.",
+            "section_image": []
+        },
+        {
+            "section_name": "Data availability",
+            "section_text": "The authors declare that the data supporting the findings of this study are available from the corresponding author upon reasonable request.",
+            "section_image": []
+        },
+        {
+            "section_name": "References",
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+            "section_image": []
+        },
+        {
+            "section_name": "Acknowledgements",
+            "section_text": "The authors are grateful for the financial support of the Research Grants Council of Hong Kong (No. 15201419), Hong Kong Polytechnic University Postdoctoral Fellowship and Endowed Professorship Fund (No. 847A). P.G. and Q.G. acknowledge funding from Shenzhen-Hong Kong Innovation Circle (No. SZSTI20EG14).",
+            "section_image": []
+        },
+        {
+            "section_name": "Author information",
+            "section_text": "These authors contributed equally: Bo Fang, Jianmin Yan.\n\nResearch Institute for Intelligent Wearable Systems, The Hong Kong Polytechnic University, 999077, Hong Kong, China\n\nBo Fang,\u00a0Jianmin Yan,\u00a0Jinli Piao,\u00a0Kit Ming Ma,\u00a0Yang Chai\u00a0&\u00a0Xiaoming Tao\n\nInstitute of Textiles and Clothing, The Hong Kong Polytechnic University, 999077, Hong Kong, China\n\nBo Fang,\u00a0Jinli Piao,\u00a0Kit Ming Ma\u00a0&\u00a0Xiaoming Tao\n\nDepartment of Applied Physics, The Hong Kong Polytechnic University, 999077, Hong Kong, China\n\nJianmin Yan\u00a0&\u00a0Yang Chai\n\nDepartment of Polymer Science and Engineering, Zhejiang University, 310027, Hangzhou, China\n\nDan Chang\n\nDepartment of Chemical and Biological Engineering, The Hong Kong University of Science and Technology, 999077, Hong Kong, China\n\nQiao Gu\u00a0&\u00a0Ping Gao\n\nAdvanced Materials Thrust, The Hong Kong University of Science and Technology (Guangzhou), 510000, Guangzhou, China\n\nQiao Gu\u00a0&\u00a0Ping Gao\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nX.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. and X.T. wrote the manuscript.\n\nCorrespondence to\n                Bo Fang, Yang Chai or Xiaoming Tao.",
+            "section_image": []
+        },
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+            "section_text": "The authors declare no competing interests.",
+            "section_image": []
+        },
+        {
+            "section_name": "Peer review",
+            "section_text": "Nature Communications thanks Jonathan Rivnay and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.\u00a0Peer reviewer reports are available.",
+            "section_image": []
+        },
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+            "section_name": "About this article",
+            "section_text": "Fang, B., Yan, J., Chang, D. et al. Scalable production of ultrafine polyaniline fibres for tactile organic electrochemical transistors.\n                    Nat Commun 13, 2101 (2022). https://doi.org/10.1038/s41467-022-29773-9\n\nDownload citation\n\nReceived: 30 November 2021\n\nAccepted: 30 March 2022\n\nPublished: 19 April 2022\n\nVersion of record: 19 April 2022\n\nDOI: https://doi.org/10.1038/s41467-022-29773-9\n\nAnyone you share the following link with will be able to read this content:\n\nSorry, a shareable link is not currently available for this article.\n\n\n\n\n                            Provided by the Springer Nature SharedIt content-sharing initiative\n                        ",
+            "section_image": [
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+            ]
+        },
+        {
+            "section_name": "This article is cited by",
+            "section_text": "npj Flexible Electronics (2025)\n\nNature Communications (2025)\n\nAdvanced Fiber Materials (2025)\n\nNature (2024)\n\nNature (2024)",
+            "section_image": []
+        }
+    ]
+}

0acd819abe48c47a84cbc21e7054100bd0d1363bbc114db43e3926604a5e536e/metadata.json

@@ -0,0 +1,146 @@
+{
+    "title": "Electrically driven spin resonance of 4f electrons in a single atom on a surface",
+    "pre_title": "Electrically Driven Spin Resonance of 4f Electrons in a Single Atom on a Surface",
+    "journal": "Nature Communications",
+    "published": "20 June 2024",
+    "supplementary_0": [
+        {
+            "label": "Supplementary Information",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-024-49447-y/MediaObjects/41467_2024_49447_MOESM1_ESM.pdf"
+        },
+        {
+            "label": "Reporting Summary",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-024-49447-y/MediaObjects/41467_2024_49447_MOESM2_ESM.pdf"
+        },
+        {
+            "label": "Peer Review File",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-024-49447-y/MediaObjects/41467_2024_49447_MOESM3_ESM.pdf"
+        }
+    ],
+    "supplementary_1": NaN,
+    "supplementary_2": NaN,
+    "source_data": [
+        "https://doi.org/10.6084/m9.figshare.24190884"
+    ],
+    "code": [
+        "/articles/s41467-024-49447-y#Fig1",
+        "/articles/s41467-024-49447-y#Fig2",
+        "/articles/s41467-024-49447-y#Fig3",
+        "/articles/s41467-024-49447-y#Fig4",
+        "https://doi.org/10.24433/CO.9869055.v1"
+    ],
+    "subject": [
+        "Nanoscale materials"
+    ],
+    "license": "http://creativecommons.org/licenses/by/4.0/",
+    "preprint_pdf": "https://www.researchsquare.com/article/rs-3385164/v1.pdf?c=1718967991000",
+    "research_square_link": "https://www.researchsquare.com//article/rs-3385164/v1",
+    "nature_pdf": "https://www.nature.com/articles/s41467-024-49447-y.pdf",
+    "preprint_posted": "06 Nov, 2023",
+    "research_square_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "A pivotal challenge in quantum technologies lies in reconciling long coherence times with efficient manipulation of the quantum states of a system. Lanthanide atoms, with their well-localized 4f electrons, emerge as a promising solution to this dilemma if provided with a rational design for manipulation and detection. Here we construct tailored spin structures to perform electron spin resonance on a single lanthanide atom using a scanning tunneling microscope. A magnetically coupled structure made of an erbium and a titanium atom enables us to both drive the erbium\u2019s 4felectron spins and indirectly probe them through the titanium\u2019s 3d electrons. In this coupled configuration, the erbium spin states exhibit a five-fold increase in the spin relaxation time and a two-fold increase in the driving efficiency compared to the 3d electron counterparts. Our work provides a new approach to accessing highly protected spin states, enabling their coherent control in an all-electric fashion.Physical sciences/Nanoscience and technology/Nanoscale materialsPhysical sciences/Physics/Condensed-matter physics",
+            "section_image": []
+        },
+        {
+            "section_name": "Additional Declarations",
+            "section_text": "There is NO Competing Interest.",
+            "section_image": []
+        },
+        {
+            "section_name": "Supplementary Files",
+            "section_text": "ErMgOESRSIsubmission.docxSupplementary Information for Electrically Driven Spin Resonance of 4f Electrons in a Single Atom on a Surface",
+            "section_image": []
+        }
+    ],
+    "nature_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "A pivotal challenge in quantum technologies lies in reconciling long coherence times with efficient manipulation of the quantum states of a system. Lanthanide atoms, with their well-localized 4f electrons, emerge as a promising solution to this dilemma if provided with a rational design for manipulation and detection. Here we construct tailored spin structures to perform electron spin resonance on a single lanthanide atom using a scanning tunneling microscope. A magnetically coupled structure made of an erbium and a titanium atom enables us to both drive the erbium\u2019s 4f electron spins and indirectly probe them through the titanium\u2019s 3d electrons. The erbium spin states exhibit an extended spin relaxation time and a higher driving efficiency compared to 3d atoms with spin \u00bd in similarly coupled structures. Our work provides a new approach to accessing highly protected spin states, enabling their coherent control in an all-electric fashion.",
+            "section_image": []
+        },
+        {
+            "section_name": "Introduction",
+            "section_text": "The last two decades have witnessed a rising focus on the control and application of quantum coherent effects, marking the advent of the so-called \u201csecond quantum revolution\u201d. Utilizing quantum coherent functionalities of materials for novel technologies, such as imaging, information processing, and communications, requires robustness of their quantum coherence, addressability, and scalability1. However, these requirements often clash since decoupling the quantum states from the environment prolongs the quantum coherent properties but hinders the possibility of efficient state manipulation.\n\nLanthanide atoms represent a promising platform to tackle this dilemma. Their well-localized 4f electrons show long spin relaxation T12,3 and coherence times T24,5. In addition, their strong hyperfine interaction facilitates the read-out of nuclear spins6,7. In bulk insulators, exceedingly long T1 and T2 have been demonstrated using optical control and detection8,9,10,11 down to the single atom level12,13. While hybrid optical-electrical approaches have been developed to access individual lanthanide atom\u2019s spins embedded in a silicon transistor14, it is still challenging to achieve efficient control of the quantum states using electrical transport methods. This necessitates the rational design of a quantum platform capable of tackling both control and detection schemes, along with their interactions with local environments. In this context, single crystal surfaces constitute an advantageous framework both for building atomically engineered nanostructures and addressing individual spin centers, in particular using scanning\u00a0probe techniques15,16,17,18. However, resonant driving and detection of surface-adsorbed lanthanide atoms have so far remained elusive.\n\nIn this work, we demonstrate the control and detection of 4f electron spins by building atomic-scale structures on a surface using a scanning tunneling microscope (STM) with electron spin resonance (ESR) capabilities19,20,21,22. The atomic structures are composed of an erbium (Er) atom as the target spin system and a magnetically coupled titanium (Ti) atom as the sensor spin. This architecture allows us to drive ESR transitions on the Er 4f electrons with a projected angular momentum of\u00a0\u0127/223 and to probe them indirectly through Ti. We observed an Er T1 of close to 1\u2009\u03bcs, which is about 5 times longer than that previously measured for 3d electrons of a remotely-driven spin-\u00bd system on the same surface18. This novel platform allows for the ESR driving and read-out of the well-screened 4f electron spin states, paving the way to integrate lanthanide atoms in quantum architectures.",
+            "section_image": []
+        },
+        {
+            "section_name": "Results",
+            "section_text": "Erbium atoms on a few monolayer-thick MgO(100) on Ag(100) present a 4f11 configuration with no unpaired electrons in the 5d and 6s shells23. The atomic-like spin and orbital momenta are coupled through the large spin-orbit interaction into a total angular momentum \\({{{{{{\\bf{J}}}}}}}_{{{{{{\\rm{Er}}}}}}}\\) with magnitude of 15\u0127/223. When adsorbed on the oxygen site of MgO (Fig.\u00a01a), the crystal field leads to a strong hard-axis magneto-crystalline anisotropy that stabilizes a doubly-degenerate ground state with an out-of-plane component of the angular momentum \\({J}_{ \\perp }=\\,\\)\u00b1\u0127/223, which splits into two singlets when an external magnetic field (B) is applied. This magnetic level scheme differs from the ones of lanthanide single atom magnets studied so far on MgO/Ag(100). For instance, dysprosium24,25 and holmium2,26,27 present a ground state characterized by a large \\({J}_{ \\perp }\\). The level scheme presents two lowest-lying states well separated by a significant anisotropy barrier and greatly suppresses the reversal of angular momentum, thereby stabilizing the magnetic states. Additionally, it impedes the first-order ESR transition induced by the exchange of a single quantum of angular momentum22. As found in a previous work23, the component of \\({{{{{{\\bf{J}}}}}}}_{{{{{{\\rm{Er}}}}}}}\\) along the magnetic field direction (z), defined as \\({J}_{z}\\), increases from \u00b1\u0127/2 to \u00b14\u0127 by rotating B from the out-of-plane (\u03d1\u2009=\u20090\u00b0) to the in-plane (\u03d1\u2009=\u200990\u00b0) direction (Fig.\u00a01b), while retaining a large probability for spin dipole transitions. Given these properties, Er can be regarded as a highly tunable two-level system allowing for efficient ESR driving. To characterize the magnetic states and anisotropy of Er, we utilized the dipole field sensing technique28 with a Ti atom on the bridge binding site of MgO as a well-known spin sensor. On this binding site, Ti has a spin STi of magnitude \u0127/2 and a relatively weak g-factor anisotropy29 compared to the oxygen binding site30.\n\na Schematic of the experimental set-up for ESR-STM measurement of an Er-Ti dimer built on MgO/Ag(100). The Ti atom (purple) is positioned close to the Er atom (orange) and located under a spin-polarized (SP) STM tip. The external magnetic field (B) defines the z-direction and is applied at an angle \u03d1 from the out-of-plane direction. b Projected total angular momentum of Er (Jz) onto the B field direction as a function of \u03d1. The strong magnetic anisotropy favors an in-plane alignment of JEr. c ESR spectra of the Ti atom placed 0.928\u2009nm apart from the Er atom at different \u03d1. At \u03d1\u2009=\u20098\u00b0, a single ESR peak is visible (pink) while, at \u03d1\u2009=\u200968\u00b0 (purple), the two ESR peaks are separated due to the magnetic interactions between the Er and Ti. For the latter, the relative peak intensity indicates a ferromagnetic interaction (set-point: Vdc\u2009=\u200950\u2009mV, Idc\u2009=\u200920 pA, Vrf\u2009=\u200912\u2009mV, B\u2009=\u20090.3\u2009T). d ESR peak separation,\u00a0\u2206f, as a function of \u03d1. The experimental points (black dots) were acquired at different set-points (Vdc\u2009=\u200950\u2009mV, Idc\u2009=\u200912\u201330\u2009pA, Vrf\u2009=\u200912\u201320\u2009mV, B\u2009=\u20090.3\u2009T). We give error bars with 95% confidence interval. The total interaction (solid purple line) calculated by the model Hamiltonian is composed of a dipolar contribution (dashed blue line) and an exchange contribution (dashed pink line). e\u2013g Schematic of the angular momenta of Er and Ti on MgO/Ag(100). The dipolar fields induced by Er are depicted as black curved arrows. When B is applied along the in-plane direction (\u03d1\u2009=\u200990\u00b0), the Jz is maximum and aligned with the spin of Ti giving the largest ferromagnetic dipolar interaction. When B is rotated, the spin of Ti follows the direction of B\u00a0while the total angular momentum of Er is aligned preferentially in-plane (f). In the out-of-plane direction (\u03d1\u2009=\u20090\u00b0), Jz is minimum and aligned with the spin of Ti (g) giving a small antiferromagnetic dipolar interaction.\n\nWe deposited Er and Ti at cryogenic temperatures (~10\u2009K) on 2 monolayers of MgO grown on Ag(100) (\u201cMethods\u201d section and Fig.\u00a0S1a). Their binding sites on the surface can be changed by atom manipulation (Supplementary Section\u00a02). When isolated, a nuclear spin-free Ti atom presents a single ESR signal under an external magnetic field (Fig.\u00a0S3a). The ESR peak of Ti splits when coupled to an Er atom (Supplementary Section\u00a04). Figure\u00a01c shows the ESR spectra obtained on Ti in an Er-Ti dimer with the atomic separation of 0.928\u2009nm (Fig.\u00a0S2b). At the magnetic field of 0.3\u2009T with \u03d1\u2009=\u20098\u00b0, we observed one ESR peak at the resonance frequency of Ti, which splits into two peaks separated by \u0394f\u2009=\u2009334\u2009\u00b1\u20093\u2009MHz when rotating B close to the in-plane direction (\u03d1\u2009=\u200968\u00b0). The two ESR peaks stem from the magnetic interaction with the Er spin fluctuating between two states28 during the measurement, with the relative peak intensity being proportional to the time-averaged population of the Er states. The pronounced difference in the relative intensity of the ESR peaks indicates a large imbalance in the Er state occupation even at B\u2009=\u20090.3\u2009T and 1.3\u2009K, which reflects the large \\({J}_{z}\\) of Er at \u03d1\u2009=\u200968\u00b0 (Fig.\u00a01b). The polarity of this asymmetry depends on the character of the magnetic interactions between the two atoms (Fig.\u00a0S4b, e). In Fig.\u00a01c, the peak at the lower frequency is less intense than the one at the higher frequency and, hence, the interaction can be regarded as ferromagnetic31, with this polarity defined as positive \u0394f in Fig.\u00a01d. We observe changes in polarity at different field directions (Fig.\u00a01d), indicating alternating couplings between ferromagnetic and antiferromagnetic states.\n\nThe angle dependence of \u0394f (Fig.\u00a01d) gives a direct measurement of the Er-Ti interaction energy28,31 and of the magnetic anisotropy23. To interpret it, we model the system through a spin-Hamiltonian including both the single atom Zeeman and anisotropy terms, as well as the interaction between the two spins:\n\nHere, \\({\\mu }_{{{{{{\\rm{B}}}}}}}\\) is the Bohr magneton, \\({J}_{ \\perp }\\) is the out-of-plane component of \\({{{{{{\\bf{J}}}}}}}_{{{{{{\\rm{Er}}}}}}}\\), \\({g}_{{{{{{\\rm{Er}}}}}}}=1.2\\) is the Er Land\u00e9 g-factor obtained from its atomic quantum numbers, and \\({\\overline{\\bar{{{{{\\rm{g}}}}}}}}_{{{{{{\\rm{Ti}}}}}}}\\) is the Ti anisotropic g-tensor29. We use a magnetic anisotropy parameter \\(D=2.4\\) meV to match the Er energy splitting found in a previous study23. The magnetic coupling consists of dipolar (\\({H}_{{{{{{\\rm{dip}}}}}}}\\)) and Heisenberg exchange interactions (\\({H}_{{{{{{\\rm{exc}}}}}}}\\)):\n\nwhere \\({\\mu }_{0}\\) is the vacuum permittivity, \\(r\\) the separation between the two atoms, \\(\\hat{{{{{{\\bf{r}}}}}}}\\) the unit vector connecting them28, and \\({{{{{{\\mathscr{J}}}}}}}_{{{{{{\\rm{exc}}}}}}}\\) the exchange interaction energy expressed in terms of \\({{{{{{\\bf{J}}}}}}}_{{{{{{\\rm{Er}}}}}}}\\)32. In our model, \\({{{{{{\\mathscr{J}}}}}}}_{{{{{{\\rm{exc}}}}}}}\\) is the only free parameter for the fit. As shown in Fig.\u00a01d, our model accurately reproduces the data for \\({{{{{{\\mathscr{J}}}}}}}_{{{{{{\\rm{exc}}}}}}}/{{{{{\\rm{h}}}}}}=\\) 48\u2009MHz, where the positive sign indicates an antiferromagnetic coupling. This value is more than 20 times smaller than that observed for a Ti-Ti dimer at the same distance (1.16\u2009GHz)33. We ascribe the smaller Er-Ti coupling to the localization of the 4f orbitals near the atom\u2019s core, which limits the overlap between Er and Ti orbitals when compared to the Ti-Ti case.\n\nThe strong angle dependence of \u0394f can be understood by considering the large magneto-crystalline anisotropy of \\({{{{{{\\bf{J}}}}}}}_{{{{{{\\rm{Er}}}}}}}\\). At \u03d1\u2009=\u200990\u00b0, \\({J}_{z}\\) is at its maximum (4\u0127), and the angular momenta of both atoms are parallel to \\(\\hat{{{{{{\\bf{r}}}}}}}\\) (Fig.\u00a01e), which maximizes the contribution of the dipolar coupling in a ferromagnetic configuration (positive \u0394f). When rotating B away from the in-plane direction, \\({{{{{{\\bf{S}}}}}}}_{{{{{{\\rm{Ti}}}}}}}\\) follows the direction of B, while the anisotropy of Er preserves a large component of \\({{{{{{\\bf{J}}}}}}}_{{{{{{\\rm{Er}}}}}}}\\) mainly aligned along the in-plane direction (Fig.\u00a01f). This misalignment between the two angular momenta reduces the dipolar interaction. Finally, as B approaches the surface normal (Fig.\u00a01g), \\({{{{{{\\bf{J}}}}}}}_{{{{{{\\rm{Er}}}}}}}\\) turns towards the out-of-plane direction with a much smaller value of \\({J}_{z}=\\) \u0127/2. With the two momenta being perpendicular to \\(\\hat{{{{{{\\bf{r}}}}}}}\\), the dipolar interaction is antiferromagnetic (negative \u0394f). Conversely, the mutual projection of \\({{{{{{\\bf{S}}}}}}}_{{{{{{\\rm{Ti}}}}}}}\\) and \\({{{{{{\\bf{J}}}}}}}_{{{{{{\\rm{Er}}}}}}}\\) is the only factor modulating the exchange interaction term, which remains negative \u0394f (antiferromagnetic coupling with positive \\({{{{{{\\mathscr{J}}}}}}}_{{{{{{\\rm{exc}}}}}}}\\)) at all angles (dashed pink curve in Fig.\u00a01d).\n\nThe direct drive of ESR in STM requires positioning the tip directly on top of the target atom19. However, despite using a tip showing ESR signal on an isolated Ti atom (Fig.\u00a0S3a), we observed no ESR when positioning the tip over an Er atom (Fig.\u00a0S3b), which we attribute to the small polarization of the 5d and 6s shells of Er and to the weak interaction between the 4f and tunneling electrons. The weak polarization of the outer shell is reflected in the absence of spin excitations in the dI/dV spectra (Fig.\u00a0S1d, e, h). These factors were found to limit the tunneling magnetoresistance at the STM junction in other lanthanide atoms24,34, possibly hindering both the ESR drive and detection23.\n\nTo overcome this limitation, we built a strongly interacting Er-Ti dimer by positioning Ti at 0.72\u2009nm from Er through atom manipulation (Fig.\u00a02a and Supplementary Section\u00a02). Similar to the isolated atom, we observed no ESR peaks at the Er position in the dimer (yellow curve in Fig.\u00a02b). However, when the tip was positioned on Ti, we observed up to 5 peaks (pink and purple curves in Fig.\u00a02b). The first two peaks below 10\u2009GHz with |\u0394f\u2009|\u2009= 2.70\u2009\u00b1\u20090.01\u2009GHz correspond to the ESR transitions of Ti that were similarly found in the dimer with larger atomic separations (Fig.\u00a01c). Hence, we label them as \\({f}_{1}^{{{{{{\\rm{Ti}}}}}}}\\) and \\({f}_{2}^{{{{{{\\rm{Ti}}}}}}}\\), respectively. In this dimer, we observed that \\({f}_{1}^{{{{{{\\rm{Ti}}}}}}}\\) shows a higher intensity than \\({f}_{2}^{{{{{{\\rm{Ti}}}}}}}\\), indicating an antiferromagnetic exchange interaction31 (Fig.\u00a0S4c, f) dominating over the dipolar coupling at this atomic separation. At higher frequencies, we further observed two peaks that are significantly blue-shifted when rotating B from \u03d1\u2009=\u200952\u00b0 (pink curve in Fig.\u00a02b) to 97\u00b0 (purple). The higher resonance frequencies and pronounced angle dependence indicate that those transitions involve the large and anisotropic angular momentum of Er, and, thus, we label them as \\({f}_{3}^{{{{{{\\rm{Er}}}}}}}\\) and \\({f}_{4}^{{{{{{\\rm{Er}}}}}}}\\). These transitions are not observed for all Er atoms, possibly due to the presence of isotopes with large nuclear spins for which the intensity of the ESR signal is spread over multiple peaks and is below the sensitivity of our measurements (Fig.\u00a0S5). In addition, their frequency separation exactly matches the one between \\({f}_{1}^{{{{{{\\rm{Ti}}}}}}}\\) and \\({f}_{2}^{{{{{{\\rm{Ti}}}}}}}\\), reflecting the same Er-Ti interaction. On the other hand, \\({f}_{3}^{{{{{{\\rm{Er}}}}}}}\\) and \\({f}_{4}^{{{{{{\\rm{Er}}}}}}}\\) are approximately equal in intensity, indicating that Ti fluctuates between two spin states with almost equal occupations. The comparable Ti states\u2019 occupation stems from the scattering with tunneling electrons and from the Zeeman splitting of Ti (~7\u2009GHz) being smaller than the thermal energy at the measurement temperature of 1.3\u2009K (~27\u2009GHz). With B at \u03d1\u2009=\u200952\u00b0, we observed one more peak at even higher frequencies. Its frequency exactly matches the sum of \\({f}_{1}^{{{{{{\\rm{Ti}}}}}}}\\) and \\({f}_{4}^{{{{{{\\rm{Er}}}}}}}\\) (or equivalently \\({f}_{2}^{{{{{{\\rm{Ti}}}}}}}\\) and \\({f}_{3}^{{{{{{\\rm{Er}}}}}}}\\)), which suggests an ESR transition involving both Ti and Er spins. We label this peak as \\({f}_{5}^{{{{{{\\rm{TiEr}}}}}}}\\). Remarkably, the sign of \\({f}_{3}^{{{{{{\\rm{Er}}}}}}}\\), \\({f}_{4}^{{{{{{\\rm{Er}}}}}}}\\) and \\({f}_{5}^{{{{{{\\rm{TiEr}}}}}}}\\) is opposite to that of \\({f}_{1}^{{{{{{\\rm{Ti}}}}}}}\\) and \\({f}_{2}^{{{{{{\\rm{Ti}}}}}}}\\), indicating a different detection mechanism for the transitions involving the Er spin, which will be discussed below. Finally, we observed an energy level crossing between Er and Ti transitions at \u03d1\u2009~\u200912\u00b0, with the Er resonance frequencies further shifting below the Ti transitions at \u03d1\u2009~\u20090\u00b0 (Fig.\u00a02c and Fig.\u00a0S6). This peculiar behavior is a consequence of the large difference in magnetic anisotropy between Er and Ti23.\n\na Constant-current STM image of the engineered Er-Ti dimer with the atomic separation of 0.72\u2009nm. The intersection of grids represents the oxygen sites of MgO. The Er atom (circled in yellow) is adsorbed on the oxygen site of MgO, while the Ti atom (circled in purple) is adsorbed on the bridge site (set-point: Vdc\u2009=\u2009100\u2009mV, Idc\u2009=\u200920 pA). b ESR spectra of the dimer given in a. When the STM tip is located on top of Er, no peaks are observed (yellow) (set-point: Vdc\u2009=\u200950\u2009mV, Idc\u2009=\u200920 pA, Vrf\u2009=\u200920\u2009mV, B\u2009=\u20090.28\u2009T, \u03d1\u2009=\u200997\u00b0). When the STM tip is located on top of Ti, 5 ESR peaks are detected (\\({f}_{{{{{\\mathrm{1,2}}}}}}^{{{{{{\\rm{Ti}}}}}}}\\), \\({f}_{{{{{\\mathrm{3,4}}}}}}^{{{{{{\\rm{Er}}}}}}}\\) and \\({f}_{5}^{{{{{{\\rm{TiEr}}}}}}}\\)) with \u03d1\u2009=\u200952\u00b0 (pink), while 4 ESR peaks are detected (\\({f}_{{{{{\\mathrm{1,2}}}}}}^{{{{{{\\rm{Ti}}}}}}}\\), and \\({f}_{{{{{\\mathrm{3,4}}}}}}^{{{{{{\\rm{Er}}}}}}}\\)) with \u03d1\u2009=\u200997\u00b0 (purple) (set-point: Vdc\u2009=\u200970, 60\u2009mV, Idc\u2009=\u200930, 40 pA, Vrf\u2009=\u200920, 15\u2009mV, B\u2009=\u20090.3\u2009T). c ESR frequencies as a function of \u03d1 at B\u2009=\u20090.32\u2009T. The ESR frequencies obtained from each measurement are given as black dots with error bars with 95% confidence interval alongside the transition energies predicted from the model Hamiltonian for \\({f}_{1}^{{{{{{\\rm{Ti}}}}}}}\\) (blue line), \\({f}_{2}^{{{{{{\\rm{Ti}}}}}}}\\) (light blue line), \\({f}_{3}^{{{{{{\\rm{Er}}}}}}}\\) (red line), \\({f}_{4}^{{{{{{\\rm{Er}}}}}}}\\) (orange line), \\({f}_{5}^{{{{{{\\rm{TiEr}}}}}}}\\) (green line), and flip-flop transition (dashed gray line). The experimental points were obtained at different set-points (Vdc\u2009=\u200960\u250070\u2009mV, Idc\u2009=\u200912\u250040 pA, Vrf\u2009=\u200915\u250025\u2009mV, B\u2009=\u20090.28\u25000.8\u2009T); the resonance frequencies were rescaled by 0.32\u2009T/B. d, e Four-level schemes corresponding to the energies of the 4 spin states of the Er-Ti dimer and the corresponding transitions depicted as colored arrows at B\u2009=\u20090.32\u2009T with different \u03d1 (90\u00b0 and 0\u00b0, respectively). At \u03d1\u2009=\u200990\u00b0 (d), the spin states are given by the Zeeman product states, while at \u03d1\u2009=\u20090\u00b0 (e), a linear combination of the Zeeman product states is needed to describe the levels.\n\nAs shown in Fig.\u00a02c, the angular dependence of the ESR frequencies is well reproduced by using Eq.\u00a01 with \\({{{{{{\\mathscr{J}}}}}}}_{{{{{{\\rm{exc}}}}}}}/{{{{{\\rm{h}}}}}}\\)\u2009=\u2009326\u2009MHz for this Ti-Er pair with 0.72\u2009nm separation. We observed small deviations for \\({f}_{1}^{{{{{{\\rm{Ti}}}}}}}\\), \\({f}_{2}^{{{{{{\\rm{Ti}}}}}}}\\) and \\({f}_{5}^{{{{{{\\rm{TiEr}}}}}}}\\), which we ascribe to different experimental conditions and magnetic interaction of Ti with the tip, which is not included in our model. Diagonalizing the Hamiltonian in Eq.\u00a01 allows us to analyze the quantum states of the Er-Ti dimer in terms of individual Er and Ti spin states. For an in-plane B\u2009=\u20090.3\u2009T, the energy detuning between the Er and Ti spins (30\u2009GHz) is much larger than the interaction energy (about 3\u2009GHz). Therefore, the Er-Ti dimer can be modeled with the 4 Zeeman product states of the Er and Ti spins. Following this picture, we can support the assignment of \\({f}_{{{{{\\mathrm{1,2}}}}}}^{{{{{{\\rm{Ti}}}}}}}\\) as Ti spin transitions occurring with no changes in the Er state, while \\({f}_{{{{{\\mathrm{3,4}}}}}}^{{{{{{\\rm{Er}}}}}}}\\) correspond to Er spin transitions without altering Ti. Finally, we attribute \\({f}_{5}^{{{{{{\\rm{TiEr}}}}}}}\\) to a double-flip transition involving both Er and Ti spins. Even though a \\(\\left|\\triangle m\\right|\\)\u2009>\u20091\u0127 process is generally forbidden to first order, anisotropic terms in the magnetic interaction can give rise to higher order matrix elements connecting states with \u0394m\u2009=\u2009\u00b12\u012735.\n\nWhen the field is oriented at \u03d1\u2009=\u20090\u00b0, both \\({{{{{{\\bf{J}}}}}}}_{{{{{{\\rm{Er}}}}}}}\\) and \\({{{{{{\\bf{S}}}}}}}_{{{{{{\\rm{Ti}}}}}}}\\) show an expectation value of \u0127/2, but a detuning still occurs due to the difference between the out-of-plane g-factors, \\({g}_{{{{{{\\rm{Er}}}}}}}\\)\u2009=\u20091.2 and \\({g}_{{{{{{\\rm{Ti}}}}}}}\\)\u2009=\u20091.989\u2009\u00b1\u20090.02429. This detuning is comparable to their interaction energy and, thus, the two middle levels are no longer described by Zeeman product states (Fig.\u00a02e). Finally, at the level crossing angle (\u03d1\u2009~\u200912\u00b0), the two Er and Ti middle levels become singlet and triplet states33. However, measuring ESR spectra under these conditions becomes challenging (Fig.\u00a0S7), possibly due to the limitation in our detection as discussed in the following.\n\nThe detection of ESR peaks exclusively occurs when the tip is positioned on top of Ti. Moving the tip from Ti to Er, the intensities of \\({f}_{3}^{{{{{{\\rm{Er}}}}}}}\\) and \\({f}_{4}^{{{{{{\\rm{Er}}}}}}}\\) gradually decrease and eventually vanish at ~0.3\u2009nm from the Ti center (Fig.\u00a0S8). This behavior indicates that driving an ESR transition on Er must induce a change in the Ti state occupation, subsequently modifying the spin polarization of the tunnel junction. In addition, while the Ti transitions always yield positive peaks \\({f}_{{{{{\\mathrm{1,2}}}}}}^{{{{{{\\rm{Ti}}}}}}}\\), Er ESR signals differ depending on specific tip conditions, i.e., different tips show positive or negative sign for \\({f}_{{{{{\\mathrm{3,4}}}}}}^{{{{{{\\rm{Er}}}}}}}\\) (Fig.\u00a03a).\n\na ESR spectra showing \\({f}_{{{{{\\mathrm{3,4}}}}}}^{{{{{{\\rm{Er}}}}}}}\\) for two different STM tips: negative peaks related to negative spin pumping (yellow line) and positive peaks related to positive spin pumping (orange line) (set-point: Idc\u2009=\u200912, 20 pA, Vdc\u2009=\u200970\u2009mV, Vrf\u2009=\u200925\u2009mV, B\u2009=\u20090.28, 0.32\u2009T, \u03d1\u2009=\u200967\u00b0). b ESR peak intensities as a function of Vrf. The measured values for \\({f}_{1}^{{{{{{\\rm{Ti}}}}}}}\\) and \\({f}_{3}^{{{{{{\\rm{Er}}}}}}}\\) are given by black dots while the intensities predicted from the rate equation model (Supplementary Section\u00a09) for \\({f}_{{{{{\\mathrm{1,2}}}}}}^{{{{{{\\rm{Ti}}}}}}}\\) and \\({f}_{{{{{\\mathrm{3,4}}}}}}^{{{{{{\\rm{Er}}}}}}}\\) are given as blue, light blue, red solid lines and an orange dashed line, respectively (set-point: Idc\u2009=\u200940 pA, Vdc\u2009=\u200970\u2009mV, B\u2009=\u20090.28\u2009T, \u03d1\u2009=\u200997\u00b0). c Four-level scheme explaining the rate equation model while driving \\({f}_{3}^{{{{{{\\rm{Er}}}}}}}\\) (red arrow). The Ti\u2019s spin relaxation rates \\({\\varGamma }_{1}^{{{{{{\\rm{Ti}}}}}}}\\) and \\({\\varGamma }_{2}^{{{{{{\\rm{Ti}}}}}}}\\) are depicted as purple arrows while the Er spin relaxation rates \\({\\varGamma }_{3}^{{{{{{\\rm{Er}}}}}}}\\) and \\({\\varGamma }_{4}^{{{{{{\\rm{Er}}}}}}}\\) are given as dashed yellow arrows. The negative spin pumping effect is represented as blue double arrows. d Normalized ESR peak intensities (\u0394I/Idc) for \\({f}_{1}^{{{{{{\\rm{Ti}}}}}}}\\) (blue circles) and for \\({f}_{4}^{{{{{{\\rm{Er}}}}}}}\\) (orange circles) at different tip heights. Here, the tip height is controlled by the set-point current Idc (set-point: Vdc\u2009=\u200970\u2009mV, Vrf\u2009=\u200910\u2009mV, B\u2009=\u20090.28\u2009T, \u03d1\u2009=\u200997\u00b0). The blue and orange lines serve as guides for the eye. The insets show two different tip-Ti distances: larger for lower Idc and smaller for higher Idc. In b and d, the error bars are given with 95% confidence interval.\n\nTo further delve into the driving and detection mechanisms of the Er spin, we measured the intensities of \\({f}_{1}^{{{{{{\\rm{Ti}}}}}}}\\) and \\({f}_{3}^{{{{{{\\rm{Er}}}}}}}\\) as a function of Vrf using a tip that shows negative Er peaks (Fig.\u00a03b). While \\({f}_{1}^{{{{{{\\rm{Ti}}}}}}}\\) exhibits a continuous increase in intensity with increasing Vrf, \\({f}_{3}^{{{{{{\\rm{Er}}}}}}}\\) reaches saturation at Vrf\u2009~\u200920\u2009mV. The result for \\({f}_{1}^{{{{{{\\rm{Ti}}}}}}}\\) aligns with previous measurements on Ti33, while the low-power saturation of Er is comparable to that of Fe, which might reflect a long T1 and/or a high Rabi rate (\u03a9)36. To understand this Vrf-dependence as well as the signs of ESR signals, we developed a rate equation model (Supplementary Section\u00a07) based on the four-level scheme depicted in Fig.\u00a03c. When driving \\({f}_{3}^{{{{{{\\rm{Er}}}}}}}\\) (red arrow), the populations of the initial and final states involved in the transition tend to equalize through a population transfer37. The changes in population are counteracted by the relaxation rates of each state (\\({\\varGamma }_{1,2}^{{{{{{\\rm{Ti}}}}}}}\\) and \\({\\varGamma }_{3,4}^{{{{{{\\rm{Er}}}}}}}\\)), which tend to repopulate the depleted states. These rates are inversely proportional to the T1 of the atom involved in the spin flip. These relaxations happen due to an exchange of energy with the environment which tends to relax the populations towards the thermal equilibrium. An exchange of energy to (from) the environment leads to a transition to a lower (higher) energy level. Since Ti located under the tip is strongly influenced by tunneling electrons, relaxation events occur on a much shorter timescale than for Er38, providing a more efficient pathway to attain the steady state. In addition, to account for the tip-dependent sign and intensity of Er ESR signals, we included a spin pumping term originating from the spin-polarized tunnel current (Fig.\u00a03c for a negatively polarized tip)17,39. In inelastic scattering events, the exchange of angular momenta occurs while retaining the total angular momentum of the system39. That is, the spin-polarized tunneling electrons lead to scattering events with preferential polarization, as depicted in the inset of Fig.\u00a03a,\u00a0c. Thus, the tunneling electrons can shift the Ti spin occupation altering the population balance with respect to the thermal equilibrium (see Supplementary Section\u00a09). The proposed detection scheme based on the change of Ti state population accurately describes the Vrf-dependence (Fig.\u00a03b) and the tip-dependent sign variations of the ESR signals (Fig.\u00a0S10b).\n\nFinally, to identify the ESR driving source of the Er spin, we follow the relative peak intensity (\u0394I/Idc) at different tip heights, as controlled by Idc. As shown in Fig.\u00a03d, \u0394I/Idc of \\({f}_{1}^{{{{{{\\rm{Ti}}}}}}}\\) increases with reducing the tip-sample distance (increasing Idc), indicating that the main driving term for Ti arises from the exchange interaction with the spin-polarized tip40,41. On the other hand, \u0394I/Idc for \\({f}_{4}^{{{{{{\\rm{Er}}}}}}}\\) remains independent of Idc, which identifies the modulation of the magnetic interaction with Ti as the ESR driving source of Er42. The modulation of the magnetic coupling43, in combination with anisotropic interaction terms35, additionally explains the drive of the double-flip transition \\({f}_{5}^{{{{{{\\rm{TiEr}}}}}}}\\).\n\nAs previously discussed about the Er-Ti dimer with 0.928\u2009nm separation, the relative peak intensity of the Ti peaks \\({f}_{1}^{{{{{{\\rm{Ti}}}}}}}\\) and \\({f}_{2}^{{{{{{\\rm{Ti}}}}}}}\\) reflects the time averaged population of the Er states (Fig.\u00a04a), i.e., changes in the time-averaged spin states of Er will induce the change of the relative peak intensity of \\({f}_{1}^{{{{{{\\rm{Ti}}}}}}}\\) and \\({f}_{2}^{{{{{{\\rm{Ti}}}}}}}\\). Thus, by monitoring the Ti ESR signals, we can observe the evolution of the Er spin state. In this way, we characterize the characteristic relaxation time \\({T}_{1}^{{{{{{\\rm{Er}}}}}}}\\) by exciting the Er into an out-of-equilibrium state and monitoring its relaxation towards the thermal state.\n\na, b Double resonance spectra in the frequency range covering Ti ESR transitions \\({{f}}_{{1}{,}{2}}^{{{{{{{\\rm{Ti}}}}}}}}\\) (a) without and (b) with simultaneous driving of Er at the ESR frequency of \\({{f}}_{{3}}^{{{{{{{\\rm{Er}}}}}}}}\\). The peak intensities of \\({{f}}_{{1}{,}{2}}^{{{{{{{\\rm{Ti}}}}}}}}\\) are related to the relative population of the Er spin states (insets). The spectra were normalized to the sum of their peak intensity. c ESR intensity ratios between \\({\\triangle I}_{{f}_{2}}^{{{{{{\\rm{Ti}}}}}}}\\) and \\({\\triangle I}_{{f}_{1}}^{{{{{{\\rm{Ti}}}}}}}\\) as a function of the driving strength Vrf2 at different Er ESR transition states (red, orange, and gray circles for \\({{f}}_{{3}}^{{{{{{{\\rm{Er}}}}}}}}\\), \\({{f}}_{{4}}^{{{{{{{\\rm{Er}}}}}}}}\\), and off-resonance, respectively). The solid curves show the correspondent simulation results by the rate equation model (Supplementary Section\u00a09) for \\({{f}}_{{3}}^{{{{{{{\\rm{Er}}}}}}}}\\) (red line), \\({{f}}_{{4}}^{{{{{{{\\rm{Er}}}}}}}}\\) (orange line) and at an off-resonance frequency (gray line). The experimental points are given as black dots with error bars corresponding to 95% confidence interval. Set-point: Idc\u2009=\u200915 pA, Vdc\u2009=\u200970\u2009mV, Vrf\u2009=\u200930\u2009mV, Vrf2\u2009=\u20091\u201350\u2009mV, B\u2009=\u20090.28\u2009T, \u03d1\u2009=\u200997\u00b0. d Schematics of the inversion recovery measurement in a pump-probe pulse scheme to determine the Er spin relaxation time \\({T}_{1}^{{{{{{\\rm{Er}}}}}}}\\). Each sequence is composed of a pump pulse at the resonance frequency of \\({{f}}_{{3}}^{{{{{{{\\rm{Er}}}}}}}}\\) (red box) and a probe pulse at the resonance frequency of \\({{f}}_{{1}}^{{{{{{{\\rm{Ti}}}}}}}}\\) (blue box). The probe pulse follows the pump pulse after a delay time \u0394t. The population of the Er states after the pump pulse relaxes back to the thermal state following its T1. e The experimental data for the inversion recovery measurement (blue circles) show the intensity of the ESR signal at the probe pulse \\({{f}}_{{1}}^{{{{{{{\\rm{Ti}}}}}}}}\\) as a function of \u0394t. The black line shows the fit using an exponential function with \\({T}_{1}^{{{{{{\\rm{Er}}}}}}}\\) of about 1\u2009\u03bcs. Set-point: Idc\u2009=\u200950 pA, Vdc\u2009=\u200970\u2009mV, Vrf pump\u2009=\u200960\u2009mV, Vrf probe\u2009=\u2009100\u2009mV, B\u2009=\u20090.28\u2009T, \u03d1\u2009=\u200997\u00b0.\n\nBy applying an additional rf voltage (Vrf2), Ti and Er spins can be simultaneously driven in the so-called \u201celectron-electron double resonance\u201d scheme44. With this scheme, it is possible to drive Er transitions and sense the change in population through the Ti ones. For instance, in double resonance experiment, the relative intensities of \\({f}_{1}^{{{{{{\\rm{Ti}}}}}}}\\) and \\({f}_{2}^{{{{{{\\rm{Ti}}}}}}}\\) are equalized when \\({f}_{3}^{{{{{{\\rm{Er}}}}}}}\\) is simultaneously driven (Fig.\u00a04b). As shown in Fig.\u00a04c, the intensity ratio of \\({f}_{1}^{{{{{{\\rm{Ti}}}}}}}\\) and \\({f}_{2}^{{{{{{\\rm{Ti}}}}}}}\\) (\\({\\Delta I}_{{f}_{2}}^{{{{{{\\rm{Ti}}}}}}}/{\\Delta I}_{{f}_{1}}^{{{{{{\\rm{Ti}}}}}}}\\)) increases with increasing Vrf only when Vrf2 is applied at the resonance frequency of \\({f}_{3}^{{{{{{\\rm{Er}}}}}}}\\) or \\({f}_{4}^{{{{{{\\rm{Er}}}}}}}\\), enabling selective modulation of the Er states to an out-of-equilibrium configuration.\n\nTaking advantage of this selective driving mechanism, we implemented an inversion recovery measurement to estimate the spin relaxation time of Er (\\({T}_{1}^{{{{{{\\rm{Er}}}}}}}\\)) in a pump-probe scheme (Fig.\u00a04d). After exciting \\({f}_{3}^{{{{{{\\rm{Er}}}}}}}\\) with a pumping rf pulse of 200\u2009ns duration that equalized the Er population, we applied a probe pulse of 500\u2009ns for \\({f}_{1}^{{{{{{\\rm{Ti}}}}}}}\\) after a delay time \u0394t. Using this sequence, we monitored the time evolution of the intensity of \\({f}_{1}^{{{{{{\\rm{Ti}}}}}}}\\) as a function of\u00a0\u0394t from the out-of-equilibrium to the thermal state (Fig.\u00a04e). The fit to an exponential function (Fig.\u00a04e) gives \\({T}_{1}^{{{{{{\\rm{Er}}}}}}}\\)\u2009=\u20090.818\u2009\u00b1\u20090.115\u2009\u03bcs, which is five times longer than that previously measured for Fe-Ti dimers in the absence of tunnel current18. We attribute this enhancement to the efficient decoupling of 4f electrons from the environment, which reduces the relaxation events arising from the scattering with substrate electrons.\n\nThe \\({T}_{1}^{{{{{{\\rm{Er}}}}}}}\\) observed through Ti likely differs from the intrinsic relaxation time of Er on this surface due to its strong interaction with the Ti atom. Nevertheless, the large \\({T}_{1}^{{{{{{\\rm{Er}}}}}}}\\) indicates that the rapid spin fluctuations of Ti occurring on the timescale of a few ns38 do not significantly perturb the stability of the Er states. This property partially originates from the large energy detuning between Er and Ti levels, which prevents the energy exchange required for spin-flip events. Using the experimentally obtained value of \\({T}_{1}^{{{{{{\\rm{Er}}}}}}}\\) in the rate equation model, we extract a driving term W\u2009=\u2009\u03a92T2/2 for Er that is two times larger than for Ti in the same dimer (Supplementary Section\u00a09). Despite the long spin lifetime and large driving term, attempts to drive Er Rabi oscillations through Ti do not yield a complete cycle (Fig.\u00a0S11b), preventing a direct measure of the Er T2. This is most likely due to a relatively low Rabi rate \u03a9 provided by the moderate Er-Ti exchange coupling, which is about 2\u25003 times smaller than in the Fe-Ti dimer42. In turn, a low value of \u03a9 together with a large driving term W would imply much longer T2 for Er than previous 3d elements, highlighting the potential of 4f electrons to realize higher performance atomic-scale qubits.",
+            "section_image": [
+                "https:////media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41467-024-49447-y/MediaObjects/41467_2024_49447_Fig1_HTML.png",
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+                "https:////media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41467-024-49447-y/MediaObjects/41467_2024_49447_Fig4_HTML.png"
+            ]
+        },
+        {
+            "section_name": "Discussion",
+            "section_text": "We demonstrated a new experimental approach to electrically drive ESR on the elusive 4f electrons in a surface-adsorbed lanthanide atom with long spin relaxation time. Given the reduced scattering with the substrate electrons, it is reasonable to anticipate an enhancement in the coherence time of Er in comparison to 3d elements. This allows one to develop more advanced pulse sequences for quantum coherent manipulation on atomic-scale spin platforms. We expect that, by employing a similar approach to different atomic structures, we can reduce the influence of the spin fluctuations of the atom used for the detection and amplify the ESR driving on the 4f electrons, enabling the use of lanthanide atoms as surface spin qubits with superior properties compared to the routinely adopted 3d elements.",
+            "section_image": []
+        },
+        {
+            "section_name": "Methods",
+            "section_text": "Our experiment was performed in a home-built STM operating at the cryogenic temperature of ~1.3\u2009K in an ultrahigh vacuum environment (<1\u2009\u00d7\u200910\u25009\u2009Torr)45. Using a two-axis vector magnet (6\u2009T in-plane/4\u2009T out-of-plane), the magnetic fields were varied from 0.28\u2009T to 0.9\u2009T at different angles from the surface normal45. To allow atom deposition on the sample kept in the STM stage, the sample is slightly tilted from the axis of the magnet by ~7\u00b0 as estimated from the fit to the data shown in Fig.\u00a01d. Considering this misalignment, all our experimental \u03d1 were offset by that amount accordingly. The magnetic tips used in our measurements were prepared by picking up ~4\u25009 Fe atoms from the MgO surface until the tips presented good ESR signals on isolated Ti atoms.\n\nWe used two different schemes to apply Vrf to the STM junction: one through the tip and one through an antenna (rf generators: Keysight E8257D and E8267D)45. In all our measurement involving a single rf sweep, we applied the Vrf using an antenna located near the sample45 except for the data in Fig.\u00a03b, where the Vrf was combined with the dc bias voltage Vdc using a bias tee at room temperature and then applied to the STM tip. The data in Fig.\u00a04a\u2500c were acquired by applying Vrf to the tip and simultaneously Vrf2 to the antenna. For the measurements reported in Figs.\u00a04e and S11, the two rf voltages (Vrf and Vrf2) were combined through a power splitter (minicircuits ZC2PD-K0244\u2009+\u2009) and applied to the STM tip. For these measurements, both rf generators were gated by an arbitrary waveform generator (Tektronix, AWG 70002B).\n\nThe surface of a Ag(100) substrate was cleaned by repeated cycles of Ar+ sputtering and annealing (700\u2009K). We grew atomically thin layers of MgO(100) on the Ag(100) by evaporating Mg metal in an oxygen atmosphere with partial pressure of 10\u25006 Torr while maintaining the sample at a temperature of ~590\u2009K, following a procedure described in a previous work46. We deposited Fe, Ti and Er atoms (<1% of monolayer) from high purity rods (>99%) using an e-beam evaporator. During the deposition the sample was held at ~10\u2009K in order to have well-isolated single atoms on the surface. As described in previous works, the Ti atoms on 2\u2009ML MgO/Ag(100) show a spin magnitude of \u0127/2 with g-factor anisotropy29, a behavior previously attributed to hydrogenation31.\n\nWe fit the ESR spectra using a model given in33 in order to extract the resonance frequency, peak intensity, and peak width for the data shown in Figs.\u00a01d, 2c, 3b, d, and 4c.\n\nFigure\u00a01c: The spectrum at \u03d1\u2009=\u20098\u00b0 (pink) was normalized at its maximum intensity, while the spectrum at \u03d1\u2009=\u200968\u00b0 (purple) was normalized to the sum of the intensities of its two peaks. The frequency detuning is defined with respect to 9.1\u2009GHz (8.1\u2009GHz) for the spectrum at \u03d1\u2009=\u20098\u00b0 (\u03d1\u2009=\u200968\u00b0).\n\nFigure\u00a02b: The spectra measured on Ti at \u03d1\u2009=\u200952\u00b0 (pink) and at \u03d1\u2009=\u200997\u00b0 (purple) were normalized at their respective maxima, while the spectrum measured on top of Er was rescaled by the same amount used for the spectrum measured on Ti at \u03d1\u2009=\u200997\u00b0. The spectra measured on Ti at \u03d1\u2009=\u200952\u00b0 and on Er are offset for clarity.\n\nFurther information on research design is available in the\u00a0Nature Portfolio Reporting Summary linked to this article.",
+            "section_image": []
+        },
+        {
+            "section_name": "Data availability",
+            "section_text": "The data used in this study are available in the figshare database under accession code [https://doi.org/10.6084/m9.figshare.24190884].",
+            "section_image": []
+        },
+        {
+            "section_name": "Code availability",
+            "section_text": "The code used to plot Figs.\u00a01d, 2c, 3b, and 4c are available alongside the relative data at https://doi.org/10.24433/CO.9869055.v1.",
+            "section_image": []
+        },
+        {
+            "section_name": "References",
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+            "section_image": []
+        },
+        {
+            "section_name": "Acknowledgements",
+            "section_text": "We thank Taehong Ahn and Leonard Edens for their support at the initial stage of the experiment and Yi Chen, Arzhang Ardavan, and Joaqu\u00edn Fern\u00e1ndez-Rossier for fruitful discussions. We acknowledge support from the Institute for Basic Science (IBS-R027-D1). Y.B. acknowledges support from Asian Office of Aerospace Research and Development (FA2386-20-1-4052). H.B. acknowledges funding from the SNSF AdG (TMAG-2_209266).",
+            "section_image": []
+        },
+        {
+            "section_name": "Author information",
+            "section_text": "Yujeong Bae\n\nPresent address: Empa, Swiss Federal Laboratories for Materials Science and Technology, nanotech@surfaces Laboratory, D\u00fcbendorf, Switzerland\n\nCenter for Quantum Nanoscience (QNS), Institute for Basic Science (IBS), Seoul, Republic of Korea\n\nStefano Reale,\u00a0Jiyoon Hwang,\u00a0Jeongmin Oh,\u00a0Andreas J. Heinrich,\u00a0Fabio Donati\u00a0&\u00a0Yujeong Bae\n\nEwha Womans University, Seoul, Republic of Korea\n\nStefano Reale\n\nDepartment of Energy, Politecnico di Milano, Milano, Italy\n\nStefano Reale\n\nDepartment of Physics, Ewha Womans University, Seoul, Republic of Korea\n\nJiyoon Hwang,\u00a0Jeongmin Oh,\u00a0Andreas J. Heinrich,\u00a0Fabio Donati\u00a0&\u00a0Yujeong Bae\n\nInstitute of Physics, Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne, Lausanne, Switzerland\n\nHarald Brune\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nS.R. and F.D. conceived the idea. S.R., F.D., and Y.B. designed the experiment. S.R., J.H., J.O., and Y.B. performed the experiments. S.R. analyzed the data and developed the model with the supervision of F.D. and Y.B.; H.B., A.J.H., F.D., and Y.B. supervised the project. S.R., F.D., and Y.B. wrote the manuscript with contributions from all authors. All authors discussed the results.\n\nCorrespondence to\n                Fabio Donati or Yujeong Bae.",
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+        },
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+            "section_name": "Peer review",
+            "section_text": "Nature Communications thanks the anonymous reviewers for their contribution to the peer review of this work. A peer review file is available.",
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+            "section_name": "About this article",
+            "section_text": "Reale, S., Hwang, J., Oh, J. et al. Electrically driven spin resonance of 4f electrons in a single atom on a surface.\n                    Nat Commun 15, 5289 (2024). https://doi.org/10.1038/s41467-024-49447-y\n\nDownload citation\n\nReceived: 09 October 2023\n\nAccepted: 05 June 2024\n\nPublished: 20 June 2024\n\nVersion of record: 20 June 2024\n\nDOI: https://doi.org/10.1038/s41467-024-49447-y\n\nAnyone you share the following link with will be able to read this content:\n\nSorry, a shareable link is not currently available for this article.\n\n\n\n\n                            Provided by the Springer Nature SharedIt content-sharing initiative\n                        ",
+            "section_image": [
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+            ]
+        },
+        {
+            "section_name": "This article is cited by",
+            "section_text": "Nature Communications (2025)\n\nnpj Quantum Information (2024)",
+            "section_image": []
+        }
+    ]
+}

0db09a99923f418955497d1d6f55a2130a934dc119e9b2f2f18766ecb87dc1ff/metadata.json

@@ -0,0 +1,171 @@
+{
+    "title": "A minority of final stacks yields superior amplitude in single-particle cryo-EM",
+    "pre_title": "Not final yet: a minority of final stacks yields superior amplitude in single-particle cryo-EM",
+    "journal": "Nature Communications",
+    "published": "10 December 2023",
+    "supplementary_0": [
+        {
+            "label": "Supplementary Information",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-023-43555-x/MediaObjects/41467_2023_43555_MOESM1_ESM.pdf"
+        },
+        {
+            "label": "Peer Review File",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-023-43555-x/MediaObjects/41467_2023_43555_MOESM2_ESM.pdf"
+        },
+        {
+            "label": "Reporting Summary",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-023-43555-x/MediaObjects/41467_2023_43555_MOESM3_ESM.pdf"
+        }
+    ],
+    "supplementary_1": [
+        {
+            "label": "Source Data",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-023-43555-x/MediaObjects/41467_2023_43555_MOESM4_ESM.zip"
+        }
+    ],
+    "supplementary_2": NaN,
+    "source_data": [
+        "https://www.ebi.ac.uk/empiar/EMPIAR-10024/",
+        "https://www.ebi.ac.uk/empiar/EMPIAR-11233/",
+        "https://www.ebi.ac.uk/empiar/EMPIAR-10097/",
+        "https://www.ebi.ac.uk/empiar/EMPIAR-11120/",
+        "https://www.ebi.ac.uk/empiar/EMPIAR-10264/",
+        "https://www.ebi.ac.uk/empiar/EMPIAR-10330/",
+        "https://www.ebi.ac.uk/empiar/EMPIAR-10269/",
+        "https://www.ebi.ac.uk/empiar/EMPIAR-10200/",
+        "https://www.rcsb.org/structure/6pcq",
+        "/articles/s41467-023-43555-x#Sec14"
+    ],
+    "code": [
+        "/articles/s41467-023-43555-x#ref-CR22",
+        "https://github.com/mxhulab/cryosieve",
+        "https://doi.org/10.5281/zenodo.10040463"
+    ],
+    "subject": [
+        "Biochemistry",
+        "Computational biophysics",
+        "Cryoelectron microscopy",
+        "Single-molecule biophysics"
+    ],
+    "license": "http://creativecommons.org/licenses/by/4.0/",
+    "preprint_pdf": "https://www.researchsquare.com/article/rs-2921474/v1.pdf?c=1702301415000",
+    "research_square_link": "https://www.researchsquare.com//article/rs-2921474/v1",
+    "nature_pdf": "https://www.nature.com/articles/s41467-023-43555-x.pdf",
+    "preprint_posted": "28 May, 2023",
+    "research_square_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Cryo-electron microscopy (cryo-EM) is widely used to determine near-atomic resolution structures of biological macromolecules. Due to the extremely low signal-to-noise ratio, cryo-EM relies on averaging many images. However, a crucial question in the field of cryo-EM remains unanswered: how close can we get to the minimum number of particles required to reach a specific resolution in practice? The absence of an answer to this question has impeded progress in understanding sample behavior and the performance of sample preparation methods. To address this issue, we have developed a new iterative particle sorting and/or sieving method called CryoSieve. Extensive experiments demonstrate that CryoSieve outperforms other cryo-EM particle sorting algorithms, revealing that most particles are unnecessary in final stacks. The minority of particles remaining in the final stacks yield superior high-resolution amplitude in reconstructed density maps. For some datasets, the size of the finest subset approaches the theoretical limit.Biological sciences/Biophysics/Molecular biophysicsBiological sciences/Biophysics/Computational biophysicscyro-EMsingle particle analysisparticle sortingfinal stacks",
+            "section_image": []
+        },
+        {
+            "section_name": "Additional Declarations",
+            "section_text": "There is NO Competing Interest.",
+            "section_image": []
+        },
+        {
+            "section_name": "Supplementary Files",
+            "section_text": "Supplementalmaterial.pdfSupplementary materials",
+            "section_image": []
+        }
+    ],
+    "nature_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Cryogenic electron microscopy (cryo-EM) is widely used to determine near-atomic resolution structures of biological macromolecules. Due to the low signal-to-noise ratio, cryo-EM relies on averaging many images. However, a crucial question in the field of cryo-EM remains unanswered: how close can we get to the minimum number of particles required to reach a specific resolution in practice? The absence of an answer to this question has impeded progress in understanding sample behavior and the performance of sample preparation methods. To address this issue, we develop an iterative particle sorting and/or sieving method called CryoSieve. Extensive experiments demonstrate that CryoSieve outperforms other cryo-EM particle sorting algorithms, revealing that most particles are unnecessary in final stacks. The minority of particles remaining in the final stacks yield superior high-resolution amplitude in reconstructed density maps. For some datasets, the size of the finest subset approaches the theoretical limit.",
+            "section_image": []
+        },
+        {
+            "section_name": "Introduction",
+            "section_text": "The transformative impact of cryo-EM single-particle analysis (SPA) on the field of structural biology has been widely recognized by the scientific community1. Cryo-EM has advanced significantly due to a series of technological innovations2,3,4,5,6,7, enabling the technique to provide macromolecular structures with up to atomic resolution at an unprecedented rate. This technological progress is commonly referred to as the resolution revolution8. Cryo-EM involves using electron microscopy images of biomolecules embedded in vitreous, glass-like ice9, which are then combined to generate three-dimensional density maps. These maps provide valuable insights into the function of macromolecules and their role in biological processes.\n\nThe stability and electron-optical performance of electron microscopes do not hinder the use of cryo-EM10. However, biological samples studied in cryo-EM are radiation-sensitive11,12. Therefore, a trade-off must be made between improving the signal-to-noise ratio (SNR) and limiting radiation damage13,14. It was concluded that statistically well-defined three-dimensional (3D) structures could not be obtained from individual biological macromolecules at atomic resolution15,16. Instead, increasing the SNR by averaging image data from many identical macromolecules is the only way to progress13,17,18. Over two decades ago, Henderson estimated that structures could be determined at a resolution of nearly 3\u2009\u00c5 by merging data from approximately 12,000 particles, even for particles as small as approximately 40 kDa19. Later, Rosenthal and Henderson argued that the electron microscopy community should adopt the same threshold criterion for structure factor quality as the X-ray protein crystallography community, which was set at a figure-of-merit of 0.5 corresponding to a phase error of 60\u00b016. The theoretical limit of the minimum number of particle images required to achieve a specific resolution can be calculated using the theory proposed by Henderson and Rosenthal16,19, given the B-factor of the instrument (e.g., electron microscopy and camera)13,14,20. In practice, the final stacks of cryo-EM still far fall short of the theoretical limit, indicating a considerable gap between what can be accomplished and the physical limit of what cryo-EM can do21. The initial particle datasets obtained by particle picking from micrographs undergo multiple rounds of laborious 2D and 3D classification to generate the final stack for model determination. The final stacks, which yield atomic or sub-atomic resolution density maps, typically comprise several orders of magnitude fewer particles than the original datasets. Therefore, the cryo-EM field faces the long-standing question of how close we can approach the theoretical limit in practice. The lack of an answer to this open question has hindered the quantification of the performance of various underdeveloped sample preparation methods and impeded the investigation of trends and the understanding of the underlying mechanisms of sample behavior. To answer the question of how close cryo-EM can approach its theoretical limit, it is crucial to determine the minimum number of particles required to achieve a high-resolution 3D reconstruction within a given dataset.\n\nIn this work, we introduce CryoSieve22, an iterative particle sorting and/or sieving algorithm that identifies the smallest subset of particles necessary to generate high-resolution density maps, which we call the finest subset. CryoSieve compares the high-frequency components of synthetic and observed particle images. A higher CryoSieve score indicates superior quality rather than typical cryo-EM damage or artifacts. Extensive experiments show that CryoSieve outperforms other particle sorting algorithms in various metrics and reveal that most particles in final stacks are futile. The finest subsets generate 3D density maps with better high-resolution amplitude, using much fewer particles than the final stacks. We propose that CryoSieve removes radiation-damaged particles within cryo-EM datasets, supported by experiments on the dataset consisting of particles exposed to various levels of electron dose. Finally, we compare the minimum particles required in theory with the size of the finest subsets obtained by CryoSieve, finding that some datasets come close to the theoretical limit after being sieved by CryoSieve. From our experiments, we suggest that advancements during the sample preparation process, aimed at increasing the proportion of the finest subset in the final stack, could potentially facilitate the development of cryo-EM.",
+            "section_image": []
+        },
+        {
+            "section_name": "Results",
+            "section_text": "We have developed a particle sorting and/or sieving model called CryoSieve that iteratively performs 3D reconstruction and particle selection, eliminating futile particles during each iteration. A flow chart scheme is provided in Supplementary Fig.\u00a03. In CryoSieve, the relion_reconstruct module of RELION is used to reconstruct a new density map with the retained particle images, which is then used in the subsequent iteration. The retained particle images in each iteration form a subset of those from the previous iteration, as shown in the following formula:\n\nwhere n(k\u22121) represents the number of retained particles. At each iteration, let bj be the j-th particle image, Aj be its forward operator defined by the estimated parameters and x(k\u22121) be the reconstructed density map from the retained particle images in the previous iteration, particles are sieved out based on their CryoSieve score, which is defined as follows:\n\nHere, H(k) is the highpass operator at the k-th iteration, and its threshold frequency increases linearly as the iteration progresses (Supplementary Table\u00a04). Given that gj relies on the accurate amplitude of the reconstructed density map x(k), CryoSPARC is not the optimal choice for reconstruction in the particle selection step (Supplementary Fig.\u00a02). It tends to deviate significantly from the true amplitude (Supplementary Fig.\u00a02c). Furthermore, the amplitude information within the CryoSieve score proves vital, and the phase residual is ineffective as a metric for particle selection (Supplementary Fig.\u00a04).\n\nThe CryoSieve score estimates the similarity between a particle and a reference projection above a given frequency. A higher CryoSieve score indicates that the particle and the reference projection share a higher proportion of signal energy, indicating better particle quality. As radiation damage mainly affects the high-frequency range, the CryoSieve score includes a highpass operator to extract the high-frequency part. We have demonstrated that the CryoSieve score can identify particles with incorrect pose parameters or components in the high-frequency range through theoretical analysis and simulation verification (Supplementary Material\u00a0I and III). Specifically, assuming that noise in particles follows a Gaussian distribution, we have shown that, with high probability, the CryoSieve score is an ideal indicator of particle image quality, distinguishing it from typical cryo-EM damage or artifacts (Supplementary Material\u00a0I). Furthermore, the CryoSieve score exhibits remarkable accuracy in removing particles with incorrect pose and CTF parameter estimations, achieving a high accuracy of over 90% (Supplementary Material\u00a0III).\n\nWe demonstrate the versatility of our method by applying it to eight experimental datasets (Table\u00a01). The first dataset is derived from the human TRPA1 ion channel (EMPIAR-10024)23. The second dataset is from influenza hemagglutinin trimer (EMPIAR-10097)24, of which the preferred orientation necessitated 40\u00b0 tilts during data acquisition. The third dataset involves LAT1-CD98hc bound to MEM-108 Fab (EMPIAR-10264)25, while the fourth features membrane-bound pfCRT complexed with Fab (EMPIAR-10330)26. Both of these datasets utilized signal subtraction during data processing. The fifth dataset is from CS-17 Fab-bound TSHR-Gs (EMPIAR-11120)27. The sixth is from TRPM8 bound to calcium (EMPIAR-11233)28. The seventh dataset is derived from human apoferritin (EMPIAR-10200)29, achievable to a resolution above 2\u00c5. The eighth dataset originates from streptavidin (EMPIAR-10269)30, with a molecular weight of only 52\u2009kDa. All datasets were obtained using a voltage of 300\u2009kV and an amplitude contrast of 0.07 or 0.1. The TEM systems and electron detectors used in the experiments are listed in Table\u00a01, along with additional metadata such as the number of particles in the final stacks, spherical aberration, symmetry and molecular weight.\n\nAll of the datasets are deposited in the Electron Microscopy Public Image Archive (EMPIAR) 31 as final stacks. These final stacks, which also contain the corresponding refined Euler angles, were used to generate the final published reconstructions. The final stacks are generated by manually selecting significantly smaller subsets through multiple rounds of 2D/3D classification, resulting in a substantially reduced number of particles compared to the original particle stacks.\n\nWe employed CryoSieve to process the eight experimental datasets. CryoSieve removed 20% of the particles in each iteration, resulting in a retaining ratio of 80.0%, 64.0%, 51.2%, and so on. The highpass cutoff frequency of CryoSieve increases linearly across iterations. The retained particles in different iterations were then used for ab initio reconstruction to determine the finest subset of particles. The finest subset only contained 21.0% to 32.8% of the particles in the final stack. However, the quality of the reconstructed map from the finest subset was consistent with that obtained from all particles in the final stack, as demonstrated in Fig.\u00a01. For some datasets, the density maps showed a certain degree of improvement, which was visualized by the restoration of some previously blurred or missing side chains in the density map (Supplementary Fig.\u00a08). The results demonstrate that CryoSieve is proficient in discarding more than half of the particles, utilizing the CryoSieve score\u2014a metric reflecting the discrepancy between the particle image and its reference projection. Crucially, this process does not compromise the quality of the final reconstruction. Moreover, the pose distribution of the removed particles was similar to those of all particles in the final stacks (Supplementary Fig.\u00a06). Therefore, CryoSieve is highly effective in selecting the most informative particles.\n\nFor all eight experimental datasets, density maps of the CryoSieve-retained particles (steel blue) and all particles in the final stack (medium purple) were compared, obtained from CryoSPARC\u2019s ab initio reconstruction after discarding the published refined Euler angles deposited on EMPIAR to avoid the bias in the final stack. The density maps were first FSC-weighted (based on FSCs given by CryoSPARC), and then B-factor sharpened using equivalent B-factors for the same protein: \u221290\u2009\u00c52 for TRPA1, \u2212180\u2009\u00c52 for hemagglutinin, \u2212100\u2009\u00c52 for LAT1, \u221260\u2009\u00c52 for pfCRT, \u221270\u2009\u00c52 for TSHR-Gs, \u221280\u2009\u00c52 for TRPM8, \u221265\u2009\u00c52 for apoferritin, and \u2212110\u2009\u00c52 for streptavidin. The central bars indicate the proportions of the retained and removed particles. The equivalent contour level was applied for each protein respectively, as indicated at the base of each ratio bar. The raw density maps corresponding to these results, unsharpened by B-factor, are given in Supplementary Fig.\u00a01.\n\nWe performed a comparative analysis of CryoSieve with other cryo-EM particle sorting criteria or software currently used in the field, including the normalized cross-correlation (NCC) method32, the angular graph consistency (AGC) approach33 and the non-alignment classification6. The parameter settings for CryoSieve and the other comparative algorithms were listed in Supplementary Material\u00a0VI. In our experiments, we used final stacks composed of relatively high-quality particles. NCC retains an equal number of particles compared to CryoSieve at each iteration, while AGC\u2019s retaining ratio is self-determined. However, AGC\u2019s retaining ratio was mainly over 90%, resulting in only a small fraction of particles being removed. Thus, the quality of the reconstructed map using the retained particles did not improve or worsen (Supplementary Table\u00a02), as these tested final stacks are composed of relatively high-quality particles. For the non-alignment classification applied to hemagglutinin, LAT1, and apoferritin, less than half of the particles were removed, resulting in some enhancement (Supplementary Material\u00a0V). However, this enhancement still falls notably short of the results achieved by CryoSieve (Supplementary Material\u00a0V). For the other five datasets, the retaining ratios using non-alignment classification exceeded 90%, resulting in the quality of maps reconstructed from the retained particles either remaining unchanged or deteriorated (Supplementary Material\u00a0V). Additionally, we randomly selected the same number of particles from the tested final stacks at each iteration to observe the baseline effect of particle number reduction.\n\nFor all the aforementioned methods (CryoSieve, NCC, AGC, non-alignment classification, and random), we discarded the refined Euler angles published and deposited on EMPIAR to prevent the inadvertent transfer of information from the removed particles to the retained particles. Thus, the retained particles were used for ab initio reconstruction by CryoSPARC to obtain refreshed sets of Euler angles and density maps. Several metrics, including FSC-based resolution16, Q-score34 and Rosenthal-Henderson B-factor16 were used to measure the quality of the refreshed density maps. Based on these metrics, our analyses reveal that CryoSieve effectively sieves out 67.2% to 79.0% (varying based on datasets) of particles from the final stacks without deteriorating the yielded density maps (Fig.\u00a02). In contrast, subsets of equal size retained by the other methods failed to reconstruct density maps of the same quality as the original (Fig.\u00a02). Therefore, CryoSieve significantly outperforms other particle sorting algorithms, demonstrating that the majority of particles are dispensable in the final stacks. A key factor in CryoSieve\u2019s superiority over both NCC, AGC and non-alignment classification is the integration of the highpass operator when computing the CryoSieve score. Without the truncation of high frequencies, scores may be predominantly influenced by low-frequency components, making it challenging to differentiate non-contributory particles in cryo-EM.\n\nWe compared the density maps reconstructed from retained particles obtained by CryoSieve (indigo), NCC (green) and cisTEM (light blue), along with random (orange) as the baseline, at different retention ratios. Density maps were ab initio reconstructed by CryoSPARC after discarding the published refined Euler angles deposited on EMPIAR. Five metrics evaluated density map quality. The first column presents FSC-based resolutions: model-to-map (solid lines with squares) and two-half-maps (solid lines with diamonds). The second column shows Q-scores for raw (dashed lines with circles) and sharpened maps (solid lines with circles), with sharpening B-factors determined by CryoSPARC. The third column depicts Rosenthal-Henderson B-factors. The iterations where CryoSieve obtained the finest subset, determined by comprehending these metrics, are labeled with hatched bars. Due to the involvement of the phase plate in the streptavidin dataset, cisTEM failed to refine the poses, and thus the corresponding analysis was omitted.\n\nCisTEM5 can report a score for each single-particle image after 3D refinement. During the 3D refinement process of cisTEM, the pose parameters of particles are re-estimated or refined. Therefore, due to differences in alignment and other image processing workflows between cisTEM and CryoSPARC, cisTEM cannot be strictly compared with CryoSieve. We compared CryoSieve and cisTEM by sorting particles using the cisTEM score and retaining equal particle counts for ab initio reconstruction in CryoSPARC (details in Supplementary Material\u00a0II). CryoSieve outperformed cisTEM in all eight experimental datasets (Fig.\u00a02).\n\nWe analyzed the differences between the particle images retained and removed using CryoSieve by performing 2D classification of the particles into 50 classes using CryoSPARC. To ensure a comparable number of particles for both retained and removed groups, we ran CryoSieve and terminated at the third iteration, yielding a retention ratio of 51.2% and a removal ratio of 48.8%. CryoSPARC reported the 2D resolution of each class, along with the number of particle images belonging to it. The particles retained by CryoSieve (Fig.\u00a03, steel blue) were distributed at a higher resolution compared to those removed by it (Fig.\u00a03, crimson). In six out of the eight datasets, particle images with the highest resolution, i.e., 7.4\u20137.1\u2009\u00c5 in TRPA1, 8.5\u20139.6\u2009\u00c5 in hemagglutinin, 6.6\u20138.2\u2009\u00c5 in LAT1, 7.2\u201311.6\u2009\u00c5 in pfCRT, 7.2\u20138.5\u2009\u00c5 in TSGH-Gs, and 11.6\u20137.5\u2009\u00c5 in TRPM8, were entirely retained by CryoSieve. For apoferritin, the majority of particles within the highest resolution range (5.5\u20135.3\u2009\u00c5) were constituted by the particles retained by CryoSieve. However, for streptavidin, possibly due to the adoption of a phase plate during data collection, unusually high resolutions were reported in the 2D classification step, rendering such a comparison between retained and removed particles ineffective. In conclusion, our analysis suggests that CryoSieve selectively retained the higher-quality particle images in the final stack while discarding lower-quality ones. It is noted that some information remains in these discarded particles, but it does not enhance the information present in the finest subset (Supplementary Material\u00a0VII).\n\nThe third iteration of CryoSieve achieved a retention ratio of 51.2% and a removal ratio of 48.8%, resulting in a similar number of particles for retention and removal. These two categories underwent CryoSPARC 2D clustering and averaging, i.e., 2D classification, with the number of 2D classes set to 50. All eight experimental datasets were tested. CryoSPARC reported the 2D resolution of each 2D class, along with the number of particle images belonging to it. We statistically analyzed the number of particles belonging to each 2D resolution and plotted histograms, demonstrating the difference between retained (steel blue) and removed (crimson) particles in terms of 2D resolution distribution. For TRPA1 and apoferritin, the bar with the highest resolution range was further finely divided and then plotted in a histogram, which is displayed to the right of the global histogram.\n\nB-factors, also known as Debye-Waller factors or temperature factors, reflect the rate at which the amplitude of high-resolution information decreases16. Lower B-factors indicate that the high-resolution signal has been better preserved during sample preparation, imaging, and image processing, implying that the particle images are of higher quality. B-factors are widely used to measure image quality in cryo-EM quantitatively35,36,37,38,39. In our eight experimental datasets, the finest subset, consisting of only 21.0% to 32.8% of particles in the final stack, generates 3D density maps with the Rosenthal and Henderson\u2019s B-factors reduced by 21.1\u2009\u00c52 to 169.0\u2009\u00c52, in comparison to those produced by the original final stacks (Table\u00a02, column D and E). The process of fitting and solving for Rosenthal and Henderson\u2019s B-factors is visualized in Supplementary Fig.\u00a05. Moreover, the B-factors determined by CryoSPARC are presented in Table\u00a02, columns B and C. In other words, the density maps reconstructed from the finest subset have a better high-resolution amplitude, meaning they contain a greater high-resolution intensity, despite the fact that the finest subsets only contain a small fraction of particles in the final stack. This indicates that CryoSieve significantly reduced the temperature factor and alleviated the amplitude contrast decay, suggesting that high-quality particles contribute to the density map and can be effectively selected by CryoSieve.\n\nWe hypothesize that some particle images in the final stacks have been subject to some degree of radiation damage and cannot be screened out by conventional methods. These particles do not contribute positively to the reconstructed density map. To verify the possibility of this conjecture, we acquired micrograph movie stacks of the proteasome using a Titan Krios 300\u2009keV cryo-EM equipped with a K3 direct electron detection camera. The defocus range was set between 0.5\u2009\u03bcm and 1.5\u2009\u03bcm. Each stack comprised 32 frames with a total electron dose of 50 e\u2212\u00c5\u22122. The electron dose was uniformly distributed across all frames. Particles were picked from identical positions using averages from frames 5\u201314, 10\u201319, 15\u201324, and 20\u201329. Consequently, we constructed a dataset consisting of 183,464 particles that represented four different levels of absorbed electron doses (Fig.\u00a04a).\n\na Particles were selected from micrograph movie stacks of the proteasome, with each stack containing 32 frames and a total electron dose of 50 e\u2212\u00c5\u22122. This electron dose was uniformly distributed across all frames. Particles were extracted from consistent positions, using averages from frames 5\u201314, 10\u201319, 15\u201324, and 20\u201329. The average electron doses absorbed are denoted at the bottom, and four representative particles are displayed for each radiation damage level. b The graph depicts the proportions of particles with varying levels of radiation damage (differentiated by colors) in the retained particles across various retention ratios (indicated on the left). A comparison was made between the particles retained by cisTEM (left horizontal bars), CryoSieve (middle horizontal bars), and NCC (right horizontal bars). CryoSieve consistently sieved out particles in a sequence from high to low radiation damage, demonstrating superior performance over both cisTEM and NCC. c Particle distribution across the four radiation damage levels was analyzed using iteration 6 (featuring a retention ratio of 26.2%) from CryoSieve, NCC, and cisTEM. The analysis also incorporated particles retained by the AGC and non-alignment classification methods, with retention ratios auto-determined for these methods. d, e The side chains of the density maps reconstructed by CryoSPARC, using retained particles, were compared alongside the corresponding model-to-map FSCs. This comparison utilized a retention ratio of 26.2% (from iteration 6) for CryoSieve, NCC, cisTEM, and random methods. The retention ratios for AGC and non-alignment classification were auto-determined. The intersection between the FSC threshold (FSC = 0.5) and the FSC curve is represented as a vertical dashed line.\n\nWe assessed the retention behavior of CryoSieve, NCC, cisTEM, AGC, and non-alignment classification in particles subjected to varying radiation damage levels, using random retention as a comparative baseline. As the number of iterations increased, the retention rate diminished. Notably, CryoSieve demonstrated enhanced proficiency in identifying particles with elevated radiation damage levels relative to NCC and cisTEM (Fig.\u00a04b). The retention ratio for cisTEM was equated to each iteration of CryoSieve (Supplementary Material\u00a0II). For AGC and non-alignment classification, the retention ratio was autonomously determined. We simultaneously compared the distribution of particles across the four radiation damage levels, selecting the sixth iteration (with a retention ratio of 26.2%) of CryoSieve, NCC, and cisTEM for this analysis. The analysis also incorporated particles retained by the AGC and non-alignment classification methods, with retention ratios auto-determined for these methods (Fig.\u00a04c). Model-to-map FSCs (Fig.\u00a04d) and a thorough comparison of density maps (Fig.\u00a04e) affirmed CryoSieve\u2019s superiority over the other methods. Retained particles, utilizing the cisTEM score as a selection criterion, exhibited a preferred orientation, resulting in diminished quality (Supplementary Fig.\u00a07).\n\nWhile the approach of grouping frames from micrograph movie stacks cannot remove other potential complications that particles might endure, such as erroneous poses, CTF parameters, and denaturation, we sought additional validation. To this end, we employed InSilicoTEM to generate synthesized particles exhibiting varying simulated radiation damage. With these simulated radiation-damage datasets, CryoSieve consistently outperformed all other methods. Notably, in the final iterations, CryoSieve exclusively retained particles unaffected by radiation damage (Supplementary Material\u00a0VIII).\n\nIt is worth noting that CryoSieve can efficiently remove particles with incorrect pose and CTF parameter estimations, achieving a high accuracy of over 90% (Supplementary Material\u00a0III). However, these particles are also removed by the non-alignment classification approach (Supplementary Material\u00a0III), making them unlikely to be present in the final stacks.\n\nThe theoretical number limit of particle images, given by Rosenthal and Henderson16, is\n\nwhere Nasym, \\(\\frac{S}{N}\\), Ne, \u03c3e, d, B stand for the number of asymmetric units, the signal-to-noise threshold criteria of the resolution, the electron dose, the elastic cross-section for carbon, the resolution, and the overall temperature factor, respectively. In the above formula, \\(\\frac{S}{N}=\\frac{1}{\\sqrt{3}}\\), which is equivalent to a phase error of 60\u00b0 or 0.143-threshold of half-maps FSC16. Meanwhile, Ne = 5\u2009e\u2212\u00c5\u22122, which is believed to be the limiting dose due to radiation damage for features near-atomic resolution16,19,40,41. The electron dose used in practice is typically a fold higher than the limiting dose. Although the additional dose does not contribute to the structure factor amplitudes at near-atomic resolution, it may have increased the signal up to the resolution limit of the final map, thus making the determination of particle parameters easier16. This conjecture agrees with the observation in the study of micrograph movie stack dose weighting, which found that only the initial few frames, not the subsequent frames, contribute to near-atomic features42,43,44. Finally, \u03c3e = 0.004\u2009\u00c52 is the elastic cross-section for carbon at 300\u2009kV45.\n\nThe overall temperature factor, or Rosenthal and Henderson\u2019s B-factor, is the dominant factor in estimating the theoretical limit. Here, we proposed a simplified assumption that limits only exist on instruments (TEM and electron detector) and that no other resolution-limiting factors exist. In other words, we assumed that all other procedures or techniques were ideal. For example, vitrified non-amorphous ice is perfectly flat and of ideal thickness, there is no beam-induced motion, and orientations of particles follow a uniform distribution, and there is no electron-charging effect. Therefore, B-factor represents a summary of all resolution-limiting factors of a given electron microscope and describes the overall quality of the instrumental setup. Holger Stark and his colleagues have summarized the current knowledge on existing state-of-the-art commercial EM hardware and their B-factors46. For the standard Titan Krios, they concluded that its B-factor is 50\u2009\u00c52, which was determined by re-evaluating data from EMPIAR-10216 as described by47, with modifications to account for off-axial aberrations by splitting the micrographs into nine subsets48. Therefore, we computed the theoretical number of particle limits at B = 50\u2009\u00c52 (Table\u00a02, column D). The sizes of the finest subsets obtained by CryoSieve were compared with such theoretical limits (Table\u00a02, column E).\n\nOut of the eight datasets examined, three (pfCRT, TSHR-Gs and apoferritin) were found to be close to their theoretical limits (Table\u00a02, column E, emphasized by bold font). However, the TRPA1 dataset fell short of the theoretical limit by approximately 22-fold. This could be due to the lower resolution capabilities of the TF30 Polara TEM used in the study compared to more advanced models like the Titan Krios. It is possible that the assumed B-factor of 50\u2009\u00c52 for the TF30 Polara is relatively low and does not accurately reflect the properties of the TEM. Moreover, the sample preparation techniques employed during the TRPA1 study in 2015 might not have been fully optimized to attain the highest possible resolution. Hemagglutinin also fell short of the theoretical limit by roughly a factor of 36 due to using a tilt-collection strategy to compensate for the preferred orientation, which resulted in a larger effective ice thickness and a degradation in the quality of particle images. Lastly, LAT1 and TRPM8 exceeded the theoretical limit by factors of 9.8 and 6.3, respectively, suggesting that improvements in sample preparation could be made for these datasets.",
+            "section_image": [
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+            ]
+        },
+        {
+            "section_name": "Discussion",
+            "section_text": "In this study, we introduced the CryoSieve algorithm, which has the ability to estimate the minimum number of particles in a dataset, referred to as the finest subset. CryoSieve demonstrated that most particles in the final stacks are superfluous and do not contribute to reconstructing density maps. On the other hand, the minority of particles that remain in the final stacks yields superior high-resolution amplitude. We also discovered that for some datasets, the size of the finest subset comes close to the theoretical limit. Therefore, CryoSieve can, to some degree, provide insight into a long-standing question in the cryo-EM field: How close can we approach the theoretical limit in practice?\n\nCryoSieve can potentially establish a metric for the quantitative evaluation of various sample preparation techniques by measuring image quality based on the gaps between the theoretical limits and the size of the finest subsets. One of the possible future directions is to address the variables encountered during sample and grid preparation and establish cause-and-effect relationships. Resolving these issues, among others, cryo-EM could become a more versatile and influential technology in structural biology, potentially addressing research questions and aiding the growth of methodologies as the field advances49.",
+            "section_image": []
+        },
+        {
+            "section_name": "Methods",
+            "section_text": "Since cryo-EM single-particle image processing software has experienced rapid development in the past few years, some of the final stacks deposited in EMPIAR can be better processed by state-of-the-art algorithms. To eliminate effects from different refinement software and their versions, ensuring fair comparisons between various particle sorting algorithms, the final stacks deposited on EMPIAR were reprocessed under a standard workflow using CryoSPARC v4.1.0 following a standard workflow. For hemagglutinin, the initial model was generated by low-pass filtering its atomic model to 30\u2009\u00c5, while for the other proteins, initial models were generated by arbitrary random initialization using CryoSPARC. Then, uniform refinement was applied for TRPA1, TRPM8, hemagglutinin, LAT1, and apoferritin, while non-uniform refinement was applied for pfCRT and TSHR-Gs. For streptavidin, we employed local refinement. This was potentially due to the use of a phase plate in the streptavidin dataset, as ab initio reconstruction failed to produce a density map for streptavidin.\n\nTo enable unbiased comparisons of density maps before and after particle sorting, the retained particles obtained from each particle sorting algorithm underwent identical refinement procedures, as previously described using CryoSPARC v4.1.0 in the standard workflow. The reconstructed density maps were used for subsequent measurements. To ensure that there\u2019s no undue influence of information from the discarded particles via their contribution to pose estimation, the former Euler angles were discarded (except streptavidin), and new sets of Euler angles were determined through the refinement of the retained particles. Moreover, in order to maintain independence between the two half sets and ensure that the Fourier Shell Correlation (FSC) served as the golden standard, half-set splits were preserved throughout the subsequent procedure by turning off the option \u201cForce re-do GS split\u201d.\n\nThe reconstructed density maps were evaluated by several metrics, including FSC-based resolution, Q-score and Rosenthal-Henderson B-factor. CryoSPARC produced two raw half maps and an auto-postprocessed density map (FSC-weighted, B-factor sharpened, two half sets averaged), accompanied by reporting half-maps FSC.\n\nFSC-based metric includes half-maps FSC (directly reported by CryoSPARC) and model-to-map FSC. Map-to-model FSC resolution was calculated using the following procedure, with the auto-postprocessed density map as input. The corresponding atomic model of the dataset was converted to the ground-truth density map by the molmap function of Chimera at Nyquist resolution. The mask was generated from the ground-truth density map (after low-pass filtering to 8\u00c5, extending by 4 pixels and applying a cosine-edge of 4 pixels) using RELION. Model-to-map FSC curves were determined between the input density map (obscured by the mask) and the ground-truth density map. The resolution threshold of the map-to-model FSC was set to 0.5.\n\nAs Q-score is sensitive to B-factor sharpening, the Q-scores of both the raw maps and the auto-postprocessed maps were measured. The auto-postprocessed maps were directly provided by CryoSPARC, while the raw maps were obtained by first averaging the two raw half maps provided by CryoSPARC, then low-pass filtering them to an appropriate resolution, in order to eliminate the impact of varying noise intensities on the density maps. The low-pass filtering threshold frequency ranged from 0.3\u2009\u00c5 to 0.5\u2009\u00c5 higher than the CryoSPARC reported half-maps FSC resolution, thus ensuring the retention of useful signals. Specifically, the threshold frequency for TRPA1 was 3.5\u2009\u00c5, for TRPM8 and TSHR-Gs it was 2.7\u2009\u00c5, for hemagglutinin it was 3.4\u2009\u00c5, for pfCRT it was 3.0\u2009\u00c5, for apoferritin it was 1.6\u2009\u00c5, for streptavidin it was 2.8\u2009\u00c5, and for LAT it was 2.8\u2009\u00c5. Q-score was calculated using the MAPQ plugin for UCSF Chimera, with all parameters set to their default values.\n\nRosenthal-Henderson B-factors were determined by fitting the formula that describes the relationship between resolution and the number of particles used for reconstruction. Five half-splitting repetitions were adopted for each dataset. After each repetition, the Euler angles were re-estimated by CryoSPARC, and the reported resolution was used for data fitting.\n\nAll conversions between CryoSPARC and RELION were performed using the pyem script.\n\nCryoSieve iteratively performs 3D reconstruction and particle sieving, while maintaining independence between two half sets by independently sieving each set of particles. 3D reconstructions of each subset were performed using RELION v4.0-beta-2, with the option \u201c\u2013-subset\u201d to preserve the half-set splitting. A mask, generated from the atomic model using RELION (low-pass filtered to 8\u2009\u00c5), was applied to the reconstructed raw density map to obtain x(k\u22121) in Eq.\u00a02 of the CryoSieve score. The same mask was applied to other particle sorting algorithms such as NCC and AGC, to ensure fair comparisons. Subsequently, particles were sieved out based on the ascending order of the CryoSieve score. In total, nine iterations were carried out, with each iteration retaining 80% of the particles from the previous iteration. The cutoff frequency of the highpass operator H(k) increased linearly as the iteration progressed. For all datasets, except for LAT1 and apoferritin, the initial cutoff frequency was set at 40\u2009\u00c5, and the final cutoff frequency was 3\u2009\u00c5. For LAT1, the initial cutoff frequency was 50\u2009\u00c5, and the final cutoff frequency was also 3\u2009\u00c5. For apoferritin, the initial cutoff frequency was 40\u2009\u00c5, and the final cutoff frequency was also 2\u2009\u00c5.\n\nFurther information on research design is available in the\u00a0Nature Portfolio Reporting Summary linked to this article.",
+            "section_image": []
+        },
+        {
+            "section_name": "Data availability",
+            "section_text": "The raw final stack datasets analyzed in this study were downloaded from the EMPIAR repository using accession codes EMPIAR-10024, EMPIAR-11233, EMPIAR-10097, EMPIAR-11120, EMPIAR-10264, EMPIAR-10330, EMPIAR-10269, EMPIAR-10200. Atomic coordinates from Protein Data Bank 6PCQ were used for the generation of simulated particles using InSilicoTEM v2.1.0.\u00a0Source data are provided with this paper.",
+            "section_image": []
+        },
+        {
+            "section_name": "Code availability",
+            "section_text": "CryoSieve22 is now open-sourced and available on GitHub [https://github.com/mxhulab/cryosieve]. A detailed tutorial can also be found on its homepage. Moreover, datasets used in this manuscript, along with the expected outputs after running CryoSieve, have been deposited on GitHub and can be accessed via CryoSieve\u2019s homepage. Code has been uploaded to Zenodo and can be accessed via [https://doi.org/10.5281/zenodo.10040463].",
+            "section_image": []
+        },
+        {
+            "section_name": "References",
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+            "section_image": []
+        },
+        {
+            "section_name": "Acknowledgements",
+            "section_text": "This work was supported by the National Key R&D Program of China (No. 2021YFA1001300) (to C.B.), the National Natural Science Foundation of China (No. 12271291) (to C.B.), the Advanced Innovation Center for Structural Biology (to M.H.), the Beijing Frontier Research Center for Biological Structure (to M.H.), Shenzhen Academy of Research and Translation (to M.H.), Natural Science Foundation of China (No. 12071244) (to Z.S.). We would like to express our gratitude to Shouqing Li and Ranhao Zhang for generously sharing their expertise in particle selection and density map reconstruction in Cryo-EM. Our thanks also go to Dr. Nan Liu for providing valuable suggestions on this work, and to Jie Xu for his assistance in constructing the real radiation damage dataset of the proteasome.",
+            "section_image": []
+        },
+        {
+            "section_name": "Author information",
+            "section_text": "These authors contributed equally: Jianying Zhu, Qi Zhang.\n\nYau Mathematical Sciences Center, Tsinghua University, Beijing, China\n\nJianying Zhu,\u00a0Zuoqiang Shi\u00a0&\u00a0Chenglong Bao\n\nKey Laboratory of Protein Sciences (Tsinghua University), Ministry of Education, Beijing, China\n\nQi Zhang\u00a0&\u00a0Mingxu Hu\n\nSchool of Life Science, Tsinghua University, Beijing, China\n\nQi Zhang\u00a0&\u00a0Mingxu Hu\n\nBeijing Advanced Innovation Center for Structural Biology, Beijing, China\n\nQi Zhang\u00a0&\u00a0Mingxu Hu\n\nBeijing Frontier Research Center for Biological Structure, Beijing, China\n\nQi Zhang\u00a0&\u00a0Mingxu Hu\n\nQiuzhen College, Tsinghua University, Beijing, China\n\nHui Zhang\n\nYanqi Lake Beijing Institute of Mathematical Sciences and Applications, Beijing, China\n\nZuoqiang Shi\u00a0&\u00a0Chenglong Bao\n\nShenzhen Academy of Research and Translation, Shenzhen, China\n\nMingxu Hu\n\nState Key Laboratory of Membrane Biology, School of Life Sciences, Tsinghua University, Beijing, China\n\nChenglong Bao\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nC.B., M.H., and Z.S. initiated the project. M.H., Q.Z., and J.Z. developed CryoSieve and carried out testing. H.Z. provided support in using InSilicoTEM. J.Z. and M.H. analyzed the data. M.H., J.Z., and C.B. wrote the manuscript.\n\nCorrespondence to\n                Zuoqiang Shi, Mingxu Hu or Chenglong Bao.",
+            "section_image": []
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+            "section_name": "Peer review",
+            "section_text": "Nature Communications thanks Qun Liu and the other anonymous reviewer(s) for their contribution to the peer review of this work. A peer review file is available.",
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+            "section_name": "About this article",
+            "section_text": "Zhu, J., Zhang, Q., Zhang, H. et al. A minority of final stacks yields superior amplitude in single-particle cryo-EM.\n                    Nat Commun 14, 7822 (2023). https://doi.org/10.1038/s41467-023-43555-x\n\nDownload citation\n\nReceived: 19 May 2023\n\nAccepted: 13 November 2023\n\nPublished: 10 December 2023\n\nVersion of record: 10 December 2023\n\nDOI: https://doi.org/10.1038/s41467-023-43555-x\n\nAnyone you share the following link with will be able to read this content:\n\nSorry, a shareable link is not currently available for this article.\n\n\n\n\n                            Provided by the Springer Nature SharedIt content-sharing initiative\n                        ",
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+        {
+            "section_name": "This article is cited by",
+            "section_text": "Nature Methods (2025)\n\nNature Communications (2025)\n\nNature (2025)\n\nCommunications Biology (2024)\n\nNature Communications (2024)",
+            "section_image": []
+        },
+        {
+            "section_name": "Associated content",
+            "section_text": "Collection",
+            "section_image": []
+        }
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+}

114b2c7af2a7edcc27507d19510f53d2b72a74abd673eef2f33846e234ceb8b7/metadata.json

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+{
+    "title": "Mechanism for fluctuating pair density wave",
+    "pre_title": "Microscopic mechanism for fluctuating pair density wave",
+    "journal": "Nature Communications",
+    "published": "01 June 2023",
+    "supplementary_0": [
+        {
+            "label": "Supplementary Information",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-023-38956-x/MediaObjects/41467_2023_38956_MOESM1_ESM.pdf"
+        },
+        {
+            "label": "Peer Review File",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-023-38956-x/MediaObjects/41467_2023_38956_MOESM2_ESM.pdf"
+        }
+    ],
+    "supplementary_1": NaN,
+    "supplementary_2": NaN,
+    "source_data": [
+        "/articles/s41467-023-38956-x#MOESM1"
+    ],
+    "code": [],
+    "subject": [
+        "Phase transitions and critical phenomena",
+        "Superconducting properties and materials"
+    ],
+    "license": "http://creativecommons.org/licenses/by/4.0/",
+    "preprint_pdf": "https://www.researchsquare.com/article/rs-1021881/v1.pdf?c=1643312156000",
+    "research_square_link": "https://www.researchsquare.com//article/rs-1021881/v1",
+    "nature_pdf": "https://www.nature.com/articles/s41467-023-38956-x.pdf",
+    "preprint_posted": "18 Nov, 2021",
+    "research_square_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "In weakly coupled BCS superconductors, only electrons within a tiny energy window around the Fermi energy, EF, form Cooper pairs. This may not be the case in strong coupling superconductors such as cuprates, FeSe, SrTiO3 or cold atom condensates where the pairing scale, EB, becomes comparable or even larger than EF. In cuprates, for example, a plausible candidate for the pseudogap state at low doping is a fluctuating pair density wave, but no microscopic model has yet been found which supports such a state. In this work, we write an analytically solvable model to examine pairing phases in the strongly coupled regime and in the presence of anisotropic interactions. Already for moderate coupling we find an unusual finite temperature phase, below an instability temperature Ti, where local pair correlations have non-zero center-of-mass momentum but lack long-range order. At low temperature, this fluctuating pair density wave can condense either to a uniform d-wave super- conductor or the widely postulated pair-density wave phase depending on the interaction strength. Our minimal model offers a unified microscopic framework to understand the emergence of both fluctuating and long range pair density waves in realistic systems.Hard Condensed-matter Physicssuperconductorsfluctuating pair density wavepairing phases",
+            "section_image": []
+        },
+        {
+            "section_name": "Additional Declarations",
+            "section_text": "There is NO Competing Interest.",
+            "section_image": []
+        },
+        {
+            "section_name": "Supplementary Files",
+            "section_text": "SMPDW.pdfSupplementary Material \u2013 Microscopic mechanism for fluctuating Pair Density Wave",
+            "section_image": []
+        }
+    ],
+    "nature_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "In weakly coupled BCS superconductors, only electrons within a tiny energy window around the Fermi energy, EF, form Cooper pairs. This may not be the case in strong coupling superconductors such as cuprates, FeSe, SrTiO3 or cold atom condensates where the pairing scale, EB, becomes comparable or even larger than EF. In cuprates, for example, a plausible candidate for the pseudogap state at low doping is a fluctuating pair density wave, but no microscopic model has yet been found which supports such a state. In this work, we write an analytically solvable model to examine pairing phases in the strongly coupled regime and in the presence of anisotropic interactions. Already for moderate coupling we find an unusual finite temperature phase, below an instability temperature Ti, where local pair correlations have non-zero center-of-mass momentum but lack long-range order. At low temperature, this fluctuating pair density wave can condense either to a uniform d-wave superconductor or the widely postulated pair-density wave phase depending on the interaction strength. Our minimal model offers a unified framework to understand the emergence of both fluctuating and long range pair density waves in realistic systems.",
+            "section_image": []
+        },
+        {
+            "section_name": "Introduction",
+            "section_text": "Spatially uniform superconducting (SC) order formed from Cooper pairs with zero center-of-mass momentum is the energetically favored ground state in the conventional theory of Bardeen, Cooper and Schrieffer (BCS)1. Equivalently, the SC instability is signaled by a divergence in the static pair-fluctuation propagator, L(q,\u2009\u03a9\u2009=\u20090), at q\u2009=\u20090 once the pair instability temperature, Ti, is achieved2. On the other hand, a non-uniform order with non-zero center-of-mass momentum Cooper pair can occur when the divergence of the pair-fluctuation propagator is shifted to non-zero q. First proposed by Fulde and Farrell (FF)3 and independently by Larkin and Ovchinnikov (LO)4, these solutions are stabilized in the presence of explicit time-reversal symmetry breaking from an external magnetic field. A modulated order parameter can also be realized in the presence of time-reversal symmetry where the spatial average of the gap vanishes. Termed pair-density waves (PDWs), these states are posited to exist in a variety of systems, including high-temperature cuprate superconductors (for a review, see ref. 5 and references therein).\n\nWhile PDWs have been subject to much theoretical6,7,8,9,10,11,12,13,14,15,16,17,18,19 and numerical20,21,22,23,24,25,26 interest, a clear-cut analytically solvable model describing their origin from microscopic ingredients is lacking. From the experimental point of view, the interest for modulated pairing phases has been triggered by increasing experimental evidence for short-ranged PDW order in the underdoped region of the phase diagram of cuprates26,27,28,29,30,31,32,33,34,35,36,37,38. In particular,32 reported the first clear observation via scanning tunneling spectroscopy of a vortex-induced PDW in Bi2Sr2CaCu2O8 at low temperature. More recent STM experiments provide further evidence in favor of a short-range PDW coexisting with the d-wave superconductivity in the SC phase and evolving into a PDW state in the pseudogap region26,38. This phase is characterized by a gap at finite temperatures but lacks long-range order, and can be characterized as a \u201cfluctuating pair density wave\u201d, locally pinned by disorder. Such a state also provides an explanation for many other experimental signatures of the cuprates, including the existence of vestigial charge density wave order arising from partial melting of a PDW5,15,39. However, there is currently no microscopic model supporting this picture. Hence it is urgent to seek a unified framework that subsumes both fluctuating and long-range ordered PDW phases under a single paradigm by providing a concrete description of their origin.\n\nIn this work, we show that a Fermi liquid subjected to a finite anisotropic interaction is unstable toward a modulated SC phase in the strong coupling limit. Whether this phase is a \u2018fluctuating\u2019 PDW (FPDW) or long-range order PDW is determined by temperature as well as the coupling strength defined by the ratio \u03b1\u2009=\u2009EB/EF, with EF the Fermi energy and EB the bound state energy for pair formation.\n\nOur strategy is to solve the self-consistent gap equation for the homogeneous d-wave superconductor and analyze the momentum dependence of the SC fluctuations. The expansion of the static pair propagator Lq in powers of momentum transfer q, can reveal, in fact, critical fluctuations of Cooper pairs with finite center-of-mass momentum, that makes the homogeneous solution unstable toward a modulated SC phase. Since we study the action only to second order in the pair field we cannot distinguish between an instability to a FF or LO state. We observe the emergence of a modulated SC state already at intermediate coupling \u03b1\u2009~\u20090.7. The appearance of such a state is linked to the existence of fluctuating terms that lower the momentum rigidity of the Cooper pairs. These terms directly follow from the anisotropy of the pairing interaction that affects the momentum dependence of the pairing susceptibility already in the normal phase.\n\nOur results are summarized in the phase diagram, Fig.\u00a01. Ti is the instability temperature of the homogeneous d-wave state obtained within the mean- field approximation. The analysis of fluctuations allows us to define two different regimes. At weak coupling, \u03b1\u2009\u226a\u20091, the uniform d-wave paired state is the ground state; at larger \u03b1 (strong coupling), SC fluctuations at finite momentum lead to two modulated pairing phases\u2014 the T\u2009=\u20090 PDW ground state and a higher temperature FPDW phase that condenses into a PDW ordered phase below a coherence temperature (Tc). The strong and weak coupling regions are separated by the line T\u2009=\u2009T*. This is the temperature at which the finite momentum fluctuations around the homogeneous solution become critical. As expected in the BCS limit, the instability temperature Ti and the coherence temperature Tc coincide at weak coupling. In the strong coupling regime, we anticipate that Ti and Tc decouple since Cooper pairs are formed but with no long range coherence. In this work, we do not perform here any calculation of the coherence temperature Tc inside the modulated phase. However, in analogy with results obtained for homogeneous s-wave superconductors in the strong coupling limit40, we expect that Tc\u2009<\u2009Ti for \u03b1\u2009>\u20091 as well. The FPDW is found for temperature Tc\u2009<\u2009T\u2009<\u2009Ti and it is characterized by pairs with finite momentum with no coherence. At T\u2009=\u20090, the ground state can be either the uniform d-wave solution or the long-range PDW depending on the value of \u03b1. Hence our model captures two key experimentally postulated modulated Cooper phases \u2014a FPDW and a long-range PDW\u2014in a single unified scheme.\n\nThe instability temperature for the d-wave superconductor, Ti, defines the transition from a Fermi liquid (light blue) to the SC state. At weak coupling the pairing state is a homogeneous d-wave superconductor (gold). Increasing \u03b1 the system develops critical fluctuations at finite momentum and the d-wave SC state becomes unstable toward a non-homogeneous SC state (pink and purple regions). T* is the temperature at which the momentum rigidity parameter c2 vanishes. The fluctuating PDW (pink) condenses below a coherence temperature Tc into a long-range ordered state that can be an homogeneous d-wave SC state (gold) or a PDW (purple) depending on the coupling strength, schematically represented by a solid line. Tc coincides with Ti at weak coupling while at strong coupling it is expected that Tc\u2009<\u2009Ti40. Note that the actual instability temperature of the FPDW, \\({\\bar{T}}_{i}\\), is somewhat higher than Ti (see Supplementary Note\u00a04). Temperatures are renormalized by the energy range of the pairing, \u039b that is the largest energy scale of our model.\n\nThe mechanism we present in this paper predicts spatially modulated pairing phases for \u03b1\u2009=\u2009EB/EF\u2009>\u20091, i.e., in strongly coupled electronic systems, with anisotropic interactions. Examples of low-density electronic materials include the Fe-based superconductor FeSe where quantum oscillations41 as well as transport and scanning tunneling spectroscopy42 show that both the electron and hole pockets are tiny with Fermi energies comparable or even smaller than the SC gap and for which we find several proposals of BCS-BEC cross-over physics in the literature43,44,45. Other \u201cmixed-band\u201d superconductors such as O vacancy- or Nb-doped SrTiO3 have one partially filled band with a large Fermi surface while the Fermi level intersects the other at or close to the band bottom46. Even if these materials typically have more than one band close to or crossing the Fermi level, the results from our minimal model may eventually provide a suitable starting-point for the analysis of possible instabilities toward modulated pairing states in dilute multiorbital superconductors. Our results may also be relevant to the recent observation of superconductivity in twisted-bilayer graphene47 where interactions can be large compared to the bandwidth leading to large inter-particle distances48 and hence possible strongly-coupled Cooper pairing.\n\nThe modulated phases we propose in this work, that include both the long-range ordered PDW as well as the FPDW at finite temperature, are distinct from earlier proposals in literature. Loder et al.10, considered similar models characterized by nearest neighbor attractive interaction with d-wave symmetry and found Cooper pairing with finite center-of-mass momentum above a critical interaction strength. In refs. 18, 19, a modulated superconducting state is found in models which have correlated pair-hopping interactions. Other models that admit modulated SC ground states were proposed in the context of cold atoms9 where local interactions were considered in systems with multiple bands. Those references focused on the analysis of the long-range ordered state (mainly at zero temperature) without exploring the FPDW phase. The key contribution of our work is it provides an analytically tractable model where both fluctuating and long-range ordered PDWs can be explained under a single unified framework.",
+            "section_image": [
+                "https:////media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41467-023-38956-x/MediaObjects/41467_2023_38956_Fig1_HTML.png"
+            ]
+        },
+        {
+            "section_name": "Results",
+            "section_text": "Let\u2019s consider a single band SC system. The kinetic part of the Hamiltonian reads H0\u2009=\u2009\u2211k\u03c3\u03bekck\u03c3ck\u03c3, where \u03bek\u2009=\u2009\u03f5k\u2009\u2212\u2009\u03bc,\u2009\u03bc is the chemical potential, \u03f5k\u2009=\u2009k2/2m the parabolic dispersion and we further assume 2m\u2009=\u20091. The pairing interaction is given by\n\ng is the constant SC coupling and \u03b8q is defined as\n\nwhere fk,q\u2009=\u2009(hk\u2212q/2\u2009+\u2009hk+q/2)/2 is a form factor. In this work hk can be any anisotropic form factor; we consider, e.g., \\({h}_{{{{{{{{\\bf{k}}}}}}}}}=({k}_{x}^{2}-{k}_{y}^{2})/\\Lambda\\) with d-wave form. The pairing energy scale is \u039b i.e., the high energy cut-off set by the inverse lattice spacing and much larger than EF. Our results do not depend qualitatively on the exact form of the anisotropy, provided it is strong enough, but they are distinct from the conventional s-wave case fk,q\u2009=\u20091. Note that the interaction Hamiltonian we choose above already assumes an attractive pairing interaction and does not begin from any repulsive Hubbard-type model. Nevertheless, the mechanism we present is \u2018microscopic\u2019 in the sense that the order parameter can be evaluated over the entire phase diagram in terms of the microscopic parameters such as Cooper binding energy and Fermi energy. Such a treatment is distinct from Ginzburg-Landau theory and consistent with terminology used in previous literature49,50.\n\nWe use the standard Hubbard-Stratonovich transformation to decouple the interaction term, Eq. (1) and to derive the effective action in term of the bosonic pairing field \u0394 (for a detailed derivation see Supplementary Note\u00a01).\n\nIn standard BCS superconductors, the mean-field value of the pairing field is defined by minimizing the action with respect to the homogeneous q\u2009=\u20090 value of \u0394 and then solving this equation together with the one for the chemical potential. To study fluctuations of the pairing field around the mean-field value, we analyze the gaussian action obtained by retaining up to the second order in the fluctuating field with arbitrary momentum q given by\n\nwhere \\({L}_{{{{{{{{\\bf{q}}}}}}}}}^{-1}\\) is the static pairing susceptibility. As discussed in51 and in the Supplementary Notes\u00a01\u20133 of this work, we need to consider in principle both the real and imaginary part of the fluctuating field. However, here we are interested in the analysis of the static limit of the fluctuation, for which real and imaginary part are decoupled. Hereafter we will analyze the gaussian fluctuation of the amplitude mode only to investigate the possible emergence of a spatially modulated pairing fluctuation out of a homogeneous d-wave SC state. The explicit form of the static pairing susceptibility for the amplitude mode is \\({L}_{{{{{{{{\\bf{q}}}}}}}}}^{-1}={g}^{-1}+{\\Pi }_{{{{{{{{\\bf{q}}}}}}}}}\\), where the particle-particle propagator reads\n\nwith \\({E}_{{{{{{{{\\bf{k}}}}}}}}}^{2}={\\xi }_{{{{{{{{\\bf{k}}}}}}}}}^{2}+{f}_{{{{{{{{\\bf{k}}}}}}}},0}^{2}{\\Delta }^{2}\\). Here T is the temperature and V the volume. Note that since 2m\u2009=\u20091, energies have dimensions of 2-D V\u22121, and \\({L}_{{{{{{{{\\bf{q}}}}}}}}}^{-1}\\) is therefore dimensionless.\n\nThe static susceptibility can be expanded in the hydrodynamic limit as\n\nThe instability temperature is defined as the highest temperature at which the susceptibility diverges, i.e., \\({c}_{0}={g}^{-1}+{\\Pi }_{0}{|}_{T={T}_{i}}=0\\), as we assume that the minimum of the action, Eq. (3), is associated with the homogeneous order parameter. The coefficient \\({c}_{2}=({\\partial }^{2}{L}_{{{{{{{{\\bf{q}}}}}}}}}^{-1}/\\partial {q}^{2}{|}_{q=0})/2\\) provides instead information about the momentum rigidity of the fluctuating Cooper pairs i.e., the energy needed to move the center-of-mass momentum of the Cooper pairs from zero to a finite value. A negative momentum rigidity, c2\u2009<\u20090, implies that finite momentum fluctuations can lower the energy of the system making the homogeneous SC solution unstable. This means that the highest temperature at which the pairing susceptibility, Eq. (5), diverges is actually associated to a critical mode with finite momentum.\n\nIn what follows we analyze the momentum-dependence of the static susceptibility, Eq. (5), looking for a sign change of the momentum rigidity parameter c2 and using it as a proxy to identify possible spatially modulated SC regions in the phase diagram. It is worth noticing that c2 is directly affected by the momentum properties of the pairing susceptibility i.e., the pairing symmetry. From Eq. (4), it is easy to verify that the anisotropy of the interactions affects the momentum dependence of the propagator not only in the SC phase via the symmetry of the SC order parameter, but also above the instability temperature Ti where \u0394\u2009=\u20090 due to the overall form factor \\({f}_{{{{{{{{\\bf{k}}}}}}}},{{{{{{{\\bf{q}}}}}}}}}^{2}\\) at the numerator. This reflects in a strong momentum dependence of the contributions to the rigidity parameter depending on the symmetry of the pairing interaction. We discuss below how this affects the development of critical finite-momentum fluctuations.\n\nThe mean-field analysis for the homogeneous d-wave superconductor is shown in Fig.\u00a02. In panels (a)\u2013(b) we report the self-consistent numerical mean-field solutions for the pairing function \u0394 and the chemical potential \u03bc as a function of temperature T for three representative cases of the pairing strength \u03b1\u2009=\u2009EB/EF\u2009=\u20090.5,\u20091.0,\u20092.0, where for simplicity the weak-coupling expression EB\u2009=\u2009\u039be\u22122/g is used at all \u03b1. In panels (c)\u2013(d) we show the same mean-field results at T\u2009=\u2009Ti and T\u2009=\u20090 as a function of \u03b1. The change of sign of the chemical potential with increasing coupling strength is well-known from the BCS-BEC crossover problem52,53,54,55,56. In the weak-coupling regime, the pairs are loosely bound and we recover the BCS expression \u03bc\u2009~\u2009EF. As the interaction increases, all fermions strongly bind in pairs and \u03bc becomes negative and proportional to\u2009\u2212\u2009EB. In both the weak and strong coupling limits, the curves are similar to those derived for s-wave superconductors in56, showing that the d-wave symmetry of the pairing interaction does not affect the mean-field results qualitatively.\n\na,b Self-consistent solutions of the pairing order parameter \u0394(T) and the chemical potential \u03bc(T) for three representative values of \u03b1. Temperatures are normalized to the instability temperature Ti defined as the temperature at which the static pairing susceptibility Lq=0 diverges, while \u0394 and \u03bc are scaled with \u039b. c Instability temperature Ti and chemical potential \u03bci\u2009\u2261\u2009\u03bc(T\u2009=\u2009Ti) as a function of \u03b1. d T\u2009=\u20090 solutions: \u03940\u2009\u2261\u2009\u0394(T\u2009=\u20090) and chemical potential \u03bc0\u2009\u2261\u2009\u03bc(T\u2009=\u20090) as a function of \u03b1. For comparison we show also the results of the isotropic s-wave case in dashed lines. Computations are performed using \u039b\u2009=\u200911,\u2009EF\u2009=\u20092.2 in units of 2m\u2009=\u20091.\n\nWe first study the SC fluctuations above the instability temperature by analyze the static pairing susceptibility in the hydrodynamic limit, Eq. (5). The mass term c0 is positive and vanishes as the temperature approaches the instability temperature as expected from a Ginzburg-Landau description of the transition.\n\nThe analysis of the momentum rigidity of the fluctuating pairs above Ti is shown in Fig.\u00a03. The weak coupling region is characterized by a standard regime of fluctuations with c2\u2009>\u20090. Here Cooper pairs with zero center-of-mass momentum are stable. Increasing \u03b1, the momentum rigidity for the d-wave pairing interaction (continuous line) monotonically decreases and becomes negative at intermediate coupling, \u03b1\u2009>\u20090.7, as shown in Fig.\u00a03(a). This means that finite momentum critical fluctuations grow, increasing the coupling strength up to a critical value of the interaction for which the homogeneous SC solution can become unstable toward a modulated phase. Notice that c2 becomes very small and eventually changes sign in the crossover between weak and strong coupling where also the chemical potential changes sign from positive to negative, see inset Fig.\u00a03(a). The result changes qualitatively for the isotropic s-wave interaction (dashed line) where the rigidity parameter decreases but remains positive even at strong coupling for the set of model parameter of our study (This result differs from the analysis of55, in which a sign change of the rigidity parameter is found for a SC system with s-wave pairing symmetry at strong coupling. In this case, however, the authors first perform a strong coupling expansion of the pairing susceptibility and only subsequently expand the approximated result in powers of q.).\n\na The momentum rigidity c2(\u03b1) for d-wave (solid line) and s-wave pairing interaction (dashed line). In the anisotropic d-wave case c2 becomes negative at intermediate coupling, \u03b1\u2009~\u20090.7 indicating that the homogeneous d-wave SC is unstable. Inset: c2(\u03bci), the sign change of the momentum rigidity occurs around the same range in which \u03bci turns from positive to negative values. The momentum rigidity for the isotropic s-wave case remains positive regardless the coupling strength. b cn(\u03b1) coefficients, n\u2009=\u20092,\u20094,\u20096, for the d-wave pairing. The positive value of c6 allows to recover the stability of the action. The computation of the higher order coefficients allows to define the finite momentum of the critical mode and the relative instability temperature. We use here the same set of parameters of Fig.\u00a02 and plot the results in dimensionless units i.e., cn\u2009\u2261\u2009cn\u039bn/2.\n\nTo characterize the modulated SC state and check its stability, we expand the static susceptibility to higher order in momentum\n\nWe report the coefficients of the momentum expansion at Ti in Fig.\u00a03(b). Results are shown as a function of \u03b1 for the coupling regime in which c2\u2009\u2272\u20090. We need to expand the susceptibility up n\u2009=\u20096 to find c6\u2009>\u20090, since for our set of model parameters c4\u2009<\u20090 as in the conventional BCS case.\n\nWe analyze the momentum dependence of the static susceptibility at Ti in Fig.\u00a04, where we show the expansion of Eq. (6) up to sixth order for different values of \u03b1. At the instability temperature, c0\u2009=\u20090 by definition and the minimum of the function is determined by the higher order coefficients. At weak coupling, where c2 is large and positive, the minimum of \\({L}_{{{{{{{{\\bf{q}}}}}}}}}^{-1}\\) is located at zero momentum. As the pairing interaction increases c2 becomes small and eventually changes sign at \u03b1\u2009~\u20090.7. Here, since c4\u2009<\u20090, the minimum shifts discontinuously to a finite momentum \\(\\bar{Q}\\), i.e., by increasing the interactions the modulated phase emerges at Ti via a first order transition from the homogeneous d-wave SC solution, in analogy with the results found at T\u2009=\u20090 in10,18. The non-zero value of \\(\\bar{Q}\\) at \u03b1\u2009~\u20090.7 signals the formation of the FPDW state with finite momentum pairing but no long range coherent order. Note that the finite order parameter jump \\(\\bar{Q}\\) is a non-universal quantity and depends on microscopic details of the chosen model, as is a feature of any generic first order transition. The momentum characterizing the modulated phase shifts toward larger values increasing the coupling parameters. In the strong coupling regime, \u03b1\u2009\u226b\u20091, the minimum occurs at \\(q/\\sqrt{\\Lambda }\\,\\gg \\,1\\), (not shown), for this range of the interaction the analysis of the momentum characterizing the modulated phase requires the implementation of a non perturbative approach.\n\nAt weak coupling, \u03b1\u2009=\u20090.22, we find the homogeneous d-wave SC. The momentum rigidity c2 is large and positive, and the minimum of the inverse of the susceptibility is at q\u2009=\u20090. At intermediate coupling, \u03b1\u2009~\u20090.7,\u2009c2 vanishes and the minimum of L\u22121 appears at a finite \\(\\bar{Q}\\) of order 1. Same set of parameters of Fig.\u00a02.\n\nTo further prove the stability and quantitatively characterize the modulated phases we expand the polynomial form, Eq. (6), around its minima \\(\\bar{Q}\\) so that we can define the susceptibility of the modulated SC phase\n\nHere \\(\\bar{{c}_{0}}\\) and \\(\\bar{{c}_{2}}\\) are the mass and the momentum rigidity parameter associated with the modulated SC phase. In the Supplementary Notes\u00a02, 3, 4, we show that \\(\\bar{{c}_{0}}=a(T-\\bar{{T}_{i}})\\quad \\,{{\\mbox{with}}}\\,\\quad \\bar{{T}_{i}}={T}_{i}+\\delta T\\quad \\,{{\\mbox{and}}}\\,,\\quad \\delta T\\, > \\,0\\), and that \\(\\bar{{c}_{2}}\\, > \\,0\\), thus demonstrating stability of the modulated phases.\n\nThe sign change of the momentum rigidity parameter discussed at T\u2009=\u2009Ti can be traced down in temperature (dashed line in Fig.\u00a01). At T\u2009=\u20090 the homogeneous d-wave state becomes unstable, now toward a PDW, for a slightly higher value of the coupling where the chemical potential \u03bc also changes sign (see Fig.\u00a02d). The stability of the PDW phase requires expanding up to the sixth-order, c4\u2009<\u20090,\u2009c6\u2009>\u20090 as we show in the Supplementary Notes\u00a02\u20134.\n\nThe results of our numerical study are summarized in the phase diagram of Fig.\u00a01. We characterized the SC region below Ti by the sign of the momentum rigidity parameter (dashed line). The sign change of the c2 coefficient at strong coupling signals the presence of critical SC fluctuations at finite momentum that make the d-wave homogeneous state unstable toward either an FPDW or PDW. The pink and purple regions indicate the FPDW and the long-range ordered PDW state at high and low temperatures respectively. We leave for future work the explicit calculation of the coherence temperature below which the FPDW condenses. The color gradient indicates approximately the expected Tc(\u03b1) behavior based on previous analysis of the coherence energy scale for the homogeneous s-wave SC state40.\n\nAnalytical calculations of the momentum rigidity can be easily performed within a simplified model in which the chemical potential is used as parameter. Both at Ti and T\u2009=\u20090, we find qualitatively the same results discussed within the numerical study. In particular, within the analytical calculations sketched in the Supplementary Note\u00a05, the momentum rigidity parameter follows the chemical potential behavior, i.e., c2(\u03bc)\u2009<\u20090 for \u03bc\u2009<\u20090. This relation is qualitatively in agreement with the numerical study performed computing self-consistently \u03bc(\u03b1), as one can see from the inset of Fig.\u00a03a.\n\nThe strategy implemented here to investigate how finite momentum fluctuations become critical at strong coupling is based on the analysis of the momentum rigidity parameter. This method presents two main advantages with respect to other theoretical approaches. On the one hand, as already discussed, it allows us to explore the finite temperature regime and analyze the FPDW state. On the other, it provides a physical understanding of the importance of the anisotropy of the pairing interactions in the development of the modulated phase. As one can see in Eq. (4), the symmetry of the pairing interactions dramatically affects the momentum dependence of the propagator not only in the SC phase, but also in the normal one when \u0394\u2009=\u20090 due to the overall form factor \\({f}_{{{{{{{{\\bf{k}}}}}}}},{{{{{{{\\bf{q}}}}}}}}}^{2}\\). This is reflected in a strong momentum dependence of the contribution to the momentum rigidity parameter. In fact, after performing analytically the Matsubara summation, the computation of the c2 coefficient reduces to an integral over the Brillouin zone \\({c}_{2}=\\frac{1}{V}{\\sum }_{{{{{{{{\\bf{k}}}}}}}}}{I}_{2}({{{{{{{\\bf{k}}}}}}}})\\). The expression for I2 is given in the Supplementary Note\u00a03, but here we show here in Fig.\u00a05 2D maps of I2(k) for both s-wave and d-wave at T\u2009=\u20090 and T\u2009=\u2009Ti. In the isotropic s-wave case, the contributions to the momentum rigidity coming from different momenta, I2(k), are positive at any (kx,\u2009ky). Whereas, in the d-wave case the contributions to the momentum rigidity coming from the nodal regions are negative and dominate the overall sign of the c2 coefficient.\n\nI2(kx,\u2009ky) color maps at T\u2009=\u20090 and T\u2009=\u2009Ti and \u03b1\u2009=\u20092.0 for the d-wave ((a, b)) and s-wave ((c, d)) case. The anisotropy of the interactions affects the momentum dependence of the propagator both in the SC and normal phase. This reflects in a strong momentum dependence of the contribution to the momentum rigidity parameter. For the d-wave case negative contributions to the rigidity are found both at T\u2009=\u20090 and T\u2009=\u2009Ti from k-points close to the nodal region. We use the same set of parameters of Fig.\u00a02 and plot the result in dimensionless units for momenta \\(|{k}_{i}|/\\sqrt{\\Lambda }\\, < \\,\\pi\\), with i\u2009=\u2009x,\u2009y.",
+            "section_image": [
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+            ]
+        },
+        {
+            "section_name": "Discussion",
+            "section_text": "A consistent explanation for the occurrence of both static and fluctuating Cooper pairs with finite momentum in the phase diagram of materials such as cuprates has been a long-standing problem. This is primarily because an identification of the microscopic ingredients driving such exotic pairing has been elusive. The results in this paper point toward a simple and unified framework that naturally promotes both fluctuating and static pair-density wave (FPDW and PDW) phases over their zero momentum counterparts. Figure\u00a01 summarizes the main conclusions of our work, supported not only by numerical evaluations but also transparent analytical estimates (see Supplementary Note\u00a05). The two key ingredients resulting in a high temperature FPDW and low temperature PDW phases are (a) anisotropic (e.g., d-wave) pair interactions and (b) intermediate to strong coupling ratio of \\(\\alpha=\\frac{{E}_{B}}{{E}_{F}}\\), where EB is the pair binding energy for two electrons on the Fermi surface in the presence of an attractive interaction, and EF is the Fermi energy. For the specific set of parameters presented here, below a critical value of \u03b1\u2009~\u20090.7, only uniform zero momentum d-wave pairing is favored. In the approximate range of 0.7\u2009\u2272\u2009\u03b1\u2009\u2272\u20091.5, the FPDW phase, characterized by a negative momentum rigidity c2 and positive c6 (see Fig.\u00a03), is stable over a range of temperatures below the instability temperature Ti. However, in this range of \u03b1 a uniform d-wave pair is still favored at zero temperature. For \u03b1\u2009\u2273\u20091.5, the PDW phase is more stable than a uniform solution at T\u2009=\u20090 and a finite momentum pair exists for all temperatures below Ti. The modulation wave vector Q of the paired phases is determined by the ratio \u03b1 and acquires a jump with increasing \u03b1 as in a first order transition (see Fig.\u00a04).\n\nIt is important to note that while in our paper the critical value of \u03b1 for which c2 changes sign appears to be of order unity, which is nominally outside the range of standard BCS weak-coupling theory, we emphasize that this value is a finite non-zero number that does not take a universal value. Depending on parameters, we can easily produce critical values of \u03b1 of order 0.3, which might be considered weak-coupling (see Supplementary Fig.\u00a02). Hence, there appears to be no physical reason that necessarily constrains FPDW and PDW phases to be in the strong coupling regime of \u03b1\u2009~\u20091.\n\nFurthermore, we note the key role of the existence of a lattice momentum cut-off. If the cut-off were taken to infinity, the modulated solution vanishes as is outlined in the Supplementary Note\u00a05. This is further highlighted in the recent exact two-body and variational wave function solution57 where it was shown that in the absence of a cut-off in the interaction, the modulated solution on a lattice loses to the homegeneous solution.\n\nRecently refs. 58, 59 discussed the possible existence of a diagonal pair density wave order in the cuprates. To obtain a diagonal pair density wave order in our analysis, the interaction must contain a dominant B2g pair-fluctuation interaction. This would imply that the form factor of the kind \\(\\sin {k}_{x}\\sin {k}_{y}\\) would be dominant in the fluctuations instead of the \\(\\cos {k}_{x}-\\cos {k}_{y}\\) form factor in Eq. (1). With this form factor, our result continues to hold but with the dominant instability now occurring along the diagonals. Note, however, that our theory does not justify which of the two (B1g or B2g) symmetry channels are the dominant fluctuations. In either of the two cases, one can obtain the finite momentum pairing instability without requiring a strong coupling treatment of the theory.\n\nThe FPDW and PDW phases are stabilized by contributions to the fluctuation free energy arising from momenta close to the nodal regions in the Brillouin zone. These contributions, which also should drive strong anisotropy in the phase stiffness near Ti, are suppressed (enhanced) at weak (strong) coupling thus leading to a modulated phase above a critical pairing strength. This simplified picture is confirmed from our numerical calculations (Fig.\u00a05). Finally, while our work primarily focuses on the instability temperature Ti in the strong coupling limit, the behavior of the condensation temperature Tc and the fluctuations around the PDW ground state in this setting are open problems that will require further investigations. Our work does not consider the competing effects of a nematic superconducting phase that has been phenomenologically found to suppress the PDW at T\u2009>\u20090 in 2D7,11. In addition, even if allowed by our model, we have not addressed the possible coexistence at low T of a PDW and a homogeneous d-wave superconductor, as suggested by cuprate experiments5,26. Our results as such set the stage for future microscopic descriptions of modulated superconductivity in strongly coupled materials.\n\nNote added: During review of the manuscript, another work based on repulsive interactions yielding PDWs became available60.",
+            "section_image": []
+        },
+        {
+            "section_name": "Methods",
+            "section_text": "We used standard many-body field theoretic methods for all computations. Details of these methods are included in the Supplementary Information provided.",
+            "section_image": []
+        },
+        {
+            "section_name": "Data availability",
+            "section_text": "All data generated or analyzed during this study are included in this published paper (and its Supplementary Information files)",
+            "section_image": []
+        },
+        {
+            "section_name": "Code availability",
+            "section_text": "All codes used to generate or analyze the results of this study are available from the corresponding author (C.S.) on reasonable request.",
+            "section_image": []
+        },
+        {
+            "section_name": "References",
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+        },
+        {
+            "section_name": "Acknowledgements",
+            "section_text": "We thank P. Abbamonte, B.M. Andersen, S. Caprara, A. Chubukov, E. Fradkin, S. A. Kivelson, M. Granath and A. Toschi for useful discussions and suggestions. C.S., L.F., and P.J.H. are supported by the DOE grant number DE-FG02-05ER46236. L.F. acknowledges support by the European Union\u2019s Horizon 2020 research and innovation programme through the Marie Sk\u0142odowska-Curie grant SuperCoop (Grant No 838526).",
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+        },
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+            "section_name": "Author information",
+            "section_text": "Department of Physics, University of Florida, Gainesville, FL, USA\n\nChandan Setty,\u00a0Laura Fanfarillo\u00a0&\u00a0P. J. Hirschfeld\n\nDepartment of Physics and Astronomy, Rice Center for Quantum Materials, Rice University, Houston, TX, 77005, USA\n\nChandan Setty\n\nScuola Internazionale Superiore di Studi Avanzati (SISSA), Via Bonomea 265, 34136, Trieste, Italy\n\nLaura Fanfarillo\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nC.S. and L.F. contributed equally to this work. C.S., L.F., and P.J.H discussed and contributed to the project design. C.S. performed the analytical calculation, L.F. performed the numerical analysis. C.S., L.F., and P.J.H. contributed to the data analysis, to the interpretation of the theoretical results, and to the writing of the text.\n\nCorrespondence to\n                Chandan Setty, Laura Fanfarillo or P. J. Hirschfeld.",
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+            "section_text": "Setty, C., Fanfarillo, L. & Hirschfeld, P.J. Mechanism for fluctuating pair density wave.\n                    Nat Commun 14, 3181 (2023). https://doi.org/10.1038/s41467-023-38956-x\n\nDownload citation\n\nReceived: 04 November 2021\n\nAccepted: 16 May 2023\n\nPublished: 01 June 2023\n\nVersion of record: 01 June 2023\n\nDOI: https://doi.org/10.1038/s41467-023-38956-x\n\nAnyone you share the following link with will be able to read this content:\n\nSorry, a shareable link is not currently available for this article.\n\n\n\n\n                            Provided by the Springer Nature SharedIt content-sharing initiative\n                        ",
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+            ]
+        },
+        {
+            "section_name": "This article is cited by",
+            "section_text": "npj Quantum Materials (2025)\n\nCommunications Physics (2025)\n\nnpj Quantum Materials (2025)",
+            "section_image": []
+        }
+    ]
+}

13b4ad41a4b6d76a4f1b69d9923f0eec1605b4ae5f7cb340e3f659fe15509df0/metadata.json

@@ -0,0 +1,145 @@
+{
+    "title": "Differential analysis of RNA structure probing experiments at nucleotide resolution: uncovering regulatory functions of RNA structure",
+    "pre_title": "Differential Analysis of RNA Structure Probing Experiments at Nucleotide Resolution: Uncovering Regulatory Functions of RNA Structure",
+    "journal": "Nature Communications",
+    "published": "22 July 2022",
+    "supplementary_0": [
+        {
+            "label": "Supplementary Information",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-022-31875-3/MediaObjects/41467_2022_31875_MOESM1_ESM.pdf"
+        },
+        {
+            "label": "Peer Review File",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-022-31875-3/MediaObjects/41467_2022_31875_MOESM2_ESM.pdf"
+        },
+        {
+            "label": "Reporting Summary",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-022-31875-3/MediaObjects/41467_2022_31875_MOESM3_ESM.pdf"
+        }
+    ],
+    "supplementary_1": NaN,
+    "supplementary_2": NaN,
+    "source_data": [
+        "https://doi.org/10.5281/zenodo.2536501",
+        "https://github.com/yub18/DiffScan",
+        "https://www.ncbi.nlm.nih.gov/geo/query/acc.cgi?acc=GSE117840"
+    ],
+    "code": [
+        "https://github.com/yub18/DiffScan"
+    ],
+    "subject": [
+        "Statistical methods",
+        "Transcriptomics"
+    ],
+    "license": "http://creativecommons.org/licenses/by/4.0/",
+    "preprint_pdf": "https://www.researchsquare.com/article/rs-800283/v1.pdf?c=1658574543000",
+    "research_square_link": "https://www.researchsquare.com//article/rs-800283/v1",
+    "nature_pdf": "https://www.nature.com/articles/s41467-022-31875-3.pdf",
+    "preprint_posted": "25 Aug, 2021",
+    "research_square_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "RNAs perform their function by forming specific structures, which can change across cellular conditions. Structure probing experiments combined with next generation sequencing technology have enabled transcriptome-wide analysis of RNA secondary structure in various cellular conditions. Differential analysis of structure probing data in different conditions can reveal the RNA structurally variable regions (SVRs), which is important for understanding RNA functions. Here, we propose DiffScan, a computational framework for normalization and differential analysis of structure probing data in high resolution. DiffScan preprocesses structure probing datasets to remove systematic bias, and then scans the transcripts to identify SVRs and adaptively determines their lengths and locations. The proposed approach is compatible with most structure probing platforms (e.g., icSHAPE, DMS-seq). When evaluated with simulated and benchmark datasets, DiffScan identifies structurally variable regions at nucleotide resolution, with substantial improvement in accuracy compared with existing SVR detection methods. Moreover, the improvement is robust when tested in multiple structure probing platforms. Application of DiffScan in a dataset of multi-subcellular RNA structurome identified multiple regions that form different structures in nucleus and cytoplasm, linking RNA structural variation to regulation of mRNAs encoding mitochondria-associated proteins. This work provides an effective tool for differential analysis of RNA secondary structure, reinforcing the power of structure probing experiments in deciphering the dynamic RNA structurome.Computational BiologyBioinformaticsBiotechnology and BioengineeringEpigenetics & GenomicsRNA structurestructure probing experimentsdifferential analysisRNA secondary structure",
+            "section_image": []
+        },
+        {
+            "section_name": "Additional Declarations",
+            "section_text": "There is NO Competing Interest.",
+            "section_image": []
+        },
+        {
+            "section_name": "Supplementary Files",
+            "section_text": "SupplementaryInformation.pdfSupplementaryInformation",
+            "section_image": []
+        }
+    ],
+    "nature_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "RNAs perform their function by forming specific structures, which can change across cellular conditions. Structure probing experiments combined with next generation sequencing technology have enabled transcriptome-wide analysis of RNA secondary structure in various cellular conditions. Differential analysis of structure probing data in different conditions can reveal the RNA structurally variable regions (SVRs), which is important for understanding RNA functions. Here, we propose DiffScan, a computational framework for normalization and differential analysis of structure probing data in high resolution. DiffScan preprocesses structure probing datasets to remove systematic bias, and then scans the transcripts to identify SVRs and adaptively determines their lengths and locations. The proposed approach is compatible with most structure probing platforms (e.g., icSHAPE, DMS-seq). When evaluated with simulated and benchmark datasets, DiffScan identifies structurally variable regions at nucleotide resolution, with substantial improvement in accuracy compared with existing SVR detection methods. Moreover, the improvement is robust when tested in multiple structure probing platforms. Application of DiffScan in a dataset of multi-subcellular RNA structurome and a subsequent motif enrichment analysis suggest potential links of RNA structural variation and mRNA abundance, possibly mediated by RNA binding proteins such as the serine/arginine rich splicing factors. This work provides an effective tool for differential analysis of RNA secondary structure, reinforcing the power of structure probing experiments in deciphering the dynamic RNA structurome.",
+            "section_image": []
+        },
+        {
+            "section_name": "Introduction",
+            "section_text": "RNA molecules play important roles in myriad cellular processes by forming specific structures1,2,3. Deciphering RNA structure is informative for understanding RNA functions. In recent years, diverse structure probing (SP) methods have been developed to study RNA secondary structure in various cellular contexts, which utilize chemicals that react differentially to nucleotides according to their local stereochemistry, pairing status, solution environment, etc4,5. Coupled with next generation sequencing technologies, SP experiments can be performed at high throughput, providing a transcriptome level view of RNA secondary structure4,5,6, i.e., RNA structurome. There are various mature high-throughput SP platforms, such as SHAPE-Seq7,8, DMS-Seq9, and icSHAPE10. These platforms offer flexible options for tackling different biological problems, and have achieved success in uncovering pervasive links between RNA structure and RNA function11.\n\nStudies have examined how the structures of particular RNA molecules change across multiple cellular conditions, revealing explicit connections between RNA structure and RNA function12. For example, the ubiquitous yybP-ykoY motif has been shown to adopt distinct structures in response to manganese ions, thus exerting regulatory consequences on protein translation in both Escherichia coli and Bacillus subtilis13. RNA structural variations have also been reported to regulate the binding of trans-acting factors and RNA stability in multiple organisms, including human, yeast, and zebrafish14,15,16,17,18.\n\nTo explore the SP experiments to uncover dynamic RNA structures, quantitative tools that contrast SP experiments to identify structurally variable regions (SVRs) are in great demand. Several methods have been proposed to identify SVRs. PARCEL19 and RASA20 directly model and compare raw read counts at each nucleotide position, and then identify regions enriched for position-level signals. However, their models are tailored for specific experimental protocols, and it is not straightforward to extend them to accommodate more emerging SP techniques. ClassSNitch21 uses machine learning methods to predict SVRs from pre-defined regions, such as segments of RNA transcripts harboring single-nucleotide mutations. It requires manually labeled SHAPE data for model training, which is based on visual judgements from experienced RNA scientists. While this method can obtain high prediction accuracy, the requirement of manual curation makes it prohibitive to generalize the strategy to more SP platforms. StrucDiff22, deltaSHAPE23, and dStruct24 take reactivities as input, which are estimated from raw read counts to summarize the pairing status at each nucleotide position. They search for SVRs with pre-specified search lengths to aggregate differential signals22,23,24. However, the choice of search length is based on prior domain knowledge, which can be subjective. Unlike the above methods which directly detect SVRs, diffBUM-HMM25 infers structural variation at position level by calculating a posterior probability of differential modification for each nucleotide position.\n\nPrevious methods have addressed the many challenges of differential analysis of SP data to varying degrees. Continued development of methods to tackle the following challenges will advance insights from SP data. First, SVRs manifest great variation in length, ranging from a few to several dozens of nucleotide positions19,24,26. As a result, searching with fixed search length can lead to insufficient detection power and inaccurate boundary mapping, when the prespecified search length deviates greatly from the true length. Second, SP platforms differ in utilization of additives, specific experimental protocols, and preprocessing pipelines, yielding distinct data types and distributions in output4,5,27. As a result, it is desirable but usually not easy to extend methods developed for one platform to another. Third, SP data can be confounded by systematic bias4,5, which should be removed from reactivities of the two compared conditions prior to differential analysis28. However, the performance of existing normalization techniques with multiple SP platforms has not been evaluated in benchmarking comparisons. Finally, rigorous error control is also highly impactful on the accuracy and biological relevance of output from SVR detection24, especially for transcriptome-scale analyses.\n\nWe advance the state of the field by developing DiffScan, a computational framework for differential analysis of SP data at nucleotide resolution. DiffScan normalizes SP reactivities via a built-in Normalization module, which is compatible with various platforms, and then looks for SVRs via a Scan module. The Scan module locates SVRs at nucleotide resolution, and rigorously controls family-wise error rate. We demonstrate with large-scale simulated datasets and benchmark datasets that DiffScan can achieves superior or comparable power and accuracy in SVR detection across various platforms, compared to state-of-art methods. We apply DiffScan to a recent icSHAPE dataset of RNA structurome in multiple subcellular compartments (e.g., nucleoplasm and cytoplasm), and reveal the potential roles of SVRs in regulating mRNA abundance, possibly mediated by RNA binding proteins such as the serine/arginine rich splicing factors.",
+            "section_image": []
+        },
+        {
+            "section_name": "Results",
+            "section_text": "DiffScan comprises a Normalization module and a Scan module (Fig.\u00a01a). SP reactivities of RNA transcripts for two conditions are taken as input, and the reactivities are normalized relative to one another in the Normalization module (Fig.\u00a01b) to correct for systematic bias. The corrected reactivities are comparable as far as possible across different cellular conditions. In the Scan module (Fig.\u00a01c), structural variations are initially evaluated at each nucleotide position, and then the algorithm scans through the transcripts with variable search lengths to identify SVRs. Finally, DiffScan returns a list of significant SVRs, with their transcript ID, nucleotide positions, and p values.\n\na Taking raw reactivities as input, DiffScan first normalizes them relative to one another in the Normalization module (b) to correct for systematic bias, and then identifies SVRs in the Scan module (c). b The Normalization module transforms raw reactivities into normalized reactivities to remove systematic bias. The raw reactivities are from the icSHAPE SRP vivo dataset which has no SVRs. The normalized reactivities are comparable as far as possible across different cellular conditions. c Taking normalized reactivities as input, the Scan module first calculates the significance of any differential signals for each nucleotide position with two-sided Wilcoxon test, and then concatenates positional p values into a regional signal via scan statistic. The significance of the scan statistic for each enumerated region is evaluated by Monto Carlo sampling, and those regions crossing a specified significance threshold are reported as SVRs.\n\nIt is known that the reactivities of particular RNA nucleotide positions can be affected by a variety of confounding factors in SP experiments28, including transcript abundance, sequencing depth, and signal-to-noise ratio (see Methods). Owing to discrepancies in these factors, the SP reactivities obtained from two conditions lacking substantial biological differences may show substantial differences29 (see Supplementary Fig.\u00a01 for example). The unwanted variations will then persist throughout the routine preprocessing steps. Thus, in practice careful adjustment between and within conditions is essential when comparing SP data obtained from samples in distinct conditions. Related challenges have been widely reported for other high-throughput sequencing experiments, such as ChIP-Seq30 and ATAC-Seq31. Inspired by normalization approaches for other high-throughput sequencing based methods, we propose the following normalization procedure for differential analysis of SP data.\n\nTo account for a potentially wide range of reactivity levels, we first rescale the reactivity values into the interval [0,1] after a 90% winsorization (see Methods). Next, the reactivities of within-condition replicates, if available, are processed by quantile normalization32,33, so that the quantiles of each replicate are matched within conditions. We subsequently normalize between-condition reactivities using an approach similar to MAnorm30. Briefly, a structurally invariant set of nucleotide positions S is determined as a \u201cpivot\u201d for normalization, and the reactivities are transformed so that the transformed reactivities are at the same level for the pivot set between conditions. The basic idea is to learn transformation rules from S and then extrapolate the learned transformation to all nucleotide positions of the transcripts. In particular, the transformation is learned from training a linear model from S, which takes reactivities in one condition as response and reactivities in the other condition as predictor. The adjusted reactivities from the Normalization module are then ready for differential analysis in the Scan module (Supplementary Fig.\u00a02). We provide theoretical justifications and empirical validations of the Normalization module in Supplementary Note\u00a0I and II, to show that the normalization explicitly corrects for between-condition differences in sequencing depth and signal-to-noise ratio. We show that when the pivot set is mis-specified, or the between-condition differences\u00a0in\u00a0sequencing depth and signal-to-noise ratio change from nucleotide to nucleotide, the performance of the proposed normalization approach is robust (Supplementary Note\u00a0III). We also demonstrate the superiority of the Normalization module over existing normalization methods, such as 2%\u20138% normalization34, with benchmark datasets (Supplementary Note\u00a0IV).\n\nFormally, \u201cscan statistics\u201d refer to statistical methods for cluster detection in time and space35,36. These methods can accurately map regional signals and control family-wise error rates during multiple testing of interrelated hypotheses. Scan statistics have been successfully applied to many areas including molecular biology37 and human genetics38. The Scan module of DiffScan was developed with the goal to identify SVRs at nucleotide resolution in a data-adaptive fashion. In brief, the Scan module slides through the transcripts to enumerate overlapping regions of different lengths, identifies regions with maximal differential signals, and evaluates their statistical significance. In detail, we first quantify positional differential signals by calculating a p value for each nucleotide position by Wilcoxon test, which contrasts reactivities between conditions in a small window surrounding the nucleotide position. Note that the Normalization module does not enforce any specific distributions of the normalized reactivities (Supplementary Fig.\u00a03), and the nonparametric test we use guarantees robust evaluation of differential signals for various SP platforms.\n\nSecond, for each region R, we propose the following scan statistic to quantify differential signals for regions,\n\nThe sum in the numerator aggregates positional differential signals, while the denominator penalizes the extension of a candidate region. A discussion of the Q function is provided in Supplementary Note\u00a0V. Intuitively, regions that are enriched with structurally variable nucleotides will obtain high Q(R) scores.\n\nWe search in the transcripts with sliding windows of different lengths, and calculate the scan statistic for each candidate region (Fig.\u00a01c). A Monte Carlo approach is then implemented to evaluate the statistical significance of the scan statistics, which addresses the multiple testing problem for the overlapping regions by controlling the family-wise error rate (see Supplementary Methods). Accordingly, we can identify SVRs with accurately mapped boundaries based on the significance of the scan statistics (Fig.\u00a01c).\n\nWe simulated RNA secondary structures in two conditions, and generated SP reactivities based on the simulated secondary structures in each condition using three types of empirical models representing different SP platforms, including two types of SHAPE reactivity27,39,40 and one type of icSHAPE reactivity17 (see Supplementary Methods). Biologically, it is often the case that a particular RNA molecule will occur as a mixture of structural conformations in a given cellular condition41,42, so SVRs detected between conditions represent altered proportions comprising these mixtures of structural conformations. Thus, the between-condition differences in RNA secondary structures can be very subtle in reality. To mimic the complexity of the landscape of RNA secondary structures, we sampled multiple structural conformations from an ensemble of energy-function-based predictions, and mixed them in varying proportions in the simulated datasets (see Methods). The reactivities were thereafter simulated based on the pairing status of each nucleotide.\n\nIn detail, we sampled 10 conformations for each of the 1000 RNA transcripts we randomly selected from transcripts in human embryonic kidney (HEK293) cells17. The lengths of the RNA transcripts ranged between 60 nt and 1,972 nt, and the simulated SVRs covered 1.6% to 67.3% of the nucleotide positions of the RNA transcripts (Supplementary Fig.\u00a04), with lengths between 1 nt and 81 nt. These data included a total of 38,317 simulated SVRs, with 12,201 being single nucleotide structural variations, 13,048 having lengths between 2 nt and 5 nt, and 13,068 SVRs with lengths greater than 5 nt (see Supplementary Fig.\u00a04 for further details). Note that these simulated data echo the real world knowledge that the lengths of SVRs vary extensively13,19,24,26,43. We varied the strength of differential signals of simulated SVRs between \u201chigh\u201d, \u201cmedium\u201d, and \u201clow\u201d. Combining different levels of signal strength and the three types of generative models of reactivity, we have in total 9 simulation settings.\n\nWe compared the performance of DiffScan with two other SVR detection methods, deltaSHAPE and dStruct. Note that DiffScan adaptively determines the lengths of SVRs from data, whereas deltaSHAPE uses a fixed search length and dStruct uses a prespecified minimum search length. We set the search length to 5 nt for deltaSHAPE (the default setting suggested by the authors23) and to three different values (1 nt, 5 nt, and 11 nt) for dStruct. The following discussions are based on dStruct with minimum search length of 5 nt. The results corresponding to minimum search length of 1 nt and 11 nt are consistent and provided in Supplementary Figs.\u00a05 and 6.\n\nFirst, to evaluate the accuracy of SVR detection at nucleotide resolution, we calculated the Jaccard index between the top predicted nucleotide positions (at varying cutoffs) and the simulated SVRs. DiffScan consistently has the largest Jaccard index in all 9 settings (Fig.\u00a02a, Supplementary Figs.\u00a07a and 8a). Note that the output of deltaSHAPE is a fixed set of regions that the threshold is internally decided, and it is represented as a single dot rather than a curve. Although dStruct also sensitively identifies SVRs, it tends to output long, contiguous regions, which include a substantial proportion of nucleotide positions without structural variations, which explains the decrease of its performance with stronger signals (Supplementary Tables\u00a01\u20133). In contrast, DiffScan locates SVRs by optimizing its scan statistic, thereby effectively distinguishes SVRs amongst overlapping regions of different lengths, leading to a finer level of granularity relative to deltaSHAPE and dStruct. Moreover, the superiority of DiffScan is consistent across different reactivity models and signal levels.\n\nDefault search length of 5 nt is used for deltaSHAPE and minimum search length of 5 nt is used for dStruct. The empirical model in S\u00fck\u00f6sd et al.40 was used to simulate reactivities. a Jaccard index between the top predicted nucleotides and the true SVRs at varying cutoffs. b Average distance between the top predicted nucleotides and the true SVRs at varying cutoffs. c Precision-Recall curves. Columns: three levels of strength of differential signals at simulated SVRs. Note deltaSHAPE does not allow external thresholding, and therefore it is represented as dots instead of curves.\n\nNext we evaluated the accuracy of SVR boundary mapping by the average distance from the predicted SVRs to the true SVRs. In the ideal case, if a predicted SVR sits within a true SVR, the distance for each nucleotide in the predicted SVR is zero. Oppositely, if a predicted SVR is off-target, i.e., containing many nucleotides that are neither in or close to the true SVRs, the distances will be large. The average distance provides complementary information of Jaccard index, as predicted SVRs that are far away from any true SVRs will have a greater distance than those close to a true SVR. An illustrative example for the average distance is provided in Supplementary Note\u00a0VI and Supplementary Fig.\u00a09. DiffScan consistently has the minimum average distance in all 9 settings (Fig.\u00a02b, Supplementary Figs.\u00a07b and 8b), demonstrating its superior performance in accurate mapping of SVR boundaries. These results again underline the advantage of DiffScan to adaptively determine SVR boundaries via scan statistic optimization, which effectively distinguishes SVRs amongst overlapping regions of different lengths.\n\nFinally, we evaluated the precision and recall rate, and the specificity (see Methods) of the SVR detection methods. Among all three methods, DiffScan achieves the best precision at the same recall rate (Fig.\u00a02c, Supplementary Figs.\u00a07c and 8c). It also has the highest specificity when the same number of nucleotides are predicted to be differential (Supplementary Fig.\u00a010).\n\nWe also considered the simulation framework in Choudhary et al.24 to compare the above methods. Briefly, DiffScan and dStruct outperform deltaSHAPE, RASA, and PARCEL regarding to Jaccard index and precision at fixed recall rate, demonstrating that the advantage of DiffScan is not specific to the simulation framework (Supplementary Fig.\u00a011). However, the relative performance of DiffScan and dStruct depends the cutoff used to select differential regions.\n\nTo assess the extent of false positive discoveries of DiffScan and other SVR detection methods, we constructed six negative control datasets (Control 1\u20136, see Methods) from multiple SP platforms, including SHAPE-Seq and icSHAPE. In these datasets, no SVRs are present between the compared conditions. Thus, any significant SVRs identified by the detection methods would represent false positives. Other SVR detection methods were included based on their applicability to the negative control datasets (Supplementary Table\u00a04). diffBUM-HMM was excluded as Bayesian approaches do not precisely control for type I error.\n\nThe false positive rates for DiffScan, dStruct, and PARCEL were below 0.05 for all tested datasets (Supplementary Fig.\u00a012, Supplementary Table\u00a05). The error rate of RASA is slightly inflated in Control 2, but is well-controlled for the other datasets. Consistent inflation is observed for deltaSHAPE across different datasets, reporting false positive results covering ~15% of nucleotide positions in the datasets. The fact that neither deltaSHAPE nor RASA control for the multiple testing problem can likely explain the observed inflation. Visualization of the prediction results by different methods are provided in Supplementary Figs.\u00a013\u201318.\n\nWe used two benchmark datasets with explicitly annotated SVRs between the compared conditions, curated by Choudhary et al.24 to evaluate different SVR detection methods. The Flu dataset26 is from a SHAPE-Seq experiment that measured the secondary structure of a Bacillus cereus crcB fluoride riboswitch in vitro in the presence or absence of fluoride. The transcript (100 nt in length) has five annotated SVRs, ranging in length between 1 nt and 8 nt. The RRE dataset43 is from a SHAPE-Seq experiment that measured the secondary structure of the HIV Rev-response element in the presence or absence of the Rev protein. There are seven annotated SVRs for Rev-RRE interactions in the transcript (369 nt in length), with lengths ranging between 7 nt and 39 nt.\n\nWe applied DiffScan, deltaSHAPE, diffBUM-HMM, dStruct, PARCEL, and RASA to identify SVRs in the two datasets. Visualization of the predicted SVRs and the annotated SVRs are provided in Supplementary Figs.\u00a019\u201322. For the Flu dataset, 60% of the top-20 nucleotides identified by DiffScan are in annotated SVRs. deltaSHAPE identified six regions, of 19 nucleotides in sum, and 63% of the nucleotides overlap with annotated SVRs. 50% of the top-20 nucleotides identified by diffBUM-HMM are in annotated SVRs. For dStruct, the identified SVR covered three annotated SVRs, with 38% of the top-20 nucleotides overlapping with annotated SVRs. PARCEL predicted a long region, covering 72% of all nucleotide positions in the transcript. Although the region spanned all five annotated SVRs, it did not effectively distinguish SVRs from flanking nucleotides between SVRs and falsely entailed many nucleotide positions without structural variations, i.e., only 33% nucleotides in the predicted SVR are in annotated SVRs. RASA did not report any significant region for the Flu dataset. Discussions of the top-40 ranked nucleotides by different methods for the Flu dataset and the results of the RRE dataset are provided in Supplementary Note\u00a0VII.\n\nIn addition, their performance is compared by the Jaccard Index and average distance to true SVRs. DiffScan had the second largest Jaccard index in the Flu dataset and the largest Jaccard index in the RRE dataset (Fig.\u00a03a). The Jaccard index of deltaSHAPE was slightly higher than DiffScan in the Flu dataset, but worse in the RRE dataset. DiffScan achieved the lowest average distance to annotated SVRs in the two benchmark datasets (Fig.\u00a03b). The results are consistent when the Jaccard index and average distance are evaluated at different cutoffs of the number of top ranked nucleotides (Supplementary Fig.\u00a023).\n\nDefault search length of 5 nt is used for deltaSHAPE and minimum search length of 5 nt is used for dStruct following the original article of the method. a Jaccard index between the top-20 ranked nucleotides and the annotated SVRs. b Average distance from the top-20 ranked nucleotides to annotated SVRs. \u201cX\u201d indicates that the corresponding method was not applicable for the dataset. \u201c*\u201d indicates that the average distance cannot be calculated since the corresponding method did not report any region.\n\nWe applied DiffScan to a recently reported icSHAPE dataset that mapped RNA secondary structure across human cellular compartments covering chromatin (Ch), nucleoplasm (Np), and cytoplasm (Cy)17. The DiffScan-predicted SVRs for the Ch versus Np (Fig.\u00a04a) and for the Np versus Cy (Supplementary Fig.\u00a024) comparisons mostly involved protein binding sites and RNA modification sites. As we also had data for RNA abundance in the Ch, Np, and Cy samples, we were interested in the potential impacts of SVRs on regulating mRNA abundance. Comparison of mRNA abundance in the Np versus Cy samples identified 61 transcripts that are significantly down-regulated in the Cy fraction (FDR < 0.05, Supplementary Fig.\u00a025). In addition, DiffScan identified SVRs in all of the 61 transcripts (p value = 1.7e-3 by Fisher\u2019s exact test, Supplementary Fig.\u00a025), suggesting an association between RNA structural variation and mRNA abundance.\n\na in regulating mRNA abundance and b shaping human traits in an icSHAPE dataset mapping RNA structure across human cellular compartments. Ch chromatin, Np nucleoplasm, Cy cytoplasm. a Predicted SVRs between Ch and Np were enriched with protein binding sites and RNA modification sites. *p value (one-sided Fisher\u2019s exact test) < 0.05, ***p value < 1e-6. P values of enrichment: m1A = 5.85e-3, m6A = 4.77e-2, \u03c8 = 2.87e-14, protein binding < 2.2e-16. b Enrichment of trait-associated SNPs in predicted SVRs. Proportion of trait-associated SNPs in SVR and non-SVR positions are plotted. P values are calculated by one-sided Fisher\u2019s exact test.\n\nTo further investigate this association, we used the FIMO module from the MEME suite44 to search for RBPs with binding motifs enriched in the predicted SVRs from the Np versus Cy comparison (see Methods). 27 RBPs were identified (FDR < 0.05, Supplementary Table\u00a06), which are most enriched in \u201cmRNA splicing, via spliceosome\u201d and \u201cRNA export from nucleus\u201d GO terms45,46 (Supplementary Table\u00a07). In particular, the identified RBPs included nine serine/arginine rich splicing factors (SRSF proteins)47, including SRSF1-SRSF6 and SRSF9-SRSF11. On the one hand, although initially discovered as splicing factors, SRSF proteins have been reported to regulate multiple steps of gene expression such as mRNA export, mRNA stability, and translation47. For example, SRSF1, SRSF3, and SRSF7 have been uncovered as adaptor proteins in mRNA export48,49. More recent studies have demonstrated that SRSF3 and SRSF7 promote the recruitment of receptor proteins for mRNA export50, hand over mRNAs to them to stimulate the nuclear export of mRNAs51, and therefore control mRNA abundance in the Cy fraction50. On the other hand, a recent study reported that RNA structural variation induced by a genetic variant influenced the binding of SRSF352. RNA structural specificities of SRSF1 and SRSF9 have also been reported in recent studies53,54. Therefore, the DiffScan-identified SVRs may regulate the binding of SRSF proteins, and consequently regulate mRNA abundance in the Cy fraction. Similar evidence was found for another significant RBP, FMRP, which is encoded by gene FMR1 (Supplementary Table\u00a06). The binding of FMPR controls the nuclear export of mRNAs55,56 and is regulated by RNA structure57,58. In summary, the DiffScan-predicted SVRs, combined with the RBP motif enrichment analysis, suggest roles of 27 RBPs in regulating mRNA abundance through mechanisms related to RNA structural variations.\n\nGiven the importance of SVRs in transcriptome regulation, we reason that SVRs may make more contributions to human complex traits than randomly selected segments in the human genome. To this end, we investigated whether DiffScan-predicted SVRs were enriched of trait-associated single nucleotide polymorphisms (SNPs) curated in the GWAS Catalog database59 (see Methods). Significant enrichment was found for the predicted SVRs from the Ch versus Np comparison and the Np versus Cy comparison (Fig.\u00a04b). The results underscore the essential roles of RNA structural variation in shaping human traits.",
+            "section_image": [
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+            ]
+        },
+        {
+            "section_name": "Discussion",
+            "section_text": "We have developed DiffScan, a computational framework for differential analysis of RNA secondary structure measured in multiple SP platforms. Our method provides several advantages. First, it adaptively estimates the lengths and locations of SVRs with single-nucleotide resolution. Compared to existing SVR detection methods, predicted SVRs by DiffScan are closer to true SVRs, both from simulated and benchmark datasets. Second, DiffScan is compatible with multiple SP platforms with robust performance. Existing SVR detection methods are usually tailored for a specific SP platform, and their generalization to other SP platforms can be prohibitive. Our method flexibly accommodates multiple SP platforms through its Normalization module and using the nonparametric test we implemented. This enables flexible analysis that is adaptable to suitable data types reflecting particular biological problems of interest. For example, the SHAPE-Seq platform with fast-acting reagent is suitable for in vitro studies of RNA folding dynamics60, while the icSHAPE platform utilizing slow-acting reagent allows in vivo transcriptome-wide structure probing16,17. As demonstrated with simulated and benchmark datasets, the excellent performance of DiffScan in terms of statistical power and accuracy for identifying SVRs is robust across different SP platforms. Third, DiffScan rigorously controls for the family-wise error rate in SVR detection, which is particularly influential for transcriptome level analyses.\n\nDiffScan has several limitations. First, the Normalization module in DiffScan relies on a structurally invariant set of nucleotide positions, which is identified via a built-in data-driven strategy. The strategy would fail in extreme cases when almost all nucleotide positions in the studied transcripts exhibit structural variations, although we expect it is rarely the case in practice4,16,17,61. In addition, when the structurally invariant set can be specified by prior knowledge, the normalization step can be easily adapted. Second, we recognize the statistical power of DiffScan is not optimized for a particular SP platform, so when the distribution of reactivities is known a priori, use of an appropriate parametric test would yield increased power. Third, proper modeling of inter-replicate variability when calculating reactivities can potentially improve the overall performance of DiffScan. Fourth, we note that the ultimate goal of studying SVRs is to understand the functional roles of RNA structure, which often involves cross-examination of other data sources, including motif analysis of RBPs, multi-omics datasets, etc. Incorporation of these multi-source data may help to accurately annotate SVRs11.",
+            "section_image": []
+        },
+        {
+            "section_name": "Methods",
+            "section_text": "We evaluated the power of DiffScan and other SVR detection methods in two SHAPE-seq datasets, of which the SVRs were curated in Choudhary et al.24. The Flu dataset probed the Bacillus cereus crcB fluoride riboswitch in vitro with and without fluoride ions, with four replicates for each condition. The transcript is 100 nt in length, and nucleotide positions 12\u201317, 22\u201327, 38\u201340, 48, and 67\u201374 were identified as SVRs between conditions. The RRE dataset studied the HIV Rev-response element, with three replicates measured in the presence and absence of Rev. The Rev-RRE interaction sites are considered SVRs. We obtained raw read counts and reactivities for the Flu dataset and reactivities for the RRE dataset, based on data availability.\n\nSynthetic negative control datasets were constructed from real SP data to assess the specificity of DiffScan and existing methods. For construction, we randomly split replicates in a single condition into two groups, and identified SVRs by contrasting the two groups. Any reported SVRs were considered false positive results. In particular, control datasets 1\u20134 were obtained by randomly splitting samples in the Flu dataset in the absence (Control 1) and presence (Control 2) of fluoride, and the RRE dataset with (Control 3) and without Rev (Control 4). To include more SP platforms in evaluation, we constructed another two control datasets from an icSHAPE dataset of mouse SRP RNA (272 nt)10, by contrasting the two in vitro samples (Control 5) and the two in vivo samples (Control 6).\n\nTo apply DiffScan in transcriptome level analysis, we downloaded the icSHAPE dataset17 in Sun et al., which mapped RNA secondary structure across HEK293 cellular compartments including chromatin, nucleoplasm, and cytoplasm. Transcripts mapped to mitochondrial genome were excluded to eliminate possible contamination by lysed mitochondria. Transcripts with RPKM less than 5 or RT stop less than 2 for all nucleotide positions were excluded17,62. Then nucleotide positions with coverage less than 10 were removed. As a result, 1,277 transcripts (covering 805,895 nucleotide positions) were compared between chromatin and nucleoplasm, and 1,815 transcripts (covering 1,203,523 nucleotide positions) were compared between nucleoplasm and cytoplasm.\n\nSuppose that there are nA replicates from condition A, and the reactivity of nucleotide position j in replicate i is \\({r}_{{ij}}^{A},1\\le i\\le {n}_{A},1\\le j\\le n\\), where n is the length of the transcript. Similarly, for nB replicates from condition B, the reactivity of nucleotide position j in replicate k is \\({r}_{{kj}}^{B},1\\le k\\le {n}_{B},1\\le j\\le n\\). We normalized reactivities using the following steps.\n\nStep 1: 90% winsorization is applied to the reactivities in each replicate separately to remove outliers, i.e., the bottom 5% of reactivities are set to the 5th percentile while the upper 5% of reactivities are set to the 95th percentile. After that, reactivities are scaled into range [0,1] by subtracting the minimum and then dividing the result by the new maximum.\n\nStep 2: Quantile normalization is applied to within-condition replicates to match the quantiles, which is frequently used in normalization analysis of genome-wide assays32,63 and has been found to be advantageous in secondary structure prediction compared to the 2\u20138% normalization method33,34.\n\nStep 3: To make between-condition reactivities comparable, we first determine a structurally invariant set S, i.e., nucleotide positions that do not exhibit structural variation across conditions. The reactivities are normalized so that the adjusted reactivities are similar between conditions in the structurally invariant set. The determination of S is described in Supplementary Methods. Then we learn a linear transformation rule from S, which converts reactivities of one condition to the same level of those of the other condition in S, and extrapolate the transformation to all nucleotide positions to obtain normalized reactivities.\n\nWe learn how to transform between-condition reactivities to the same level in S by fitting the following robust regression utilizing iterated re-weighted least squares with Huber\u2019s M estimate64. (For the sake of simplicity, we will still use \\({r}_{{ij}}^{A},{r}_{{ij}}^{B}\\) to denote reactivities processed by Step 1 and Step 2).\n\nwhere log \u03b1 corrects for the difference in sequencing depth and \u03b2 corrects for the difference in signal-to-noise ratio. Given that within-condition replicates are normalized by quantile normalization, it follows that \\(\\widetilde{{r}_{{ij\\;}}^{A}}\\approx \\widetilde{{r}_{{kj\\,}}^{B}}\\) in S if we transform \\({r}_{{kj}}^{B}\\) into \\(\\widetilde{{r}_{{kj\\,}}^{B}}={{\\exp }}(\\widehat{{{\\log\\ }}\\alpha }+\\hat{\\beta }\\,{{\\log}}\\,{r}_{{kj}}^{B})\\) and let \\(\\widetilde{{r}_{{ij\\;}}^{A}}={r}_{{ij}}^{A},{j}\\in S\\). Based on this, we extrapolate the fitted model to all nucleotide positions to obtain normalized reactivities \\(\\widetilde{{r}_{{ij\\;}}^{A}}={r}_{{ij}}^{A}\\) and \\(\\widetilde{{r}_{{kj\\,}}^{B}}={{\\exp }}(\\widehat{{{\\log\\ }}\\alpha }+\\hat{\\beta }\\,{{\\log}}\\,{r}_{{kj}}^{B}),1\\le j\\le n\\).\n\nWith normalized reactivities as input, we first test position-level differences between conditions to derive positional p values. To encompass various SP platforms, a nonparametric Wilcoxon test is used, which evaluates the structural variation at nucleotide position j by contrasting reactivities between conditions in a small window surrounding j. Technically, we define\n\nwhere \\(\\widetilde{{r}_{{it\\,}}^{A}},\\widetilde{{r}_{{kt}}^{B}}\\) are normalized reactivities, Cj is a small window centering at nucleotide position j with radius r, and pj is the two-sided p value. By default, we set r to 2 nt.\n\nTo concatenate position-level signals into regional signals, a scan statistic is defined for each region R,\n\nWith penalty of region length |R|, extending a candidate region will accumulate position-level signals at the expense of penalization. As a result, SVRs with accurately mapped boundaries can be distinguished based on the magnitude of the scan statistic.\n\nIn view of the dynamic locations and lengths of SVRs, we scan the transcripts by enumerating all candidate regions with suitable lengths, i.e., every region in \\({{{{{\\mathcal{R}}}}}}\\) = {R|Lmin \u2264 |R| \u2264 Lmax}. To determine whether a region R is selected as an SVR, we test\n\nbased on the magnitude of Q(R). We implemented a Monte Carlo approach to control the family-wise error rate for DiffScan (see Supplementary Methods).\n\nWe simulated reactivities for two conditions through the following three steps.\n\nStep 1. 1000 human RNA sequences in an icSHAPE dataset17 were randomly selected (length no more than 2000 nt due to computational burden). For each RNA sequence, we sampled 10 conformations from the Boltzmann distribution of secondary structure65 utilizing the RNAsubopt program in ViennaRNA version 2.4.1566.\n\nStep 2. Conditional on the pairing status of each nucleotide in a transcript, the reactivities can be sampled from pre-trained reactivity distributions. Three distributions were used: Cordero et al.39 and S\u00fck\u00f6sd et al.40 as fitted from SHAPE data, and also reactivity distributions we fitted from icSHAPE data (Supplementary Methods).\n\nStep 3. Different biological conditions were characterized by differential compositions of the 10 conformations generated in Step 1. The reactivities of each conformation were linearly combined accordingly to generate the observed reactivities in each condition. Specifically, for condition A, the 10 conformations of a transcript were assigned with weights \\({w}_{c}^{A},1\\le c\\le 10\\), with \\({w}_{c}^{A}\\) corresponding to the weight of the cth conformation in condition A, with \\(0\\le {w}_{c}^{A}\\le 1,\\,{\\Sigma }_{c=1}^{10}{w}_{c}^{A}=1\\). For condition B, the weight of the cth conformation was \\({w}_{c}^{B}\\), with \\(0\\le {w}_{c}^{B}\\le 1,{\\Sigma }_{c=1}^{10}{w}_{c}^{B}=1\\). To simulate SVRs that cover a reasonable proportion (approximately 20%16,17) of all nucleotide positions of the 100 transcripts, we allocated 90% of the weight to the first two conformations and randomly distributed the remaining 10% to the other eight conformations. We then generated reactivities in condition A and B separately by changing the weights of the first two conformations. Thus, nucleotide positions with different pairing status between the first two conformations form SVRs. Furthermore, replicates were simulated by adding random noise (\\({{{{{\\rm{N}}}}}}\\left({0,0.1}^{2}\\right)\\)) to the weights of the first two conformations. Finally, simulations were conducted at three levels of signal strength respectively by setting (i) \\(({w}_{1}^{A},{w}_{2}^{A})=(0.4,0.5),({w}_{1}^{B},{w}_{2}^{B})=(0.5,0.4)\\), (ii) \\(({w}_{1}^{A},{w}_{2}^{A})=(0.3,0.6),({w}_{1}^{B},{w}_{2}^{B})=(0.6,0.3)\\), and (iii) \\(({w}_{1}^{A},{w}_{2}^{A})=(0,0.9),({w}_{1}^{B},{w}_{2}^{B})=(0.9,0)\\).\n\nIn the simulated datasets, we evaluated the performance of different methods with four metrics. First, to evaluate the accuracy of SVR detection at nucleotide resolution, we calculated the Jaccard index between predicted SVRs and true SVRs. Jaccard index between nucleotide position sets A and B is defined as \\(\\frac{\\left|A\\cap B\\right|}{\\left|A\\cup B\\right|}\\). Second, to evaluated the accuracy of SVR boundary mapping, we calculated the average distance from predicted SVRs to true SVRs. For each nucleotide position in a predicted SVR, the distance to true SVRs is the number of nucleotides between itself and the nearest nucleotide in all true SVRs. The nucleotide distance of a predicted SVR is calculated by taking the average of the distances of all its nucleotides. An illustrative example for the average nucleotide distance is provided in Supplementary Fig.\u00a09. Third, we calculated the Precision-Recall curve. At varying significance levels, the value of precision was calculated as the number of correctly predicted nucleotide positions divided by the number of all predicted nucleotide positions. The value of recall rate was calculated as the number of correctly predicted nucleotide positions divided by the number of all nucleotide positions in the simulated SVRs. Fourth, we calculated the specificity of predicted SVRs as the number of correctly predicted non-SVR nucleotide positions divided by the number of all true non-SVR nucleotide positions.\n\nIn the negative control datasets (Control 1\u20136), to access whether the false positive discoveries of a method can be controlled at a nominal level, we calculated the position-level false positive rate as the number of predicted nucleotide positions at significance level 0.05 divided by the length of the transcript.\n\nIn the benchmark datasets with annotated SVRs (Flu and RRE)\u2014similar to our processing of the simulated datasets\u2014we calculated the Jaccard index and average distance between top predicted nucleotide positions and annotated SVRs.\n\nThe software deltaSHAPE version 1.0 available at the Weeks lab website23 was utilized to implement deltaSHAPE. As far as we know, there is no official software release for PARCEL or RASA; and we implemented them utilizing custom scripts from existing literature24. The R package dStruct version 1.0.0 was utilized to implement dStruct. The scripts in Paolo Marangio\u2019s GitHub page (https://github.com/marangiop/diff_BUM_HMM) were used to implement diffBUM-HMM.\n\nTo calculate reactivities, we assumed that \\({{{{{{\\rm{RT}}}}}}}_{j}\\sim {{{{{\\rm{Binomial}}}}}}({N}_{j},{p}_{j}),\\) in which \\({{{{{{\\rm{RT}}}}}}}_{j}\\) is the RT stop at position j in the case experiment, Nj is the number of times that position j is exposed to the probing molecules, and pj is the probability that position j is modified. The maximum likelihood estimator for pj is \\(\\widehat{{p}_{j}}=\\frac{{{{{{{\\rm{RT}}}}}}}_{j}}{{N}_{j}}\\). On the other hand, the coverage at position j in the control experiment (\\({{{{{{\\rm{cove}}}}}}{{{{{\\rm{rage}}}}}}}_{j}^{{{{{{\\rm{control}}}}}}}\\)) is approximately proportional to Nj. Therefore, we calculated the reactivity at position j as \\({r}_{j}=\\frac{{{{{{{\\rm{RT}}}}}}}_{j}}{{{{{{{\\rm{coverage}}}}}}}_{j}^{{{{{{\\rm{control}}}}}}}}\\)67. Based on this, four reactivity replicates of each condition were generated by enumerating the four pairings of the two count replicates from case experiments and the two count replicates from control experiments.\n\nWe collected 1193 motifs of 159 RBPs from the ATtRACT database68. For each motif, we searched in the predicted SVRs for significant motif hits utilizing the FIMO module (\u2013norc\u2013thresh 0.001) from the MEME suite version 5.2.044, and the number of significant hits in each SVR were counted.\n\nTo evaluate the significance of motif enrichment, we randomly sampled null regions in non-SVR regions in the same transcripts, with region length matched to the predicted SVRs. The number of significant hits in each null region is recorded. After that, we performed a one-sided Wilcoxon signed-rank test for the two count vectors of significant hits to evaluate the significance of enrichment. Motifs with corrected p value (Benjamini-Hochberg method) less than 0.05 were considered significantly enriched.\n\nWe downloaded the summary statistics of the published genome-wide association studies (GWAS) curated in the GWAS catalog database (v1.0)59. Proportions of trait-associated SNPs (GWAS p value < 1e\u20135) in SVR and non-SVR positions were compared, and the statistical significance was evaluated with Fisher\u2019s exact test.\n\nFurther information on research design is available in the\u00a0Nature Research Reporting Summary linked to this article.",
+            "section_image": []
+        },
+        {
+            "section_name": "Data availability",
+            "section_text": "The data that support this study are available from the corresponding authors upon reasonable request. The raw benchmark datasets used in this study are available at https://doi.org/10.5281/zenodo.2536501. The processed negative control datasets (Control 1\u20136) and benchmark datasets (Flu and RRE) are available at https://github.com/yub18/DiffScan. The icSHAPE datasets for transcriptome level analysis are available in the GEO database under accession code GSE117840.",
+            "section_image": []
+        },
+        {
+            "section_name": "Code availability",
+            "section_text": "The DiffScan software is available at https://github.com/yub18/DiffScan. The scripts and data for the reproduction of the analyses and results are also provided.",
+            "section_image": []
+        },
+        {
+            "section_name": "References",
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+        },
+        {
+            "section_name": "Acknowledgements",
+            "section_text": "L.H. acknowledges research support from the National Natural Science Foundation of China (Grant No. 12071243). The work was done partially while L.H. was participating in the virtual program of the Institute for Mathematical Sciences, National University of Singapore, in 2022. Q.C.Z. acknowledges the State Key Research Development Program of China (Grant No. 2019YFA0110002) and the National Natural Science Foundation of China (Grants nos. 32125007 and 91940306). We would like to thank Professor Jun S. Liu for the helpful discussions.",
+            "section_image": []
+        },
+        {
+            "section_name": "Author information",
+            "section_text": "Center for Statistical Science, Department of Industrial Engineering, Tsinghua University, Beijing, China\n\nBo Yu\u00a0&\u00a0Lin Hou\n\nMOE Key Laboratory of Bioinformatics, School of Life Sciences, Tsinghua University, Beijing, China\n\nPan Li,\u00a0Qiangfeng Cliff Zhang\u00a0&\u00a0Lin Hou\n\nCenter for Synthetic and Systems Biology, Beijing Advanced Innovation Center for Structural Biology, Tsinghua-Peking Joint Center for Life Sciences, School of Life Sciences, Tsinghua University, Beijing, China\n\nPan Li\u00a0&\u00a0Qiangfeng Cliff Zhang\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nB.Y., Q.C.Z., and L.H. conceived the study and wrote the manuscript. B.Y. and L.H. developed the computational framework. B.Y. and P.L. performed the data preparation and statistical analysis. B.Y., Q.C.Z., and L.H. interpreted the results. All authors approved the manuscript.\n\nCorrespondence to\n                Qiangfeng Cliff Zhang or Lin Hou.",
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+            "section_text": "Yu, B., Li, P., Zhang, Q.C. et al. Differential analysis of RNA structure probing experiments at nucleotide resolution: uncovering regulatory functions of RNA structure.\n                    Nat Commun 13, 4227 (2022). https://doi.org/10.1038/s41467-022-31875-3\n\nDownload citation\n\nReceived: 14 August 2021\n\nAccepted: 05 July 2022\n\nPublished: 22 July 2022\n\nVersion of record: 22 July 2022\n\nDOI: https://doi.org/10.1038/s41467-022-31875-3\n\nAnyone you share the following link with will be able to read this content:\n\nSorry, a shareable link is not currently available for this article.\n\n\n\n\n                            Provided by the Springer Nature SharedIt content-sharing initiative\n                        ",
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+            ]
+        },
+        {
+            "section_name": "This article is cited by",
+            "section_text": "Nature Reviews Molecular Cell Biology (2024)",
+            "section_image": []
+        }
+    ]
+}

15fcceacea9659ccc9a268ffbc146771eb89eaeda09f1967fcb353a755448031/metadata.json

@@ -0,0 +1,137 @@
+{
+    "title": "Excitonic Mott insulator in a Bose-Fermi-Hubbard system of moir\u00e9 WS2/WSe2 heterobilayer",
+    "pre_title": "Excitonic Mott insulator in a Bose-Fermi-Hubbard system of moir\u00e9 WS2/WSe2 heterobilayer",
+    "journal": "Nature Communications",
+    "published": "14 March 2024",
+    "supplementary_0": [
+        {
+            "label": "Supplementary Information",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-024-46616-x/MediaObjects/41467_2024_46616_MOESM1_ESM.pdf"
+        },
+        {
+            "label": "Peer Review File",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-024-46616-x/MediaObjects/41467_2024_46616_MOESM2_ESM.pdf"
+        }
+    ],
+    "supplementary_1": NaN,
+    "supplementary_2": NaN,
+    "source_data": [
+        "https://doi.org/10.6084/m9.figshare.25246012.v1",
+        "https://doi.org/10.6084/m9.figshare.25246006.v1",
+        "https://doi.org/10.6084/m9.figshare.25246009.v1",
+        "https://doi.org/10.6084/m9.figshare.25246015.v1"
+    ],
+    "code": [],
+    "subject": [
+        "Phase transitions and critical phenomena",
+        "Quantum simulation",
+        "Two-dimensional materials"
+    ],
+    "license": "http://creativecommons.org/licenses/by/4.0/",
+    "preprint_pdf": "https://www.researchsquare.com/article/rs-2861185/v1.pdf?c=1710500788000",
+    "research_square_link": "https://www.researchsquare.com//article/rs-2861185/v1",
+    "nature_pdf": "https://www.nature.com/articles/s41467-024-46616-x.pdf",
+    "preprint_posted": "15 Jun, 2023",
+    "research_square_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Understanding the Hubbard model is crucial for investigating various quantum many-body states and its fermionic and bosonic versions have been largely realized separately. Recently, transition metal dichalcogenides heterobilayers have emerged as a promising platform for simulating the rich physics of the Hubbard model. In this work, we explore the interplay between fermionic and bosonic populations, using a $\\rm{WS}_2$/$\\rm{WSe}_2$ heterobilayer device that hosts this hybrid particle density. We independently tune the fermionic and bosonic populations by electronic doping and optical injection of electron-hole pairs, respectively. This enables us to form strongly interacting excitons that are manifested in a large energy gap in the photoluminescence spectrum. The incompressibility of excitons is further corroborated by measuring exciton diffusion, which remains constant upon increasing pumping intensity, as opposed to the expected behavior of a weakly interacting gas of bosons, suggesting the formation of a bosonic Mott insulator. We explain our observations using a two-band model including phase space filling. Our system provides a controllable approach to the exploration of quantum many-body effects in the generalized Bose-Fermi-Hubbard model.Physical sciences/Physics/Condensed-matter physics/Phase transitions and critical phenomenaPhysical sciences/Materials science/Nanoscale materials/Two-dimensional materialsPhysical sciences/Physics/Quantum physics/Quantum simulationPhysical sciences/Physics/Condensed-matter physics/Phase transitions and critical phenomenaPhysical sciences/Materials science/Nanoscale materials/Two-dimensional materialsPhysical sciences/Physics/Quantum physics/Quantum simulation",
+            "section_image": []
+        },
+        {
+            "section_name": "Additional Declarations",
+            "section_text": "There is NO Competing Interest.",
+            "section_image": []
+        },
+        {
+            "section_name": "Supplementary Files",
+            "section_text": "GaoetalSM.pdf",
+            "section_image": []
+        }
+    ],
+    "nature_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Understanding the Hubbard model is crucial for investigating various quantum many-body states and its fermionic and bosonic versions have been largely realized separately. Recently, transition metal dichalcogenides heterobilayers have emerged as a promising platform for simulating the rich physics of the Hubbard model. In this work, we explore the interplay between fermionic and bosonic populations, using a WS2/WSe2 heterobilayer device that hosts this hybrid particle density. We independently tune the fermionic and bosonic populations by electronic doping and optical injection of electron-hole pairs, respectively. This enables us to form strongly interacting excitons that are manifested in a large energy gap in the photoluminescence spectrum. The incompressibility of excitons is further corroborated by observing a suppression of exciton diffusion with increasing pump intensity, as opposed to the expected behavior of a weakly interacting gas of bosons, suggesting the formation of a bosonic Mott insulator. We explain our observations using a two-band model including phase space filling. Our system provides a controllable approach to the exploration of quantum many-body effects in the generalized Bose-Fermi-Hubbard model.",
+            "section_image": []
+        },
+        {
+            "section_name": "Introduction",
+            "section_text": "The rich physics of the Hubbard model has brought fundamental insights to the study of many-body quantum physics1. Initially proposed for electrons on a lattice, different fermionic and bosonic versions of this model have been simulated in various platforms, ranging from ultracold atoms2 to superconducting circuits3. Recently, bilayer transition metal dichalcogenides (TMDs) have become a versatile platform to study the Hubbard model thanks to the coexistence of several intriguing features such as the reduction of electron hopping due to the formation of moir\u00e9 lattice with large lattice constant, and the existence of both intra- and interlayer excitons. These characteristics have enabled the realization of numerous effects of many-body physics such as metal-to-Mott insulator transition4,5,6,7,8,9, generalized Wigner crystals10,11,12,13,14, exciton\u2013polaritons with moir\u00e9-induced nonlinearity15, stripe phases16, light-induced ferromagnetism17. Moreover, there have been recent exciting perspectives of exploring such effects in light\u2013matter correlated systems3,18,19. While typically the fermionic and bosonic versions of the Hubbard model are explored independently, combining these two models in a single system holds intriguing possibilities for studying mixed bosonic-fermionic correlated states20,21.\n\nIn this work, we demonstrate Bose\u2013Fermi\u2013Hubbard physics in a TMD heterobilayer. We independently control the population of fermionic (electronic) particles by doping with a gate voltage (Vg), and the population of bosonic (excitonic) states by pumping with a pulsed optical drive of intensity I. Harnessing these two control methods, we realize strongly interacting excitons. In particular, we show the incompressibility of excitonic states near integer filling by observing an energy gap in photoluminescence, accompanied by an intensity saturation. Remarkably, we observe the suppression of diffusion, a strong indication of the formation of a bosonic Mott insulator of excitons.",
+            "section_image": []
+        },
+        {
+            "section_name": "Results",
+            "section_text": "To demonstrate these effects, we use a moir\u00e9 lattice created by stacking two monolayers of WS2 and WSe2, with symmetric top and bottom gates. Figure\u00a01a shows a schematic illustration of the heterobilayer device (see Supplementary Note\u00a01 for details). Due to the type-II band alignment of the heterostructure (Fig.\u00a01b), negative doping results in a population of electrons in the WS2 subject to the moir\u00e9 potential of the bilayer. The ratio between the density of this population and the density of moir\u00e9 sites in the structure determines the so-called electronic filling factor (\u03bde). The optical pump results in the formation of an energetically favorable interlayer exciton (X)22, by pairing between an electron in WS2 and a hole in WSe2 (represented in Fig.\u00a01b). In order to explore different regimes of Bose\u2013Fermi\u2013Hubbard model, we control the bosonic and fermionic populations by changing I and Vg, respectively. This can be compared to the ultracold atom implementation of Bose\u2013Fermi mixture where the respective populations are fixed in each experiment23. Before discussing our experimental observation, we discuss three limiting cases that determine the phase space of our system, as indicated in Fig.\u00a01c. The corresponding physical scenarios are represented in panels d\u2013f. First, in the weak excitation limit and low electronic filling factor (\u03bde ~0) regime, the system\u2019s photoluminescence (PL) emission originates exclusively from the few X states in the quasi-empty lattice (panel d). This emission comes from excitons in lattice sites where they are the only occupant particles, namely, \u201csingle occupancy states\u201d (X1). Upon increasing \u03bde, the number of singly occupied sites decreases, and in the limiting case of \u03bde \u2265 1, as represented in panel e, the optically generated excitons can only form in lattice sites already occupied by charged particles. In this case, the required energy to form the exciton increases due to the on-site Coulomb repulsion, and hence the PL emission has new branch with higher energy than the previous regime. Consequently, the PL originates from lattice sites with an electron-exciton double occupancy (X2). Finally, we consider the case where the electronic doping is below the threshold required to reach a fermionic Mott insulator (0\u2009<\u2009\u03bde\u2009<\u20091) but I is strong enough to optically saturate the single-occupancy states. The extra excitons create a number of sites with electron-exciton or exciton\u2013exciton double occupancies (panel f). In this case, the PL emission corresponds to mixed contributions from exciton\u2013exciton and exciton\u2013electron interaction (Uex-ex and Uex-e); the individual peaks cannot be distinguished in a single spectrum due to the broadness of linewidths. Therefore, in this regime, the emitted light is only a combination of the X1 and X2 PL emission. This interplay between exciton and electron occupancy can lead to situations in which the moir\u00e9 lattice is completely filled with a mixed population of fermions and bosons, forming a hybrid incompressible state. Specifically, in the limit of weak electronic tunneling, excitons can form a Mott insulating state, in the remainder of sites that are not filled by electronic doping. Note the line in Fig.\u00a01c denoting panel f is an asymptote since optical pumping can not fully saturate an exciton line. At \u03bde\u2009=\u20090, this intensity is denoted as I* (see Supplementary Note\u00a08 for details).\n\na Schematic of the WS2/WSe2 dual-gate device. The TMD heterobilayer is embedded between two symmetric gates: top gate (TG) and bottom gate (BG). b Depiction of the type-II band alignment of the bilayer. The blue and red curves denote bands from WS2 and WSe2, respectively. The shaded ellipse indicates the formation of interlayer excitons composed of an electron from the WS2 conduction band and a hole from the WSe2 valence band. c Phase diagram of the system. The population of the moir\u00e9 lattice can be controlled via two independent parameters: the gate voltage changes the electronic filling factor (\u03bde), and the optical pump creates a population of excitons, proportional to the input intensity. In the gray area, the system behaves as a mixed gas of bosonic and fermionic particles. As one approaches the upper limit (black line), the system becomes incompressible due to the saturation of single-occupancy states. d\u2013f Interlayer exciton formation under optical excitation for three different regimes governed by the pump intensity (I) and \u03bde: c low I and \u03bde\u2009~\u20090, d low I and \u03bde\u2009~\u20091, e high I and 0\u2009<\u2009\u03bde\u2009<\u20091. X1 (X2) denotes PL emission from singly (doubly) occupied moir\u00e9 lattice sites. X2 can originate from either electron-exciton (Uex-e) or exciton\u2013exciton (Uex-ex) double occupancies.\n\nTo experimentally investigate these regimes, we perform PL measurements, with varying pump power and backgate voltage. A detailed description of the optical setup can be found in Supplementary Note\u00a02. We use pulsed excitation to achieve high exciton density while reducing thermal effects by keeping low average power. Experiments with CW excitation are consistent with the presented data, as shown in Supplementary Note\u00a06. Figure\u00a02a\u2013c shows the PL dependence at three different intensities as schematically shown in panel d. Figure\u00a02a shows the normalized doping-dependent PL spectrum for low/(0.08\u2009\u03bcW/\u03bcm2), which corresponds to low bosonic occupation. The fermionic occupation \u03bde is varied between 0 and 1.1. For low \u03bde, PL emission is detected only from X1. However, at Vg\u2009\u2248\u20092.98\u2009V, we detect a transition in the PL emission to X2. This transition corresponds to the formation of X\u2019s in the presence of an incompressible fermionic Mott insulator24,25. From the reflectivity measurement and calculations from a capacitor model, we attribute Vg\u2009=\u20092.98\u2009V to \u03bde\u2009=\u20091 (see Supplementary Note\u00a03). The energy gap between X1 and X2 is \u0394E\u2009\u2248\u200929\u2009meV, which corresponds to the on-site Coulomb repulsion energy between an electron and an exciton (Uex-e). We elaborate on this energy gap later in the sub-section \u201cEnergy map along the phase space\u201d. The dim mid-gap features between X1 and X2 at \u03bde ~1 are strongly position-dependent and disappear at higher power. This indicates that such emission is from localized excitons. Figure\u00a02b shows the PL spectrum under pump intensity equal to 12.1\u2009\u03bcW/\u03bcm2. It is worth noticing that the Vg at which the PL signal from X2 is detected is lower than in panel a. The system is therefore in the regime depicted in Fig.\u00a01f. Upon further increasing the pump intensity X2 can be detected even at \u03bde\u2009=\u20090, as observed in Fig.\u00a02c. In this case, the PL emission originates solely from double occupancy of excitons in a moir\u00e9 lattice site, suggesting that, for high I, purely bosonic states of strongly interacting excitons are created. Comparing Fig.\u00a02a, c, one can observe that in the former case, the emergence of the X2 peak corresponds to a sharp suppression of X1, while in the latter case, both peaks coexist. This indicates the nature of the double occupancy: in the first scenario, the exciton is forming in the presence of an electron, and after its recombination, there are no other optical excitations in the system. In contrast, the coexistence of both peaks in panel c shows that upon double exciton occupancy, the recombination of X2 precedes the recombination of X1.\n\na\u2013c Normalized PL spectrum as a function of gate voltage (\u03bde) for three different pump intensities: I\u2009=\u20090.08\u2009\u03bcW\u03bcm2 (a), I\u2009=\u200912.1\u2009\u03bcW/\u03bcm2 (b) and I\u2009=\u20091229\u2009\u03bcW/\u03bcm2 (c). The peaks associated with single (X1) and double (X2) occupancy are indicated on each panel. The dashed lines indicate the gate voltages at which the PL intensity X2 exceeds X1. The dashed black lines of (d) indicate the measurement ranges of (a\u2013c). e\u2013g Evolution of the PL intensity for X1 (red) and X2 (blue) as a function of gate voltage for the same values of pump intensities displayed in (a\u2013c). The electron filling factor at which X2 exceeds X1 decreases as pump intensity increases. h shows the gate voltage at which the intensity of X2 exceeds that of X1, as a function of the total PL intensity. The error bars represent the standard errors for the parameter estimates in the fitting routine.\n\nFrom the observation described in the previous paragraph, we conclude that the detection of PL emission with X1 and X2 energies benchmarks the formation of exciton states in singly and doubly occupied lattice sites, respectively. At \u03bde\u2009=\u20090, the X1 peak in Fig.\u00a02c is blueshifted with respect to Fig.\u00a02a. We associate this feature with a mean-field effect due to exciton\u2013exciton interaction. As we increase the electronic doping, fewer sites are available to create X1 excitons and on those occupied sites, only X2 is created. Consequently, the effective population of X1 excitons is decreased. Therefore the mean-field shift is suppressed to the point that at high filling (\u03bde ~1) the X1 energy is the same as in the case of low pump intensity. Next, in order to understand the interplay between fermionic and bosonic lattice occupancies in each regime, we perform a quantitative analysis of their respective integrated intensity. We extract these values from the collected PL spectra using a computational fitting method (see Supplementary Note\u00a07 for further details). Figure\u00a02e\u2013g displays this intensity dependence on \u03bde for the same I range of panels a\u2013c. We notice that as electrons fill the system\u2019s phase space (upon increasing Vg), the number of accessible single-occupancy states decreases. As a consequence, the integrated intensity of X1 reduces with increasing \u03bde. Remarkably, for each intensity, there is a critical \u03bde after which the PL emission of X2 exceeds that of X1. The gate voltage at which the crossing takes place (\\({V}_{{{{{{{{\\rm{g}}}}}}}}}^{{{{{{{{\\rm{cr}}}}}}}}}\\)) is highlighted on each panel by a vertical dashed line. This line indicates a constant ratio between the X1 and X2 populations. The crossing takes place at lower \u03bde upon increasing I, as expected. In Fig.\u00a02h, we track \\({V}_{{{{{{{{\\rm{g}}}}}}}}}^{{{{{{{{\\rm{cr}}}}}}}}}\\) as a function of the total collected PL emission, which gives an indication of the total number of excitons in both X1 and X2 branches. We observe a clear trend: a higher total population of excitons results in a faster saturation of the single-occupancy states and hence an increasing number of double occupancy states.\n\nNext, in order to trace the role of the optical pump and the optical saturation that leads to the formation of incompressible bosonic states, we investigate the PL for varying I for different \u03bde. In Fig.\u00a03a\u2013c, we focus on three different values of \u03bde, as indicated in panel d, and study the PL spectrum for increasing emitted PL power. For zero fermionic occupancy (panel a), X2 contributes to the emission only at very high total PL emission intensity. In panels b and c, we increase the electronic doping to \u03bde\u2009=\u20090.7 and \u03bde\u2009=\u20090.95, respectively, and as expected, the total PL at which we detect X2 decreases. In the low-power region, panel c shows the PL emission from mid-gap states also observed in Fig.\u00a02a. Apart from the energy gap in the emission, we observe a blueshift of the X1 line with increasing PL power. Assuming the weak tunneling regime, this shift should be equal to \\({U}_{{{{{{{{\\rm{ex}}}}}}}}{{\\mbox{-}}}{{{{{{{\\rm{ex}}}}}}}}}\\langle {\\hat{x}}^{{{{\\dagger}}} }\\hat{x}\\rangle\\), where \\({\\hat{x}}^{{{{\\dagger}}} }\\) is the creation operator of an exciton. For example, in Fig.\u00a03b for total PL power at 2 counts/s, the bosonic occupation is \\(\\langle {\\hat{x}}^{{{{\\dagger}}} }\\hat{x}\\rangle \\simeq 0.2\\). This corroborates with the energy gap that occurs at 10 counts/s for an estimated unity filling (\\(\\langle {\\hat{x}}^{{{{\\dagger}}} }\\hat{x}\\rangle \\simeq 1\\)). We present a fully quantum theoretical analysis of this observation in Supplementary Note\u00a010. Panels e\u2013g show the intensities of X1 and X2 for the values of \u03bde in panels a\u2013c. As expected, in panel e, one can observe that the intensity of the X1 PL emission increases monotonically, and it starts to saturate only at very high total PL emission regimes. Upon filling the moir\u00e9 lattice with one exciton or one electron per site, the X1 PL intensity saturates. With higher \u03bde, the saturation occurs at lower I, as shown in panels f and g. Since this saturation corresponds to filling the single-occupancy states, we associate it with the establishment of an incompressible bosonic Mott insulator. Note that this bosonic Mott insulator is in a drive-dissipative regime, similar to the demonstration in superconducting qubit systems26.\n\na\u2013c Normalized PL spectrum as a function of the total collected PL power for three different electronic filling factors. The peaks associated with single (X1) and double (X2) occupancy are indicated on each panel. d indicates the ranges of I and \u03bde for the measurements shown in (a\u2013c). e\u2013g evolution of the PL power for X1 (red) and X2 (blue) as a function of the total collected PL power for the same values of \u03bde displayed in (a\u2013c). f displays the fitting function (dashed black line) employed to extract Psat and \\({\\,{{\\mbox{P}}}\\,}_{1}^{\\max }\\) (described in the text). h Evolution of Psat (brown) as a function of the gate voltage (\u03bde). As expected from our phase-space filling model, its value reduces with increasing filling factor. The quantity \\({{{\\mbox{P}}}}_{{{{{{{{\\rm{sat}}}}}}}}}/{\\,{{\\mbox{P}}}\\,}_{1}^{\\max }\\) (green) shows good agreement with the theoretical model. The error bars represent the standard errors for the parameter estimates in the fitting routine.\n\nTo quantitatively analyze this saturation effect, we fit the X1 PL power (P1) to the function \\({\\rm{P}}_{1}={\\,{{\\mbox{P}}}\\,}_{1}^{\\max }\\frac{{{{{{{{\\rm{P}}}}}}}}}{\\,{{\\mbox{P}}}\\,+{{{{{{{{\\rm{P}}}}}}}}}_{{{{{{{{\\rm{sat}}}}}}}}}}\\), where P is the total PL power. From the fitting, we extract \\({\\rm{P}}_{1}^{\\max }\\) which is the asymptotic value of the X1 emitted PL power, and Psat which determines the total PL of saturation. This functional form corresponds to the expected system behavior when the charge gap U is sufficiently large to permit the utilization of a phase-space filling model to treat both single and double occupancy states (details in Supplementary Note\u00a08). Figure\u00a03f includes an example of the fitting function (dashed black line). According to our model, the value of Psat should decrease with increasing \u03bde because a lower excitonic population is required to achieve the incompressible states. The compiled data for the full range of \u03bde, shown in panel h with brown marks, is in good agreement with the expected trend. From the model, we can also infer that the quantity \\({{{\\mbox{P}}}}_{{{{{{{{\\rm{sat}}}}}}}}}/{\\,{{\\mbox{P}}}\\,}_{1}^{\\max }\\) should be independent of the electronic doping level because both quantities depend linearly on 1\u2009\u2212\u2009\u03bde; higher electronic occupancy implies less single-occupancy states available to host an exciton. The green marks in Fig.\u00a03h represent this behavior, which is in good agreement with the model. We conclude that the saturation of single-occupancy states is directly reflected in the intensity of X1, enabling the extraction of the conditions under which the incompressible states occur. Importantly, this enables a direct calibration of the bosonic and fermionic fractions in the system.\n\nIn order to further validate the incompressible nature of excitonic states, we perform diffusion measurements of the interlayer excitons27. For a steady population of excitons created by a continuous-wave laser pump, the diffusion length carries information about the nature of the state: an incompressible bosonic state is expected to have a lower diffusion length than a weakly interacting one. We spatially image the diffusion pattern with spectral resolution and extract the diffusion length (LX1) of the single-occupancy excitons. The choice of LX1 as an appropriate quantity to benchmark the incompressibility of bosonic Mott insulating states, assumes a constant exciton lifetime with varying population. This is supported by previous reports in the literature that show the independence of this quantity over three orders of magnitude of pumping power28. The downward diffusion image has patterns that originate in the inhomogeneous surface of the bilayer. Although the inhomogeneities on that side hinder the extraction of LX1, the optically induced suppression of the diffusion length for constant \u03bde can be clearly observed in this region (Fig.\u00a04a, b). The population injected at y\u2009=\u20090 (dotted line) propagates, and its emission pattern is monitored along a range of 5\u2009\u03bcm (dashed rectangle). The color scale is the same for both panels. Panel b shows a reduction of the diffused X1 population in comparison to panel a. For the quantitative analysis of this observation, it is necessary to use a fitting routine, for which the smooth pattern on top of the injection point (y\u2009<\u20090) is more reliable. Figure\u00a04c shows the extracted LX1 as a function of Vg for different pump intensities from the exponentially decaying spatial diffusion pattern in this region. We provide more details about the analysis of the diffusion data in Supplementary Note\u00a09. For low electronic density, the exciton diffusion length increases as the power is augmented. This trend, highlighted by the upward arrow, is in agreement with the expected behavior for weakly interacting bosons28,29. Remarkably, as the electronic filling factor increases, the trend completely inverts (inset). This is a direct signature of the bosonic Mott insulator formation since the bulk is incompressible and the melting only occurs at the edge.\n\nSpectrally and spatially resolved diffusion pattern at \\({\\nu }_{e}=0.73\\left.\\right({{{{{{{{\\rm{V}}}}}}}}}_{{{{{{{{\\rm{g}}}}}}}}}=2.34\\)V) for low (a) and high (b) I. The dashed rectangle highlights the region where the suppression of diffusion can be observed. c Exciton diffusion length as a function of the gate voltage for a range of \u03bde and for different input intensities. For low \u03bde, the diffusion length increases with I due to exciton repulsive interaction. Upon further filling the moir\u00e9 lattice, the trend inverts, indicating the optical realization of incompressible states. The inset is a zoom-in of the red dotted rectangle to highlight the reduction of LX1 with increasing I. The error bars represent the standard errors for the diffusion length estimated from the exponential fitting.\n\nThe implemented fitting algorithm allows us to track the changes in the energy of both species of excitons and the energy gap between them. These results are presented in Fig.\u00a05. Panels a and b show the central energies of the peaks X1 and X2 in the space of parameters for which each peak is detectable. In the range where both of them can be detected, their energy difference \u0394E (panel c) provides important information about the nature of the interactions taking place in the system. In the case of low electronic occupancy and high exciton density (top left corner of the panel), \u0394E corresponds to the exciton\u2013exciton interaction gap (Uex-ex ~32\u2009meV). Conversely, at high \u03bde and low exciton density (bottom right corner), this gap depends on the exciton\u2013electron interaction (Uex-e ~27\u2009meV). The gradual change in the nature of the interactions taking place in the system along the parameters space is reflected in the change of \u0394E. Interestingly, the largest energy gap takes place for states with high occupation of bosons and fermions (top right corner), which is consistent with a blueshift of the X2 PL peak due to the high population of excitons with large Bohr radius repelling through dipolar interaction.\n\nEnergy of the X1 (a) and X2 (b) PL emission as a function of gate voltage and pump intensities. The white areas correspond to the range of parameters where the corresponding peak completely vanishes. When X1 and X2 coexist, we extract the energy difference, as shown in (c).",
+            "section_image": [
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+            ]
+        },
+        {
+            "section_name": "Discussion",
+            "section_text": "In summary, we demonstrated a Mott insulating state of excitons in a hybrid Bose\u2013Fermi Hubbard system formed in a TMD heterobilayer. While our incompressibility observation was based on spatially resolved diffusion in the steady-state limit, one can explore interesting non-equilibrium physics due to the relatively long lifetime of interlayer excitons. More generally, spatiotemporally resolved measurements, combined with independent tunability of fermionic and bosonic populations, make it possible to investigate the equilibrium and non-equilibrium physics of Bose\u2013Fermi mixtures. Moreover, a quantum microscopic model capable of fully describing such a driven-dissipative Bose\u2013Fermi mixture remains an open area of research. The novel experimental diffusion method used to benchmark the excitonic incompressibility opens exciting perspectives for the simulation of complex dynamics in many-body quantum systems that range from a single bosonic particle in a Fermi sea to a strongly interacting gas of bosons. Particularly intriguing examples are the optical investigation of charge and spin physics in integer and fractional fillings, e.g., Mott excitons30,31 or spin liquids32,33,34,35, and fractional Chern insulators36,37.",
+            "section_image": []
+        },
+        {
+            "section_name": "Methods",
+            "section_text": "The WSe2/WS2 heterostructure was fabricated using a dry-transfer method with a stamp made of a poly(bisphenol A carbonate) (PC) layer on polydimethylsiloxane (PDMS). All flakes were exfoliated from bulk crystals onto Si/SiO2 (285\u2009nm) and identified by their optical contrast. The top/bottom gates and TMD contact are made of few-layer graphene. The PC stamp and samples were heated to 60\u2009\u00b0C during the pick-up steps and released from the stamp to the substrate at 180\u2009\u00b0C. The PC residue on the device was removed in chloroform, followed by a rinse in isopropyl alcohol and ozone clean. Sample transfer was performed in an argon-filled glovebox for improved interface quality. The electrodes consist of 3.5\u2009nm of chromium and 70\u2009nm of gold. They were fabricated using standard electron-beam lithography techniques and thermal evaporation.\n\nThe sample is kept in a dilution refrigerator at a temperature of 3.5\u2009K. For PL measurements, we use a confocal microscopy setup. Our pumping source is a pulsed Ti:Sapphire laser tuned at 720\u2009nm (1.722\u2009eV), with a pulse duration of 100\u2009fs and a repetition rate of ~80\u2009MHz. In addition, an optical chopper system at 800\u2009Hz is used to prevent sample heating while having a high pump intensity. The residual pump is removed with a spectral filter before collecting the PL emission in a spectrometer-CCD camera device. A complete description of the setup is presented in the Supplementary Note\u00a02.\n\nFor the diffusion measurements, we used a continuous-wave (CW) laser. The rest of the optical measurement setup was similar.",
+            "section_image": []
+        },
+        {
+            "section_name": "Data availability",
+            "section_text": "The PL and diffusion data generated in this study have been deposited in the Figshare database under accession links: https://doi.org/10.6084/m9.figshare.25246012.v1; https://doi.org/10.6084/m9.figshare.25246006.v1; https://doi.org/10.6084/m9.figshare.25246009.v1; https://doi.org/10.6084/m9.figshare.25246015.v1 .",
+            "section_image": []
+        },
+        {
+            "section_name": "References",
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+            "section_image": []
+        },
+        {
+            "section_name": "Acknowledgements",
+            "section_text": "The authors acknowledge fruitful discussions with N. Schine and A. Kollar. This work was supported by AFOSR FA95502010223, MURI FA9550-19-1-0399, FA9550-22-1-0339, NSF IMOD DMR-2019444, ARL W911NF1920181, and Simons and Minta Martin foundations. Ming Xie is supported by the Laboratory for Physical Sciences. R. Ni and Y. Zhou are supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences Early Career Research Program under Award No. DE-SC-0022885.",
+            "section_image": []
+        },
+        {
+            "section_name": "Author information",
+            "section_text": "These authors contributed equally: Beini Gao, Daniel G. Su\u00e1rez-Forero, Supratik Sarkar.\n\nJoint Quantum Institute (JQI), University of Maryland, College Park, MD, USA\n\nBeini Gao,\u00a0Daniel G. Su\u00e1rez-Forero,\u00a0Supratik Sarkar,\u00a0Tsung-Sheng Huang,\u00a0Deric Session,\u00a0Mahmoud Jalali Mehrabad,\u00a0Pranshoo Upadhyay,\u00a0Jonathan Vannucci,\u00a0Sunil Mittal\u00a0&\u00a0Mohammad Hafezi\n\nDepartment of Materials Science and Engineering, University of Maryland, College Park, MD, USA\n\nRuihao Ni\u00a0&\u00a0You Zhou\n\nCondensed Matter Theory Center, University of Maryland, College Park, MD, USA\n\nMing Xie\n\nNational Institute for Materials Science, Tsukuba, Japan\n\nKenji Watanabe\u00a0&\u00a0Takashi Taniguchi\n\nInstitute for Quantum Electronics, ETH Zurich, Zurich, Switzerland\n\nAtac Imamoglu\n\nMaryland Quantum Materials Center, College Park, MD, USA\n\nYou Zhou\n\nInstitute for Theoretical Physics, ETH Zurich, Zurich, Switzerland\n\nMohammad Hafezi\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nB.G., D.G.S.F., S.S. and M.H. conceived and designed the experiments. K.W. and T.T. supplied the necessary material for the fabrication of the sample. B.G., D.S. and R.N. designed and fabricated the sample. J.V. and S.M. collaborated with the preparation of the setup at its initial stage. B.G., D.G.S.F. and S.S. performed the experiments. B.G., D.G.S.F., S.S., T.S.H., M.J.M., M.X., A.I., Y.Z. and M.H. analyzed the data and interpreted the results. T.S.H. and M.H. elaborated on the theoretical models presented in the manuscript. B.G., D.G.S.F., S.S., M.J.M. and M.H. wrote the manuscript, with input from all authors.\n\nCorrespondence to\n                Daniel G. Su\u00e1rez-Forero or Mohammad Hafezi.",
+            "section_image": []
+        },
+        {
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+            "section_text": "The authors declare no competing interests.",
+            "section_image": []
+        },
+        {
+            "section_name": "Peer review",
+            "section_text": "Nature Communications thanks the anonymous reviewers for their contribution to the peer review of this work. A peer review file is available.",
+            "section_image": []
+        },
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+            "section_image": []
+        },
+        {
+            "section_name": "About this article",
+            "section_text": "Gao, B., Su\u00e1rez-Forero, D.G., Sarkar, S. et al. Excitonic Mott insulator in a Bose-Fermi-Hubbard system of moir\u00e9 WS2/WSe2 heterobilayer.\n                    Nat Commun 15, 2305 (2024). https://doi.org/10.1038/s41467-024-46616-x\n\nDownload citation\n\nReceived: 30 May 2023\n\nAccepted: 04 March 2024\n\nPublished: 14 March 2024\n\nVersion of record: 14 March 2024\n\nDOI: https://doi.org/10.1038/s41467-024-46616-x\n\nAnyone you share the following link with will be able to read this content:\n\nSorry, a shareable link is not currently available for this article.\n\n\n\n\n                            Provided by the Springer Nature SharedIt content-sharing initiative\n                        ",
+            "section_image": [
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+            "section_name": "This article is cited by",
+            "section_text": "Nature Communications (2025)\n\nNature Photonics (2025)\n\nNature Communications (2025)\n\nNature Reviews Physics (2025)\n\nNature Communications (2025)",
+            "section_image": []
+        }
+    ]
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181d4c4630c34a4672d2fc1e3cae257c0bd4ea34482bf51a132436daa4f25a99/metadata.json

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+        "Carbon nanotubes and fullerenes",
+        "Chemical engineering",
+        "Design, synthesis and processing",
+        "Natural gas"
+    ],
+    "license": "http://creativecommons.org/licenses/by/4.0/",
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+        {
+            "section_name": "Abstract",
+            "section_text": "The elimination of soot is particularly crucial in the pursuit of reducing pollutant emissions and achieving a circular economy. The generation of soot is a significant challenge in industries. The most effective approach to eliminate soot is to oxidize it in the high-temperature furnace. In this study, soot with different properties was produced the by non-catalytic partial oxidation process at high temperatures. The real-time oxidation processes of soot nanoparticles at 900\u00b0C were studied by in situ transmission electron microscopy (TEM). The industrial soot performs various oxidation models. The corresponding mathematical expressions of different oxidation models were developed. The incipient soot of shrinking core model (SCM) has a faster reaction rate than the partially matured soot of internal oxidation model (IOM) and the mature soot of SCM. A rare core-shell separation model (CSM) was studied. The nanostructures of soot in different oxidation models were characterized, and the relationship between macroscopic properties and nanostructures was established by Raman results and lattice fringe analysis, effective in the prediction of soot oxidation behavior.Physical sciences/Chemistry/Chemical engineeringPhysical sciences/Energy science and technology/Fossil fuels/Natural gasnon-catalytic oxidationin situ TEMhigh temperatureoxidation modelsoot nanostructure",
+            "section_image": []
+        },
+        {
+            "section_name": "Additional Declarations",
+            "section_text": "There is NO Competing Interest.",
+            "section_image": []
+        },
+        {
+            "section_name": "Supplementary Files",
+            "section_text": "Creditauthorstatement.docx",
+            "section_image": []
+        }
+    ],
+    "nature_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Soot generation is a major challenge in industries. The elimination of soot is particularly crucial to reduce pollutant emissions and boost carbon conversion. The mechanisms for soot oxidation are complex, with quantified models obtained under in situ conditions still missing. We prepare soot samples via noncatalytic partial oxidation of methane. Various oxidation models are established based on the results of in situ transmission electron microscopy experiments. A quantified maturity parameter is proposed and used to categorize the soot particles according to the nanostructure at various maturity levels, which in turn lead to different oxidation mechanisms. To tackle the challenges in the kinetic analysis of soot aggregates, a simplification model is proposed and soot oxidation rates are quantified. In addition, a special core-shell separation model is revealed through in situ analysis and kinetic studies. In this study, we obtain important quantified models for soot oxidation under in situ conditions.",
+            "section_image": []
+        },
+        {
+            "section_name": "Introduction",
+            "section_text": "Soot is a byproduct of incomplete combustion and contributes to pollution1. It is produced in large quantities not only in internal combustion engines2 but also during many chemical industrial processes involving fossil fuels, such as entrained flow gasification of coal or biomass and noncatalytic partial oxidation (NCPOX) of gaseous hydrocarbons3. In industrial processes that utilize fossil fuels, the production of soot results in carbon loss and a low yield of syngas (H2 and CO). Soot is easily entrained out by syngas and influences subsequent processes. Soot is thought to have a considerable influence on global warming4, second to that of CO25,6 and even greater than those of methane and other halocarbon greenhouse gases7. In addition, soot can be inhaled by humans and thus increases the risk of respiratory diseases8. Therefore, eliminating soot is quite important for environmental protection and the stable operation of industrial installations.\n\nThe most effective approach to eliminate soot is to oxidize it before emission. The oxidation of soot can be categorized into two types: high-temperature oxidation (>800\u2009\u00b0C) and low-temperature oxidation (300\u2009\u00b0C~700\u2009\u00b0C)9. The oxidation rate is low at low temperatures, and it is necessary to use catalysts to effectively eliminate soot10. There have been sufficient studies on low-temperature oxidation11,12,13,14, which were based on the exhaust systems of engines. However, temperatures in industrial furnaces typically exceed 800\u2009\u00b0C. In this range, the reaction rate of oxidation is greater. The competition between the formation and consumption of soot is greater. Soot undergoes cracking to form fine particles by oxidation in the furnace. We even collected a large quantity of highly oxidized soot particles in the NCPOX industrial furnace3. Therefore, it is possible to eliminate soot before emission at high temperatures.\n\nOn the macroscopic scale, the oxidation reactivity of soot is correlated to its physicochemical properties. Extensive studies have shown that the oxidation reactivity of soot is related to its carbon structure3,15,16. The soot ageing process in high-temperature furnaces involves carbonization, surface growth, and coagulation, resulting in the formation of soot particles with different degrees of graphitization17. More crystal layer defects, shorter lattice fringe lengths, and a less graphite-like structure endow soot with better reactivity and a lower oxidation activation energy18,19. However, these studies required estimating the oxidation mechanisms, which were not understood in detail.\n\nOn the microscopic scale, some empirical oxidation models, such as the shrinking core model20, the homogeneous reaction model21, and the random pore model22,23, describe the oxidation processes of carbonaceous materials. However, the oxidation of soot is very complex because of the special particle nanostructures of soot. These nanostructures make oxidation process modeling quite challenging. For example, mature soot consists of an onion-like graphitized carbon shell and an amorphous carbon core24. Studies have reported the hollow nature of soot particles during oxidation25,26,27, and but its evolution has not yet been revealed by in situ observations. Gao et al.28 found that soot particles collected from an industrial furnace at high temperature had hollow nuclei. This finding indicated that soot presented a selective oxidation phenomenon in high-temperature furnaces. It is thus necessary to study the effect of nanostructures on soot oxidation.\n\nIn situ transmission electron microscopy (TEM) provides detailed real-space information with a high spatial resolution. It allows researchers to directly analyze a particle\u2019s real-time reactions at the atomic scale. During in situ TEM experiments in the gas phase, the differentially pumped environmental TEM approach (ETEM, open type) and the windowed gas cell approach (closed type)29,30 are normally utilized. Sediako et al.31 observed noncatalytic oxidation of soot by ETEM. Through observations on the soot particles, it was hypothesized that soot has different oxidation modes. Sediako et al.32 and Toth et al.33 conducted in situ observations under various pressures and temperatures. The surface reaction and densification during soot oxidation were observed, and soot with larger diameters was likely to undergo highly nonreactive surface oxidation. Naseri et al.34 and Dadsetan et al.35 further discovered that the electron beams of TEM also have impacts on carbon black particle conversions under in situ oxidation conditions using ETEM and scanning transmission electron microscopy (STEM). However, most studies have been limited to qualitative research on soot oxidation, and kinetic studies have not been conducted on oxidation modes of soot by in situ conditions.\n\nSoot samples always consist of particles with different properties. The properties of soot produced under turbulent conditions can be more inhomogeneous because of the complex production environment in the furnace. These different particles always present various oxidation behaviors. Therefore, there is no basis to predict the oxidation mode of a soot sample. Most current characterization methods provide only the average properties of the soot samples. It is quite challenging to distinguish between different particles. To our knowledge, the mechanism and quantitative model of soot oxidation at high temperatures have rarely been studied due to the limitations of the in situ method. Therefore, it is necessary to establish an in situ strategy to obtain a reliable model to accurately describe the high-temperature oxidation behavior of soot.\n\nIn this study, a series of soot samples were produced at different molar ratios of O2 to CH4 (O2/CH4\u2009=\u20090.5, 0.6, 0.7, and 0.8), which was denoted as S1, S2, S3, and S4. The nanostructure of soot was characterized. A maturity parameter was established to quantify the differences in the nanostructures of soot particles at various maturity levels. The oxidation behaviors of these soot particles were evaluated by in situ TEM. The results can be used in kinetics studies by establishing a variety of oxidation models. A simplification approach was proposed for oxidation models of soot aggregates. The relationship between the nanostructure and macroproperties was established by considering the maturity parameters and various characterization methods, including energy dispersive X-ray spectroscopy (EDS), Raman spectroscopy, high-resolution TEM (HRTEM), and thermogravimetric analysis. The application of oxidation models in real combustion modeling was discussed by proposing two approaches. This study developed good correlations between quantitative mathematical models and advanced in situ TEM observations for the characterizations of soot oxidation.",
+            "section_image": []
+        },
+        {
+            "section_name": "Results and discussion",
+            "section_text": "Solid products and liquid products were separated at higher temperatures. No soot precursors or liquid-like incipient soot (<10\u2009nm) were observed in the TEM images. The collected particle size ranged from ~26\u2009nm to ~391\u2009nm. The morphology of the soot is shown in Supplementary Fig.\u00a0S1. The average particle size, \\({\\bar{D}}_{{{{{{\\rm{P}}}}}}}\\), decreased from 133.76\u2009nm to 83.22\u2009nm along with an increase in the O2/CH4 ratio from 0.5 to 0.8 during the production processes. Compared with the soot collected from the laminar flame, the soot from high-temperature furnace had a much larger average particle size. The effects of coalescence and surface growth were more significant in high-temperature furnace. The soot samples also presented a turbulent flame soot character. In the NCPOX process, the turbulent jet flame in the furnace was divided into a jet flow zone, a recirculation zone, and a reforming zone36. The different particle residence times in these zones resulted in an inhomogeneous distribution of the primary particle size of each soot sample.\n\nThe nanostructures of particles of different sizes were observed by HRTEM. According to the different nanostructures, soot particles were divided into 3 types, as shown in Fig.\u00a01a: young soot, partially matured soot, and mature soot.\n\na The classification of soot particles was based on the nanostructure of soot particles. b The particle size distribution of three types of soot. There were overlaps in the size ranges of different types of particles. It was more accurate to assess the maturity of particles based on their structure than relying on particle size alone. c The maturity of soot samples became younger with the O2/CH4 increased. Source data are provided as a Source Data file.\n\nThe young soot was in the early stage of ageing37,38. Soot transitions from coalescence to agglomeration and forms a particle structure from liquid-like incipient soot. Therefore, the particle size of young soot was larger than that of incipient soot. The particle boundaries were rough, and the interior showed a loose and multipored structure. The polycyclic aromatic hydrocarbon (PAH) crystalline layers presented irregular orientations. The most obvious characteristic was that there was no graphitic shell. The main particle size of the young soot ranged from 26\u2009nm to 100\u2009nm. The partially matured soot was in the middle stage of ageing39. Spherical structures had formed in the primary particles. This stage involves mainly dehydrogenation and surface reactions. The particles began to form graphitic shells, but the boundaries were still rough. The arrangement of PAH crystals changed to a concentric orientation. The main particle size was from 53\u2009nm to 143\u2009nm. The mature soot was in the late stages of ageing. The particles had formed smooth graphitic shells with a highly spherical shape. Mature soot formed larger aggregates at this stage. The main particle size was from 58\u2009nm to 281\u2009nm. The particle size distribution of the soot sample is shown in Fig.\u00a01b.\n\nThe concentrations of the three types of soot are shown in Fig.\u00a01c. The proportion of mature soot decreased with increasing O2/CH4 ratio. The proportion of partially matured soot peaked at O2/CH4\u2009=\u20090.7. The proportion of young soot increased obviously from O2/CH4\u2009=\u20090.7. The soot type of the samples was controlled by the O2/CH4 ratio. Researchers can produce soot of a particular structure to utilize or facilitate elimination.\n\nThere was a significant difference in the nanostructure of the three types of soot. However, the evolution of the nanostructure was the same for different soot samples. The three types of soot were at different maturity levels. A maturity parameter M was established to quantify the differences in the nanostructure of soot particles.\n\nSoot maturity mainly depends on two independent parameters, the C/H ratio and the primary particle size40. The C/H ratio reflects the degree of dehydrogenation and carbonization at high temperatures. The particle size reflects the degree of surface growth. However, the C/H ratio of individual particles is difficult to obtain. In addition, it is not possible to determine the maturity from the particle size alone. Studies have shown that particle growth and graphitization result in the development of a fine carbon-lattice structure during maturation41,42,43. Therefore, a parameter described by the nanostructure was adopted. The fringe length and C/H ratio can reflect the size increase and carbonization.\n\nThe carbon atom number of PAH molecules can be calculated by using Eq. (1)44.\n\nwhere \\({L}_{a,i}\\) is the fringe length of the ith PAH determined by HRTEM. The carbon-to-hydrogen ratio of \\({\\left(\\frac{C}{H}\\right)}_{{{{{{\\rm{PAH}}}}}},i}\\) can be expressed as shown in Eq. (2)45.\n\nWe found that Eq. (2) was suitable for plane PAHs. Therefore, it is appropriate for the prediction of immature soot. During maturation, defects can cause PAHs to curve from a plane structure to a three-dimensional structure. The mature soot contains more curved PAHs, which have higher C/H ratios. Here, we established a dimensionless parameter, \u03c4, to correct the hydrogen number of curved PAHs. As shown in Fig.\u00a02a, b, the H atoms are distributed only on the edge of the PAH. The actual number of H atoms is related to the length of the sides. In HRTEM, \u03c4 reflects the tortuosity of a fringe. As shown in Fig.\u00a02c, \u03c4 can be defined as shown in Eq. (3), where La is the fringe length and D is the distance between the two endpoints.\n\na, b When the plane PAHs curved to form three-dimensional structures, the number of hydrogen atom decreases further. c The tortuosity was defined as the ratio of fringe length to endpoints distance. d The maturity level of particles can be determined from the relationship between maturity parameter, M, and C/H ratios. Source data are provided as a Source Data file.\n\nThe corrected number of hydrogen atoms, \\({H}_{{{{{{\\rm{PAH}}}}}},i}\\), can be expressed as shown in Eq. (4).\n\nFor a PAH with fewer than six rings, the molecule is too small to bend. Curved PAHs often form due to the five-membered carbon rings inside them. We selected corannulene (C20H10) as the first molecule to be curved. Corannulene is a PAH with nearly circular symmetry and 20 carbon atoms. When the carbon atom number of partially matured soot and mature soot is below 20, \u03c4\u2009=\u20091. Therefore, we defined the maturity \\({M}_{{{{{{\\rm{particle}}}}}},j}\\) of a single particle j as the ratio of the number of C atoms to the corrected number of H atoms of all PAHs, as shown in Eq. (5).\n\nWhen \\({L}_{a,i} \\, < \\,0.652,\\,{\\tau }=1\\);\\(\\,{L}_{a,i}\\ge 0.652,\\,{\\tau }=\\frac{{L}_{a}}{D}\\). The same method can be used to determine the average maturity of multiple particles, as shown in Eq. (6).\n\nWhen \\({L}_{a,i,j}\\, < \\, 0.652,\\,{\\tau }=1;{L}_{a,i,j}\\ge 0.652,\\,{\\tau }=\\frac{{L}_{a}}{D}\\). The \\({M}_{{{{{{\\rm{sample}}}}}}}\\) values of the soot samples were determined and compared to the results of elemental analysis. The relationship is shown in Fig.\u00a02d. Since the curve passes through the origin, the allometric function was performed.\n\nDue to the different analytical principles of instruments, the macroscopic C/H ratio determined through Eq. (7) may be underestimated. The significance of \\({M}_{{{{{{\\rm{sample}}}}}}}\\) lies in reflecting the extent of growth and carbonization of the sample. It is generally recognized that the C/H ratio of incipient soot is 1.4~2.5 and that of mature soot is 8~2046,47,48,49. It can be determined from Eq. (7) that the \\({M}_{{{{{{\\rm{sample}}}}}}}\\) value of incipient soot is 0.83~1.42, and that of mature soot is 4.21~9.91. Most of the samples were found to be in the middle stage of maturation. This was attributed to the high concentration of partially matured soot in the samples. We correlated the 3 types of soot with the general sample by calculating the \\({M}_{{{{{{\\rm{sample}}}}}}}\\) value. The young soot corresponded to the soot samples with C/H ratios of 2.5~4.1, the partially matured soot corresponded to samples with C/H ratios of 4.1~8, and the mature soot corresponded to samples with C/H ratios or 8~20.\n\nThe calculated maturity level of soot samples well matched the corresponding nanostructure obtained by TEM, which further proved the rationality of \\({M}_{{{{{{\\rm{sample}}}}}}}\\). This enables the characterization of soot nanoparticles through quantitative analysis and correlates the nanostructures with macroproperties of soot. As the maturation process of soot is the same50,51,52, the maturity level and corresponding oxidation model of soot from different conditions can be determined by \\({M}_{{{{{{\\rm{sample}}}}}}}\\).\n\nIn situ oxidation experiments of soot particles were carried out. The oxidation modes depended greatly on the nanostructures of soot with different maturity levels.\n\nThe oxidation process of young soot is shown in Fig.\u00a03a. The particles shrank and formed a core during oxidation. The primary particle size continued to decrease throughout the process. The reaction was very fast in the initial stage of oxidation. The particle size decreased, and the bond between particles was broken. The soot aggregate was divided into small particles. In the middle stage, the small particles formed many pore structures and cracked into pieces. The pieces agglomerated to form spherical clusters, which may be caused by van der Waals interactions53. In the final stage, the spherical clusters were continuously oxidized until a small amount of poorly reactive fragments remained. The in situ oxidation showed fragmentation and agglomeration during oxidation. This was related to the low carbonization degree of young soot. The oxidation of young soot was named the fast-shrinking core model (SCM).\n\na Young soot, b, c partially matured soot, and d mature soot.\n\nThe oxidation of partially matured soot occurred in two different modes. One is shown in Fig.\u00a03b. The oxidation started from the interior of the particles, and the particle size was unchanged. Several hollow structures appeared inside the particles, which did not necessarily originate from the center of the primary particle. As the oxidation progressed, the hollow structures increased in size. The particles outside the aggregates were consumed earlier than the middle particles. The final stage was the oxidation of the carbon shell. When the hollow structures occupied most of the particle, the particles were not able to maintain the spherical structure and cracked into small pieces. These small pieces agglomerated and were oxidized.\n\nThe formation of hollow regions and the shell fragmentation of partially matured soot were evaluated by in situ TEM. The surface of partially matured soot is not dense enough, and oxygen easily entered the interior of the particles through pores. The reactivity of amorphous carbon inside the particles was much greater than that of the graphitized shell. Therefore, the interior was preferentially oxidized and formed an internal oxidation model (IOM).\n\nAnother kind of core-shell separation model (CSM) was observed by in situ TEM, as shown in Fig.\u00a03c. In the early stage of the reaction, the reaction was very slow, and no apparent change was observed. As the reaction proceeded, the shell and the core were separated, and the core began to shrink. The core was always oxidized and remained spherical, and no hollow structures were observed in the core. The core did not always contract around the center of the particle sphere. Finally, a graphitized shell remained, which was difficult to oxidize. The particle size remained constant throughout the CSM oxidation process.\n\nTo study the CSM mechanism, the soot particle structure was further analyzed by HRTEM and EDS. Figure\u00a04a shows the HRTEM image, HAADF-STEM image, and corresponding EDS elemental maps of C and O in particles subjected to the CSM. Figure\u00a04b shows images of other soot particles. Some fine PAHs were observed in the shell part of the particles subjected to the CSM. The locations of these PAHs were consistent with the separated interfaces. These PAH structures caused carbon atoms to bond with sp3 or mixed sp2-sp3 hybridization, which induced bending and defects in the crystalline layers54. This is one possible reason for core-shell separation during oxidation. As shown in Fig.\u00a04c, the shell of soot aggregated according to the CSM was held together by chemical bonds. The shell was formed by surface growth, and the separated interface was likely to be the initial position of surface growth. The oxidation reactivity of carbon on either side of the separated interface was significantly different. According to the EDS results, the distribution of C was uniform in the two kinds of particles. However, the concentration of O was much greater at the separated interface. These oxygen-containing functional groups can cause surface defects in graphite crystal layers. Furthermore, these functional groups reduced the reactivation energy for oxidation, which caused the carbon in the corresponding position to be preferentially consumed by oxidation55,56. This is another possible reason for the core-shell separation during the oxidation of partially matured soot.\n\nThere are some fine PAHs locating at the separated interface of a soot particles of CSM, comparing to b other soot particles. Oxygen functional groups (yellow) are more concentrated at the separation interface, compared to carbon (red). c The graphitic shell of the soot remains intact and was not fragmented or oxidized.\n\nCSM is different from the previously reported models, and the evolution mechanism of the CSM was revealed in this study. This provides researchers with a more comprehensive understanding of soot oxidation processes. The cage structure of soot formed by the CSM was stable and had strong oxidation resistance, which can be potentially used as a storage and transportation medium for drugs or protein57.\n\nThe reaction time of mature soot was the longest among the oxidation models, as shown in Fig.\u00a03d. The oxidation process started from the surface and proceeded only on the surface. The particle size decreased slowly. The periphery of the particles was damaged, resulted in the formation of several small-scale defects. However, no internal oxidation was observed in this case. It is indicated that the graphitized shell of mature soot is dense and thick enough. Naseri et al.34 noted that the graphitic shell of soot was highly resilient to O2, and the activation energy for surface oxidation was high. The mature soot presented an oxidation mode of slowly shrinking throughout the process with spherical particles. It was described as slow SCM.\n\nThe in situ oxidation showed that the oxidation modes were highly dependent on the nanostructure of the soot particles. The nanostructure changed with the maturation process, and the oxidation mode changed. At the same time, these nanostructures maintained the sphericity of the particles. As oxidation proceeded, these structures were destroyed, leading to fragmentation of the spherical particles.\n\nTo accurately calculate the reaction rate of soot from the experimental results, mathematical models describing the oxidation process of soot were established. The intrinsic oxidation reaction rate was expressed as Eq. (8)58 according to reaction (9)59. There was a first-order dependency on the oxygen concentration60.\n\nwhere \u03bb is the number density of the surface reactive site, \\({S}_{{{{{{\\rm{soot}}}}}}}\\) is the area of the reaction surface on the soot particle, \\(K(T)\\) is the reaction rate coefficient at the reactive site related to temperature, and \\({c}_{{{{{{\\rm{O}}}}}}_2}\\) is the concentration of oxygen. The temperature term, \\(K(T)\\), can be expressed as shown in Eq. (10) according to the Arrhenius equation.\n\n\\({S}_{{{{{\\rm{soot}}}}}}\\) is related to the conversion rate x, and x can be obtained by experiments. Therefore, accurate models must be established to calculate the x values of different soot oxidation processes, and then kinetic parameters can be obtained. According to the reaction process of soot particles, it is assumed that the primary particles of soot are solid carbon spheres with uniform density. Based on the in situ oxidation process, the conversion rate x of soot particles can be obtained from the projected area S.\n\nThe oxidation models of young soot and mature soot are shown in Fig.\u00a05a, b. According to the volume formula for a sphere, the primary particle volume V at a certain conversion and the initial volume V0 can also be given by S and S0 as Eqs. (11) and (12):\n\nwhere S0 denotes the initial projected area. Since the particle density is uniform, x can be obtained by using Eq. (13).\n\na SCM of young soot particles. b IOM of partially matured soot particles. c CSM of partially matured soot particles. d SCM of mature soot particles. e, f The simplification approach divided or merged the soot aggregates (yellow) into multiple adjacent equivalent spheres (black). The radius and projected area of the equivalent sphere were used for calculation as new parameters instead of the radius and projected area of soot aggregates. g, h The conversion rate and reaction rate of different particles were obtained by various simplified models. The reaction rate of models varied with time, which resulted in a challenge in the selection of models during the oxidation of multiple particles. Source data are provided as a Source Data file.\n\nAs shown in Fig.\u00a05a, b, the surface area, Ssoot, decreases as the oxidation progresses. Thus, the surface area of the particle can be expressed as a function of x.\n\nwhere Ssoot,0 is the surface area at x\u2009=\u20090, and S0 is the initial projected area. Substituting Eqs. (13), (14), and (15) into Eq. (8) results in Eq. (16).\n\nTherefore, the activation energy of the oxidation reaction can be obtained.\n\nFor the IOM, it was assumed that hollow structures were formed at random positions inside the particles and that the particle size remained unchanged during oxidation. The hollow structure was regarded as spherical and grew from the nuclei to the boundary of the particle until the reaction was complete, as shown in Fig.\u00a05c. Notably, the projection area measured during the experiment was the area of the annular part. The volume of the remaining unoxidized part is determined as shown in Eq. (17).\n\nAccording to Eq. (13), the expression of the conversion rate can be obtained by Eq. (18).\n\nFor the IOM, the active area was the inner surface area of the particle, and the surface area increased gradually with the reaction progress. Thus, the surface area of the particle can be expressed as shown in Eq. (19).\n\nThe oxidation model of partially matured soot is shown in Fig.\u00a05d. According to the in situ oxidation process in Fig.\u00a03c, the contrast of the shell part was much lower than that of the core, indicating that the shell part was very thin. Assuming that the volume of the shell part is a certain value V\u2019, the volume of the particle can be expressed as shown in Eq. (20).\n\nConsequently, the conversion rate was found to be\n\nwhere\n\nIn the CSM, the reactivity of the residual shell was very poor; accordingly, the reactive area \\({S}_{{{{{{\\rm{soot}}}}}}}\\) was the surface area of the core.\n\nThe proposed models are suitable for soot samples with C/H ratios >2.5 and soot particles with \\({M}_{{{{{{\\rm{sample}}}}}}}\\) greater than 1.42. They may not be suitable for liquid-like incipient soot (<10\u2009nm).\n\nSoot is often found in aggregates. The fractal dimension of aggregates is much larger than that of primary particles, which leads to a large error of x calculated by means of Eq. (13). Models for soot aggregates are needed.\n\nPrimary particles in TEM images can be identified by computer programming61, which yields the equivalent radius (R1, R2, R3,\u2026\u2026) and center coordinates (x1, x2, x3,\u2026\u2026y1, y2, y3,\u2026\u2026) of the primary particles in aggregates. Consequently, x of soot aggregates can be obtained by these parameters. Nevertheless, the expressions for x and Ssoot are too complicated, and they cannot be integrated by Eq. (8). The activation energy cannot be obtained by this approach. The complicated formula is unfriendly for engineering applications.\n\nTo address this issue, a simplified approach was established to obtain a suitable expression of x for soot aggregates. The aggregates were processed as shown in Fig.\u00a05e, f.\n\nWhen the spherical center of the smaller primary particle was inside the larger particle, the two particles were treated as one spheroid (Fig.\u00a05e). When the center of the smaller primary particle was outside the larger particle, the two particles were divided into two nonoverlapping spheroids at the intersection. Subsequently, a new equivalent spherical radius (r1, r2, r3, \u2026\u2026) and projected area (s1, s2, s3, \u2026\u2026) were obtained. The total projected area of the soot aggregate was the sum of the projected area of new spheroids, as shown in Eq. (24). Since the projected areas of new spheroids were calculated from the in situ TEM images, the total projected area was not affected by the simplification approach. The approach did not require calculating the volume of intersecting parts. The total volume was expressed as Eq. (25). Therefore, the conversion rate of soot aggregates x was determined by means of Eq. (26).\n\nThe simplified aggregates no longer consisted of spherical particles but consisted of hypothetical equivalent spheres. The best advantage was that the conversion expression of aggregates was similar to that of single particles. This means that the model of aggregates is suitable for subsequent kinetic calculations. This simplified approach facilitated rapid and precise calculation of the reaction rates for various types of soot by the researchers.\n\nSometimes, small particles on the outside of the aggregate were eliminated first, which required researchers to track the oxidation progress of individual primary particles for accurate results. When the primary particle sizes in one aggregate were not very different, the projected area and volume were expressed as follows.\n\nwhere n is the number of primary particles. Thus, Eq. (26) was reduced to Eq. (29), which is the same as Eq. (13).\n\nIn this situation, the in situ TEM results were used for kinetics studies.\n\nThe conversion rates of aggregates oxidized with the IOM and the CSM were expressed as Eq. (30) and Eq. (31) by the same approach. The simplification approach facilitates the kinetic calculations of soot aggregates oxidations, and these models could be used to quantify the oxidation process of soot.\n\nThe developed mathematical models were verified based on the experimental results obtained by in situ TEM. The relationships of the conversion rate and reaction rate changing with time are shown in Fig.\u00a05g, h. The processed results accurately describe the soot oxidation behavior compared with the real-time oxidation processes. The first 50\u2009seconds was the heating stage, and the reaction rate increased with increasing temperature. Young soot shows the highest reactivity. In the constant-temperature reaction stage, the reaction rate decreased gradually. This was related to the decrease in the active surface area. For the partially matured soot oxidized with the IOM, the reaction rate was very high in the early stage. This was due to the oxidation of amorphous carbon with high reactivity in the particle core. The reaction rate decreased gradually when the conversion rate exceeded 86.8%. This was related to the oxidation of the less active graphitic shell. For partially matured soot oxidized with the CSM, the reaction rate was very low in the early stage, which was due to shell separation. When the separation stage finished, the reaction rate began to increase, while the conversion rate was only 0.6%. As the oxidation proceeded, the core of the particle began to shrink. The reaction transitioned from the oxidation of a small amount of graphitized carbon to that of amorphous carbon. In the later stage, the reaction rate decreased rapidly when the conversion rate exceeded 83.8%. Finally, a highly graphitized shell with poor reactivity was left. Partially matured soot oxidized with CSM had the highest instantaneous reaction rate. The average reactivity of soot oxidized with the IOM and the CSM was similar for partially matured soot. The instantaneous reaction rate of mature soot was the lowest. The reaction rate of mature soot oxidized with SCM gradually increased with carbon conversion. The reaction rate eventually fluctuated around 0.5%\u2009s\u22121. As the oxidation proceeded, the reactivity increased. The oxidation rate change during the processes reflected the nanostructure of soot particles.\n\nThe reaction rate varied greatly among different models, so it is very important to choose the correct oxidation model according to the maturity level of soot particles.\n\nThe oxidation reactivity of the four samples is shown in Fig.\u00a06a. The reactivity, R0.9, of soot increased as the ratio of O2/CH4 increased from 0.5 to 0.8 during the NCPOX process. The reactivity of soot depends greatly on the carbon structure3. The carbon structure of the samples was analyzed by Raman spectroscopy. With an increase in the O2/CH4 ratio from 0.5 to 0.8 during the NCPOX process, the integral band area ratio of the D band to G band (ID1/IG) of soot samples increased from 3.23 to 3.80, while the degree of graphitization of the particles decreased.\n\na The reactivity of soot increased as the ratio of O2/CH4 increased from 0.5 to 0.8. b The increase of reactivity was because the graphitization degree of soot samples decreased. c The oxidation models can be selected by maturity parameters. Source data are provided as a Source Data file.\n\nThe relationship between ID1/IG and R0.9 is shown in Fig.\u00a06b. The oxidation reactivity of soot was negatively correlated with ID1/IG. An increase in the maturity of the soot samples led to an increase in the average graphitization degree of the samples. This in turn resulted in a decrease in the oxidation reactivity. The quantified relationships between O2/CH4 ratio and maturity parameters are shown in Fig.\u00a06c. According to the \\({M}_{{{{{{\\rm{sample}}}}}}}\\) of samples, S1 (O2/CH4\u2009=\u20090.5) belongs to the SCM, and S2, S3, and S4 (O2/CH4\u2009\u2265\u20090.6) belong to the IOM, which corresponds to the concentration distribution of soot shown in Fig.\u00a01c. It was found that the selection of the oxidation model depends on the main particle type in the soot sample. For more macroscopic conditions in the flame, the nanostructures change differently. The effect of various macroscopic conditions on application of our oxidation models can be ultimately evaluated by the maturity parameter of soot samples.\n\nTwo approaches are proposed to obtain the maturity parameter for real combustion modeling. (1) In the situation that soot samples can be obtained, the maturity parameter is directly calculated from the nanostructure as proposed above. (2) In the situation that soot samples cannot be obtained, the maturity parameter can be theoretically calculated using the number density function by quantifying the carbon atom number and C/H ratio62 of the as-formed soot in combustion modeling. The oxidation models can be selected on that basis to calculate the reaction rate in population balance equations which has been applied in counter flow flame, diffusion flame, and premixed flame63,64,65,66. As soot maturation progresses, the oxidation model can be changed with maturity parameters. Compared to the current modeling using empirical equations, the oxidation models provide more detail about oxidation process thereby more accurate results. This means that the soot oxidation behavior can be theoretically predicted by given the macroscopic parameters. More details can be referred to the Supplementary Discussion.\n\nThis study established three soot oxidation models applicable to different types of soot basing on the particle oxidation behavior. The corresponding oxidation behavior can be predicted by soot maturity under specific combustion conditions. The models can be used for kinetic calculations and optimize soot oxidation process in engine system and industrial furnace.",
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+        {
+            "section_name": "Methods",
+            "section_text": "NCPOX is a mature technology that involves a typical turbulent fuel-rich flame resulting from the combustion of gas fuels. The soot produced during the NCPOX process has properties similar to those of other soot obtained from gas fuels. The specific differences in properties have been discussed in our previous work3,27. The soot samples in this study were produced by a lab-scale device via the NCPOX process. The conditions used for soot production are listed in Table\u00a01. We quantified all the reactants and products. The properties of soot were characterized. These samples have certain regularity in properties and are more suitable for comparative study than ordinary commercial carbon black.\n\nCH4 and O2 reacted in a corundum tube at atmospheric pressure. The molar ratio of H2 to CO at the outlet was ~2. The reaction temperature was controlled to be constant at 1200 \u00b0C. Soot was collected at the outlet through a hopper with a filter screen. The hopper was covered by alumina bulk fiber, which prevented the soot precursor from condensing in the hopper. As a result, no soot was adsorbed on the surface of the soot particles, which was verified by the Soxhlet extraction method. The samples were dried at 105\u2009\u00b0C for 24\u2009hours for further oxidation and characterization.\n\nThe oxidation behaviors of individual soot particles were determined by in situ TEM. In situ aberration-corrected STEM experiments were performed using a Climate S3 in situ TEM holder (DENS Solutions Company), allowing dynamic observation at high temperatures. The oxidation reaction was confined to a tiny gas cell within 5\u2009\u03bcm in thickness. The reaction gas cell consisted of a pair of microelectromechanical system (MEMS) chips with an amorphous silicon nitride (SiNx) membrane for TEM observation in real time. A total of 0.5\u2009mg of each soot sample was sonicated with 20\u2009mL of ethyl alcohol for 10\u2009min at 45\u00b0C and finally deposited on chips. It was verified that this method can yield the best concentration in the windows of the membrane. The reaction pressure was 100 mbar. The pressure was selected to control the oxidation processes at an appropriate reaction rate, facilitating the clear observation of particle evolution. The oxidation agent (0.5% O2 and 99.5% N2) was continuously pumped into the gas cell from the inlet. The oxidation agent was in full contact with the soot particles before the reaction. During the reaction, a very small quantity of the CO2 product was pumped out. At this microscale, the diffusion effect was negligible, and the reaction was considered an intrinsic reaction.\n\nThe soot samples were heated to 400\u2009\u00b0C from ambient temperature through chips in the vacuum. The observation position and magnification of the soot samples were adjusted. Then, the oxidation agent was pumped in until the pressure stabilized. The soot samples could not be oxidized at 400\u2009\u00b0C. Oxidation was initiated by rapidly increasing the temperature to 900\u2009\u00b0C at a heating rate of 10\u2009\u00b0C\u2009s\u22121. Images of the samples during oxidation were recorded by TEM, clearly capturing the evolution of the internal structure of the particles. The experimental process was shown in Supplementary Fig.\u00a0S2. The magnifications of the images obtained during in situ oxidation were controlled below 350 kx with less electron beam irradiation, ensuring a low level of ionization of O2. The continuous flow from the inlet to the outlet further minimized the effect of ionized oxygen on the reaction.\n\nThe oxidation of soot groups at 900\u2009\u00b0C was analyzed by means of a thermogravimetric analyser (NETZSCH STA 2500 Regulus). Approximately 3\u2009mg of soot sample was heated to 900\u2009\u00b0C at a heating rate of 20\u2009\u00b0C\u2009min\u22121 in a N2 atmosphere. Then, it was switched to an oxidation atmosphere. The oxidation atmosphere consisted of 0.5% O2 and 99.5% N2, and the concentration of O2 was the same as that in the in situ oxidation processes. This lower O2 concentration can prevent soot from combusting too rapidly at high temperatures. A total flow rate of 200\u2009mL\u2009min\u22121 of oxidation agent was employed to eliminate the diffusion effects. The conversion ratio, x, of the soot oxidation process was defined as shown in Eq. (32).\n\nwhere m0 is the initial mass of the sample, m is the mass of the sample at a certain moment, and m\u221e is the remaining mass of the sample. The oxidation reactivity was evaluated by the reactivity index R0.9, which was defined as follows in Eq. (33).\n\nwhere \\({t}_{x=0.9}\\) is the oxidation time required for x\u2009=\u20090.9.\n\nTEM images were obtained for primary particle size analysis. The boundary of each primary particle was fitted to an ellipse by a manual approach. The maximum Feret\u2019s diameter, \\({d}_{\\max }\\), and the minimum Feret\u2019s diameter, \\({d}_{\\min }\\), of the ellipse were determined by means of ImageJ software. The primary particle diameter, \\({D}_{{{{{{\\rm{P}}}}}}}\\), was determined from the arithmetic average of \\({d}_{\\max }\\) and \\({d}_{\\min }\\). The primary particle size, \\({\\bar{D}}_{{{{{{\\rm{P}}}}}}}\\), of the soot sample was the average of \\({D}_{{{{{{\\rm{P}}}}}}}\\). The specific formula is shown in the Supplementary Methods. More than 2000 particles from 4 samples were measured in this study.\n\nThe HRTEM images of the static nanostructure of soot were obtained on a ThermoFisher Talos F200X. The original images were processed by contrast enhancement, top-hat transformation, binarization, and skeletonization, and then the meaningless fringes that were shorter than the size of the aromatic cycle (0.246\u2009nm) were removed67. The final image was used for fringe analysis. The example of image processing is shown in Supplementary Fig.\u00a0S3. Statistical results were obtained by the same processing of multiple groups of images.\n\nThe C/H ratio of the soot samples was determined by an elemental analyser (VARIO EL CUBE) on a dry and ash-free basis.\n\nThe carbon structures were characterized by Raman spectroscopy (ThermoFisher DXR), which was carried out by using a He-Ne laser (0.5\u2009mW, 455\u2009nm). The Raman results in the first-order Raman spectrum region were deconvoluted by means of the five-band method68 with the following bands: G (1580\u2009cm\u22121), D1 (1350\u2009cm\u22121), D2 (1610\u2009cm\u22121), D3 (1550\u2009cm\u22121), and D4 (1180\u2009cm\u22121). The distributions of different carbon structures of the soot samples are shown in the Supplementary Fig.\u00a0S4. The integral band area ratio of the D band to G band (ID1/IG) was used to quantify the degree of graphitization of soot samples69.\n\nSTEM characterization was performed by means of a ThermoFisher Themis Z microscope equipped with two aberration correctors under 300\u2009kV. HAADF-STEM images were recorded using a convergence semi-angle of 11 mrad and inner and outer collection angles of 59 and 200 mrad, respectively. EDS was carried out using 4 in-column Super-X detectors.\n\nFurther information on research design is available in the\u00a0Nature Portfolio Reporting Summary linked to this article.",
+            "section_image": []
+        },
+        {
+            "section_name": "Data availability",
+            "section_text": "All data that support the plots within this manuscript are available. Source Data file has also been deposited in Figshare under accession link https://doi.org/10.6084/m9.figshare.2403918070.\u00a0Source data are provided with this paper.",
+            "section_image": []
+        },
+        {
+            "section_name": "References",
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+            "section_image": []
+        },
+        {
+            "section_name": "Acknowledgements",
+            "section_text": "This work was financed by the National Natural Science Foundation of China (22178114) (F.C.W.) and the China Scholarship Council (M.G.), the Science and Technology Commission of Shanghai Municipality (22ZR1415700) (S.D.), Shanghai Rising-star Program (20QA1402400) (S.D). Thanks for the support of the Frontiers Science Center for Materiobiology and Dynamic Chemistry and the Feringa Nobel Prize Scientist Joint Research Center at East China University of Science and Technology.",
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+        },
+        {
+            "section_name": "Author information",
+            "section_text": "Institute of Clean Coal Technology, East China University of Science and Technology, Shanghai, 200237, P.R. China\n\nMing Gao,\u00a0Lu Ding,\u00a0Yunfei Gao,\u00a0Zhenghua Dai,\u00a0Guangsuo Yu\u00a0&\u00a0Fuchen Wang\n\nDepartment of Mechanical Engineering, National University of Singapore, Singapore, 117576, Singapore\n\nMing Gao\u00a0&\u00a0Wenming Yang\n\nEngineering Research Center of Resource Utilization of Carbon-containing Waste with Low-carbon Emissions, Ministry of Education, Shanghai, 200237, P.R. China\n\nMing Gao,\u00a0Lu Ding,\u00a0Yunfei Gao,\u00a0Zhenghua Dai,\u00a0Guangsuo Yu\u00a0&\u00a0Fuchen Wang\n\nKey Laboratory for Advanced Materials and Feringa Nobel Prize Scientist Joint Research Center, Institute of Fine Chemicals, School of Chemistry & Molecular Engineering, East China University of Science and Technology, Shanghai, 200237, P.R. China\n\nYongjun Jang\u00a0&\u00a0Sheng Dai\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nM.G. and Y.J.J. conducted the experiments; M.G. designed the research, analyzed the data, and wrote the paper; L.D., Y.F.G. and W.M.Y. contributed to writing and editing; Z.H.D., G.S.Y. and F.C.W. supervised the work; F.C.W. and S.D. conceptualized and directed the project.\n\nCorrespondence to\n                Lu Ding, Sheng Dai, Wenming Yang or Fuchen Wang.",
+            "section_image": []
+        },
+        {
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+            "section_text": "The authors declare no competing interests.",
+            "section_image": []
+        },
+        {
+            "section_name": "Peer review",
+            "section_text": "Nature Communications thanks Alberto Baldelli and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. A peer review file is available.",
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+        {
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+            "section_text": "Open Access  This article 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. The images or other third party material in this article are included in the article\u2019s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article\u2019s 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/.\n\nReprints and permissions",
+            "section_image": []
+        },
+        {
+            "section_name": "About this article",
+            "section_text": "Gao, M., Jang, Y., Ding, L. et al. Mechanism of the noncatalytic oxidation of soot using in situ transmission electron microscopy.\n                    Nat Commun 14, 6256 (2023). https://doi.org/10.1038/s41467-023-41726-4\n\nDownload citation\n\nReceived: 14 April 2023\n\nAccepted: 15 September 2023\n\nPublished: 06 October 2023\n\nVersion of record: 06 October 2023\n\nDOI: https://doi.org/10.1038/s41467-023-41726-4\n\nAnyone you share the following link with will be able to read this content:\n\nSorry, a shareable link is not currently available for this article.\n\n\n\n\n                            Provided by the Springer Nature SharedIt content-sharing initiative\n                        ",
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+        "https://github.com/NLykoskoufis/fenrichcpp",
+        "/articles/s41467-023-42405-0#ref-CR38"
+    ],
+    "subject": [
+        "Cancer genetics",
+        "Cancer genomics",
+        "Colorectal cancer",
+        "DNA transposable elements",
+        "Gene regulation"
+    ],
+    "license": "http://creativecommons.org/licenses/by/4.0/",
+    "preprint_pdf": "https://www.researchsquare.com/article/rs-1138340/v1.pdf?c=1639790329000",
+    "research_square_link": "https://www.researchsquare.com//article/rs-1138340/v1",
+    "nature_pdf": "https://www.nature.com/articles/s41467-023-42405-0.pdf",
+    "preprint_posted": "17 Dec, 2021",
+    "research_square_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Transposable elements (TEs) are interspersed repeats that contribute to more than half of the human genome, and TE-embedded regulatory sequences are increasingly recognized as major components of the human regulome. Perturbations of this system can contribute to tumorigenesis, but the impact of TEs on gene expression in cancer cells remains to be fully assessed. Here, we analyzed 275 normal colon and 276 colorectal cancer (CRC) samples from the SYSCOL colorectal cancer cohort and discovered 10,111 and 5,152 TE expression quantitative trait loci (eQTLs) in normal and tumor tissues, respectively. Amongst the latter, 376 were exclusive to CRC, likely driven by changes in methylation patterns. We identified that transcription factors are more enriched in tumor-specific TE-eQTLs than shared TE-eQTLs, indicating that TEs are more specifically regulated in tumor than normal. Using Bayesian Networks to assess the causal relationship between eQTL variants, TEs and genes, we identified that 1,758 TEs are mediators of genetic effect, altering the expression of 1,626 nearby genes significantly more in tumor compared to normal, of which 51 are cancer driver genes. We show that tumor-specific TE-eQTLs trigger the driver capability of TEs subsequently impacting expression of nearby genes. Collectively, our results highlight a global profile of a new class of cancer drivers, thereby enhancing our understanding of tumorigenesis and providing potential new candidate mechanisms for therapeutic target development.",
+            "section_image": []
+        },
+        {
+            "section_name": "Additional Declarations",
+            "section_text": "Yes there is potential Competing Interest.\nEmmanouil T. Dermitzakis is currently an employee of GSK. The work presented in this manuscript was performed before he joined GSK. All other authors declare no competing interests.",
+            "section_image": []
+        },
+        {
+            "section_name": "Supplementary Files",
+            "section_text": "SupplementaryTables.xlsxAll tables",
+            "section_image": []
+        }
+    ],
+    "nature_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Transposable elements (TEs) are prevalent repeats in the human genome, play a significant role in the regulome, and their disruption can contribute to tumorigenesis. However, TE influence on gene expression in cancer remains unclear. Here, we analyze 275 normal colon and 276 colorectal cancer samples from the SYSCOL cohort, discovering 10,231 and 5,199 TE-expression quantitative trait loci (eQTLs) in normal and tumor tissues, respectively, of which 376 are colorectal cancer specific eQTLs, likely due to methylation changes. Tumor-specific TE-eQTLs show greater enrichment of transcription factors, compared to shared TE-eQTLs suggesting specific regulation of their expression in tumor. Bayesian networks reveal 1,766 TEs as mediators of genetic effects, altering the expression of 1,558 genes, including 55 known cancer driver genes and show that tumor-specific TE-eQTLs trigger the driver capability of TEs. These insights expand our knowledge of cancer drivers, deepening our understanding of tumorigenesis and presenting potential avenues for therapeutic interventions.",
+            "section_image": []
+        },
+        {
+            "section_name": "Introduction",
+            "section_text": "Understanding the mechanisms underlying tumorigenesis has been one of the main research questions in cancer biology. While somatic mutations, chromosomal rearrangements and gene amplification are the three main hallmarks driving cancer progression, they are unable to provide a complete explanation of tumorigenesis. Recent discoveries have demonstrated that transposable elements (TEs) have contributed to the evolution of gene regulation and can alter the landscape of gene expression in development and disease1,2,3,4,5. Transposable elements (TEs) are interspersed repeats that contribute more than half of the human genome. TEs, more specifically TE-embedded regulatory sequences (TEeRS) are broadly active during the phases of genome reprogramming that occur in the germline and the early embryo, and then controlled by epigenetic mechanisms that still allow their finely orchestrated participation in biological events as diverse as brain development, immune responses, and metabolic control. The aberrant re-activation of TEeRSs is observed under certain conditions and disease states, notably cancer6,7,8. Transcription is defined by the coordinated activity of regulatory elements which are modulated by genetic variation. Thus, we speculate that transposable element expression is influenced by regulatory non-coding variants, also called expression Quantitative Trait Loci (eQTLs), known to contribute to the onset and progression of complex diseases like cancer9,10. To build on this concept, we set out to analyze the interplay between regulatory variants (eQTLs), transposable elements and gene expression to characterize the genetic perturbation of TE and gene expression in cancer. In this paper, we integrated genome-wide genotyping data (genotype array) and transcriptomic profiles (bulk RNA-sequencing) from the Systems Biology of Colorectal Cancer (SYSCOL) cohort comprising of 275 and 276 normal and tumor samples, respectively. We discovered thousands of eQTLs regulating TE expression both in normal and tumor as well as many tumor specific TE-eQTLs likely driven by methylation changes. Notably, we observed that tumor-specific TE-eQTLs show a greater enrichment of transcription factors compared to shared TE-eQTLs suggesting that TEs more specifically regulated in tumor. Furthermore, by using Bayesian networks, we discovered thousands of TEs acting as mediators of genetic effects, significantly altering the expression of nearby genes, including many known cancer driver genes and showed that tumor-specific TE-eQTLs trigger the driver capability of TEs. Overall, we show that TEs are important mediators of genetic effects onto nearby genes, specifically in cancer, highlighting, their importance during tumorigenesis.",
+            "section_image": []
+        },
+        {
+            "section_name": "Results",
+            "section_text": "To measure the expression of TEs in CRC, we examined transcriptomes obtained by RNA-seq from 275 normal and 276 CRC samples from the SYSCOL cohort11. We quantified TE and gene expression using an in-house curated TE annotation list originating from the RepBase database12 that contains approximately 4.6 million individual TE loci. These annotations were merged with gene annotation from ensembl (v19). Filtering for uniquely mapped reads (Methods) to obtain robust estimates of TE expression resulted in 50,921 TEs and 17,430 genes (protein coding and lincRNAs). We observed that the majority of expressed TEs present in our dataset are SINEs (Alu and MIR), LINEs (L1 and L2) as well as different subfamilies of Long Terminal Repeats (LTRs) and DNA transposons. However, when we looked at the proportion of expressed TEs per subfamily, SVA and ERVK were most prominent (Fig.\u00a01a, Supplementary Fig.\u00a01). Additionally, we used available data from Encode13 and miRbase14 to generate a list of regulatory regions and discovered that 13,590 expressed TEs overlapped with at least one previously identified regulatory element. We also discovered that expressed TEs are significantly enriched for most regulatory regions, except for enhancers, compared to non-expressed TEs (Supplementary Data\u00a01; Fig.\u00a01b, Supplementary Fig.\u00a02) highlighting their potential role in gene expression regulation.\n\na Barplot showing the proportion of uniquely mapped and quantified TE subfamilies in our dataset. b Pie chart showing the proportion of TEs with different types of regulatory elements within their sequence. We uniquely mapped and quantified 50,921 TEs. The majority of them are SINEs from the Alu and MIR family, L1 and L2 TEs from the LINE family and different subfamilies of LTRs as well as some DNA transposons. When we looked at the proportion of expressed TE per subfamily, we observed that SVA and ERVK are most prominent. Additionally, 13,590 out of the 50,921 TEs contain regulatory elements within sequence.\n\nUsing TE expression quantifications and genotype data we first sought to assess the impact of inter-individual genetic variation on TE expression. We conducted cis-eQTL analysis followed by a forward backward stepwise conditional analysis (Methods) and discovered a total of 10,231 and 5199 TE-eQTLs as well as 6955 and 1552 gene eQTLs in normal and tumoral tissue, respectively (Supplementary Figs.\u00a03 and 4; Supplementary Data\u00a02, 3). Similarly to gene-eQTLs, TE-eQTLs displayed stronger effects and density closer to the transcription start site (TSS) in both normal and tumor samples (spearman rho\u2009=\u2009\u22120.33, p\u2009<\u20092.2e\u221216 in normal, spearman rho\u2009=\u2009\u22120.25, p\u2009<\u20092.2e\u221216 in tumor) (Fig.\u00a02a, b), yet were more proximal to the TSS compared to gene-eQTLs (two-sided Wilcoxon p\u2009=\u20092.4e\u221212 in normal; two-sided Wilcoxon P\u2009=\u20094.8e\u221207 in tumor; Supplementary Fig.\u00a05). We observed that TEs displayed fewer independent eQTLs per TE than genes (Fig.\u00a02c, d) while the minor allele frequencies of TE- and gene-eQTL variants were similar (Supplementary Fig.\u00a06). Proximal distance of TE-eQTLs to TSS and the smaller number of independent signals per TE could be due to smaller evolutionary time of TE regulatory landscapes in the human genome compared to genes, making proximal effects much more likely.\n\neQTL variant distance to TSS in a normal and b in tumor. We observe stronger eQTL effect close to the transcription start site of TE and genes in both normal (two-sided Wilcoxon, p\u2009=\u20092.4e\u221212) and tumor (two-sided Wilcoxon, p\u2009=\u20094.8e\u22127). Number of secondary eQTLs for TEs and genes in c normal and d tumor. Gene eQTLs have more functionally independent eQTLs per gene than TEs do. Source data are provided as a Source Data file.\n\nTo corroborate our findings, we used external datasets to replicate our eQTL discoveries. We downloaded available data from GTEx for colon transverse (N\u2009=\u2009174) and TCGA for colon adenocarcinoma (TCGA-COAD, N\u2009=\u2009251). We processed both datasets in a similar way as we did with the SYSCOL dataset (methods 2-3). Not all variant-feature pairs were present in the GTEx colon transverse dataset after all filtering steps. Out of the 10,231 TE-eQTLs and 6955 gene-eQTLs discovered in normal, 8380 (82%) and 5930 (85%) TE- and gene-eQTLs, respectively were present in the dataset and could be replicated. From the 5199 TE- and 1552 gene-eQTLs discovered in SYSCOL tumor, only 3221 (62%) TE- and 1164 (75%) gene-eQTLs were present in the TCGA-COAD dataset. We observe a high replication of our original results (Supplementary Fig.\u00a07A\u2013C; Supplementary Data\u00a04) in normal (pi1 TE-eQTLs\u2009=\u20090.831 pi1 gene-eQTLs\u2009=\u20090.686) and tumor (pi1 TE-eQTLs\u2009=\u20090.884; pi1 gene-eQTLs\u2009=\u20090.783) (Supplementary Fig.\u00a07D\u2013F; Supplementary Data\u00a05) corroborating our findings.\n\nGiven previously established roles of tumor-specific gene-eQTLs in tumorigenesis11, we aimed next at investigating whether tumor-specific TE-eQTLs could similarly contribute as cancer driving factors. To this end, we used linear mix models with an interaction term between variant and tissue (normal/tumor). We discovered that 429 (8%) of the tumor TE-eQTLs are tumor-specific and 1697 (24%) of the normal TE-eQTLs are normal-specific, with 525 TE-eQTLs shared between both settings (Fig.\u00a03a; Supplementary Data\u00a06). For genes, we found 117 (%) tumor gene-eQTLs to be tumor-specific and 902 (%) normal gene-eQTLs to be normal-specific, of which 175 were shared (Supplementary figure\u00a08A; Supplementary Data\u00a07). Shared TE- and gene-eQTLs were closer to the TSS of TEs/genes compared to tissue-specific eQTLs (two-sided Wilcoxon p\u2009<\u20092.2e\u221216) (Fig.\u00a03b, Supplementary Fig.\u00a08B). Additionally, we observed that shared eQTLs conserved their effect in both normal and tumor (Fig.\u00a03c, Supplementary Fig.\u00a08C). These results indicate that TE expression is under strong genetic control and that non-coding germline variants act as drivers of TE expression in cancer as similarly observed for gene expression11.\n\na Mosaic plot of tissue specificity of TE-eQTLs. b Tissue specificity and distance of TE-eQTL to transcription start site (TSS). The shared TE-eQTLs (black) are closer to the TSS than are the tissue specific TE-eQTLs (red) (two-sided Wilcoxon p\u2009<\u20092.2e\u221216). c TE-eQTL slopes for the normal specific TE-eQTLs in blue, the tumor specific in red and shared in black. d Boxplot of the absolute value difference of median methylation betas between normal and tumor samples for shared (n\u2009=\u2009248) and tumor-specific (n\u2009=\u2009675) TE-eQTLs. We observe significant increase in methylation change for tumor-specific TE-eQTLs compared to shared TE-eQTLs between normal and tumor (two-sided Wilcoxon test, p\u2009=\u20092.5e\u221211). Shared TE-eQTLs box plot values: minima\u2009=\u20091.987e\u22123; 1st quartile\u2009=\u20099.550e\u22123; median\u2009=\u20090.025; mean\u2009=\u20090.046; 3rd quartile\u2009=\u20090.062; maxima\u2009=\u20090.274. Tumor-specific TE-eQTLs box plot values: minima\u2009=\u20099.908e\u22124; 1st quartile\u2009=\u20090.021; median\u2009=\u20090.05; mean\u2009=\u20090.072; 3rd quartile\u2009=\u20090.11; maxima\u2009=\u20090.438. Source data are provided as a Source Data file.\n\nTo corroborate the biological relevance of the discovered TE-eQTL variants we performed functional enrichment analysis of TE and gene eQTLs in normal and tumor using available ChIP-seq data from the Ensembl Regulatory Build15 for 202 TFs and 29 histone marks. We then proceeded with multiple test correction with a given FDR of 5% (methods section 1.6.4). We found significant enrichment for many TF binding sites overlapping the eQTL loci highlighting the functional relevance of the variants discovered (Fig.\u00a04a, b; Supplementary Figs.\u00a09 and 10; Supplementary Data\u00a08, 9). At 5% FDR, we discovered 5 significant hits (4 TFs and 1 histone marks) and 16 significant hits (12 TFs and 4 histone marks) that displayed stronger enrichment for TE eQTLs compared to gene eQTLs in normal and tumor, respectively. The TF most enriched over TE-eQTLs in normal tissues was ZNF274, a Kr\u00fcppel-associated box (KRAB) domain-containing zinc-finger protein (KZFP), whereas the most enriched over tumor TE-eQTLs was TRIM28, the master corepressor that is recruited by the KRAB domain of many TE-binding KZFPs and serves as a scaffold for a heterochromatin-inducing complex capable of repressing TEs via histone H3 Lys9 trimethylation (H3K9me3), histone deacetylation and DNA methylation16,17. Additionally, BDP1 and BRF1, two subunits of the RNA polymerase III transcription initiation factor, were more enriched over TE-eQTLs compared to gene eQTLs highlighting potential transcription of Alu or MIR TEs of the SINE family18. These results corroborate the biological relevance of TE eQTLs and point to possible transcription and repression of certain TEs.\n\na The ratio between TE-eQTL enrichment and gene-eQTL enrichment in log2 scale discovered in normal. 5 TFs show stronger enrichment for TE-eQTLs in normal compared to gene-eQTLs. b The ratio between TE-eQTL enrichment and gene-eQTL enrichment in log2 scale discovered in tumor. We observed 16 TFs to have a stronger enrichment for TE-eQTLs than gene-eQTLs in normal. c log2 ratio between tumor-specific TE-eQTL enrichment and shared TE eQTL enrichment. We observe 60 TFs with a stronger enrichment for the tumor-specific TE-eQTLs than the shared eQTLs indicating that these TFs regulate TE expression specifically in tumor. Source data are provided as a Source Data file.\n\nTo assess the differential effects of tumor-specific versus shared eQTLs, we performed functional enrichment analyses using available ChIP-seq data from LoVo colorectal cancer cells for 220 TFs and 2 histone marks19 (methods section 1.6.4). We observed that in the case of genes, all tested TFs had a stronger enrichment for shared compared to tumor-specific eQTLs, indicating that these TFs are regulating gene expression in both the normal and tumor state. (Supplementary Fig.\u00a011, Supplementary Data\u00a010). In contrast, we found at 5% FDR, 60 significant hits (58 TFs and 2 histone marks) displaying stronger enrichment for tumor-specific versus shared TE-eQTLs, pointing to tumor-specific TE regulation (Fig.\u00a04c; Supplementary Fig.\u00a012; Supplementary Data\u00a011). Of these, 23 were upregulated and 25 downregulated in tumors (12 were missing from our expression data and could not be tested for differential expression analysis), but we did not observe any significant correlation between the tumor-specific TE-eQTL enrichment to shared TE-eQTL enrichment ratio and fold change in the expression of the corresponding transcription factors (Pearson R\u2009=\u20090.019, p-value\u2009=\u20090.86; Supplementary Fig.\u00a013). Thus, differential expression of these TFs is not driving the tumor-specific TE-eQTL effects. However, 61 of the 88 tumor-specific TE-eQTLs overlapping the binding sites of the 60 aforementioned TFs are not significantly associated (FDR\u2009=\u20095%) with any nearby (\u00b11\u2009Mb from TSS) TE or gene in normal, indicating that these regulatory regions are inactive in the normal state (Supplementary Fig.\u00a014). Additionally, we compared methylation levels between normal and tumor samples for the tumor-specific and shared eQTLs and observed significantly increased (Wilcoxon rank sum test p-value\u2009=\u20092.5e\u221211 for TEs and p-value\u2009=\u20090.0037 for genes) methylation over tumor-specific compared to shared eQTLs for both gene and TEs (Fig.\u00a03d; Supplementary Fig.\u00a08D).\n\nAltogether these results suggest that many TFs are regulating TE expression. The inactivity of some of the TE eQTLs in normal and the significant changes in methylation between tumor-specific and shared TE-eQTLs indicate that regulatory switches involving the recruitment of these TFs might underlie the effects of tumor-specific TE eQTLs.\n\nHaving established that TEs are under genetic control, we next sought to assess the causal relationship between eQTL variants, TEs and genes and discover the extent to which TEs act as drivers of gene expression in tumor. To this end, we focused on regulatory variants affecting both TEs and genes and detected these in an unbiased manner by first associating TEs with genes using a similar approach to QTL mapping. Next, we quantified the identified 20,083 TE-gene pairs found in normal samples and 140,274 TE-gene pairs found in tumor at 1% FDR and used this quantified TE-gene pairs to find all eQTL-TE-gene triplets by performing a standard eQTL analysis (Methods; Supplementary Figs.\u00a015\u201317). At 5% FDR, we discovered 11,937 and 9528 triplets in normal and tumor, respectively, for which we inferred the most likely causal relationship using Bayesian networks (Methods)20,21,22. We tested three models, (i) the causal model where the eQTL variant affects TE expression and then gene expression, (ii) the reactive model where the eQTL variant affects gene expression and then TE expression and (iii) the independent model where the eQTL variant affects independently TE and gene expression (Supplementary Fig.\u00a018). Bayesian Networks were shown to be an adequate method for testing these three models23. We observed significantly more causal models in tumor (47%) compared to normal (23%) (Fisher p-value\u2009<\u20092e\u221216) indicating that TEs are causal for gene expression predominantly in tumor and to a lesser extent in normal (Fig.\u00a05a, b; Supplementary Fig.\u00a019; Supplementary Data\u00a012, 13). We also show that the proportion of causal models correlated with the genomic position of the TE with respect to the gene; intronic TEs tend to be reacting to gene expression. whereas TEs outside the gene body tended to be causal. We believe that the predominance of reactive model from intronic TEs and downstream of genes is a consequence of the transcription of the gene and not the transcription of the TE via the TE promoter. Interestingly, there were significantly more causal scenarios when the eQTL variant lied within the TE, rather than outside (Fisher p-value\u2009<\u20092e\u221216) pinpointing to direct regulatory effects of the TE onto gene expression (Supplementary Fig.\u00a020).\n\na Barplot representing the mean probability for each of the three models in normal and tumor. We observe significantly more causal cases in tumor compared to normal (two-sided Wilcox P-value\u2009<\u20092e\u221216). b Barplot representing the model substitutions for the 9528 tumor triplets from normal to tumor. Independent models tend to shift to a causal in tumor. This is true also for the reactive models in normal but to a much smaller extent. c Barplot representing the number of triplets that do not switch models, that switch to a causal model or that switch to reactive/independent from normal to tumor. The majority of triplets do not switch models between normal and tumor. However, 2584 triplets are switching to a causal model making the corresponding TEs potential drivers of gene expression. d Each point represents a TE-gene for each of the 2584 tumor triplets. All points are significant in tumor but not in normal (gray points). We observe that in most cases, TEs are positively correlated with genes except for a few cases. Most cancer driver genes have no significant correlation with any TE in normal indicating that for most part, TEs impact them specifically in tumor. Source data are provided as a Source Data file.\n\nWe then proceeded with replicating the causal inference of the eQTL\u2014TE\u2014gene triplets to corroborate our findings. We tested the triplets where all three molecular phenotypes were present in either GTEx colon transverse for the SYSCOL normal colon triplets or in TCGA-COAD for the SYSCOL tumor triplets, yielding 9577 (80%) triplets and 5893 (62%) triplets in common, respectively. We performed BNs similarly to the original discoveries. We observe a high replication of both normal (62% similarity) and tumor (74% similarity) results (Supplementary Fig.\u00a021; Supplementary Data\u00a014, 15). We believe that the reason the replication of our normal colon eQTLs is lower than for the tumor eQTLs is because of sample size differences between SYSCOL normal colon (N\u2009=\u2009275) and GTEx colon transverse (N\u2009=\u2009174) decreasing our statistical power. These results corroborate our findings and highlight that our discoveries are valid.\n\nAltogether, these results show that TEs are significantly more causal for changes in gene expression in tumor than in normal tissue.\n\nThese results suggested that genetic variations in TE expression might drive tumorigenesis. To test this hypothesis, we considered the union of all triplets, i.e. the eQTL variant, TE and gene expression, discovered across tumor and normal tissue and using the same BN approach as previously mentioned, we inferred the causal relationship between the triplets in both states (methods). We similarly looked for shared triplets across the 11,937 normal and 9528 tumor triplets (eQTL-TE-gene triplets are the same in both states or the eQTL for TE-gene pair is in high LD (R2\u2009>\u2009=\u20090.9)). In both shared and union triplets, we observed a significant increase in the causal model in tumor (Fisher Exact Test p-value\u2009<\u20092.2e\u221216 for shared and union triplets) mainly due to independent models and to a lesser extent reactive model shifting to causal. (Supplementary Fig.\u00a022; Supplementary Data\u00a016, 17). Focusing on the 9528 tumor triplets, we discovered 2584 (27%) triplets that switched to a causal model in tumor compared to normal, highlighting regulatory changes whereby TEs impacted the expression of nearby genes (Fig.\u00a05c). These 2584 triplets constituted of 1766 unique TEs impacting 1558 unique genes. Interestingly, we observed that TEs switching to causal were significantly up-regulated compared to TEs that did not switch models between normal and tumor or that switched but not to causal (Wilcoxon p-value 2.2e\u221214; Supplementary Fig.\u00a023). These results suggest that upregulation of TEs could give rise to their gene expression driver capability.\n\nWhile expression of most TEs was positively correlated with the expression of the associated gene in tumor (n\u2009=\u20092575) (Fig.\u00a05d), only a few showed negative correlation (n\u2009=\u20099). Of the significant tumor TE-gene pairs tested in normal colon, we observed that 930 maintained the same effect (in terms of size and direction) whereas 36 showed an opposite effect in tumor samples. Interestingly, of the 1558 genes, 55 were cancer driver genes (CDG) (3 CRC specific; based on Cancer Gene Census24) but we did not find a significant enrichment of CDGs in triplets switching to causal compared to all other tumor triplets (Fisher exact test p-value\u2009=\u20090.2185; odds-ratio\u2009=\u20091.276). For 41 out of the 55 CDGs, we did not find a significant correlation between their expression and the expression of the corresponding TEs in normal samples pinpointing that these TEs have no impact on these genes in the normal state. Taken together, these results suggest an important role of TEs as drivers of gene expression during tumorigenesis.\n\nWe investigated whether any of the 9528 tumor triplets were constituted of any previously identified tumor-specific or shared TE-eQTLs and assess how the model likelihood changed between normal and tumor. We identified 320 and 133 tumor triplets constituted of a shared or a tumor-specific TE-eQTL, respectively (Fig.\u00a06a, b) and observed that the 133 tumor triplets constituted with a tumor-specific TE-eQTL are significantly enriched for triplets switching to causal compared to the 320 tumor triplets constituted with a shared TE-eQTL (Fisher Exact test p-value\u2009=\u20096.6e\u22124; Odds-ratio\u2009=\u20092.04) (Fig.\u00a06b). Additionally, we observed that for 120 triplets with tumor-specific TE-eQTLs, the eQTL variant was not a significant eQTL for the corresponding gene in the triplet (Fig.\u00a06c), highlighting that the eQTLs get activated in the tumor state influencing TE expression that subsequently impact gene expression. Altogether, these results suggest that tumor-specific TE-eQTLs contribute to tumorigenesis by impacting genes through TEs, adding additional proof that germline variants can be contributing to tumorigenesis.\n\na The barplot represent the frequency of the causal, reactive and independent model for the triplets with shared or tumor-specific TE-eQTLs. b The barplot represents the model changes from normal to tumor for the triplets constituted of shared or tumor-specific TE-eQTLs. c Barplot that represent the number of tumor-specific TE-eQTLs that are inactive eQTLs for the triplet associated gene. Source data are provided as a Source Data file.\n\nIt has been shown that TEs could impact gene expression by acting as alternative promoters for nearby genes and creating chimeric transcripts (transpochimeric transcripts (tcGTs))25,26. To assess whether any of the tumor triplets with causal TEs were affected by tcGT events, we looked for cases where transcripts started from a TE and spliced into a single or multiple nearby genes (methods). We only kept tcGTs made up of the same TE and gene as in the 9528 tumor triplets and that were significantly more abundant in tumor samples compared to normal samples using a Fisher exact test. At 5% FDR, we discovered 126 tcGTs present in 147 tumor triplets. Of these, 78 triplets (66 TcGTs) were causal and 46 triplets (39 TcGTs) switched to causal from normal to tumor. Interestingly, we detected tcGT events with a known tumor suppressor gene RNF43 and two oncogenes ETS2 and SLCO1B3 supporting the extensive contribution of TEs during tumorigenesis.",
+            "section_image": [
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+            ]
+        },
+        {
+            "section_name": "Discussion",
+            "section_text": "Transposable elements are important contributors to tumorigenesis and provide supplementary means by which gene expression can be altered in cancer. While many studies have used a hypothesis-driven approach and focused at specific TEs or their subfamilies for discovering TEs that alter the expression of nearby genes in cancer27,28,29, applying a genome-wide scan could allow to obtain a better picture of the effects of TEs on gene expression during tumorigenesis.\n\nHere, we present a global profile of tumor drivers and show that TEs are highly prevalent mediators of genetic effects on genes altering their expression, specifically in tumor. By combining genome and transcriptome data together we, show that TEs are under tight genetic control and discover that transcription factors regulate TE expression much more in tumor than in normal. By looking at the interplay between eQTL variants, transposable elements, and gene expression, we are able to dissect eQTL effects and show that for several genes, the genetic effect of an eQTL is passed on genes through TEs which act as mediators and drive gene expression. We observe this to occur significantly more in cancer than in normal and show that the majority of TEs increase the expression of affected nearby genes. Interestingly, we discover that TEs affecting known cancer driver genes in cancer have for most part no significant effect on these genes in normal suggesting a tumor-specific effect of these TEs. Additionally, in our study we show that alongside predisposing alleles and somatic mutations, germline variants are crucial contributors to tumorigenesis as these allow for transcriptional changes to occur at the level of TEs that in turn result in altered expression of nearby genes in cancer as shown previously11.\n\nIt is known that TEs are much more active in tumor than in normal, primarily due to a global hypomethylation in cancer driving their expression26. However, in our analysis we observe a higher number of eQTLs in normal than in tumor which may sound contradictory. This has to do with the nature of the tumor tissue being much more heterogeneous increasing the variance in the expression data subsequently affecting statistical power, leading to fewer eQTLs being discovered. By increasing sample size we could minimize this problem and increase the eQTL discovery in tumor.\n\nTo assess the function of these eQTLs, we used functional enrichment analysis. Even though we discover more eQTLs in normal, we observe that tumor TE-eQTLs are significantly enriched for more transcription factors compared to normal TE-eQTLs and the higher number of TFs significantly associated with tumor-specific TE-eQTLs indicates that TEs are more active in cancer compared to normal. Interestingly, we observed that for 61 tumor-specific TE-eQTLs, the eQTL loci is not an eQTL for any nearby gene or TE (\u00b11\u2009Mb) in the normal state. This indicates that these loci are probably inactive in normal and get activated during tumorigenesis, driving the expression of nearby TEs, specifically in cancer. Interestingly, we observed significant difference between DNA methylation changes at tumor-specific TE-eQTLs than shared TE-eQTL loci (eQTL active in both normal and cancer) which pinpoints that DNA methylation changes at these specific loci to be one of the causes of the activation of these eQTLs in cancer.\n\nWhile we focused on TEs impacting the expression of nearby genes in an independent manner, it is highly plausible that synergistic effects occur from both cis- and trans- acting TEs. Performing such an analysis could give a fuller picture of the regulatory network behind the regulation of gene expression through TE effects, requiring, however, a high sample size for sufficient statistical power. Nevertheless, because of the highly repetitive nature of transposable element sequences and their evolutionary relatedness among TE families, mapping short reads originating from TEs is a real challenge18,30. Our RNA-seq dataset having a read length of 49\u2009bp, it is highly possible that we did not map all expressed TEs subsequently leading to missing information, as shown previously18,30. Future studies where RNA-sequencing is performed with longer read lengths could allow for better mapping of expressed TEs and give us a fuller picture of the number of these driver TEs in cancer.\n\nIt is known that certain TE subfamilies, especially the younger ones like L1HS get reactivated during tumorigenesis and are able to retrotranspose creating tumor-specific integrations, perturbing the human genome. This is also a limitation in our study, as the assessment of tumor-specific TE integrations require Whole-Genome Sequencing (WGS) to be assessed. Additionally, our study is focused more on the effects of older TE subfamilies as these have accumulated sufficient mutations in their genomic sequence to make the various integrants distinguishable from each other. We believe that long-read sequencing technologies could be a good approach for studying younger TE subfamilies.\n\nAltogether, we have outlined that TEs are important mediators of genetic effects onto genes that could potentially be used as risk factors or therapeutic targets for future drug development and aid in cancer treatment.",
+            "section_image": []
+        },
+        {
+            "section_name": "Methods",
+            "section_text": "The Systems Biology of Colorectal cancer (SYSCOL) dataset (accession number: EGAC00001000204) contains data from genotypes and RNA-sequencing for matched normal-tumor samples (i.e., both tumor and normal samples originate from the same patient). Samples that had genotype data and molecular phenotype quantifications from tumor and normal (normal adjacent to tumor) tissue were analyzed, yielding 275 normal samples and 276 tumor samples. In case of multiple tumor samples from the same patient, only samples with quantifications from the most advanced tumor were kept.\n\nWe used imputed genotypes and only kept variants with a minor allele frequency (MAF) \u22655%, yielding a total of 6,132,240 variants that were used for all downstream analyses.\n\nSYSCOL samples were sequenced using 49\u2009bp, 75\u2009bp and 100\u2009bp read lengths using paired-end non-stranded mRNA-sequencing. We first started by trimming all samples with 75\u2009bp (N\u2009=\u200973) and 100\u2009bp (N\u2009=\u20094) reads down to 49\u2009bp to reduce any bias in downstream analysis stemming from read length. For this we used cutadapt31 with the following command \u201ccutadapt -u\u2014Nreads -o <output_file><input_file>\u201d. All trimmed samples were mapped to the human reference genome (hg37) using hisat232.\n\nGene and transposable element counts were generated using the featureCounts software33. We provided a single annotation file in gtf format to featureCounts containing both genes and transposable elements. This prevents any read assignation ambiguity to occur. For transposable elements, we used an in-house curated version of the Repbase database12 where we merged fragmented LTR and internal segments belonging to a single integrant. We only used uniquely mapped reads for gene and TE counts. Molecular phenotypes that did not have at least one sample with 20 reads and for which the sum of reads across all samples was lower than the number of samples, were discarded. Furthermore, we normalized molecular phenotypes (TEs and genes) for sequencing depth using the TMM methodology as implemented in the limma package of Bioconductor34 and used gene counts as library size for both TEs and genes. Finally, we removed any molecular phenotype that had more than 50% of missing data (zeros) in tumor and normal samples separately and took the union of molecular phenotypes, yielding 17,430 genes and 50,921 TEs for a total of 68,351 molecular phenotypes.\n\nThe observed variability in molecular phenotypes from RNA-sequencing data can be of biological or technical origin. To correct for technical variability, while retaining biological variability, we residualised the molecular phenotype data for the covariates as described below:\n\nTo correct for population stratification that is observed between the SYSCOL samples, we used Principal Component analysis (PCA) results obtained from genotypes of SYSCOL patients. We only retained the first three principal components (PCs) as covariates.\n\nIn order to capture experimental/technical variability in the expression data, we performed PCA, centering and scaling, using pca mode from QTLtools software package35. To ascertain the number of PCs that capture technical variability, we used QTL mapping (see method 3.4.1 for the description of QTL mapping) to identify the best eQTL discovery power in both tumor and normal samples. To this end, we carried out multiple rounds of eQTL mapping for tumor and normal samples separately, each time using the 3 PCs from genotypes and incrementally adding 0, 1, 2, 5, 10, 20, 30, 40, 50, 60 and 70 PCs as covariates. This approach resulted in identifying 30 PCs in tumor and normal samples for maximizing eQTL discovery.\n\nIn total, 33 covariates were regressed out from tumor and normal sample expression data using QTLtools correct mode35. We additionally rank-normalized on a per phenotype basis across all samples such that quantifications followed normal distribution with mean 0 and standard deviation 1\u2009N(0,1) using QTLtools --normal option35.\n\nWe used microarray based DNA methylation data from the SYSCOL project, accession number EGAD00010001888, and a similar approach to a previous study to find differential methylation of eQTLs11. In brief, we calculated the absolute value difference of the medians of normalized methylation probe betas in normal and tumor that we call median differential methylation. We then compared the distribution of their medians in tumor-specific TE and genes eQTLs vs. the shared TE and gene eQTLs and calculated a P-value using the Mann\u2013Whitney U test. P-values were corrected for multiple testing using the R/qvalue package with a given FDR threshold of 5%.\n\nThe DESeq2 R package36 was used in calculating differentially expressed genes and TEs. We normalized the raw TE/gene counts within the DESeq2 package using the sequencing date, GC mean and insert size as covariates. The differential expression P-values were corrected for multiple testing using an FDR threshold of 5%.\n\nAll analyses were performed separately for normal and tumor samples. We used imputed genotypes with MAF\u2009\u2265\u20095%, gene expression data with normalized counts per million (CPMs) (as described above) for both eQTL and conditional eQTL mapping.\n\nFor eQTL mapping, we used cis mode of the QTLtools software package35. For each molecular phenotype:\n\nWe counted all genetic variants in a 1\u2009Mb window (+/\u22121\u2009Mb) around the transcription start site (TSS) of the phenotype and tested all variants within this window for association with the phenotype. We only retained the best hits which are defined as the ones with the smallest nominal p-value.\n\nNext, we used permutations to adjust the nominal p-values for the number of variants tested. More specifically, we randomly shuffled the quantifications of the phenotypes 1000 times and retained only the most significant associations. This created a null distribution of 1000 null p-values. Then, we fitted a beta distribution on the null distribution and used the resulting beta distribution to adjust the nominal p-value. Principally, this strategy allows to quantify the chance of getting a smaller p-value than the nominal one in random datasets.\n\nThis effectively gave us the best variant in cis together with the corresponding adjusted p-value of association for each molecular phenotype. Finally, to correct for the number of phenotypes being tested we used False Discovery Rate (FDR) correction approach. More specifically, we used the R/qvalue package37 to perform genome-wide FDR correction which ultimately facilitated to extract all phenotype-variant pairs that are significant at a pre-determined FDR threshold, 5% FDR in this case.\n\nThe cis mode informs us on the best phenotype-variant pair only. Given that the expression of molecular phenotypes can be affected by multiple cis eQTLs, we proceeded with conditional analysis to discover all eQTLs with independent functional effects on a given phenotype. Principally, discoveries are made after conditioning on previous ones. Again, cis mode in the QTLtools software package was used35. In brief, after running permutations (method 1.4.1) for each phenotype, we calculated a nominal p-value threshold of being significant. We first determined the adjusted p-value threshold that corresponds to the targeted FDR level and then used the beta quantile function to go from adjusted p-value to a specific nominal p-value threshold. For conditional analysis, forward-backward methodology is used to discover all independent QTLs and to identify the most likely candidate variants, while at the same time controlling for a given FDR (5% FDR in this case). We only kept the top variant for each signal.\n\nTo discover tissue specific and shared eQTLs, we used the eQTL results obtained after running the conditional pass. In total, we tested 17,186 eQTLs to discover normal-specific eQTLs and 6751 to discover tumor-specific eQTLs. To do that, we used linear mix models using an interaction term between dosage and tissue (i.e tumor or normal) to test whether the slopes in normal and tumor are significantly different. Linear mix models are needed here because normal and tumor samples are originating from the same patient thus genotypes will be identical. We did this for tumor and normal eQTLs separately. Then we performed multiple test correction using the R/qvalue package37 with a given FDR threshold of 5%. Additionally, for all significant results at 5% FDR, if eQTL slopes (slopes given from conditional QTL mapping using QTLtools) in normal and tumor had the same direction, then we only kept the ones where the SNP-phenotype association in the opposite tissue was not nominally significant (P\u2009>\u20090.05) as given by the cis nominal pass mode in the QTLtools package35.\n\nShared eQTLs are defined as the ones where the P-value for the interaction term is not significant but need to be significant eQTLs (5% FDR) in both normal and tumor as assessed by the conditional QTL mapping.\n\nTo compare the QTL variants to a null distribution of similar variants without regulatory association, we sampled for each eQTL variant 100 random regulatory genetic variants matching for relative distance to TSS (withing 2.5\u2009kb) and minor allele frequency (within 2%) and only kept variants that are not eQTLs for any other TE or gene (nominal p-value\u2009>\u20090.05). The enrichment for a given category was calculated as the proportion between the number of regulatory associations in a given category and all regulatory variants over the same proportion in the null distribution of variants. The p-value for this enrichment is calculated with the Fisher exact test. Finally, we corrected for multiple testing using an FDR threshold of 5% using the \u201cp.adjust\u201d function in the R programming language. The code for performing the functional enrichment analysis can be accessed here: https://github.com/NLykoskoufis/fenrichcpp38.\n\nChIP-seq data was downloaded from the FTP site (http://ftp.ensembl.org/pub/grch37/current/regulation/homo_sapiens/). The dataset contains ChIP-seq data from 88 human cell types for a total of 209 transcription factors and 29 histone marks (build hg19). For each of the TFs and histone marks, we took the union of all peaks together from all 88 cell types. Overlapping peaks were merged together using the \u201cmerge\u201d options in the BEDtools software39. This allowed us to create an extensive annotation of peaks for 209 TFs and 29 histones genome-wide.\n\nWe used publicly available ChIP-seq data from colorectal cancer LoVo cell line with accession code GSE49402. The dataset comprises of 202 TFs and 2 histone marks (build hg19). We used BED files containing the coordinates of the peaks for each TF and histone mark for functional enrichment of our eQTLs.\n\nFor gene and TE eQTLs in normal and tumor, we used the peak annotation generated from the Ensembl Regulatory Buil data to get an extensive comprehension of which TFs regulate the expression of TEs. Regarding the tumor-specific vs. shared TE and gene eQTLs, we used available ChIP-seq data from the colorectal cancer LoVo cell line19. We used a cancer specific dataset as we were interested in discovering cancer specific effects.\n\nTo discover associations between TEs and genes, we proceeded in a similar way to what we did for QTL mapping (method 1.4.1). Effectively, we used TE expression as our \u201cgenotypes\u201d and genes as our phenotype. Then, we corrected for multiple testing using the R/qvalue package with a given FDR of 1%. We then estimated the nominal p-value thresholds for each phenotype being tested as described in (method 1.4.2) with a given FDR of 1%. Given the nominal threshold we get for each gene, we then extracted all TEs with an association P-value below this threshold which could give multiple TEs for a gene in some cases.\n\nTo quantify each of TE-gene pairs that have been found to be significant, we used a dimensionality reduction approach based on PCA as previously described22. Specifically, for each TE-gene pair, we aggregated gene expression together with TE expression by using the coordinates on the first principal component. This effectively built a quantification matrix with rows and columns corresponding to the number of TE-Gene pairs and individuals, respectively. All quantifications have been rank-normalized on a per phenotype basis so that the values match a normal distribution N(0,1). This prevents outlier effects in downstream association testing. This is all implemented in the clomics software package22.\n\nBayesian networks (BNs) are a type of probabilistic graphical model that uses Bayesian inference to compute probabilities. BNs aim to model conditional dependencies and therefore causation by representing conditional dependencies as edges and random variables as nodes in a directed acyclic graph. The flow of information between two nodes is reflected by the direction of the edges, giving an idea of their causal relationship. BNs have been previously used in a genetic framework20 to get insight into the most likely network from which the observed data originates.\n\nIn BNs, the joint probability density can be divided into marginal probability functions and conditional probability functions for the nodes and edges, respectively. Additionally, BNs satisfy the local Markov property where each variable is conditionally independent of its non-descendants given its parent variables. In the context of this study, we used BNs to learn the causal relationships between triplets of variables, each one containing a genetic variant, a transposable element and a gene. In practice, only three distinct network topologies where relevant to the hypotheses we wanted to test (Supplementary Fig.\u00a012). More specifically, we looked at:\n\nThe causal scenario where the genetic variant affects first the TE and then the gene.\n\nThe reactive scenario where the genetic variant affects the gene first and then the TE.\n\nThe independent scenario in which the variant affects the gene and the TE independently.\n\nOf note, we only retained network topologies that assume that the signal systematically originates from the genetic variant. In practice, we applied BNs on data that was obtained from running an QTL mapping using the TE-gene pairs using a similar approach to QTL mapping described above (Method 1.4.1) and only kept significant results at 5% FDR which corresponds to 11,937 QTL-TE-gene triplets in normal and 9528 QTL-TE-gene triplets in tumor.\n\nFor each triplet, we build a 275 \u00d73 matrix in normal and 276 \u00d73 matrix in tumor containing normalized quantifications and used it to compute the likelihood of the 3 BN topologies using the R/bnlearn package (Version 4.5)40. As a last step, we went from likelihoods to posterior probabilities by assuming a uniform prior probability on the three possible topologies. Posterior probabilities where used for all BN-related analyses.\n\nFirst, a per sample transcriptome was computed from the RNA-seq bam file using StringTie41 with parameters \u2013j 1 \u2013c 1. Each transcriptome was then crossed using BEDTools39 to both the ensembl hg19 coding exons and curated RepBase12 to extract TcGTs for each sample. Second, a custom python program was used to annotate and aggregate the sample level TcGTs into counts per groups (normal, tumor). In brief, for each dataset, a GTF containing all annotated TcGTs was created and TcGTs having their first exon overlapping an annotated gene or TSS not overlapping a TE were discarded. From this filtered file, TcGTs associated with the same gene and having a TSS 100\u2009bp within each other were aggregated. Finally, for each aggregate, its occurrence per group was computed.\n\nWe downloaded available data for colon transverse (N\u2009=\u2009174) and germline genotypes from dbGAP (accession code: phs000424.v8.p2).\n\nWe used the already filtered VCF file provided by GTEx. The following filters were applied and kept all variants with a MAF\u2009\u2265\u20095%, yielding a total of 6,494,417 variants.\n\nThe RNA-seq dataset was treated similarly to SYSCOL RNA-seq data. We first trimmed the reads down to 49\u2009bp using cutadapt31. Then we mapped and quantified the samples using the exact same approach as for SYSCOL (methods section 1.3.2). Finally, we combined all samples together into a multi-sample bed file and kept all features (TEs, genes) that had less than 50% of missing expression data across all samples, yielding a total cd of 167,429 TEs and 18,472 genes. Then, we corrected our expression data using the first 3 principal components (PCs) obtained from genotypes, the sex of the samples, the platform they were sequenced and the first 20 PCs obtained from the expression data, for a total of 25 covariates used.\n\nWe downloaded available germline genotypes and RNA-seq data for colon adenocarcinoma (N\u2009=\u2009251) from The Cancer Genome Atlas (TCGA) database, accession code phs000178.v11.p8.\n\nGermline genotypes were downloaded from the legacy archive GDC portal. We downloaded all germline genotypes for TCGA-COAD in birdseed format. We used birdseed2vcf python tool (https://github.com/ding-lab/birdseed2vcf) to convert birdseed to VCF format. We then combined all samples together creating a multi-sample VCF file that we spitted per chromosome and uploaded to the Michigan Imputation Server42 for imputation and phasing using the Haplotype Reference Consortium (HRC) as reference panel, Eagle v2.4 software43 for phasing and European (EUR) population. Finally, we merged all chromosome VCFs into a single VCF file and kept variants with a MAF\u2009\u2265\u20095%, HWE\u2009>\u20091e\u221206 and R2\u2009>\u20090.3, yielding a total of 5,511,779 variants.\n\nAs the read length of TCGA-COAD samples is the same as SYSCOL, we did not need to trim the reads. We mapped, quantified, and filtered our RNA-seq data in a similar way as for SYSCOL and GTEx colon transverse samples yielding a total of 19,376 genes and 75,815 TEs. Expression data was corrected using the same approach as for SYSCOL (methods section 1.3.3) using the first 3 principal components (PC) obtained from genotypes and the first PC obtained from expression data for a total of 4 covariates used.\n\nFor the replication of our normal and tumor eQTL discoveries, we used the \u201crep\u201d mode in the QTLtools software44.We then used the pi1 metric to estimate the proportion of significance of our eQTLs in GTEx colon transverse. The pi1 is equal to 1\u2014pi0 where pi0 is the proportion of true null p-values obtained using pi0est from the Qvalue R package45.\n\nWe used the same eQTL\u2014TE\u2014gene triplets discovered in normal and tumor and replicated them in GTEx or TCGA-COAD, respectively. We used the exact same approach as previously (methods section 1.8). We then calculate the mean probability of the causal, reactive and independent model. Finally, we compared the percentage of triplets with the same model predicted in both SYSCOL and the replication dataset.\n\nFurther information on research design is available in the\u00a0Nature Portfolio Reporting Summary linked to this article.",
+            "section_image": []
+        },
+        {
+            "section_name": "Data availability",
+            "section_text": "All data generated during the current study are available in Supplementary Data\u00a01\u201317. Supplementary Data\u00a01\u201317 contains results obtained from the various analysis performed using raw publicly available datasets. The RNA-sequencing data and genotype arrays for the 275 normal colon and 276 colorectal cancer samples from SYSCOL is available in the European Genome-Phenome Archive (EGA) under accession code EGAC00001000204. This restricted data can be requested through EGA or cla@ki.au.dk. Questions regarding the processed data can be emailed to Dr. Nikolaos Lykoskoufis at nikolaos.lykoskoufis@gmail.com. The microarray based DNA methylation data from the SYSCOL project is available in EGA under accession code EGAD00010001888. The RNA-sequencing and germline genotypes from the GTEx dataset can be obtained through dbGAP under accession code phs000424.v8.p2. The RNA-sequencing and germline genotypes from TCGA database can be obtained through dbGAP under accession code phs000178.v11.p8. Both GTEx and TCGA datasets are restricted data and access can be requested through dbGAP. Colorectal cancer LoVo cell line ChIP-seq data can be obtained from Gene Expression Omnibus (GEO) under accession code GSE49402. Transcription factors and histone marks ChIP-seq data can be downloaded from the Ensembl FTP site [http://ftp.ensembl.org/pub/grch37/release-100/regulation/homo_sapiens/Peaks/] where we downloaded all compressed bed files for all cell types. The full list of hyperlinks of all ChIP-seq datasets from Ensembl used in the current study can be found in Supplementary Dataset\u00a018.\u00a0Source data are provided with this paper.",
+            "section_image": []
+        },
+        {
+            "section_name": "Code availability",
+            "section_text": "All custom scripts used can be accessed here: https://github.com/NLykoskoufis/te_project. The code for the functional enrichment analysis can be accessed here: https://github.com/NLykoskoufis/fenrichcpp38.",
+            "section_image": []
+        },
+        {
+            "section_name": "References",
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+        },
+        {
+            "section_name": "Acknowledgements",
+            "section_text": "The computations were performed at the University of Geneva on the Baobab cluster. This work was supported by grants from Louis-Jeantet Foundation support (to E.T.D.) and SNSF grant (to E.T.D.). This work was supported by grants from the European Research Council (KRABnKAP, No. 268721; Transpos-X, No. 694658), the Personalized Health and Related Technologies (PHRT-508) program, the Swiss National Science Foundation (310030_152879 and 310030B_173337), the Swiss Cancer League and the Aclon Foundation to D.T. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.",
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+            "section_name": "Author information",
+            "section_text": "These authors contributed equally: Halit Ongen, Didier Trono, Emmanouil T. Dermitzakis.\n\nDepartment of Genetic Medicine and Development, University of Geneva Medical School, 1211, Geneva, Switzerland\n\nNikolaos M. R. Lykoskoufis,\u00a0Halit Ongen\u00a0&\u00a0Emmanouil T. Dermitzakis\n\nInstitute for Genetics and Genomics in Geneva (iGE3), University of Geneva, 1211, Geneva, Switzerland\n\nNikolaos M. R. Lykoskoufis,\u00a0Halit Ongen\u00a0&\u00a0Emmanouil T. Dermitzakis\n\nSwiss Institute of Bioinformatics, 1211, Geneva, Switzerland\n\nNikolaos M. R. Lykoskoufis,\u00a0Halit Ongen\u00a0&\u00a0Emmanouil T. Dermitzakis\n\nNGS-AI JSR Life Sciences, Route de la Corniche 3, 1066, Epalinges, Switzerland\n\nNikolaos M. R. Lykoskoufis\n\nSchool of Life Sciences, Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne (EPFL), 1015, Lausanne, Switzerland\n\nEvarist Planet\u00a0&\u00a0Didier Trono\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nN.M.R.L., H.O. and E.T.D. designed the study. N.M.R.L. analyzed the data and wrote the manuscript and N.M.R.L., H.O., D.T. and E.T.D. interpreted the results. E.P. shared the quantifications data. H.O., D.T. and E.T.D. jointly supervised this work.\n\nCorrespondence to\n                Nikolaos M. R. Lykoskoufis or Emmanouil T. Dermitzakis.",
+            "section_image": []
+        },
+        {
+            "section_name": "Ethics declarations",
+            "section_text": "E.T.D. is currently an employee of GSK. The work presented in this manuscript was performed before he joined GSK. N.M.R.L. is currently an employee of NGS-AI JSR Life Sciences. The work presented in this manuscript was performed before he joined NGS-AI. All other authors declare no competing interests.",
+            "section_image": []
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+        {
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+        },
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+            "section_name": "About this article",
+            "section_text": "Lykoskoufis, N.M.R., Planet, E., Ongen, H. et al. Transposable elements mediate genetic effects altering the expression of nearby genes in colorectal cancer.\n                    Nat Commun 15, 749 (2024). https://doi.org/10.1038/s41467-023-42405-0\n\nDownload citation\n\nReceived: 03 December 2021\n\nAccepted: 10 October 2023\n\nPublished: 25 January 2024\n\nVersion of record: 25 January 2024\n\nDOI: https://doi.org/10.1038/s41467-023-42405-0\n\nAnyone you share the following link with will be able to read this content:\n\nSorry, a shareable link is not currently available for this article.\n\n\n\n\n                            Provided by the Springer Nature SharedIt content-sharing initiative\n                        ",
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+            "section_name": "This article is cited by",
+            "section_text": "Nature Communications (2025)\n\nScientific Reports (2024)",
+            "section_image": []
+        }
+    ]
+}

1a09553a5e30c2d41c7355bea1f342bc1fb51d884fd725dfd36895e83eeb9e8f/metadata.json

@@ -0,0 +1,139 @@
+{
+    "title": "Soliton walls paired by polar surface interactions in a ferroelectric nematic liquid crystal",
+    "pre_title": "Domain patterns with paired soliton walls stabilized by polar surface interactions in a ferroelectric nematic liquid crystal",
+    "journal": "Nature Communications",
+    "published": "07 July 2022",
+    "supplementary_0": [
+        {
+            "label": "Supplementary Information",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-022-31593-w/MediaObjects/41467_2022_31593_MOESM1_ESM.pdf"
+        },
+        {
+            "label": "Peer Review File",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-022-31593-w/MediaObjects/41467_2022_31593_MOESM2_ESM.pdf"
+        },
+        {
+            "label": "Reporting Summary",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-022-31593-w/MediaObjects/41467_2022_31593_MOESM3_ESM.pdf"
+        }
+    ],
+    "supplementary_1": NaN,
+    "supplementary_2": NaN,
+    "source_data": [],
+    "code": [],
+    "subject": [
+        "Ferroelectrics and multiferroics",
+        "Liquid crystals"
+    ],
+    "license": "http://creativecommons.org/licenses/by/4.0/",
+    "preprint_pdf": "https://www.researchsquare.com/article/rs-1157479/v1.pdf?c=1657278745000",
+    "research_square_link": "https://www.researchsquare.com//article/rs-1157479/v1",
+    "nature_pdf": "https://www.nature.com/articles/s41467-022-31593-w.pdf",
+    "preprint_posted": "19 Jan, 2022",
+    "research_square_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Surface interactions are responsible for many properties of condensed matter, ranging from crystal faceting to the kinetics of phase transitions. Usually, these interactions are polar along the normal to the interface and apolar within the interface. Here we demonstrate that polar in-plane surface interactions produce stable domain structures in the bulk of a ferroelectric nematic liquid crystal. Monodomains form in micron-thick cells, while thicker cells feature quasiperiodic stripes of an alternating uniform electric polarization, separated by domain walls, within which the polarization rotates by 180\u00b0. The surface polarity makes these walls paired with a total rotation by 360\u00b0. Analysis of the domain structures allows one to determine the polar contribution to the surface anchoring potential. The 360\u00b0 pairs of domain walls resemble domain walls in cosmology models with biased vacuums and ferromagnets in an external magnetic field. The polarity-biased ferroelectric structures are highly susceptible to weak electric fields and could lead to applications in advanced electro-optics, sorting of polar inclusions, sensing, memory, and grating devices.ferroelectric nematic liquid crystaldomain wallspolar surface anchoringsoliton-soliton pairs",
+            "section_image": []
+        },
+        {
+            "section_name": "Additional Declarations",
+            "section_text": "There is NO Competing Interest.",
+            "section_image": []
+        },
+        {
+            "section_name": "Supplementary Files",
+            "section_text": "SupplementaryInformationDec92021.pdfDomain patterns with paired soliton walls stabilized by polar surface interactions in a ferroelectric nematic liquid crystal",
+            "section_image": []
+        }
+    ],
+    "nature_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Surface interactions are responsible for many properties of condensed matter, ranging from crystal faceting to the kinetics of phase transitions. Usually, these interactions are polar along the normal to the interface and apolar within the interface. Here we demonstrate that polar in-plane surface interactions of a ferroelectric nematic NF produce polar monodomains in micron-thin planar cells and stripes of an alternating electric polarization, separated by 180o domain walls, in thicker slabs. The surface polarity binds together pairs of these walls, yielding a total polarization rotation by 360o. The polar contribution to the total surface anchoring strength is on the order of 10%. The domain walls involve splay, bend, and twist of the polarization. The structure suggests that the splay elastic constant is larger than the bend modulus. The 360o pairs resemble domain walls in cosmology models with biased vacuums and ferromagnets in an external magnetic field.",
+            "section_image": []
+        },
+        {
+            "section_name": "Introduction",
+            "section_text": "Domains and domain walls (DWs) separating them are important concepts in many branches of physics, ranging from cosmology and high-energy science1 to condensed matter2,3,4. When the system cools down from a symmetric (\u201cisotropic\u201d) state, it might transition into an ordered state divided into domains. For example, domains in solid ferroic materials such as ferromagnets and ferroelectrics exhibit aligned magnetic moments or electric polarization2,3,4. Within each domain, the alignment is uniform, following some \u201ceasy direction\u201d set by the crystal structure. These easy directions are nonpolar, thus opposite orientations of the polar order are of the same energy. The boundary between two uniform domains is a DW, within which the polar ordering either gradually disappears or realigns from one direction to another. By applying a magnetic or electric field, one can control the domains and DWs, which enables numerous applications of ferroics, ranging from computer memory to sensors and actuators2,3,4.\n\nRecent synthesis and evaluation5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22 of new mesogens with large molecular dipoles led to a demonstration of a fluid ferroelectric nematic liquid crystal (NF) with a uniaxial polar ordering of the molecules13,14. The ferroelectric nature of NF has been established by polarizing optical microscopy observations of domains with opposite orientations of the polarization density vector P and their response to a direct current (dc) electric field E13,14. The surface orientation of P is set by buffed polymer layers at glass substrates that sandwich the liquid crystal13,14. This sensitivity to the field polarity and in-plane surface polarity makes NF clearly different from its dielectrically anisotropic but apolar paraelectric nematic counterpart N.\n\nIn this work, we demonstrate that the surface polarity of in-plane molecular interactions produces stable polar monodomains in micron-thin slabs of NF and polydomains in thicker samples. The polar contribution to the in-plane surface anchoring potential is on the order of 10%. The quasiperiodic polydomains feature paired domain walls (DWs) in which P realigns by 360o. The reorientation angle is twice as large as the one in 180o DWs of the Bloch and N\u00e9el types that are ubiquitous in solid ferromagnets and ferroelectrics2,3 and in a paraelectric nematic N23. The polar bias of the \u201ceasy direction\u201d of surface alignment explains the doubled amplitude of the 360o DWs and shapes them as coupled pairs of 180o static solitons. The width of DWs, on the order of 10 \u03bcm, is much larger than the molecular length scale, which suggests that the space charge produced by splay of the polarization within the walls is screened by ions and that the splay modulus K1 in NF is significantly higher than the bend K3 counterpart. The enhancement of K1 is evidenced by the textures of conic-sections in NF films with a degenerate in-plane anchoring, in which the prevailing deformation is bend. Numerical analysis of the DW structure suggests that K1/K3 >\u20094 in the NF phase of the studied DIO material.",
+            "section_image": []
+        },
+        {
+            "section_name": "Results",
+            "section_text": "We explore a material abbreviated DIO7, synthesized as described in the Supplementary Figs.\u00a01\u20137. On cooling from the isotropic (I) phase, the phase sequence is I\u2212174\u2009\u00b0C \u2212 \u2009N\u221282\u2009\u00b0C \u2212 SmZA\u221266\u2009\u00b0C \u2212NF\u221234\u2009\u00b0C\u2212Crystal, where SmZA is an antiferroelectric smectic with a partial splay24, geometrically reminiscent of the splay N model proposed by Mertelj et al.10 The sandwich-type cells are bounded by two glass plates with layers of polyimide PI-2555 buffed unidirectionally. The plates are assembled in a \u201cparallel\u201d fashion, with the two buffing directions R at the opposite plates being parallel to each other. We use Cartesian coordinates in which R\u2009=\u2009(0,\u22121,0) is along the negative direction of the y-axis in the xy plane of the sample. The electric field is applied along the y-axis.\n\nThe N and SmZA phases show a uniform alignment of the optical axis (director n^) along the rubbing direction R, Fig.\u00a01a, b. In the absence of the electric field, depending on the thickness d of the liquid crystal layer, NF forms either polydomain structures, when d > 3\u2009\u03bcm, Fig.\u00a01c, or polar monodomains in thin samples, d = 1\u20132\u2009\u03bcm, Fig.\u00a01d. At the bounding plates, P and n^ are parallel to the surface, as evidenced by the measurement of optical retardance \u0393=250nm at wavelength \u03bb=535\u2009nm of a cell with d=1.35\u03bcm, which yields the DIO birefringence \u0394n=\u0393/d = 0.19, close to the values reported by other groups22,24. Similar values of \u0394n are obtained in homogeneous (free of DWs) regions of thicker cells, Supplementary Fig.\u00a08. The monocrystal textures of thin cells and homogeneous regions of thick cells, Fig.\u00a02a, become extinct when P and n^ are parallel to the direction of polarizer or analyzer of a polarizing optical microscope (POM). These facts demonstrate planar alignment with little or no \u201cpretilt\u201d and exclude the possibility of director twist in DW-free regions of both thin and thick cells. The planar monocrystal structure of cells with parallel assembly of unidirectionally buffed substrates should be contrasted to the textures in cells with antiparallel assembly, in which P and n^ twist along the normal z-axis13,14.\n\na\u2013c Polarizing optical microscopy of a thick d = 4.7\u2009\u03bcm sample and d, e PolScope Microimager textures of a thin 1.35\u2009\u03bcm sample. a, b Uniform N and SmZA textures, respectively. c polydomain NF texture; the polarization P is antiparallel to the rubbing direction R in the wider domains and is parallel to R in the narrower domains; two 180\u00b0 DWs enclosing the narrow domain reconnect (circles mark some reconnection points). d Field-induced realignment of P from the direction \u2212R to R. e Reversed field polarity realigns P back into the ground state P \u2191\u2193 R. f Scheme of P reorientation in (e); there are two 180o twist DWs of the Bloch type near the plates. g Azimuthal surface anchoring potential for different ratios of the polar WP and apolar WQ coefficients.\n\na Textures observed between crossed polarizers with P \u2193\u2193 R in the narrow central domain separated by two bright 180o DWs from the wide domains with P \u2191\u2193 R at the periphery; the electric field realigns P in the narrow or wide domains, depending on the field polarity. b The same textures, observed with an optical compensator that allows one to establish the reorientation direction of P. c Topologically nontrivial structure of the 360o W-pair of DWs; along the line \u03b3, the polarization vector P rotates by 360o, thus covering the order parameter space S1 once, which yields the topological charge Q = 1. Cell thickness d = 4.7\u2009\u00b5m.\n\nThe planar alignment avoids a strong surface charge. Even a small tilt \u03c8\u223c5o of P from the xy plane would produce a surface charge density Pz ~ P\u03c8 ~ 4 \u00d7 10\u22123 C m\u22122, which is larger than the typical surface charge (10\u22124 \u2212 10\u22125)C m\u22122 of adsorbed ions reported for nematics25,26; here P\u22484.4\u00d710\u22122Cm\u22122 is the polarization of DIO7. Therefore, we expect that the out-of-plane (zenithal) polar anchoring is much stronger than the in-plane azimuthal anchoring.\n\nThin cells, \u03bcd=1\u22122\u03bcm, filled in the N phase at 120\u2009\u00b0C, and cooled down with the rate 2\u2009\u00b0C/min, show a monodomain texture, with the polarization P=P(0,1,0) antiparallel to R=(0,\u22121,0), Fig.\u00a01d. A dc electric field E=E(0,1,0) directed along P and of an amplitude E=(1\u221210)kV/m causes no textural changes, while the opposite field polarity reorients n^ and P beginning with E\u2193=\u22121.0kV/m, Fig.\u00a01d. As the field increases, the optical retardance \u0393 diminishes, Fig.\u00a01d, which indicates that n^ twists away from the rubbing direction in the bulk. Above a critical field Ec=\u221211kV/m, the surface anchoring that keeps P antiparallel to R (P\u2191\u2193R) is broken, and a uniformly aligned state P\u2193\u2193R nucleates and propagates across the cell, swiping away the twisted state. Once formed, the P\u2193\u2193R state is stable for days, even in the absence of the field. A field E=E(0,1,0) that is antiparallel to R realigns P back to the ground state P\u2191\u2193R, beginning with E\u2191=0.6kV/m, which is noticeably lower than |E\u2193|, Fig.\u00a01e. Figure\u00a01f schematizes the polarization realignment from the local anchoring minimum P\u2193\u2193R to the global one at P\u2191\u2193R, which is accompanied by the formation of horizontal left- and right-twisted 180o DWs of the Bloch type near the plates. Multiple cycles of switching leave E\u2191 and E\u2193 intact, which means that the electric field realigns the polarization P in the liquid crystal bulk but does not switch the polarity of the rubbing direction R. Note also that heating the material into I and then cooling it down to NF restores P antiparallel to R.\n\nThe difference in the electric fields |E\u2193| and |E\u2191| that deviate P from the states P\u2191\u2193R and P\u2193\u2193R, respectively, demonstrates that the in-plane anchoring in the cells with the parallel assembly of the buffed plates exhibits two energy minima, one global at \u03c6=0, and another local at \u03c6 = \u00b1\u03c0. Here, \u03c6 is the angle that P makes with the y-axis. The azimuthal surface anchoring potential that captures these features is\n\nwhere WQ \u2265 0 and WP \u2265 0 are the apolar (quadrupolar, or nematic-like) and polar anchoring coefficients, respectively, Fig.\u00a01g. This form follows the one proposed by Chen et al.14 and places a global minimum at \u03c6=0. When WP = 0, the anchoring is polarity-insensitive, and the minima at \u03c6=0,\u00b1\u03c0 are of an equal depth. As WP increases, the minima at \u03c6=\u00b1\u03c0 raise to the level \u0394W=2WP and become local, until disappearing at WP\u2265WQ, Fig.\u00a01g. The energy barrier Wmax = WQ(1 + \u03c9)2/2 at \u03c6 = arccos(\u2212\u03c9) separates the global and local minima; \u03c9=WP/WQ is the relative strength of the in-plane polar anchoring.\n\nThe surface anchoring torques27 \u2202W(\u03c6)\u2202\u03c6|z=0,d=(WQsin\u03c6cos\u03c6+WPsin\u03c6)|z=0,d resist the realigning action of the field, Fig.\u00a01f. For a small deviation from the preferred state \u03c6=0, the torque is WQ+WP; for a deviation from the metastable state \u03c6=\u00b1\u03c0 the torque is weaker, WQ\u2212WP. These torques compete with the elastic torque K2/\u03beE=K2PE caused by the field-induced twist of P in subsurface regions of a characteristic thickness \u03beE=K2/PE, where K2 is the twist elastic constant, Fig.\u00a01f. The difference in the surface torques explains the difference in the reorienting fields, WQ+WPWQ\u2212WP=|E\u2193E\u2191|\u22481.3, which allows one to determine the relative strength of the polar anchoring, \u03c9=WP/WQ\u22480.13. The measured E\u2191=0.6kV/m, E\u2193=\u22121.0kV/m, reported7 P=4.4\u00d710\u22122C/m2, and a reasonable assumption27 K2\u22485pN, lead to the estimates \u03beE\u22480.3\u03bcm, WQ\u22481.3\u00d710\u22125J/m2, and WP\u22481.7\u00d710\u22126J/m2. The estimated WQ is within the range reported for nematics at rubbed polyimides28,29.\n\nNote here that in the thin cell under study, the material was filled in the N phase at 120\u2009\u00b0C by a capillary flow along the \u2212R direction, Fig.\u00a01d. Filling a cell by a flow at 120\u2009\u00b0C along R yields E\u2193=\u22121.4kV/m and E\u2191=1.0kV/m, which implies a weaker polar bias: \u03c9\u22480.08. This flow effect on the surface anchoring deserves further study, but to describe the polydomain patterns in thick cells, we avoid it by filling the cells in at 180\u2009\u00b0C and then rapidly cooling the sample through the N phase with a rate 30\u2009\u00b0C/min, followed by slow cooling through SmZA and NF with the rate 2\u2009\u00b0C/min. Thin d=1.1 \u03bcm monodomain samples show E\u2193=\u22120.4kV/m, E\u2191=0.3kV/m, which yields \u03c9\u22480.07. With the values of P and K2 above, one estimates WQ\u22488.8\u00d710\u22126J/m2, and WP\u22480.63\u00d710\u22126J/m2. In what follows, we discuss the data for cells filled in the isotropic phase at 180\u2009\u00b0C; the domain structures are similar to those in cells filled at 120\u2009\u00b0C.\n\nCooling cells of thickness \u03bcd=3\u221216\u03bcm from the SmZA phase results in a quasiperiodic domain texture of NF, Fig.\u00a01c, with alternating homogeneous P\u2191\u2193R and P\u2193\u2193R stripes, as established by the response to the in-plane electric field, Figs.\u00a02 and 3. For example, the cell of the thickness d=4.7\u03bcm shows relatively wide (5\u2013150 \u03bcm) regions in which P\u2191\u2193R and narrow (1\u20132\u2009\u03bcm) regions in which P\u2193\u2193R, respectively, Figs.\u00a01c, 2 and 3. Once formed, the domains remain stable for days. Repeating heating-cooling cycles, even following a crystallization or transition into the isotropic phase, reproduces the same qualitative NF patterns.\n\na\u2013d POM textures of topologically trivial S-pair that are smoothly realigned into a uniform state by the electric field of an appropriate polarity. e An opposite field polarity tilts P in two wide domains, but does not cause a complete reorientation, contrary to the case of the narrow domain in (d). f Topological scheme of the S-pair shown in (a). P rotates CW in the left DW and CCW in the right DW, thus Q = 0. g Topological scheme of the S-pair shown in (c). P in the central narrow domain could rotate only CCW as the field increases. h, i POM textures (with an added waveplate) of a topologically stable 360o W-pair of DWs, Q = 1; increase of the electric field could cause both CW and CCW rotations of P within the same DW pair, as schematized in (j). Cell thickness 4.7\u2009\u00b5m in all textures.\n\nBoth narrow and wide domains are extinct when aligned along the polarizers of POM, Fig.\u00a02a, and show optical retardance \u0393\u2009=\u2009900\u2009nm at \u03bb=\u2009535\u2009nm and \u03bcd=4.7\u03bcm, which means that \u0393/d coincides with \u0394n and thus P and n^ must be in the xy plane of the cell.\n\nDomains of opposite polarization are separated by DWs. Within each DW, P and n^ must realign by 180o. The DWs enclosing the narrow domains always exist and terminate in pairs, Figs.\u00a01c, 2 and 3, so that the reorientation within the DW pair is 360o in the plane of the sample. To elucidate the structures in a greater detail, we use thicker cells (d=6.8\u03bcm), in which the narrow domains are slightly wider, Supplementary Fig.\u00a09, and perform POM observations with monochromatic light, using a blue interferometric filter of a central wavelength \u03bb = 488\u2009nm, full width at half maximum (FWHM) 1\u2009nm, and a red filter (\u03bb = 632.8\u2009nm, FWHM 1\u2009nm), Fig.\u00a04.\n\na Polychromatic texture of a DW pair running parallel to one of the crossed polarizers; wide P \u2191\u2193 R (\u03c6 = 0, 2\u03c0) and narrow P \u2193\u2193 R (\u03c6 = \u03c0) domains are extinct. b The same texture, observed with a blue filter; the stripes with \u03c6 = \u03c0/2 and 3\u03c0/2 where P is perpendicular to the DWs are also extinct. c Transmitted light intensity along the dashed line in (b). d Polychromatic texture of a DW pair running at 45o to the crossed polarizers; wide P \u2191\u2193 R (\u03c6 = 0, 2\u03c0) and narrow P \u2193\u2193 R (\u03c6 = \u03c0) domains show similar optical retardance. e The same texture, observed with a red filter that yields destructive interference at locations \u03c6 = 0,\u03c0/2, \u03c0, 3\u03c0/2, 2\u03c0. f Transmitted light intensity along the dashed line in (e). Cell thickness 6.8\u2009\u00b5m in all textures.\n\nIn crossed polarizers aligned parallel and orthogonal to the DWs, the regions in which P\u2191\u2193R (\u03c6=0,2\u03c0) and P\u2193\u2193R (\u03c6=\u03c0) appear dark in both polychromatic, Fig.\u00a04a, and blue light, Fig.\u00a04b, c. The blue filter observations reveal that the regions located approximately half-way between \u03c6=0,2\u03c0 and \u03c6=\u03c0 are also dark, apparently corresponding to \u03c6=\u03c0/2,3\u03c0/2, Fig.\u00a04b, c. The dark stripes associated with \u03c6 = 0, \u03c0/2, \u03c0, 3\u03c0/2, 2\u03c0, are separated by bright stripes, corresponding to intermediate \u03c6\u2019s, Fig.\u00a04a\u2013c. The textures in Fig.\u00a04a\u2013c make it clear that the described DWs are indeed walls with a 360o reorientation of P and n^, as opposed to the \u201cbend texture with line disclination\u201d of other NF materials presented by Li et al.21, 180o surface disclination lines and 180o DWs described by Chen et al.13 and Li et al.21. The transmitted intensity profile in Fig.\u00a04c allows one to introduce the characteristic width parameters of the DW pairs: distances L\u03c0/2 between the two central bright stripes, L\u03c0 between two dark narrow stripes, and L3\u03c0/2 between two outermost stripes. These distances, although small (8\u201315\u2009\u03bcm), are clearly wider than the cores of singular disclinations, and 180o walls or surface disclinations described previously. Importantly, besides the in-plane 360o reorientation of P and n^, the textures in \u03bcd=6.8\u03bcm cells also suggest tilts of these vectors away from the cell\u2019s xy plane, as described below.\n\nWhen the crossed polarizers are at 45o with respect to the DWs, polychromatic light observations reveal the same interference colors in narrow (\u03c6=\u03c0) and wide (\u03c6=0,2\u03c0) domains, Fig.\u00a04d. The chosen \u03bcd=6.8\u03bcm allows us to achieve destructive interference of the ordinary and extraordinary waves in POM observations with a red filter (\u03bb\u2009=\u2009632.8\u2009nm), at which \u0394n=0.189, since the factor \u03c0d\u25b3n2\u03bb=3.19 associated with the interference of the two modes27 is close to \u03c0. Although the crossed polarizers are at 45o to the DWs, destructive interference causes extinction in the regions with \u03c6 = 0, \u03c0, and 2\u03c0, where P and n^ are in the xy plane; regions \u03c6=\u03c0/2,3\u03c0/2 also appear dark. A notable exception are four narrow peaks of transmission, at 0<\u03c6<\u03c0/2, \u03c0/2<\u03c6<\u03c0, \u03c0<\u03c6<3\u03c0/2, and 3\u03c0/2<\u03c6<2\u03c0, Fig.\u00a04f, which signal the appearance of a polar z-component of P and n^.\n\nThere are two types of the 360o DW pairs. In the first, called W-pairs because of the shape of the director field, Fig.\u00a02c, P rotates by 180o in the same fashion in both DWs, either clockwise (CW) or counterclockwise (CCW). In the second type, called 360o S-pairs for their geometry, Fig.\u00a03f, the rotation directions alternate: if P rotates CW by 180o in one DW, it rotates CCW by 180o in the next one. The splay-bend schemes of Figs.\u00a02c and 3f demonstrate only the topological features of the in-plane realignments; polar tilts and associated twists add to the complexity of the splay-bend and will be treated in the section on numerical simulations.\n\nThe difference between the W- and S-pairs is topological, as illustrated by mappings of the oriented line \u03b3 threaded through the DWs pair and the enclosed domain, into the order parameter space, a circle S1\u200927, Figs.\u00a02c and 3f. Each point on S1 corresponds to a certain \u03c6. The line \u03b3 in Fig.\u00a02c produces a CCW-oriented closed contour \u03a5 encircling S1 once. The W-pair of CCW walls thus carries a topological charge Q= 127. A DW pair with a CW 360o rotation of P would carry Q=\u22121. Neither could be transformed into a uniform state Q= 0 without breaking the surface anchoring and overcoming a large elastic energy barrier. S-pairs of 180o-walls with alternating sense of rotations are topologically trivial, Q= 0: the corresponding contour \u03a5 does not encircle S1 fully and could be contracted into a single point \u03c6=0 without the need to overcome the elastic energy barrier, Fig.\u00a03g.\n\nThe elastic energy density stored within a DW, KL\u03c02\u223ckBTaL\u03c02, where K is the average Frank elastic constant, kBT is Boltzmann\u2019s energy, a\u223c1nm is the molecular size, and L\u03c0\u2248(5\u221220)\u03bcm is the characteristic width of a DW pair, defined as the distance between the x-coordinates of two bend regions, \u03c6 = \u03c0/2 and 3\u03c0/2, Figs.\u00a02c and 4c, f, is much lower than the energy density kBTa3 of the orientational order. Therefore, P\u2225n^ and realignment of P preserves the magnitude P. This feature makes the observed DWs similar to N\u00e9el DWs in ferroics, as opposed to Ising DWs, in which P\u21920.\n\nReorientation of P within each DW generates a \u201cbound\u201d space charge of density \u03c1b = \u2212div P. If the polarization charge is not screened by ionic charges, then the balance of the elastic energy (per unit area of the wall) KL\u03c0 and the electrostatic energy P2L\u03c0\u03b5\u03b50 suggests30 that a DW would be of a nanoscale width, equal the so-called polarization penetration length \u03beP=\u03b5\u03b50KP2, where \u03b50 is the electric constant, \u03b5 is the dielectric permittivity of the material. For the DIO polarization density7 P=4.4\u00d710\u22122C/m2 and assumed K=10pN, \u03b5\u2009=\u200910, one finds \u03beP\u22481 nm, much smaller than the observed L\u03c0, Fig.\u00a04. Note here that the estimated \u03b5 is lower than the often reported value 104, which might be exaggerated by the effect of polarization realignment31. The polarization charge of density \u03c1b\u223cPL\u03c0\u223c(0.2\u22120.9)\u00d7104C/m3 at the splay region of a DW should be screened by mobile free charges, supplied by ionic impurities, ionization, and absorption effects. To achieve a comparable screening charge \u03c1f\u223cen\u223c(0.2\u22120.9)\u00d7104C/m3, where e=1.6\u00d710\u221219C is the elementary charge, the concentration of ions at the DW should be n\u223c(1022\u22121023)/m3. A high ion concentration n\u223c1023/m3 has been reported as a volume-averaged value for ferroelectric smectics32, although conventional nematics usually yield smaller values33, n\u223c(1020\u22121022)/m3. It is reasonable to assume that even when the volume-averaged n is less than n\u223c(1022\u22121023)/m3, mobile charges could move from the uniform regions of the material and accumulate at local concentrations sufficient to screen the splay-induced polarization charge.\n\nAs envisioned by Meyer34 and detailed theoretically in the subsequent studies35,36,37, the ionic screening enhances the splay elastic constant K1 associated with (div n^)2 in the Frank\u2013Oseen free energy density: K1=K1,0(1+\u03bbD2/\u03beP2), where K1,0 is the bare modulus, of the same order as the one normally measured in a conventional paraelectric N, and \u03bbD=\u03b5\u03b50kBTne2 is the Debye screening length, which, for the typical parameters specified above and n=1023/m3, is on the order of 10nm. With \u03bbD\u223c10nm,\u03beP\u223c1 nm, the enhancement factor, \u03bbD2\u03beP2\u223c102, could be strong. Thus, K1 in NF can be much larger than K1 in N. Very little is known about the elastic constants in the N phase of ferroelectric materials and practically nothing is known about the elasticity of NF. Chen et al.24 measured K1\u224810K2 in the N phase of DIO and expected37 K1\u22482pN. Mertelj et al.10 reported that in the N phase of another ferroelectric material RM734, K1 is even lower, about 0.4 pN. Since the bend elastic constant K3 of NF is not supposed to experience an electrostatic renormalization, it is expected to be a few tens of pN; for example, Mertelj et al.10 found K3\u224810-20 pN for the N phase of RM734. Therefore, the ratio \u03ba=K1/K3 in NF could be larger than 1, ranging from a single-digits value to ~102. The next section presents qualitative evidence that K1>K3 in NF.\n\nThe textures of N and NF are strikingly different when there is no in-plane anchoring. Figure\u00a05 shows the textures of thin (d=5\u22127\u03bcm) films of DIO spread onto glycerin; the upper surface is free. Thermotropic N films are known to form 2\u03c0 domain walls of the W type, stabilized by the hybrid zenithal anchoring, tangential at the glycerin substrate and tilted or homeotropic at the free surface38; these 2\u03c0 domain walls contain both splay and bend and are clearly distinguished in DIO as bands with four extinction bands, Fig. 5a. The NF textures feature an optical retardance that is consistent with the director being tangential to the film. The most important feature is that the curvature lines of P and n^ are close to circles and circular arches, Fig.\u00a05b, c, which implies prevalence of bend and signals that splay is energetically costly. One often observe disclinations of strength +1 with predominant bend, Fig.\u00a05b, c. The regions with +1 disclinations are separated from regions with a straight or nearly straight P by defects shaped as parts of ellipses and parabolas, Fig.\u00a05b, while two neighboring domains with a +1 disclination in each are separated by hyperbolic defects, Fig.\u00a05c.\n\na N film shows 2\u03c0 domain splay-bend walls. b, c NF texture of conic-sections with prevailing circular bend; in (b), elliptical defects separate regions between mostly circular bend and mostly uniform P field, while in (c), hyperbolic shapes separate domains with predominantly circular bend. Film thickness 7\u2009\u00b5m in (a, c), and 5\u2009\u00b5m in (b); n^ is depicted by white lines.\n\nThe conic-sections textures (CSTs) of NF in Fig.\u00a05b, c resemble focal conic domain (FCD) textures of a smectics A, in which the layers are shaped as the so-called Dupin cyclides27 that preserve equidistance and avoid bend and twist of the normal to the layers (which is the smectic director). The distinct feature of the Dupin cyclides is that their focal surfaces reduce to conic-sections, such as a confocal ellipse and hyperbola, or pairs of parabolas. The CSTs in Fig.\u00a05b, c shows similar conic-sections as the boundaries between regions of different director curvatures. In NF, the director avoids splay; twist is not prohibited, but the degenerate anchoring does not require it. The FCD textures in a smectic A reflect the inequality K3\u226bK1, while the CSTs in NF suggest K1>K3; a detailed analysis of CSTs will be presented elsewhere. In what follows, we explore the DW pairs in planar samples theoretically, first in a simplified one-constant approximation, and then accounting for the possibility of elastic anisotropy K1>K3 and non-planar geometry of the director.\n\nThe observed coexistence of the wide P\u2191\u2193R and narrow P\u2193\u2193R domains in planar cells results from the two-minima surface potential W(\u03c6), Fig.\u00a01g, balanced by the bulk elasticity of NF. According to the experiments, the director within the DW pair experiences a reorientation by 2\u03c0 along the x axis, which must incorporate both splay and bend, Figs.\u00a02\u20134. The experimental data in Fig.\u00a04e, f also demonstrate a polar tilt towards the z-axis; this tilt adds a twist of P. To make the theoretical analysis tractable, the overall director field could be approximated as\n\nwhere the azimuthal angle \u03c6(x) between P and the y-axis varies only along the x-axis and the polar angle \u03b8(x,z) between P and the xy plane could change along both the x- and z-axes. Far from the DW pair, the boundary conditions are \u03c6(x)=\u03b8(x,z)=0. We also measure \u03b8(x,z) = 0 at the locations with \u03c6 = 0, \u03c0, and 2\u03c0, where optical retardance is close to d\u0394n, Fig.\u00a04e, f. Since the polar tilt at the bounding plates is penalized by a large surface charge, we assume that the zenithal polar anchoring is infinitely strong and approximate the bulk variations of the polar angle as\n\nwhich satisfies the boundary condition \u03b8(x,z)=0 at z=\u00b1d/2; \u03b8a is the tilt amplitude.\n\nThe Frank\u2013Oseen free energy with the bulk, saddle-splay, and the azimuthal surface anchoring terms reads\n\nwhere K1, K2, K3, and K24 are the elastic constants of splay, twist, bend, and saddle-splay, respectively. The equilibrium director field n^||P minimizing the free energy in Eq. (4) could be found only numerically. However, analytical solutions useful for the understanding of the DW pairs could be found if \u03b8(x,z)=0 and K1=K3=K; the planar geometry with \u03b8=0 excludes twists.\n\nSetting the variation of the energy (4) to zero leads to the first integral of the Euler\u2013Lagrange equation:\n\nFor an apolar anchoring, \u03c9=0, and the boundary conditions \u2202\u03c6\u2202x(\u00b1\u221e)=0, \u03c6(\u2212\u221e)=0, \u03c6(\u221e)=\u03c0, the constant of integration is 0 and the solution\n\nrepresents a static \u03c0-soliton with a characteristic width \u03be=Kd2WQ, within which P realigns into \u2212P. This solution is an \u201cinversion wall\u201d of the N\u00e9el type observed by Nehring and Saupe in planar N cells23. The energy per unit length of each \u03c0-soliton, obtained by integrating f with WP=0 over the range \u2212\u221e<x<\u221e, is finite, F\u03c0=22KdWQ.\n\nWhen WP>0, the single-wall solution (6) is no longer valid since \u03c6=\u00b1\u03c0 is only a local minimum of W(\u03c6). With WP>0, Eq. (5) is a double-sine-Gordon equation, extensively studied in high-energy physics and cosmology39 and physics of ferromagnets4, in which case the analogs of the surface WQ and WP terms are of a bulk nature, associated, e.g., with the crystal anisotropy of a ferromagnet and the external magnetic field, respectively. With boundary conditions \u2202\u03c6\u2202x(\u00b1\u221e)=0, \u03c6(\u00b1\u221e)=0,2\u03c0, among the solutions of Eq. (4) are topologically protected \u03c0\u03c0 soliton-soliton pairs with 360o in-plane reorientation of P and a topological charge Q=\u00b11:\n\nwhere \u03be\u03c0\u03c0=\u03be11+\u03c9, \u03b4\u03c0\u03c0=2arcsinh1\u03c9; \u201c+\u201d signs correspond to a Q=1 pair in Fig.\u00a02c, e and Supplementary Fig.\u00a010a. The solution is a superposition of two \u03c0-walls located at x=\u00b1\u03be\u03c0\u03c0\u03b4\u03c0\u03c02 and limiting a stripe of a nearly uniform P\u2193\u2193R, Fig.\u00a06a. The \u03c0\u03c0-soliton (7) is topologically equivalent to the 360o DW pair of the W type in Figs.\u00a02, 3h, 3i and 4. The energy per unit length of this \u03c0\u03c0-soliton is finite: F\u03c0\u03c0=2F\u03c0[1+\u03c9+\u03c9arccoth1+\u03c9].\n\na In-plane polarization field for \u03c9 = 0.1. b The corresponding texture observed between crossed polarizers with the intensity of transmitted light calculated with Eq.(8). c Polarization profile \u03c6\u03c0\u03c0(x) for different surface anchoring anisotropies \u03c9; the separation L\u03c0 between two extinction bands at \u03c6\u03c0\u03c0 = \u03c0/2 and \u03c6\u03c0\u03c0 = 3\u03c0/2 is shown for the profile with \u03c9 = 0.001. d Characteristic widths of the \u03c0\u03c0 soliton-soliton pairs defined in (b) vs. \u03c9; note that \u0394x \u2245 L\u03c0 for \u03c9 < 0.1, but \u0394x < L\u03c0 for \u03c9 > 0.1.\n\nThe intensity of unpolarized monochromatic light, transmitted through two crossed polarizers enclosing a birefringent sample with a DW pair described by Eq. (7) and running parallel to one of the polarizers27,\n\nproduces a texture with maximum light transmission at \u03c6\u03c0\u03c0 = \u03c0/4, 3\u03c0/4, 5\u03c0/4, and 7\u03c0/4 and extinction at \u03c6\u03c0\u03c0 = 0, \u03c0/2,\u03c0,3\u03c0/2,and 2\u03c0, Fig.\u00a06b, which is qualitatively similar to the experimental textures in Fig.\u00a04.\n\nTo facilitate a comparison with the experiment, the width of the DW pairs is characterized by distances L\u03c0/2 between the two central bright stripes, L\u03c0 between two dark narrow stripes, L3\u03c0/2 between two outermost stripes, Fig.\u00a06b. L\u03c0/2 measures the extension of mostly splay deformations between \u03c6\u03c0\u03c0 = 3\u03c0/4 and 5\u03c0/4, while the quantity L3\u03c0/2 \u2212 L\u03c0/2 characterizes the extension of predominant bend. The characteristic width \u0394x=\u03b4\u03c0\u03c0\u03be\u03c0\u03c0 appearing in Eq. (7) is close to L\u03c0 when \u03c9<0.1, but is smaller than L\u03c0 when \u03c9>0.1, as shown in Fig.\u00a06d.\n\nAn increase of the elastic modulus K makes the DWs wider and farther apart, to weaken the gradients of n^ and P. When the polar in-plane anchoring is weak, \u03c9\u226a1, the DWs are far away from each other, Fig.\u00a06c, with L\u03c0=\u25b3x\u2248Kd2WQln4\u03c9 and a characteristic width \u03be\u03c0\u03c0\u2248Kd2WQ(1\u2212\u03c92) close to \u03be. The pair\u2019s energy approaches the sum of the energies of two individual \u03c0-solitons, F\u03c0\u03c0\u22482F\u03c0[1+\u03c92(1+ln4\u03c9)]. A larger \u03c9 pushes the walls towards each other, shrinking the narrow P\u2193\u2193R stripe, where the polarization is in the local minimum of the anchoring potential, Fig.\u00a06c, d.\n\nThe soliton-antisoliton \u03c0\u03c0\u00af or \u03c0\u00af\u03c0 pairs with alternating \u03c0 -rotations of P satisfying Eq. (5) with the boundary conditions \u2202\u03c6\u2202x(\u00b1\u221e)=0, \u03c6(\u00b1\u221e)=0 and corresponding to the S-pairs, are illustrated in Supplementary Figs.\u00a010b and 11. Finally, solutions in which the boundary conditions are \u2202\u03c6\u2202x(\u00b1\u221e)=0, \u03c6(\u00b1\u221e)=\u00b1\u03c0 are also possible; they exhibit interesting spreading dynamics, as shown in Supplementary Fig.\u00a012.\n\nFor \u03ba\u2261K1/K3\u22601 and \u03b8(x,z)=0, the free energy per unit area of an NF cell, after integration over the cell thickness, writes\n\nThe first integral of the Euler-Lagrange equation is\n\nwhere \u03be3=K3d2WQ is the extrapolation length associated with the bend modulus and quadrupolar anchoring. Equation (10) could be solved numerically if rewritten as an expression describing a dynamic \u201cparticle\u201d of a kinetic energy 12\u03be32(\u2202\u03c6\u2202x)2 (with the coordinate x representing \u201ctime\u201d) rolling through a double-welled potential V[\u03c6]=2\u03c9(cos\u03c6\u22121)\u2212sin2\u03c62(\u03bacos2\u03c6+sin2\u03c6), with zero total energy:\n\nThe \u03c0\u03c0-soliton solution corresponds to the particle rolling down the potential V[\u03c6] starting at \u03c6=0, where V=0, through the two wells, and arriving at \u03c6=2\u03c0. Because energy is conserved, the soliton would be stable as the maxima at \u03c6=0,2\u03c0 are both at V=0. To find \u03c6(x), one needs to impart a small initial \u201cmomentum\u201d forcing the particle to start the motion.\n\nFigure\u00a07 shows the results of numerical analysis. The width parameters L\u03c0/2,L\u03c0, and L3\u03c0/2 of the DW pairs are not much affected by the elastic anisotropy when K1/K3\u226a1, but increase, approximately as L\u03c0\u221dK1/K3, when K1/K3>1, Fig.\u00a07b. Because of their topological 2\u03c0-rotation nature, the DW pairs must incorporate both splay and bend, no matter the value of K1/K3. A notable qualitative feature of the director profile \u03c6(x) of the DW pairs is that as K1/K3 increases, the stripes of splay widen, Fig.\u00a07a. The structure tends to decrease the high splay energy by extending the length over which the splay develops; in contrast, it could afford a shorter bend development since K3 is low. Domain walls in a chiral smectic C (SmC*) stabilized by a magnetic field show similar features40, with the difference that, in SmC*, it is K3 that is increased by the ionic screening. Thus, it is the bend stripes that are wider in SmC* than their splay counterparts.\n\na Director profiles of DWs pairs for \u03c9 = 0.1 and different elastic ratios K1/K3. b The width parameter L\u03c0 vs K1/K3 for different anchoring anisotropies \u03c9. c Ratio of width parameters L3\u03c0/2/L\u03c0/2 vs K1/K3 for different anchoring anisotropies \u03c9; the dashed line shows L3\u03c0/2/L\u03c0/2 = 1.8 obtained by averaging experimental data for 64 DW pairs.\n\nThe effect of elastic anisotropy on the ratio L3\u03c0/2/L\u03c0/2 is very strong when K1/K3 is in the range 0.1\u201310, Fig.\u00a07c. As K1/K3 increases, the width of the splay region progressively expands and L\u03c0/2 approaches L3\u03c0/2. When compared to the experimental value L3\u03c0/2/L\u03c0/2=1.8 obtained by averaging data of 64 DW pairs of both W and S types, the model of a planar \u03c0\u03c0-soliton suggests K1/K3\u223c10 if \u03c9=0.1. A more detailed comparison with the experiment is given below.\n\nThe planar model neglects the possibility of director tilts towards the z-axis. Unless the cells are very thin, such a possibility should not be ignored. Figure\u00a04e demonstrates that the director indeed tilts away from the xy-plane. To explore the effect, we return to Eq. (4) and use the ansatz in Eq. (3) for the tilt angle \u03b8(x,z). For small \u03b8, the Frank\u2013Oseen free energy density per unit area of the cell is\n\nEquation (12) demonstrates that in areas of strong splay, where cos2\u03c6(\u2202x\u03c6)2 is large, a non-zero tilt \u03b8a>0 decreases the splay contribution by introducing twist (the terms proportional to K2). The introduction of tilt becomes energetically costly when the cell is thin, with the tilt magnitude bounded by \u03b8a\u2272d2\u03c0\u03be32=12\u03c0WQdK3. For a 6.8 \u03bcm cell, K3/WQ=1\u03bcm, we expect \u03b8a\u22720.4. Significantly thinner cells would hardly experience polar tilt at all: a strong zenithal anchoring (associated with the tilts away from the xy plane) makes the energetic costs of a vertical gradient over a short d prohibitively high. Note, however, that our analysis is limited to a particularly simple z-dependence for both \u03b8 and \u03c6 and the quantitative estimates above might be changed by a more rigorous analysis.\n\nTo find the tilt configuration \u03b8a(x), we minimize the Frank\u2013Oseen free energy in Eq. (4) using gradient descent. The sharp bend of \u03c6(x) at large K1/K3 introduces computational challenges. To get a qualitative picture while ensuring the numerical convergence of the gradient descent procedure, we take K1/K3=10 and d/\u03be3=15, for which we expect a noticeable tilt. The resulting configurations of the polar angle \u03c6(x) and the tilt \u03b8a(x) are shown in Fig.\u00a08a, c, d. Note that the director reorients to point nearly vertically (\u03b8a approaches \u03c0/2) in the middle of each of the two \u03c0-solitons, Fig.\u00a08a. In these high tilt regions, the polar angle \u03c6 rotates very rapidly as a function of x. This allows for a lower anchoring free energy as \u03c6 maintains values close to 0,2\u03c0 for a larger range of x, Fig.\u00a08a. The introduction of the tilt reduces the domain wall energy by about 20%, Fig.\u00a09a. This measured decrease becomes even more substantial for larger values of d/\u03be3, Fig.\u00a09a. It also represents a lower bound on the energy reduction as we use a constrained z-dependence of the azimuthal and polar angles. It would be interesting to minimize both \u03c6 and \u03b8 without any constraints to find the true global energy minimum.\n\na Tilt magnitude \u03b8a(x) and polar angle \u03c6(x) profiles calculated by numerical minimization of the Frank\u2013Oseen energy in Eq. (4) using the ansatz in Eq. (3) for K1/K3 = 10. The largest tilt occurs near \u03c6=\u03c02,3\u03c02. b Transmitted light intensity through a cell and a filter of the type shown in Fig.\u00a04e, where the wavelength \u03bb of light is chosen such that \u03c0d\u25b3n2\u03bb=\u03c0. Note the favorable comparison between these results and the experimental data in Fig.\u00a04c, f. Transmission is strong whenever \u03c6=\u03c04,3\u03c04,5\u03c04,7\u03c04. c, d Two projected schemes of the polarization field in the one-quarter of the \u03c0\u03c0-soliton in which we find the largest tilt \u03b8, with the same parameters as in (a). In all simulations, d = 15 \u03be3, K2 = K3/2, and \u03c9 = 0.1.\n\na Energy ratio of a planar domain wall (\u03b8 = 0) versus one with a tilt (\u03b8 > 0), as calculated from minimizing the Frank\u2013Oseen energy in Eq. (4) using the ansatz in Eq. (3) for various values of K1/K3 and d/\u03be3. Note the marked energy gain from introducing a tilt for thick cells. For thinner cells, d/\u03be3<10, the gain is negligible, especially at large ratios K1/K3. b Ratio of width parameters L3\u03c0/2/L\u03c0/2 vs K1/K3 for different cell thicknesses d/\u03be3. Note that this ratio is expected to be smaller whenever there is substantial tilt in the director configuration. For thinner cells, d/\u03be3<10, the ratio approaches the planar value (black line) for large K1/K3 as the tilt becomes negligible. In all simulations, \u03c9=0.1 and K2/K3=0.5. The dashed line shows L3\u03c0/2/L\u03c0/2=1.8 obtained by averaging experimental data for 64 DW pairs. The lines connecting the data points in these plots are a guide to the eye.\n\nTaking the results for \u03c6,\u03b8, we simulate the transmitted light intensities of the cell viewed through crossed polarizers with a monochromatic light of a particular wavelength \u03bb, Fig.\u00a08b. Choosing a wavelength at which the transmission through regions with P\u2191\u2193R and P\u2193\u2193R is suppressed, we find the results in Fig.\u00a08b for two orientations of the polarizers. The simulated intensities in Fig.\u00a08b compare favorably to Fig.\u00a04c (blue curve) and Fig.\u00a04f (red curve). The red curve has an additional small peak between the two main peaks at around \u03c6\u2248\u03c04,3\u03c04. This small peak is not resolved in the experiment in Fig.\u00a04f. One potential reason is that the intensity peak is very narrow, less than \u03be32; with d= 6.8 \u03bcm, K3/WQ=1\u03bcm, we expect \u03bc\u03be32\u22480.9\u03bcm. Another reason is that the regions with \u03b8>0 present a lower refractive index to the propagating beam as compared to the regions with \u03b8=0; the index gradient bends the propagating rays away from the regions with \u03b8>0 towards the regions with \u03b8=0, which might further mitigate the small central peaks in the red curve in Fig.\u00a08b. Note that the central peak would further narrow when the elastic anisotropy increases, K1K3>10, so that the reorientation of the angle \u03c6 is even more rapid.\n\nThe tilted configurations depend sensitively on the cell thickness as \u03b8a decreases with decreasing d/\u03be3: the tilt becomes energetically less favorable since the director gradients along the z-axis become stronger under the condition of an infinite polar zenithal anchoring at the bounding plates. The ratio of the energy of a purely planar configuration, Eplanar, to the energy of a configuration with a tilt, Etilt, is shown in Fig.\u00a09a. The numerical simulations suggest that the tilt is strongly reduced for d/\u03be3<10. For K3/WQ=1\u03bcm, and d in the range (3\u201316) \u03bcm, one finds 2<d/\u03be3<6. Our experimental results are likely near the transition region when the tilt becomes energetically favorable, as suggested by the transmission peaks in Fig.\u00a04e.\n\nThe width ratio L3\u03c0/2/L\u03c0/2 depends on the presence of tilt and the cell thickness, Fig.\u00a09b. In thicker cells, the width ratio is smaller as the tilt allows for a faster reorientation of the azimuthal angle \u03c6, as shown in Fig.\u00a08a. The decrease, however, depends on the value of K1/K3, Fig.\u00a09b. The dependence is subtle, with the width ratio approaching the planar value for small K1/K3\u223c(1\u22124), but reaching a smaller value for K1/K3\u224810.\n\nThe width ratio L3\u03c0/2/L\u03c0/2 can be used to estimate K1/K3, Fig.\u00a09b. We analyzed the profiles of transmitted monochromatic light intensities similar to the one in Fig.\u00a04c for DWs pairs in samples of thickness ranging from 4.6 \u03bcm to 15.9 \u03bcm, which implies 3<d/\u03be3<6. In this range, there is no clear thickness dependence of the width ratio. The experimental data, averaged over 64 DWs pairs, yield L3\u03c0/2/L\u03c0/2=1.8\u00b10.3. According to the model predictions in Fig.\u00a09b, the value L3\u03c0/2/L\u03c0/2=1.8 corresponds to K1/K3=(4\u22127) in the model with polar tilts and d/\u03be3=10, and to K1/K3=10 in the model of planar DWs. However, a relatively large standard deviation in the measured width parameter, \u00b10.3, embraces the possibility of much higher elastic anisotropy. An additional factor of uncertainty is in the strong dependence of the geometrical parameters and thus of K1/K3 on the in-plane polar anchoring parameter \u03c9, Fig.\u00a07c. We thus conclude that the experiments on the structure of DW pairs place the lower bound on the elastic anisotropy of NF, K1/K3\u22654, which is supported by both Figs.\u00a07c and 9b.",
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+            ]
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+        {
+            "section_name": "Discussion",
+            "section_text": "The polar nature of the azimuthal surface anchoring of NF planar cells brings about patterns of polar monodomains and polydomains with alternating directions of the polarization P. Cooling the samples down to NF produces both P\u2191\u2193R and P\u2193\u2193R local surface alignments. These directions could be the same at the opposing plates, \u03c6(z=0)=\u03c6(z=d), or the opposite. In the latter case, the two different orientations must be connected by a twisted P, \u03c6(z)=(\u03c6d\u2212\u03c60)z/d+\u03c60, where \u03c60 and \u03c6d are the actual alignment directions at the two plates, which are found from the balance of the elastic and anchoring torques, Supplementary Eqs. (S5\u2013S9). This twisted structure carries an energy ft=2WP+\u03c022K2(1\u2212\u03c92)d(1\u2212\u03c92)+2\u03be2 per unit area, where \u03be2=K2/WQ. In thin cells, ft could be large enough to eliminate the energy barrier between the \u03c6=0 and \u03c6=\u03c0 states and cause the system to relax directly into the ground state \u03c6(z)=0, see Supplementary Eq.\u00a0(S10) and Supplementary Fig.\u00a013. In cells thicker than dc\u2248\u03c02K28WP\u22483.6\u03bcm, ft is smaller than the energy 4WP of the metastable uniform state \u03c6(z)=\u03c0. In these thick cells, the local energy minimum at \u03c6=\u03c0 and the energy barrier that separates \u03c6=\u03c0 and \u03c6=0 directions are preserved (Supplementary Fig.\u00a013); thus the system could relax into either the ground state, \u03c6(z)=0, or the metastable state \u03c6(z)=\u03c0, which explains the observed domain structures with DWs in the thick samples.\n\nWe limited our analysis by the structures observed in the deep NF phase, but the experiments show rich dynamics of the emerging patterns during cooling in the high-temperature end of the NF phase, most likely caused by the temperature dependencies of WQ, WP, and the elastic constants; these will be described elsewhere.\n\nA unique and unusual topological consequence of the surface polarity is that the DWs that separate domains of uniform polarizations form only as 360o pairs, of either the topologically protected soliton-soliton W-type or topologically trivial S-type. The DW pairs in which the order parameter varies from one global energy minimum to another while surpassing an energy barrier makes them similar to the DWs studied in cosmology models with \u201cbiased\u201d vacuums39, in which two vacuums have a slightly different energy and are separated by an energy barrier, similarly to the surface anchoring potential in Eq. (1) and Fig.\u00a01g. In solid ferroics, surface interactions are polar along the normal to interfaces, which leads to the well-known patterns of alternating domains separated by 180o walls of the Bloch or N\u00e9el type2,3; 360o pairs could be observed only in the presence of an external field that competes with the apolar easy directions of the crystal structure4. DWs with 360o rotation of the director could also be observed in a smectic C liquid crystal30,40,41,42,43,44, in which case they are attributed to an externally applied electric field30 or to the asymmetry of the film along the normal direction44. In a uniaxial apolar nematic N, 360o DWs connect surface point-defects, called boojums, in a hybrid aligned film, Fig.\u00a05a, in which one surface imposes a tangential orientation of n^ and another one sets a perpendicular alignment of n^, i.e., again the reason is the asymmetry with respect to the normal direction38,45. Under hybrid alignment of N, the 360o DW carries an elastic energy \u221dRL proportional to their length R and width L<<R, which is smaller than the elastic energy of an isolated boojum with an energy \u221dR2, where R is the characteristic size of the system45. Unlike all listed examples, the 360o DWs in NF are caused by interactions that are polar in the plane of the bounding surfaces. The observed 360o pairs of DWs are also different from 180o DWs in NF cells with an antiparallel assembly of buffed plates that preset twist deformations13,14,24. The coupling between the surface polarity and the bulk structures allows us to estimate the polar contribution \u03c9\u2261WPWQ\u223c0.1 to the in-plane anchoring of P.\n\nWhen the surfaces impose no restrictions on the in-plane orientation of P, NF films feature the conic-sections textures, Fig.\u00a05b, c, similar to focal conic domain textures in a smectic A. In a smectic A, the predominant director deformations are splay, signaling K1/K3\u226a1, while in NF, the prevailing curvatures are bend, Fig.\u00a05b, c, suggesting K1/K3>1. The last condition makes the NF textures also similar to the textures of developable domains in columnar phases in which bend is the only allowed deformation of the director27. When the elastic constants show a strong disparity, liquid crystal textures often respond by introducing additional deformation modes (such as the effect of splay-canceling46 or structural twist in the N droplets47,48,49). The DW pairs are no exception: the experiments, Fig.\u00a04e, and numerical analysis, Figs.\u00a08, 9, suggest that the in-plane splay-bend of P could be accompanied by out-of-plane tilts of P, which introduce the twist of P and reduce the overall energy of the DWs. The analysis of the experimentally observed DW pairs suggests K1/K3>4.\n\nThe geometry of the domains and DW pairs is defined primarily by the balance of the polar and apolar terms in the surface potential, suggesting potential applications as sensors and solvents capable of spatial separation of polar inclusions. The advantage of NF is that the material is fluid and is thus easy to process in various confinements. Since the domains form in an optically transparent and birefringent NF fluid with a high susceptibility to low electric fields, other potential applications might be in electro-optics, electrically-controlled optical memory, and grating devices.",
+            "section_image": []
+        },
+        {
+            "section_name": "Methods",
+            "section_text": "The aligning agent PI-2555 and its solvent T9039, both purchased from HD MicroSystems are combined in a 1:9 ratio. Glass substrates with ITO electrodes are cleaned ultrasonically in distilled water and isopropyl alcohol, dried at 95\u2009oC, cooled down to the room temperature and blown with nitrogen. An inert N2 environment is maintained inside the spin coater. Spin coating with the solution of the aligning agent is performed according to the following scheme: 1\u2009s @ 500\u2009rpm \u2192 30\u2009s @ 1500\u2009rpm \u21921\u2009s @ 50\u2009rpm. After the spin coating, the sample is baked at 95\u2009\u00b0C for 5\u2009min, followed by 60\u2009minutes baking at 275\u2009\u00b0C. The spin coating produced the PI-2555 alignment layer of thickness 50\u2009nm.\n\nThe PI-2555 layer is buffed unidirectionally using a Rayon YA-19-R rubbing cloth (Yoshikawa Chemical Company, Ltd, Japan) of a thickness 1.8\u2009mm and filament density 280/mm2 to achieve a homogeneous planar alignment. An aluminum brick of a length 25.5\u2009cm, width 10.4\u2009cm, height 1.8\u2009cm and weight 1.3\u2009kg, covered with the rubbing cloth, imposes a pressure 490\u2009Pa at a substrate and is moved ten times with the speed 5\u2009cm/s over the substrate; the rubbing length is about 1\u2009m. Unidirectional rubbing of a polyimide-coated substrates is known to align a nematic in a planar fashion, with a small pretilt of the director n^. For example, the director of a conventional nematic 5CB in contact with a buffed PI-2555 makes an angle 3\u2218\u00b11\u2218 with the substrate; the tilt direction correlates with the direction R of buffing50. The pretilt in NF is expected to be smaller because of the surface polarization effect, as evidenced by the fact that the optical retardance of the uniform domains equals \u0394nd; however, the rubbing is still expected to produce nanoscale in-plane polarity because of the separation of oppositely charged moieties.\n\nTwo PI-2555-coated glass plates are assembled into cells in \u201cparallel\u201d geometry, with the two buffing directions R at the opposite plates being parallel to each other. One plate contains a pair of parallel transparent indium tin oxide (ITO) stripe electrodes separated along the R-direction by a distance l = 5\u2009mm in the studies of monodomains and 3\u2009mm in the case of polydomains. A Siglent SDG1032X waveform generator and an amplifier (Krohn-Hite corporation) are used to apply an in-plane dc electric field E = E(0, \u00b11, 0). The observations are limited to an area 1 mm2 at the center of the gap. Since the cell thickness d is much smaller than l, the electric field in this region is predominantly horizontal and uniform.\n\nThe films with degenerate azimuthal surface anchoring are prepared by depositing a thin DIO film onto the surface of glycerin (Fisher Scientific, CAS No. 56-81-5 with assay percent range 99\u2013100 %w/v and density 1.261\u2009g/cm3 at 20\u2009\u00b0C) in an open Petri dish. A piece of crystallized DIO is placed onto the surface of glycerin at room temperature, heated to 120\u2009\u00b0C, and cooled down to the desired temperature with a rate of 5\u2009\u00b0C/min. In the N, SmZA and NF phases, DIO spreads over the surface and forms a film of a thickness defined by the deposited mass. For example, in Fig. 5a, a film of a thickness 5\u2009\u00b5m resulted from a deposited 2.55\u2009mg of the material.\n\nThe optical textures are recorded using a polarizing optical microscope Nikon Optiphot-2 with a QImaging camera and Olympus BX51 with an Amscope camera. PolScope MicroImager (Hinds Instruments) is used to map the director patterns and measure the optical retardance.\n\nTo simulate the optical transmission through the cell, we employ the Jones matrix formalism. Assuming light propagation along the z-axis, the polarization in the xy-plane is described by a two-component vector, with (10) polarization along x^ and (01) along y^. The cell is represented as a 2\u00d72 matrix consisting of a product of elements corresponding to thin slices of the uniaxial material. Given a tilt \u03b8(x,z) and polar angle \u03d5(x) of the optical axis, a thin slab i of material of thickness \u0394z will modify the electric field polarization at position (x,zi) according to a sequence of rotations and a phase retardance:\n\nwhere \u03bb is the wavelength of the light, which we take to satisfy \u03bb=(ne\u2212n0)d/2. The dielectric eigenvalues are \u03c30z=n0=1.5 and\n\nwhere ne=1.7. The entire cell consists of N slabs, such that N\u0394z=d. The full optical matrix for the cell is given by the product\n\nwhere we take the locations zi to be the midplanes of the thin slabs: zi=\u2212d/2+(i\u22121/2)\u0394z. We then choose a large enough N such that our matrix converges. Note that the intensity for crossed polarizers can be easily extracted from the matrix elements Mij. We have the following expressions for the intensities when the polarizers are aligned along the x and y axes and when they are at 45\u2218 to these axes, respectively:\n\nFurther information on research design is available in the\u00a0Nature Research Reporting Summary linked to this article.",
+            "section_image": []
+        },
+        {
+            "section_name": "Data availability",
+            "section_text": "All data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.",
+            "section_image": []
+        },
+        {
+            "section_name": "References",
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+            "section_image": []
+        },
+        {
+            "section_name": "Acknowledgements",
+            "section_text": "The authors thank N.A. Clark for illuminating discussions and for providing us with refs. 37,40. This work was supported by NSF grant ECCS-2122399 (ODL).",
+            "section_image": []
+        },
+        {
+            "section_name": "Author information",
+            "section_text": "These authors contributed equally: Bijaya Basnet, Mojtaba Rajabi, Hao Wang.\n\nAdvanced Materials and Liquid Crystal Institute, Kent State University, Kent, OH, 44242, USA\n\nBijaya Basnet,\u00a0Mojtaba Rajabi,\u00a0Hao Wang,\u00a0Priyanka Kumari,\u00a0Kamal Thapa,\u00a0Sanjoy Paul\u00a0&\u00a0Oleg D. Lavrentovich\n\nMaterials Science Graduate Program, Kent State University, Kent, OH, 44242, USA\n\nBijaya Basnet,\u00a0Priyanka Kumari\u00a0&\u00a0Oleg D. Lavrentovich\n\nDepartment of Physics, Kent State University, Kent, OH, 44242, USA\n\nMojtaba Rajabi,\u00a0Kamal Thapa\u00a0&\u00a0Oleg D. Lavrentovich\n\nDepartment of Physics and Astronomy, University of Tennessee, Knoxville, TN, 37996, USA\n\nMaxim O. Lavrentovich\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nB.B. performed the experiments on polydomain structures and analyzed the data; M.R. performed the experiments on monocrystal states and analyzed the data; H.W. designed and performed the synthesis, purification, and chemical characterization of DIO; P.K. performed studies of films at the surface of glycerin and analyzed the data, K.T. assisted in cell preparation and experiments; S.P. assisted in the experimental set-ups; M.O.L. performed numerical analysis, O.D.L. conceived the project, analyzed the data, and wrote the manuscript with the inputs from all co-authors. All authors contributed to scientific discussions.\n\nCorrespondence to\n                Oleg D. Lavrentovich.",
+            "section_image": []
+        },
+        {
+            "section_name": "Ethics declarations",
+            "section_text": "The authors declare no competing interests.",
+            "section_image": []
+        },
+        {
+            "section_name": "Peer review",
+            "section_text": "Nature Communications thanks J Jones and the other anonymous reviewer(s) for their contribution to the peer review of this work.\u00a0Peer reviewer reports are available.",
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+            "section_image": []
+        },
+        {
+            "section_name": "About this article",
+            "section_text": "Basnet, B., Rajabi, M., Wang, H. et al. Soliton walls paired by polar surface interactions in a ferroelectric nematic liquid crystal.\n                    Nat Commun 13, 3932 (2022). https://doi.org/10.1038/s41467-022-31593-w\n\nDownload citation\n\nReceived: 09 January 2022\n\nAccepted: 24 June 2022\n\nPublished: 07 July 2022\n\nVersion of record: 07 July 2022\n\nDOI: https://doi.org/10.1038/s41467-022-31593-w\n\nAnyone you share the following link with will be able to read this content:\n\nSorry, a shareable link is not currently available for this article.\n\n\n\n\n                            Provided by the Springer Nature SharedIt content-sharing initiative\n                        ",
+            "section_image": [
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+            ]
+        },
+        {
+            "section_name": "This article is cited by",
+            "section_text": "Nature Communications (2025)\n\nNature (2025)\n\nNature Communications (2025)\n\nNature Physics (2025)\n\nNature Communications (2025)",
+            "section_image": []
+        }
+    ]
+}

1a99039586ef68e3c10ab28a022b5167155f5a8a0303222dba71ea9bdae0eb2f/metadata.json

@@ -0,0 +1,143 @@
+{
+    "title": "How urban form impacts flooding",
+    "pre_title": "How Urban Form Impacts Flooding",
+    "journal": "Nature Communications",
+    "published": "19 August 2024",
+    "supplementary_0": [
+        {
+            "label": "Supplementary Information",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-024-50347-4/MediaObjects/41467_2024_50347_MOESM1_ESM.pdf"
+        },
+        {
+            "label": "Peer Review File",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-024-50347-4/MediaObjects/41467_2024_50347_MOESM2_ESM.pdf"
+        },
+        {
+            "label": "Description of Additional Supplementary Files",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-024-50347-4/MediaObjects/41467_2024_50347_MOESM3_ESM.pdf"
+        },
+        {
+            "label": "Supplementary Data 1",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-024-50347-4/MediaObjects/41467_2024_50347_MOESM4_ESM.xlsx"
+        }
+    ],
+    "supplementary_1": NaN,
+    "supplementary_2": NaN,
+    "source_data": [
+        "/articles/s41467-024-50347-4#Fig4",
+        "/articles/s41467-024-50347-4#MOESM4"
+    ],
+    "code": [],
+    "subject": [
+        "Hydrology",
+        "Natural hazards",
+        "Water resources"
+    ],
+    "license": "http://creativecommons.org/licenses/by/4.0/",
+    "preprint_pdf": "https://www.researchsquare.com/article/rs-3650683/v1.pdf?c=1724151925000",
+    "research_square_link": "https://www.researchsquare.com//article/rs-3650683/v1",
+    "nature_pdf": "https://www.nature.com/articles/s41467-024-50347-4.pdf",
+    "preprint_posted": "29 Nov, 2023",
+    "research_square_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Urbanization and climate change are contributing to severe flooding globally, damaging infrastructure, disrupting economies, and undermining human well-being. Approaches to make cities more resilient to floods are emerging, notably with the design of flood-resilient structures, but relatively little is known about the role of urban form and its complexity in the concentration of flooding. We leverage statistical mechanics to reduce the complexity of urban flooding and develop a mean-flow theory that relates flood hazards to urban form characterized by the ground slope, urban porosity, and the Mermin order parameter which measures symmetry in building arrangements. The mean-flow theory presents a dimensionless flood depth that scales linearly with the urban porosity and the order parameter, with different scaling for disordered square- and hexagon-like forms. A universal scaling is obtained by introducing an effective mean chord length representative of the unobstructed downslope travel distance for flood water, yielding an analytical model for neighborhood-scale flood hazards globally. The proposed mean-flow theory is applied to probe city-to-city variations in flood hazards, and shows promising results linking recorded flood losses to urban form and observed rainfall extremes.Earth and environmental sciences/HydrologyEarth and environmental sciences/Natural hazards",
+            "section_image": []
+        },
+        {
+            "section_name": "Additional Declarations",
+            "section_text": "There is NO Competing Interest.",
+            "section_image": []
+        },
+        {
+            "section_name": "Supplementary Files",
+            "section_text": "SupplementaryMaterial.pdfSupplementary Information",
+            "section_image": []
+        }
+    ],
+    "nature_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Urbanization and climate change are contributing to severe flooding globally, damaging infrastructure, disrupting economies, and undermining human well-being. Approaches to make cities more resilient to floods are emerging, notably with the design of flood-resilient structures, but relatively little is known about the role of urban form and its complexity in the concentration of flooding. We leverage statistical mechanics to reduce the complexity of urban flooding and develop a mean-flow theory that relates flood hazards to urban form characterized by the ground slope, urban porosity, and the Mermin order parameter which measures symmetry in building arrangements. The mean-flow theory presents a dimensionless flood depth that scales linearly with the urban porosity and the order parameter, with different scaling for disordered square- and hexagon-like forms. A universal scaling is obtained by introducing an effective mean chord length representative of the unobstructed downslope travel distance for flood water, yielding an analytical model for neighborhood-scale flood hazards globally. The proposed mean-flow theory is applied to probe city-to-city variations in flood hazards, and shows promising results linking recorded flood losses to urban form and observed rainfall extremes.",
+            "section_image": []
+        },
+        {
+            "section_name": "Introduction",
+            "section_text": "Flooding is one of the most frequent and costliest natural disasters1,2, and impacts are often concentrated in cities3,4. The severity of flooding is increasing from more intense storms driven by a warming climate5, expanding development into hazardous areas6, and high levels of physical and social vulnerability3,7. Vulnerabilities include building and infrastructure designs that do not tolerate exposure to rising and fast-moving flood waters8, economies that are hindered by infrastructure impacts and job losses9, and flooding that disproportionately exposes disadvantaged and marginalized communities7. In a future marked by more extreme weather events and populations concentrated in cities, attention to the physical form of cities and their vulnerability to flood impacts is of growing importance. This includes the development and application of climate-resilient architectural design approaches10,11, so communities and households can significantly limit the severity of flood losses and more readily bounce back from severe events. But this also calls for attention to the urban form of the community, including the density of development and the configuration of the street network and its relation to ground slopes which drive the movement of flood water.\n\nResearch to date suggests that the configuration of urban forms has the potential to alter the patterns and severity of flooding substantially12,13, but an understanding of the role of urban forms, globally, in shaping flood impacts is limited. Indeed, urban planning initiatives are underway in cities around the world to adapt at-risk communities to more intense flooding and other climate risks, meet needs for housing and commerce, and manage ecosystem health and the provision of ecosystem services; these would benefit from foundational knowledge\u2013a mean-flow theory\u2013describing the effect of urban form on the concentration of flood severity. That is, the goal here is to relate how the depth and velocity of urban flooding at neighborhood scales relate to the orientation and configuration of street layouts and buildings, given the volumetric flow rate. When combined with data and models estimating volumetric flow rates in cities, for example, from heavy rainfall, stormwater surcharge, and overbank streamflows, a mean-flow theory could aid analyses of factors driving present-day flooding hotspots across cities and inform future urban planning with respect to flood risk. Such mean-flow theory is, in principle, akin to the empirical Manning equation for the flow properties of streams14, \\(Q=A{R}^{2/3}\\sqrt{\\alpha }/{n}_{M}\\), where flow rate Q is related to Manning\u2019s roughness nM, flow cross-section and hydraulic radius A and R, and the bottom slope \u03b1, respectively. The Manning equation and other empirical models (e.g., Chezy) have proven instrumental and robust for designing flood channels, and here we seek an equivalent for urban flood plains.\n\nOur inspiration for an urban flooding mean-flow theory is taken from how complex systems are approached in statistical mechanics. Urban forms epitomize a complex system much akin to granular media15, disordered porous solids16, glassy systems17, and complex fluids18, to name only a few. When viewed deterministically, flooding through a complex urban form depends on the location of each obstruction. However, in an average sense, the flow behavior should be governed by a few characteristic state variables reflective of the urban form, e.g., building density, and indicators of how clusters of buildings are configured. This averaging is motivated by Boltzmann\u2019s treatise that proves the equilibrium properties of non-interacting classical particles remain independent of their location and instead rely on the system\u2019s volume\u2014a fundamental thermodynamic state variable19. To reduce the complexity of urban flooding, we need a large ensemble of refined flow observations to build our mean-flow theory. Experimental studies20 and field measurements21 have proven insightful when studying the role of obstructions on urban flooding, yet to date, they remain strictly limited to extremes of simplified obstruction arrangements or case-specific urban forms. Hence, computational modeling is the only viable approach to collect statistically significant data on urban flooding dynamics over a representative spectrum of urban forms.\n\nThe flow structure and boundary layers of urban flooding can be simulated with Reynolds-averaged Navier-Stokes, large-eddy simulation, and direct numerical simulation22. However, in pursuit of computational efficacy, we rely on a shallow-water hydrodynamic model23 and produce thousands of fine-resolution, building-resolved simulations for different realizations of urban form. Shallow-water theory builds on the assumption of hydrostatic pressure and nearly horizontal flow, and shallow-water models have been validated at neighborhood and larger scales by extensive laboratory and field studies and urban flood modeling20,24,25,26,27,28,29. While urban flooding can involve high levels of complexity, such as flows into basements, subway systems, and usually involves a mix of underground flows through storm pipes and overland flow along streets30, we are specifically interested here in the depth and velocity of overland flow through cities caused by the amount of overland flow in response to hazard drivers (e.g., rainfall, overbank flows, stormwater surcharge). Hence, our simulation approach involves measuring the steady-state depth and velocity of flooding for a given flow rate under a wide range of urban forms.\n\nIn this work, we assemble an ensemble of urban flood simulations and reduce the complexity of urban flooding through dimensional analysis of simulation results and consideration of conservation laws into a master curve that constitutes a mean-flow theory. This theory establishes a mathematical equation that relates flooding attributes\u2013notably depth and intensity defined as the product of flood depth and velocity\u2013to the ground slope, urban form, and flow rate encountered across cities. Moreover, we seek a model that explains the global variability of urban flooding hazards at neighborhood and larger scales and provides planning-level support for more flood-resilient cities.",
+            "section_image": []
+        },
+        {
+            "section_name": "Results and discussion",
+            "section_text": "City building arrangements are highly varied globally, as indicated in Fig.\u00a01 (Supplementary Note\u00a0I and Materials and \u201cMethods\u201d Section A). For example, the alignment of buildings in Chicago, USA (Fig.\u00a01c) is structured, while Lagos, Nigeria is unstructured (Fig.\u00a01h). A mean-flow theory of urban flooding applicable to global variations in building layouts (e.g., Fig.\u00a01(a\u2013h)) calls for a systematic parameterization of urban form, and here we draw from studies of the physics of phase transition and disordered materials31,32, where the Mermin order parameter33 (\u03c7) has been used to quantify the spatial degree of order/disorder of a system of particles. At the scale of individual particles (or buildings), the Mermin order parameter determines the symmetry of cn nearest neighbors to the reference particle34. For instance, for building arrangements with square symmetry, cn\u2009=\u20094, and those with hexagonal symmetry feature cn\u2009=\u20096. Furthermore, the local order parameter can be averaged to extract a collective disorder attribute representative of an urban region, as follows:\n\nwhere \\({\\theta }_{kj{k}_{0}}\\) is the angle between the central building j and its neighbors k and k0, where k0 is a fixed neighbor and k permutes over all possible neighbors of the jth building. When \\({\\chi }_{{c}_{n}}\\) is greater than 0.9, the synthetic urban form exhibits a pronounced symmetry and resembles a planned urban layout, e.g., Chicago, Fig.\u00a01c. As disorder increases, the symmetry diminishes, and the synthetic urban form features characteristics of an organically nucleated and grown urban environment, e.g., Jakarta, Fig.\u00a01e. Here, we adopt the order parameter concept to quantitatively characterize the disorder of buildings within a city alongside the urban porosity \u03d5, which characterizes the amount of pore space and is inversely related to the building density.\n\nSelected areas from (a) Boston, (b) Virginia Beach, (c) Chicago, (d) London, (e) Jakarta, (f) Sao Paulo, (g) Tokyo, and (h) Lagos. The building footprints, streets, highways, parks, and rivers are displayed in gray, yellow, orange, green, and blue, respectively. The coordinates of each city are defined along the top and left sides of the panel. Basemaps provided by OpenStreetMap (https://www.openstreetmap.org/copyright) used in conjunction with Microsoft\u2019s Building Footprints and Google\u2019s Open Buildings, data made available via an Open Database License (https://opendatacommons.org/licenses/odbl/).\n\nEnsembles of synthetic city urban forms at a given porosity and disorder are developed using hybrid reverse Monte Carlo35,36 (HRMC); see Materials and \u201cMethods\u201d Section B and Supplementary Notes\u00a0II\u2013III for detail. Furthermore, to support shallow-water modeling and specifically the characterization of steady-state, uniform flow conditions, a rectangular urban domain is created with a length (L), width (W), longitudinal slope (\u03b1), and a Manning coefficient for bottom resistance (nM), and the domain is populated with N square buildings of side length (D). Due to HRMC\u2019s computational cost, we only generate building patterns in a unit cell of length lu and repeat the unit cell to cover the entire channel length. The chosen level of disorder controls the irregularity of building locations (see Supplementary Fig.\u00a0S1), and the urban porosity follows as \u03d5\u2009=\u20091\u2009\u2212\u2009ND2/(WL). To characterize flooding, the shallow-water equations are solved on a fine-resolution, unstructured computational mesh (ParBreZo), where mesh edges are aligned with building walls to enforce a no-flow boundary condition23,28, see Materials and \u201cMethods\u201d Section C, Supplementary Figs.\u00a0S2\u2013S3.\n\nOur simulations resolve flooding within the pore space between buildings, and solutions reflect the bulk effect of building form drag. Moreover, using a Godunov-type finite volume scheme for solving the shallow-water equations allows us to resolve supercritical flows, subcritical flows, and flows with hydraulic jumps23. Solutions include localized super-critical flows (Fr\u2009>\u20091) along steep slopes, but average flows across neighborhoods are found to be largely sub-critical (Fr\u2009<\u20091). As has been observed in experiments37, simulations show that a hydraulic jump occurs when localized supercritical flows encounter obstructions37.\n\nFigure\u00a02a\u2013f show the color map of non-dimensionalized flood velocity in the downslope direction (uD2/Q) as a function of flow velocity (u), flow rate (Q), and building size (D), for neighborhoods of varying porosity and disorder. Relative to square symmetry at \u03d5\u2009=\u20090.6, we observe the choking of flow with decreasing \u03c74. This indicates that increasing disorder restricts the flood flow in urban forms that possess a near square symmetry (regular layout), but has an opposite effect in synthetic urban models with nearly hexagonal symmetry (or a staggered layout) representative of flow paths along diagonal directions. In particular, at \u03d5\u2009=\u20090.6, the disorder opens new flood flow pathways through clusters of buildings much akin to flow pathways through disordered granular media38.\n\nNon-dimensionalized flood velocity maps for unit cells of urban forms with (a\u2013c) square and (d\u2013f) hexagon-like patterns with porosity \u03d5=0.6 and Mermin order \u03c7=1.0, 0.8, and 0.6, respectively. The color bar on the right represents the velocity scale for all velocity maps. Gray squares represent flow obstructions. While the unit cell lu is\u2009~\u200933D, the channel length is set to 20lu to mitigate size effects. The normalized chord length distribution \\(P({l}_{c}^{{\\prime} })\\) for each urban form is placed below each velocity map in panels (g\u2013l); see the text for the definition.\n\nThese qualitative observations suggest that both the symmetry and irregularity of street grids in cities contribute to the tortuosity and constriction of flow paths at neighborhood and larger scales, which in turn shape the distribution of flood depths and velocities responsible for safety risks and losses39. To characterize how the symmetry and irregularity interact with ground slope to control the neighborhood-scale flood levels, we leverage the non-dimensionalized chord length distribution \\(P({l}_{c}^{{\\prime} }(\\theta ))\\), which represents the distribution of randomly placed line segments fitting within pore space between two building walls40 in all directions (\u03b8), see Supplementary Note\u00a0IV and Supplementary Fig.\u00a0S4 for detail. For simplicity, we here focus on chord length in the direction of the steepest descent. The chord length represents the distance over which a fluid particle can accelerate under the influence of gravity and bottom shear before being blocked by an obstruction, and Fig.\u00a02(g\u2013l) show the distribution of \\(P({l}_{c}^{{\\prime} })\\) for the building patterns shown in Fig.\u00a02(a\u2013f), respectively. The floodplain with perfect square symmetry exhibits a bimodal distribution of long and short chord lengths corresponding to the unit cell\u2019s length and nearest neighbor distance. By introducing disorder, additional peaks appear at intermediate values of chord length. The perfectly hexagonal floodplain also displays a bimodal distribution and behaves similarly; however, the large chord length corresponds to the second nearest neighbor. A representative chord length for any urban form follows with the expectation of \\({l}_{c}^{{\\prime} }\\) excluding the first and second nearest neighbor chords that do not effectively contribute to the flood drainage due to stagnation effects. Focusing on chord lengths beyond three building sizes, we define the normalized average effective chord length as:\n\nwhere \\({l}_{c}^{{\\prime} }={l}_{c}/D\\) and lu is the length of the unit cell. The corresponding \\(\\bar{{l}_{c}}\\) and average non-dimensionalized velocity for each distribution also appear in Fig.\u00a02g\u2013l. We observe qualitatively that the average flood velocity is directly correlated with \\(\\bar{{l}_{c}}\\), meaning that long \\(\\bar{{l}_{c}}\\) results in higher average velocities regardless of the underlying urban symmetry.\n\nTo reduce the observed complexity in urban form-induced flood behavior, we consider the mass and momentum conservation laws for dense urban forms, where the bottom shear is negligible compared to the distributed form drag. In a spatially large enough control volume that sufficiently represents the flow heterogeneity, the average gravitational force (\\(\\bar{{F}_{g}}=g\\bar{h}A\\phi \\,cos(\\alpha )sin(\\alpha )\\)) balances the resultant form drag (\\(\\bar{{F}_{D}}={C}_{D}{A}_{p}\\overline{u| V| }\\)) in the steady-state limit, Fig.\u00a03(a). In this case, while gravity (g) drives the flow with average vertical height (\\(\\bar{h}\\)) through available urban pore space (A\u03d5), the drag resists the flow. This resistive force is proportional to the drag coefficient (CD), the so-called projected area (\\({A}_{p}=\\bar{h}{W}_{p}cos(\\alpha )\\))41, and spatially averaged velocity squared component (\\(\\overline{u| V| }=\\overline{u| \\sqrt{{u}^{2}+{v}^{2}}| }\\)). The average perpendicular component of flow velocity (v) is zero, and its magnitude should be smaller than u, meaning \\(\\overline{u| V| }\\approx \\overline{{u}^{2}}\\). Invoking mass conservation (\\(q=\\overline{uh}\\phi \\,cos(\\alpha )\\)), we can eliminate the drag dependence on velocity and estimate this force using average height, \\(\\bar{{F}_{d}} \\, \\approx \\, {C}_{D}{W}_{p}{q}^{2}/(\\bar{h}{\\phi }^{2}\\,cos(\\alpha ))\\). Therefore, through force balance (\\(\\bar{{F}_{g}}=\\bar{{F}_{d}}\\)), we can estimate the average flood height as follows,\n\nThe main challenge in determining the average flood height pertains to the exact measurement of projected width (Wp), an extensive quantity that depends on urban form. Therefore, A\u03d53/Wp can be viewed as a characteristic length scale whose size is proportional to the building size, A\u03d53/Wp\u2009=\u2009D/\u03a02, where similar to \\({C}_{D}\\left(\\frac{{{{{{{\\bf{r}}}}}}}_{i}}{D}\\right)\\), \\(\\Pi \\left(\\frac{{{{{{{\\bf{r}}}}}}}_{i}}{D}\\right)\\) is a dimensionless function of the building arrangements (ri) in the urban layout. For the maximum 10% slope considered in this study, the approximation of \\(cos(\\alpha )\\sqrt{sin(\\alpha )}\\propto \\sqrt{\\alpha }\\) introduces less than 1% error.\n\na A schematic of the control volume through which water, shown in blue, flows between gray square obstacles. In dense urban environments, the floor shear is negligible compared to the other forces, and the gravitational force balances the form drag at the steady state. A limited number of one-factor-at-a-time flow simulations corroborate with the proposed dimensionless relationship, showing the flood height (b) scales linearly with flow rate per width (q), and (c) is proportional to the inverse square root of the bottom slope (\u03b1\u22121/2).\n\nThe average flood height in Eq. (3) is deterministic if the locations of all buildings are known. However, when viewed through statistical mechanics, the flood height should, in principle, be only dependent on a small number of statistical attributes of the floodplain rather than the unique locations of all buildings. While this is an unconventional concept in the context of urban flooding, it is a well-established concept for studying the thermodynamics of granular media and glassy systems17. In this sense, the ensemble-averaged dimensionless flood height can be thought of as a hydrodynamic state function of the city that depends on hydrodynamic state variables \u03d5, \u03c7, and \\({\\bar{l}}_{c}\\), which yields the following dimensionless relation:\n\nwhere \u3008.\u3009 denotes the ensemble average and modified drag coefficient \\({C}_{D}^{{\\prime} }=\\langle \\Pi \\sqrt{{C}_{D}}\\rangle\\). Interestingly, we derive the same relation through considerations of dimensional homogeneity, see Supplementary Note\u00a0V. Regardless of the derivation method, the theory suggests the ensemble-averaged dimensionless flood height (\\(\\langle \\bar{h}\\rangle \\sqrt{gD}/q\\)) should depend on dimensionless geometric factors, the bottom slope, and the drag coefficient that depends on the porosity, order parameter, and average chord length in the flow direction. To test this theory, we perform one-factor-at-a-time flow simulations varying slope and flow rate per width for different urban forms with various porosity and order parameters, Fig.\u00a03(b\u2013c). Corroborating with the proposed theory, the numerical simulations show \\(\\langle \\bar{h}\\rangle\\) scales linearly with q and is inversely proportional to the square root of the bottom slope, \\(1/\\sqrt{\\alpha }\\). We note that while our theory and Manning equation show \\(\\langle \\bar{h}\\rangle \\propto 1/\\sqrt{\\alpha }\\), they differ in predicting the exponent in \\(\\langle \\bar{h}\\rangle \\propto {q}^{m}\\) scaling relation. In an empty wide rectangular channel, where flow is driven by gravity and bottom shear, the Manning equation predicts \\(\\langle \\bar{h}\\rangle \\propto {q}^{3/5}\\). However, as discussed before, in a densely-packed urban flood channel, the form drag balances the gravity leading to a new scaling relation, i.e., \\(\\langle \\bar{h}\\rangle \\propto {q}^{1}\\). Therefore, the proposed change in exponent m is intimately related to the change in underlying physical processes governing momentum transfer.\n\nTo further verify the proposed theoretical framework, we need to demonstrate that \\({C}_{D}^{{\\prime} }(\\phi,\\chi,\\bar{{l}_{c}})\\) can solely explain the distributions of flood depth over a range of flow simulations with varying 0.4\u2264\u03d5\u22641, 0.3\u2264\u03c74,\u2009\u03c76\u22641, \u03b1, and q. In an attempt to collapse the results, we first neglect the impact of urban order, i.e.,\\({C}_{D}^{{\\prime} }={f}_{1}(\\phi )\\propto {(1+{a}_{{c}_{n}}\\phi )}^{{s}_{{c}_{n}}}/{\\phi }^{{p}_{{c}_{n}}}\\), where \\({a}_{{c}_{n}}\\), \\({s}_{{c}_{n}}\\) and \\({q}_{{c}_{n}}\\) are specific to square and hexagonal symmetries as denoted by the coordination number cn. This approach reduces the search for the state function to an optimization problem. Regardless of the underlying symmetry, \\({s}_{{c}_{n}}\\approx 1\\), \\({p}_{{c}_{n}}\\approx 0\\) and \\({a}_{{c}_{n}}\\) converges to -1, meaning f1\u2009\u2248\u2009(1\u2009\u2212\u2009\u03d5), better known as the packing fraction in the physics of granular media. This parameter mirrors the urban building coverage, which is suggested to be the most influential factor affecting flood depth via a sensitivity analysis12. The coverage parameter also appears in flow through channels covered by vegetation and is shown to scale flow resistance42. However, the packing fraction collapses data only at high porosity and becomes increasingly insufficient in dense textures, where the disorder becomes a controlling factor, see Supplementary Fig.\u00a0S8a.\n\nTo account for the disorder effects at low porosity, we assume \\({C}_{D}^{{\\prime} }={f}_{1}(\\phi )\\times {f}_{2}(\\chi )\\). For simplicity, we focus on linear functions through the Taylor expansion, \\({C}_{D}^{{\\prime} }\\approx {c}_{{c}_{n}}(1-\\phi )(1+{b}_{{c}_{n}}{\\chi }_{{c}_{n}})\\), where \\({b}_{{c}_{n}}\\) and \\({c}_{{c}_{n}}\\) are fitting parameters. In particular, we arrive at the following relation:\n\nwhere slopes c4 and c6 are 5.31 and 2.54, and b4 and b6 are -0.5 and 1.1, respectively, as noted in Fig.\u00a04a. Interestingly, we note c4/c6\u2009\u2248\u20092 and b4/b6\u2009\u2248\u2009\u2212\u20091/2.\n\nThis depth depends on (a) separate functions of slope, porosity, and order for rectangular and hexagonal symmetry and (b) a single function of slope, porosity, and average chord length.\n\nAs qualitatively observed in Fig.\u00a02, the introduction of disorder into square and hexagonal urban forms has an opposite effect on flood behavior. This is now quantitatively confirmed by the change in the \\({b}_{{c}_{n}}\\) sign. We also note the proposed linear relationships do not capture the flood depth for floodplains without obstructions. The relevant dimensionless quantity in the limit of high \u03d5 is \\({\\langle \\bar{h}\\rangle }^{5/3}/(q{n}_{M})\\), which is confirmed by the convergence of simulation data when \\((1-\\phi )(1+{b}_{{c}_{n}}{\\chi }_{{c}_{n}})/\\sqrt{\\alpha }\\) tends to zero, see Supplementary Fig.\u00a0S8b.\n\nWe can now examine the impact of urban form on flood depth in synthetic city neighborhoods. Leveraging Eq. (5) at constant porosity, the flood depth ratio between square- and hexagon-like patterns becomes c4(1\u2009+\u2009b4\u03c74)/(c6(1\u2009+\u2009b6\u03c76)). This ratio is\u2009\u2248\u20091/2 for perfectly ordered cities, meaning flood depth is twice as severe in hexagonal cities. As the disorder increases to the point that the underlying patterns become indistinguishable, i.e.,\u03c74\u2009=\u2009\u03c76\u2009=\u20090.5, the ratio becomes\u2009\u2248\u20091, and as expected, there is no difference in flood depth. In this scenario, the disorder increases flood depth by\u2009\u2248\u20091/2 in a square urban pattern, while it decreases the flood depth by\u2009\u2248\u20091/4 in hexagonal form.\n\nThe inherent drawback of Eq. (5) as a mean-flow theory is that it does not provide a universal relation between dimensionless quantities due to dependence on the underlying symmetry. As noted in Fig.\u00a02, the flood depth is associated with open flow pathways characterized by \\(\\bar{{l}_{c}}\\). This prompts proposing \\({C}_{D}^{{\\prime} }(\\phi,\\bar{{l}_{c}})={f}_{1}(\\phi )\\times {f}_{3}(\\bar{{l}_{c}})\\). Focusing on an f3 function of the form \\({\\bar{{l}_{c}}}^{\\beta }\\), we find through optimization that \u03b2\u2009\u2248\u2009\u2212\u20091/2. As shown in Fig.\u00a04b, this heuristic approach collapses the bifurcated results into a linear relationship as follows:\n\nwhere d0\u2009=\u20090.07 and d1\u2009=\u20095.62. Eqs. (5)\u2013(6) are valid in the range of 0.4\u2264\u03d5 considered here. Eq. (5) becomes increasingly inaccurate at lower porosity as flood depth should increase non-asymptotically at \u03d5\u2009=\u20090. Eq. (6), however, becomes singular at \u03d5\u2009=\u20090, since \\(\\bar{{l}_{c}}\\) tends to zero in this regime. This equation constitutes a mean-flow theory of urban flooding that relates the average flood depth to urban form attributes. Note that increasing slopes and increasing chord length act to decrease flood depth due to increases in flood velocity. Hence, the mean-flow theory predicts shallow, high-velocity flows along streets oriented in the downslope direction, an especially dangerous flow regime that has been described as ultrahazardous flooding43,44.\n\nThe proposed mean-flow theory is now applied to examine the city-to-city variability of urban flooding hazards; see Materials and \u201cMethods\u201d Section D. Selecting twenty cities across five continents, we analyze urban porosity and chord length in the direction of the steepest slope at a km2 grid resolution as shown in Fig.\u00a05(a\u2013b). Similar to the synthetic floodplains, we observe a correlation between urban porosity and normalized average chord length, Fig.\u00a05c. The denser cities feature smaller chord lengths, as evident in San Francisco and Lagos. However, a notable outlier to this trend is S\u00e3o Paulo, where long streets in densely developed neighborhoods create long corridors for flood passage. Loosely-packed cities such as Virginia Beach also exhibit longer chord lengths due to the sparsity of flow obstructions.\n\nFlood hazards across cities worldwide are examined by (a) Subdividing cities into 1 km x 1 km tiles (shown in Vancouver, BC, Canada) and evaluating the topographic slope \u03b1, porosity \u03d5, and order \u03c7 and (b) estimating the average chord length in the direction of descent to reveal (c) the porosity and chord length across 20 twenty cities; error bars show the margin of error with 90 percent confidence. Application of the mean-flow theory reveals: (d) the flow rate-normalized flood inundation \\({H}^{*}=\\langle \\bar{h}\\rangle /{h}_{ref}\\) and non-dimensionalized flood intensity \\({P}^{*}=\\langle \\bar{hu}\\rangle /h{u}_{ref}\\) for twenty cities with constant flow rate of Q\u2009=\u20091m3/s, (e) the theoretical flow rate-normalized flood inundation H* and non-dimensionalized flood intensity P* for recorded flood events. Finally, (f) The normalized monetary damages \\({{{{{\\mathcal{L}}}}}}\\) are compared to the product of the inflow rate q and urban form factor \\({{{{{\\mathcal{F}}}}}}(\\phi,\\, {l}_{c},\\, \\alpha,\\, D)\\) among different flash flooding events. In panels (c-f), the markers' colors represent the average bottom slope of each city defined by the color bar to the right side. Building footprint data for Karachi and Mumbai may not be sufficient. Basemaps provided by OpenStreetMap (https://www.openstreetmap.org/copyright) used in conjunction with Microsoft\u2019s Building Footprints and Google\u2019s Open Buildings, data made available via an Open Database License (https://opendatacommons.org/licenses/odbl/).\n\nTo characterize cities in terms of their flood hazards, we define two dimensionless flood hazard indicators: flood depth and intensity; see Supplementary Note\u00a0VI. For the dimensionless flood depth hazard H*, we use our mean-flow theory in Eq. (6), which is independent of the underlying symmetry and more applicable to real-world complex urban forms. Flow rates required by the mean-flow theory, q, are estimated as the product of an extreme event precipitation intensity and a length scale for runoff accumulation, taken here to be 1 km. We then divide \\(\\langle \\bar{h}\\rangle\\) by href, the reference flood depth in an obstruction-free channel with \u03b1ref\u2009=\u20090.1 and qref\u2009=\u20090.001 m2/s, which are respectively representative of average slopes and precipitation rates observed in our twenty cities. We also define the dimensionless flood intensity as the average product of flood depth and velocity normalized by the flood intensity in an obstruction-free channel inundated by qref, \\({P}^{*}=\\langle \\overline{hu}\\rangle /{\\bar{(hu)}}_{ref}\\). This dimensionless quantity is controlled by the inflow rate at the steady state, meaning P*\u2009=\u2009q/(qref\u03d5). This indicates the normalized flood intensity at the urban scale is independent of its form and bottom slope, and controlled by porosity and flow rate only; see Supplementary Fig.\u00a0S9.\n\nHow susceptible are cities to urban flood hazards based on urban form alone? We can now address this question by computing the dimensionless flood depth and intensity given the urban porosity, chord length, and slope for each city, as shown in Fig.\u00a05d. Note that with q computed with a 1 km runoff accumulation length scale for all cities, differences in flood depth and intensity are completely attributable to differences in urban form and precipitation intensity, and not to differences arising from larger scale drainage patterns or urban drainage infrastructure that contribute to the accumulation of urban flood flows. Most cities are clustered toward the low-hazard region, i.e., low flood depth and intensity. Chicago\u2019s urban form is conducive to high flood depth due to its relatively low porosity and flat terrain. San Francisco faces the opposite hazard, where the flood intensity overshadows flood depth due to the steep topography and low urban porosity. High-hazard cities are marked by high levels of flood depth and intensity and include Tokyo, Lagos, Jakarta, Karachi, and S\u00e3o Paulo. Compared to other cities in this study, these cities exhibit a very low porosity and mild slope. In the case of S\u00e3o Paulo, there are also long and steep flow pathways characterized by high chord length and bottom slope.\n\nWe reviewed the Emergency Events Database (EM-DAT)45 for extreme events that occurred within the 20 cities considered in this study and used archives of historical precipitation and a simple rainfall-runoff approximation to estimate the inflow rate, q, see Materials and \u201cMethods\u201d Section D. Figure\u00a05(e) maps hazard severity for sixteen extreme events classified as flash floods using our dimensionless flood depth and intensity. S\u00e3o Paulo, Jakarta, Karachi, Toyko, and Houston emerge as the cities that have experienced the most intense flash flood hazards, based on dimensionless flood depth, intensity, or a combination of the two. Moreover, the occurrence of multiple events in S\u00e3o Paulo, Jakarta, and Karachi suggests that these cities are amongst the most hazardous cities in the world for flash floods based on a combination of extreme event frequency and urban form.\n\nValidating the proposed mean-flow theory for describing city-to-city variations in urban flooding is extremely difficult because extreme event flooding of street grids is not systematically documented with ground-based sensors and satellite-based remote sensing methods for flood inundation do not perform well in urban areas46. EM-DAT includes metrics of economic losses, which we expect to be associated with precipitation, flood depths, and flood velocity. However, flood losses depend on many physical and social vulnerabilities in addition to hazard severity. Thus any attempt to link hazard severity to economic impacts is expected to be highly uncertain. We focused on five flash flooding events from EM-DAT with economic loss data within the twenty selected cities of this study. Due to the economic variability of the impacted cities, we normalize the reported damages by the respective country\u2019s gross domestic product and re-scale the damage values between zero and unity. Figure\u00a05(f) reveals a correlation between the normalized monetary damages, \\({{{{{\\mathcal{L}}}}}}\\), and a linear combination of flood hazard indicators as follows:\n\nwhere\n\nThis relationship provides a rather intuitive yet insightful finding that flood damages are linearly related to q and an urban form factor, \\({{{{{\\mathcal{F}}}}}}\\). The positive correlation between \\({{{{{\\mathcal{L}}}}}}\\) and F is in general alignment with established theories and models for flood damage, including widely used depth-damage curves [e.g.,47]. If we set \u03ba\u2009=\u20090 in our damage model, Eq. (8), it is simplified to a linear depth-damage curve. However, we find that the reported EM-DAT damages cannot be solely explained by flood height, which necessitates the consideration of flood intensity as a damage-driving factor.\n\nThe Houston (2016) event appearing in Fig.\u00a05f was the most costly of the flash flood events recorded across the cities examined for this study. However, the most costly extreme events in recorded history were all classified by EM-DAT as tropical cyclones, not flash floods, and the top six events as of 2019 all occurred in the U.S.2. When we compared tropical cyclone losses and our estimates of urban flood hazards from rainfall, we did not find a correlation. Indeed, damage from tropical storms results from several hazard drivers, including wind, storm surge, and rainfall2.\n\nWe acknowledge several limitations of our approach, including the representation of urban forms with arrays of square obstructions as opposed to more organic forms, assumed uniformity in the runoff accumulation length scale, the approximation of urban flooding as a two-dimensional flow without fully resolving the turbulent boundary layers that contribute to form drag, and the limited number of cities sampled for the development of our mean-flow theory. Additional research could help with understanding the importance of each of these methodological factors relative to the development of a mean-flow theory for urban flooding. Nevertheless, given the range of urban porosity, order values, and floodplain slopes considered herein, our approach systematically considers an immense spectrum of urban forms. Indeed, we successfully reduce the complexity of urban flood flow data into a master curve that provides an intuitive explanation of the distribution of flood hazards globally across cities, and that aligns with observations of flood losses.\n\nThe mean-flow theory presented here thus offers a foundational approach for examining how urban form affects the physical vulnerability of cities to flooding. Application of the mean-flow theory at neighborhood and larger scales could help to understand why specific cities, or even neighborhoods within cities, are most susceptible to flood impacts. The mean-flow theory could also support the planning of new developments in anticipation of flood exposure, and the development of flood resilience plans and programs. Hence, the mean-flow theory offers a promising entry point for urban planning of safer and more resilient cities.",
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+            "section_name": "Methods",
+            "section_text": "We assimilate publicly available building footprints, digital elevation models (DEMs), and city boundary data sets for twenty cities worldwide, see Supplementary Notes\u00a0I. For cities in the United States, building footprint data is obtained through Microsoft Maps\u2019 nationwide open building footprints data set48. For most cities outside the United States, we extract building footprints from OpenStreetMap49, a publicly available crowd-sourced database. To supplement this database, we also obtain building footprints for African and Southeast Asian countries through Open Buildings, a building footprint database developed through deep learning of satellite imagery50. We obtain the elevation data from MERIT51, a high-accuracy global digital elevation model at roughly 90-meter resolution. While the MERIT DEM was found to contain an RMSE of\u2009~\u20094m52, this error translates to a\u2009\u00b1\u20090.008 change in slope and is likely present in all cities, having little effect on our overall findings. At a finer resolution of 30 meters, FABDEM53 was also considered but was ultimately found to contain building heights that skewed the terrain elevations. We delineate the urban region based on the administrative boundaries of each city.\n\nWe conceptualize city urban form with rectangular landscape panels of length (L), width (W), slope (\u03b1) and Manning coefficient (nM) populated with N square buildings of side length (D). Ensembles of urban landscapes representative of a specified porosity \u03d5 and order \u03c7 are generated through a hybrid reverse Monte Carlo (HRMC) algorithm, which was first introduced to improve upon the modeling of amorphous carbon structures35,36. Using user-defined constraints to inform the placement of buildings and an energy penalty to avoid unrealistic or physically improbable configurations, this probabilistic and iterative algorithm is capable of generating ensembles of urban forms with the targeted porosity and order (See Supplementary Note\u00a0II and Supplementary Fig.\u00a0S1 for additional detail).\n\nUrban landscape panels were constructed with a length L=10,000 m, W=500 m, building size D=15 m, and a range of slopes, \u03b1=0.001-0.1. The channel was configured sufficiently long to balance gravitational effects and flow resistance from bottom shear and form drag, sufficiently wide to avoid edge effects, and sufficiently small to make fine-resolution modeling feasible over thousands of scenarios. Manning\u2019s roughness (nM) is 0.02 s/m1/3 in all simulations, representing a concrete surface, and an ensemble of M=3 realizations are utilized for each combination of porosity, order, and slope. We confirmed that a set of three simulations was sufficient for estimating the mean flood depth by checking sixteen different urban forms using M=30 realizations and seeing only a negligible difference.\n\nFlood flow for each realization of urban form is simulated using ParBreZo, which uses a Godunov-type, finite volume scheme to solve the full two-dimensional shallow-water equations on an unstructured grid of triangular cells constrained by building walls23. Hence, buildings are represented by the so-called building-hole method28.\n\nEvery realization of urban form is independently meshed through constrained Delaunay triangulation using the Triangle mesh generation software54. To ensure a quality mesh, all cell angles are restricted to greater than 20\u2218, and a spatially-dependent maximum area constraint on cell size is utilized. Within the upstream section of the urban form where we seek to achieve a uniform flow in which gravity and flow resistance balance each other, i.e., 0\u2009<\u2009x\u2009<\u2009L/D\u2009=\u200933.3, the maximum area constraint is Ac/D2\u2009=\u20090.02, where Ac is the maximum area of a triangular cell. Hence, we use a cell size that is no larger than 2% of the size of a building. In the downstream portion of the urban form, i.e.,L/D\u2009=\u200933.3\u2009<\u2009x\u2009<\u2009L/D\u2009=\u2009666.7, the mesh coarsens to a maximum cell area of Ac/D2\u2009=\u20090.13 to reduce computational costs without impacting precision. See Supplementary Fig.\u00a0S2 for a visual of the mesh.\n\nTo capture uniform flow within the upstream portion of each urban form, a flow rate of Q is evenly spread over the upstream edge of the domain, the downstream edge is treated as a free-overfall boundary condition, and the sides of the domain are treated as free-slip walls. The model is initialized with an initially dry floodplain and integrated into a steady state with an adaptive time step that maintains a Courant number of 0.8. Upon convergence, the uniform depth and velocity distribution are evaluated based on the flow conditions within the upper 100 m of the channel. For each model, the urban form and flow attributes \u03d5, \\({\\chi }_{{c}_{n}}\\), Q, \\(\\bar{{l}_{c}}\\), and \u03b1, along with the resulting flow height h, velocity u, and their product hu, are provided in the spreadsheet \u2018Supplementary Data\u00a01\u2019.\n\nWe note that the domain length and width specification, grid refinement criteria, and convergence conditions were checked from an uncertainty perspective, and sensitivities were found to be negligible. Moreover, our multi-step simulation workflow, including (1) construction of synthetic urban forms, (2) mesh generation, (3) shallow water simulation, and (4) data post-processing, is implemented as a high-throughput framework. This framework runs on a high-performance computing cluster and streamlines the execution of parametric studies such as this one; see Supplementary Note\u00a0III for details.\n\nEach of the 20 cities identified for this study is decomposed into 1 km x 1 km panels, Fig.\u00a05a. While many cities have street drains with O(100m) spacing to collect rainwater, these systems are only designed to contain flows from relatively frequent events (e.g., ten-year return period) and thus substantially longer overland flow runs occur with the most severe events. The use of a value of 1 km allows us to resolve both the amount of overland flow and the slope of the ground, thus providing an assessment of urban flooding at the neighborhood scale. Moreover, we find that the trends in flood hazards revealed by the mean-flow theory do not depend on a specific value of the rainfall accumulation length scale. Scarcely developed regions with a porosity higher than 90%, and within city boundaries, are disregarded. For each panel, urban porosity and average building side length are calculated from the building footprint data. Additionally, the DEM of each panel is analyzed to find the maximum slope and direction. We subsequently calculate the effective chord length in the direction of maximum slope in each cell, Fig.\u00a05b and Supplementary Table\u00a0S1 provide the complete set of urban attributes computed for the twenty cities studied in this work.\n\nThe Emergency Events Database (EM-DAT)45 is cross-referenced for \u201cflash flood events\u201d and \u201ctropical cyclones\u201d since 2000, which lead to direct runoff from impervious surfaces into the urban form and the concentration of flooding. A total of sixteen flash flood events are identified, and five of these contain estimates of monetary damages, see Supplementary Table\u00a0S2. Additionally, a total of seven tropical cyclone events are identified and all contain information about monetary damages. For each event, we collect precipitation data from the PERSIANN system55. Precipitation data is reported hourly for the extent of each event, and the highest rate is applied to the city area to produce flow rate Q using the rational method and assuming that all precipitation becomes runoff (i.e., no interception or infiltration).\n\nWe do not consider flooding events that occurred before the year 2000 because PERSIANN satellite data for systematically estimating precipitation is not available, and because of substantial urban growth over the past twenty years. We also note that monetary losses recorded in the EM-DAT database are usually not confined to a city\u2019s boundaries but include all regions affected by the event. This may cause an over- or under-estimation of damages reported for a city. We also note that monetary losses from tropical cycles may be caused by multiple hazard drivers including wind, storm surge, and rainfall, whereas monetary losses from flash floods are mainly the result of intense rainfall2.",
+            "section_image": []
+        },
+        {
+            "section_name": "Data availability",
+            "section_text": "The results of the flow simulations through synthetic urban forms of varying porosity and order, presented in Fig.\u00a04, generated in this study are provided in the spreadsheet \u2018Supplementary Data\u00a01\u2019.",
+            "section_image": []
+        },
+        {
+            "section_name": "References",
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+            "section_image": []
+        },
+        {
+            "section_name": "Acknowledgements",
+            "section_text": "M.J.A.Q. was partly supported by NSF CAREER Award No. 2145537 and NSF Award No. 2103125. B.F.S. was supported by NSF Award No. 2031535. S.B. was supported as a GAANN Fellow through the UCI Civil and Environmental Engineering GAANN grant funded by the US Department of Education (P200A210077). S.B. also gratefully acknowledges the Bridge Fellowship from UCI\u2019s Henry Samueli School of Engineering.",
+            "section_image": []
+        },
+        {
+            "section_name": "Author information",
+            "section_text": "Department of Civil and Environmental Engineering, University of California, Irvine, Irvine, CA, USA\n\nSarah K. Balaian,\u00a0Brett F. Sanders\u00a0&\u00a0Mohammad Javad Abdolhosseini Qomi\n\nDepartment of Urban Planning and Public Policy, University of California, Irvine, Irvine, CA, USA\n\nBrett F. Sanders\n\nDepartment of Materials Science and Engineering, University of California, Irvine, Irvine, CA, USA\n\nMohammad Javad Abdolhosseini Qomi\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nB.F.S. and M.J.A.Q designed the research. S.B. developed the high-throughput computational framework for the parametric study, performed numerical simulations, and gathered the simulation results. S.B. collected and assimilated urban, precipitation, and disaster data from multiple public sources. M.J.A.Q and B.F.S. developed the theoretical framework based on dimensional analysis. All authors analyzed the results and wrote the manuscript.\n\nCorrespondence to\n                Brett F. Sanders or Mohammad Javad Abdolhosseini Qomi.",
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+            "section_text": "Balaian, S.K., Sanders, B.F. & Abdolhosseini Qomi, M.J. How urban form impacts flooding.\n                    Nat Commun 15, 6911 (2024). https://doi.org/10.1038/s41467-024-50347-4\n\nDownload citation\n\nReceived: 22 November 2023\n\nAccepted: 08 July 2024\n\nPublished: 19 August 2024\n\nVersion of record: 19 August 2024\n\nDOI: https://doi.org/10.1038/s41467-024-50347-4\n\nAnyone you share the following link with will be able to read this content:\n\nSorry, a shareable link is not currently available for this article.\n\n\n\n\n                            Provided by the Springer Nature SharedIt content-sharing initiative\n                        ",
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+            ]
+        },
+        {
+            "section_name": "This article is cited by",
+            "section_text": "npj Urban Sustainability (2025)\n\nNature Sustainability (2025)\n\nNature Communications (2025)\n\nEnvironmental Processes (2025)\n\nWater Resources Management (2025)",
+            "section_image": []
+        },
+        {
+            "section_name": "Associated content",
+            "section_text": "Collection",
+            "section_image": []
+        }
+    ]
+}

1c5b985c2be84959f29ad76dc11cefabcef013d6b77c77d88f37cd6c8208e884/metadata.json

@@ -0,0 +1,159 @@
+{
+    "title": "Signal-processing and adaptive prototissue formation in metabolic DNA protocells",
+    "pre_title": "Signal-Processing and Adaptive Prototissue Formation in Metabolic DNA Protocells",
+    "journal": "Nature Communications",
+    "published": "08 July 2022",
+    "supplementary_0": [
+        {
+            "label": "Supplementary Information",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-022-31632-6/MediaObjects/41467_2022_31632_MOESM1_ESM.pdf"
+        },
+        {
+            "label": "Peer Review File",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-022-31632-6/MediaObjects/41467_2022_31632_MOESM2_ESM.pdf"
+        },
+        {
+            "label": "Description of Additional Supplementary Files",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-022-31632-6/MediaObjects/41467_2022_31632_MOESM3_ESM.pdf"
+        },
+        {
+            "label": "Supplementary Video 1",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-022-31632-6/MediaObjects/41467_2022_31632_MOESM4_ESM.mp4"
+        },
+        {
+            "label": "Reporting Summary",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-022-31632-6/MediaObjects/41467_2022_31632_MOESM5_ESM.pdf"
+        }
+    ],
+    "supplementary_1": [
+        {
+            "label": "Source Data",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-022-31632-6/MediaObjects/41467_2022_31632_MOESM6_ESM.xlsx"
+        }
+    ],
+    "supplementary_2": NaN,
+    "source_data": [
+        "/articles/s41467-022-31632-6#Fig2",
+        "/articles/s41467-022-31632-6#Fig4",
+        "/articles/s41467-022-31632-6#Sec15"
+    ],
+    "code": [],
+    "subject": [
+        "Biopolymers",
+        "DNA",
+        "Chemical origin of life",
+        "Self-assembly"
+    ],
+    "license": "http://creativecommons.org/licenses/by/4.0/",
+    "preprint_pdf": "https://www.researchsquare.com/article/rs-999587/v1.pdf?c=1657817005000",
+    "research_square_link": "https://www.researchsquare.com//article/rs-999587/v1",
+    "nature_pdf": "https://www.nature.com/articles/s41467-022-31632-6.pdf",
+    "preprint_posted": "01 Nov, 2021",
+    "research_square_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "The fundamental life-defining processes in living cells, such as replication, division, adaptation, and tissue formation, take place via intertwined metabolic reaction networks orchestrating downstream signal processing in a confined, crowded environment with high precision. Hence, it is crucial to understand and reenact some of these functions in wholly synthetic cell-like entities (protocells) to envision designing soft-materials with life-like traits. Herein, we report on a programmable all-DNA protocell (PC) composed of a liquid DNA interior and a hydrogel-like shell, harboring DNAzyme active sites in the interior whose catalytic bond-cleaving activity leads to a downstream phenotype change in the protocells, as well as triggers prototissue formation. In this regard, we coupled several tools of DNA nanoscience, such as RNA cleavage, dynamic strand displacement reactions, and multivalent palindromic interactions, in a synchronize pathway so that the input signal can be processed inside the protocells and generate downstream cues giving rise to metabolic adaptive behavior. For example, the compartmentalized DNAzyme catalyzes the bond-cleavage of a substrate that releases a DNA strand in situ to trigger a strand displacement reaction at the shell of the protocells leading to a change in color resembling a \u201cphenotype-like\u201d change in cells, and finally to establish communication with other protocells via multivalent interactions.Materials Chemistrymetabolic reaction networkscell communicationsignal processing",
+            "section_image": []
+        },
+        {
+            "section_name": "Additional Declarations",
+            "section_text": "There is NO Competing Interest.",
+            "section_image": []
+        },
+        {
+            "section_name": "Supplementary Files",
+            "section_text": "SIDzCatPCNatCommun.pdfSuppVideoDzCatPC.mp4Supplementary Video_ FRAP on active Protocell",
+            "section_image": []
+        }
+    ],
+    "nature_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "The fundamental life-defining processes in living cells, such as replication, division, adaptation, and tissue formation, occur via intertwined metabolic reaction networks that process signals for downstream effects with high precision in a confined, crowded environment. Hence, it is crucial to understand and reenact some of these functions in wholly synthetic cell-like entities (protocells) to envision designing soft materials with life-like traits. Herein, we report on all-DNA protocells composed of a liquid DNA interior and a hydrogel-like shell, harboring a catalytically active DNAzyme, that converts DNA signals into functional metabolites that lead to downstream adaptation processes via site-selective strand displacement reactions. The downstream processes include intra-protocellular phenotype-like changes, prototissue formation via multivalent interactions, and chemical messenger communication between active sender and dormant receiver cell populations for sorted heteroprototissue formation. The approach integrates several tools of DNA-nanoscience in a synchronized way to mimic life-like behavior in artificial systems for future interactive materials.",
+            "section_image": []
+        },
+        {
+            "section_name": "Introduction",
+            "section_text": "Living cells execute numerous complex functions, such as division, differentiation, adaptation, and tissue formation, by guiding the flux of materials and information via intertwined metabolic reaction networks in a crowded intracellular environment or even in liquid/liquid phase-segregated (LLPS) membraneless organelles1,2,3,4,5. In recent years, the bottom-up reenactment of fundamental cellular processes inside artificial synthetic compartments has emerged as an appealing strategy to investigate biological pathways from molecular to macroscopic length-scale in a controlled environment6,7,8,9. These approaches not only pave the way towards constructing a wholly man-made synthetic cellular equivalent (protocells, PCs) with life-like functionality and adaptivity but also provide an insight into fundamental reaction network-driven processes in natural cells. Historically, liposomes10,11,12,13,14,15, polymersomes16,17,18, colloidosomes19,20, and proteinosomes21 based PC models have been used for encapsulation of bio-inspired transformations or also communication networks. This involves, for instance, DNA-mediated signal cascades, self-replication, and in-vitro protein synthesis22. However, such systems may suffer from low and heterogeneous encapsulation efficiency, absence of molecularly crowded interior resembling the cytoplasmic matrix, and lack control over stoichiometry of components in the case of multimeric active cargoes. In contrast, PC models23,24,25,26 based upon complex coacervates, aqueous two-phase systems, and LLPS of intrinsically disordered proteins have been suggested as more appropriate cytoplasmic model systems because their inherent macromolecular-rich crowded interior and high loading capacity resemble the cytoplasmic matrix27,28,29,30,31,32,33. Various studies reported the use of such macromolecularly crowded PCs for gene expression34, ribonucleic acid catalysis35,36, and multienzyme iterative processing in multicomponent microdroplets37,38. In spite of these recent examples, functional adaptation in crowded PCs using metabolic transformations based upon an external signal using an encapsulated catalyst with precisely organized downstream action, such as \u201cphenotype-like changes\u201d or communication and prototissue39,40 formation, remain challenging and are rarely explored19. Recently, we reported the functional and morphological adaptation ability of all-DNA PCs41 via in situ generation of a self-reporting non-DNA metabolite upon ring-closing metathesis reaction based on genetically modified artificial metalloenzymes immobilized in PCs42. The non-DNA metabolite could interact with double-stranded DNA (dsDNA) in the shell, which led to metabolic growth, mechanical stress built up, and ultimately PC fusion. Since adaptivity is imperative for life\u2019s survival in a dynamic environment, it is of critical importance to establish strategies capable of converting chemical signals from diverse origins to allow for intra- or inter-PC downstream processes such as functional adaptation and communication.\n\nDNA has become a relevant biomacromolecule for nanoscience and systems chemistry research for its programmable structure formation and its ability to rationally design reaction networks and concatenated logic operations, demonstrating its potential as a toolbox in molecular computing43,44,45,46,47,48,49. Among other DNA principles, catalytic nucleic acids (DNAzymes and ribozymes)50,51,52,53 have emerged as one relevant tool in the DNA reaction network toolbox. Towards the first combination of DNAzymes with PCs, recently, it has been shown that the ribozyme activity of bond cleavage is enhanced inside membraneless coacervate droplets36. However, a higher-level function integration of such systems in protocell research remains elusive.\n\nHerein we introduce catalytic signal processing inside highly programmable all-DNA protocells (PC) formed by LLPS of specific single-stranded DNA (ssDNA) strands. As a key tool, we encapsulate a DNAzyme that cleaves RNA positions in DNA-RNA chimera substrates that serve as signals. We demonstrate enhanced metabolic signal conversion by RNA bond cleavage inside the PCs and capitalize on this understanding by using the signal output to instigate downstream phenotype-like changes in the PC, as well as prototissue formation by PC clustering via induction of multivalent self-complementary interaction at the PC surface. Moreover, we also show an interprotocellular communication of the metabolites between catalytically active sender PCs and inactive receiver PCs, leading to the formation of largely sorted prototissue-like colonies. All strategies are enabled by engaging the metabolized output of the initial signal downstream in dynamic DNA strand displacement (DSD) reactions.",
+            "section_image": []
+        },
+        {
+            "section_name": "Results and discussion",
+            "section_text": "Building upon our previous work41,42,54, we prepared PCs composed of liquid ssDNA interiors and DNA hydrogel shells by rapid self-compartmentalization during a temperature ramp (ca. 10\u2009min) of an aqueous solution containing two ssDNA-multiblock copolymers (p(A20-m) and p(T20-n)). A20 and T20 denote homo-repeats of 20 adenine and 20 thymine nucleotides (nt), while m and n stand for defined, so-called barcode domains, which are used for functionalization using their complementary counterparts (Fig.\u00a01a). In short, during heating, the A20/T20 duplexes dissociate, and p(A20-m) undergoes LLPS during the heating step, while p(T20-n) remains dissolved. During cooling, re-hybridization of A20/T20 happens rapidly at the periphery of the p(A20-m) phase-separated droplets, giving rise to a hydrogel-like shell stabilized by A20/T20 duplexes. Eventually, the p(A20-m) dissolves below its cloud point temperature (ca. 45\u2009\u00b0C)41, but stays entrapped in a liquid state under high osmotic pressure and macromolecular crowding, as confined by a compact hydrogel-like shell. Apart from the facile preparation and providing a cytosol-like DNA-based crowded, confined platform, one of the significant advantages of such PCs is the selective addressability and orthogonal functionalization of the interior and the shell using the barcode domains (m,n) (Supplementary Fig.\u00a02 and Supplementary Table\u00a01).\n\na Synthesis of sequence-specific two multiblock ssDNA polymers via rolling circle amplification (RCA). A buffered mixture of the ssDNA polymers is subjected to a fast-heating ramp (3\u2009\u00b0C/min) in the presence of Mg2+ (50\u2009mM). Heat-induced phase-separation of p(A20-m) during heating and antagonistic duplex (A20-T20) hybridization (at the coacervate surface) during the cooling step, resulting in the self-assembly of kinetically-trapped all-DNA PCs. The core and shell barcodes are denoted with m and n, respectively. The immobilization of DNAzymes (Dz) is achieved using duplex hybridization between m* residues of the Dz and the core barcodes (m). b The system properties are demonstrated in three different pathways. Firstly, a self-reporting substrate (Subs-1) carrying an RNA linkage is used to investigate the catalytic efficiency of Dz in the confined state, in which Cy5 fluorescence (magenta color) increases upon cleaving the RNA linkage. Secondly, the downstream signal processing and phenotype-like change in PCs are demonstrated using a caged substrate (Subs-3). The Dz-catalyzed bond cleavage at the Loop-1 and subsequent release of Cy5-n* substitutes Atto488-nshort*, changing the shell color from green to magenta. Thirdly, the metabolic prototissue formation is demonstrated by a similar loop substrate (Subs-4) bearing a palindromic (p) sequence, which gets exposed at the PC periphery after the intra-protocellular metabolic bond cleavage and a DSD reaction at the shell, leading to crosslinking of the PCs via p\u2013p duplex formation. Lastly, the formation of sender and receiver prototissue formation via downstream interprotocellular signal transduction from active to dormant PCs is prompted by catalytic bond cleavage of Subs-4. All the strands are listed in Supplementary Table\u00a02.\n\nTo realize the catalytic metabolism inside the PCs, we introduced a specific Mg2+-dependent RNA-cleaving DNAzyme (Dz). This specific DNAzyme cleaves a single RNA linkage embedded in a DNA substrate efficiently52. For the facile loading of Dz in the PC core, we separated it into two ssDNA sequences, so-called split DNAzymes (Figs.\u00a01a, 2a and Supplementary Fig.\u00a01). Each sequence contains one-half of the complementary barcode domain (m1/2*), a stem part (s or s*), an active site sequence (t1 or t2), and a substrate docking site (u1 or u2). After annealing both parts to form the acting Dz, these Dzs were added to a buffered PC dispersion containing 50\u2009mM Mg2+ (for all the experiments hereafter), whereupon the Dzs rapidly dock inside the PC core via binding with every m-barcode sequence present in the p(A20-m) chains. Since the concentration of m-barcode in the PC interior can be precisely determined, all the barcodes can be easily functionalized with Dzs using proper amounts added to the dispersion. Any excess Dz in the solution is removed by washing the PCs via centrifugation.\n\na Schematic representation of a catalytic cycle for RNA linkage cleavage in Subs-1 in PC interior and fluorescence enhancement upon uncaging the Cy5-appended product. b Schematic representation of two scenarios, where the DCBC is performed in (i) a buffered solution where the Dz is hybridized with a monomeric m-sequence, and (ii) in Dz\u2282PCs. c Time-dependent spectrofluorimetric investigation of DCBC in PC and solution. A control experiment in which the auto-cleavage of Subs-1 is also presented in the absence of Dz (gray trace). d The percentage of bond cleavage of Subs-1 in the three scenarios mentioned above. e PCs were identified in the forward scatter (FSC) versus side scatter (SSC) plot. f, g Intra-protocellular Atto488 and Cy5 fluorescence were monitored over time by flow cytometry. Black line shows the moving median. h The time-dependent CLSM images for DCBC induced Cy5-appended sequence uncaging in an Atto488-labeled PC system. The shell of all the PCs is labeled with Atto488-n* (green channel). At t\u2009=\u20090 (before the addition of Subs-1), all the PCs are visualized as green circles since the fluorescent Atto488-n* is hybridized with the shell barcode domain (n) of p(T20-n) polymer. The DCBC in Dz\u2282PCs is monitored over 8\u2009min time period, and a gradual increase of Cy5 fluorescence (magenta channel) at the PC core is observed. i\u2013k Line segment analysis in both channels (green and magenta) of Line-1, Line-2, and Line-3 at t\u2009=\u20090, 1, and 8\u2009min, respectively. l CLSM image of dormant PCs (without the Dz, only with Split-Dz-1) at t\u2009=\u200910\u2009min after adding Subs-1. Data were the means\u2009\u00b1\u2009standard deviation of duplicate reactions. Scale bars: 5\u2009\u03bcm. The error regions in panel c represent the standard deviation of two independent experiments. The error bar in d represents the standard deviation of three independent experiments (N\u2009=\u20093). Condition: for spectroscopic measurements: [Dz\u2282PCs], [Dz in solution]\u2009=\u20092\u2009\u03bcM, [Subs-1]\u2009=\u20095\u2009\u03bcM, for cytometry experiments: [Dz\u2282PCs]\u2009=\u20090.5\u2009\u03bcM, [Subs-1]\u2009=\u20091.3\u2009\u03bcM and for the microscopic experiments: [Dz\u2282PCs]\u2009=\u20097\u2009\u03bcM, [Subs-1]\u2009=\u200916.6\u2009\u03bcM, at 25\u2009\u00b0C, TE buffer.\n\nFigure\u00a01 summarizes the analysis of the catalytic activity of the Dz-loaded PCs (Dz\u2282PCs), as well as the strategies for downstream signal processing in a step-by-step manner using three different thoughtfully designed substrates (Fig. 1b): (1) A self-reporting substrate (Subs-1) with an RNA linkage, in which a fluorescence resonance energy transfer (FRET) pair (fluorophore\u2009+\u2009quencher) is separated upon bond cleavage helps to analyze the catalytic conversion. (2) Subs-3 with a cleavage domain at its loop (Supplementary Fig.\u00a03), concealing a sequence (n*) complementary to the shell barcode that is released upon catalytic loop cleavage, is used for the phenotype-like change by DSD of shell-immobilized shorter Atto488-nshort*. (3) A loop substrate Subs-4 with a palindromic sequence connected to n* (Cy5-n*-p) is used to prompt inter-PC communication by multivalent binding scenarios.\n\nFirstly, to investigate the catalytic activity of the Dz inside and outside the PCs, we used a self-reporting substrate (Subs-1) with an RNA linkage and a FRET pair (Cy5 and a black hole quencher (BHQ)) covalently attached at both ends. Upon Dz-catalyzed breaking of the RNA bond in Subs-1, Cy5, and BHQ are separated (Fig.\u00a02a), giving rise to the enhancement of fluorescence intensity (represented in magenta color). Spectrofluorometric (for investigating catalytic efficiency), cytometric (for statistical analysis), and microscopic (for real-time visualization) techniques were used purposefully to characterize the intra-protocellular catalysis and to optimize the sequences for the next step. The stoichiometric ratio of Subs-1 to Dz is fixed at 2.5 for comparing the catalyst activity. In more detail, Subs-1 binds to the u1 and u2 residues of the Dz, but after cleavage, the two parts of the initial ssDNA signal melt away due to the low melting temperature (Tm\u2009=\u2009~20\u2009\u00b0C) of each individual half. The corresponding fluorescence traces show a 2-fold more efficient Dz-catalyzed bond cleavage (DCBC) in the PC (~62% turnover of Subs-1) as compared to the solution (~35% turnover of Subs-1). The higher activity of the DNAzyme inside the PC can be addressed by the crowding effect of the liquid DNA core and the different environmental conditions that the DNAzyme experiences inside the PC compared to those in the solution. The polarity of the liquid DNA environment and high ionic strength could play an important role. The reaction rates are also faster (Fig.\u00a02c), and the turnover number is ca. 1.6, indicating multiple turnovers per Dz. We, however, also observe that the encapsulated Dz\u2282PCs reduce its activity beyond this turnover, which indicates that the cleaved product reaches an equilibrium between the free and bound state due to its stickiness to the catalytic site at 25\u2009\u00b0C (Supplementary Fig. 4). The slight decrease in the fluorescence intensity of the cleaved product after 15\u2009min of substrate addition can be attributed to the PC sedimentation at the bottom of the well plate (Fig.\u00a02c). The negative control shows almost no product formation in the absence of the Dz.\n\nTo achieve more detailed insights into the level of the PC population, we performed flow cytometry experiments. In this case, the shells of Dz\u2282PCs (p(T20-n)) were labeled with Atto488-n* (green color in Fig.\u00a02a, f), and Subs-1 was added after ~2\u2009min of measurement. PCs were identified in the forward scatter (FSC, size) versus side scatter (SSC, complexity/granularity) plot, and signals without Atto488 and Cy5 fluorescence were excluded from the analysis (<3% of all protocells, Fig.\u00a02e). The fluorescence intensity in the Cy5 channel increases after the addition of Subs-1 and reaches a plateau after 350\u2009s (Fig.\u00a02g). This corresponds to the Dz-catalyzed cleavage of Subs-1. In contrast, the Atto488 fluorescence of the shell remains unaltered over the measurement window (Fig.\u00a02f). The consistent evolution of the cytometry data underscores a homogeneous PC population. Control experiments with dormant PCs (without the whole Dz) do not show a steady increase in fluorescence in the Cy5 channel (Supplementary Fig.\u00a05).\n\nFurthermore, we selected the Atto488-labeled Dz\u2282PCs for in situ morphological studies using confocal laser scanning microscopy (CLSM). The PCs are initially visualized with a green shell and empty core (t\u2009=\u20090\u2009min, Fig.\u00a02h). Once Subs-1 is injected into the PC suspension, a magenta fluorescence (excitation 637\u2009nm) appears in the core of the Dz\u2282PCs, which confirms that the compartmentalized DNAzyme catalyzes the RNA bond cleavage, producing the Cy5-appended output. The rate of product formation correlates with both fluorescence spectroscopy and the cytometry results (Fig. 2c, g). Interestingly, the magenta fluorescence persists in the PC core after the completion of the reaction, and an immediate diffusive leveling into the solution does not occur at 25\u2009\u00b0C, which is also supported by the cytometry results (Fig.\u00a02g). The line segment analysis of the confocal micrographs before the substrate addition (0\u2009min, line-1), after the addition (1\u2009min, Line-2), and at the reaction completion (8\u2009min, Line-3) exhibit an increase of magenta fluorescence along the lines throughout the reaction (Fig.\u00a02i\u2013k). In contrast, the green fluorescence at the shell remains unchanged. In a relevant control experiment, no Cy5 fluorescence enhancement is observed in the PC core when the same amount of Subs-1 was injected into a dormant PC (without the encapsulated Dz; Fig.\u00a02l).\n\nTo better understand the diffusivity of the output product of the DCBC and the potential binding to the substrate recognition site (u1 and u2), we performed FRAP (fluorescence recovery after photobleaching) cycles inside the Dz\u2282PC interior. The repeated photobleaching on a PC after completion of the reaction (cleaving the Subs-1) in both Atto488 (green) and Cy5 (magenta) channels exhibits different diffusion patterns. The green fluorescence at the PC shell (region of interest 1, ROI-1) does not show any recovery after every bleach cycle and attains a fully bleached state after the fifth cycle (Fig.\u00a03a, b). This corresponds to a hydrogel-like shell structure with negligible fluorophore diffusion. In contrast, the magenta fluorescence at the PC core (ROI-3) exhibits almost complete recovery after each bleach cycle, confirming rapid diffusion of the product inside the PC (Fig.\u00a03a, c). Note that a control area outside of the PC (ROI-4) also shows bleaching of Cy5 fluorescence and recovery due to some slowly leaked product (Supplementary Fig.\u00a06).\n\na CLSM image of a Dz\u2282PC after the completion of DCBC of Subs-1 and the photobleaching is performed within the dotted rectangles. The row of CLSM images depicts the pre-bleach state, the post-bleach state immediately after the second bleach cycle, and another post-bleach state after the recovery, hence just before the third bleaching cycle. b The relative fluorescence intensities from ROI-1 and ROI-2 (green channel for Atto488) over the seven bleach cycles. c The relative fluorescence intensities from ROI-3 and ROI-4 (magenta channel) over seven bleach cycles, depicting Cy5 fluorescence recovery. The black downward arrows represent the bleaching events. Scale bars: 3\u2009\u03bcm. d Schematic representation of catalyst recovery after completion of the Subs-1 cleavage and the confirmation of the free DNAzyme active sites using Subs-2, a self-reporting substrate with a second fluorophore (Cy3, cyan). e CLSM image of Dz\u2282PCs with fully-cleaved Subs-1 (merged channel: Atto488 and Cy5). f CLSM image of Dz\u2282PCs after 60\u2009min of Subs-1 addition. g, h The line segment analysis in both channels of Line-1 and Line-2, before and after the product release from PC core, respectively. i CLSM images Dz\u2282PCs after the addition of Subs-2 (t\u2009=\u20091\u2009min and t\u2009=\u20098\u2009min). Three channels represent the PC shell (green, Atto488), the residual product of Subs-1 (magenta, Cy5), and the product generated from Subs-2 (cyan, Cy3). Scale bars: 5\u2009\u03bcm. j The line segment analysis of Line-3 of three channels. Conditions: [Dz\u2282PCs]\u2009=\u20095\u2009\u03bcM, [Subs-1] and [Subs-2]\u2009=\u200912.5\u2009\u03bcM in TE buffer at pH 8.\n\nFurthermore, to demonstrate the continued operation and also refreshed use of the encapsulated Dz, we injected a second substrate (Subs-2) with a different fluorophore (Cy3) to the Dz\u2282PCs after completion of the Subs-1 cleavage (Fig. 3d). Prior to the addition of Subs-2, the release of the cleaved product Subs-1 (with Cy5) from the Dz active site and the PC core is confirmed using CLSM images (Fig.\u00a03e, f). A detailed 1-h kinetic study on the product release from the PC is shown in Supplementary Fig.\u00a07. The line segment analysis obtained from CLSM reveals 82% of product releases from the PCs in 1\u2009h (Fig.\u00a03g, h). Upon addition of Subs-2, the Cy3 fluorescence (cyan) increases rapidly inside the PC core, indicating the cleavage of the RNA linkage in Subs-2 (Fig.\u00a03i). Figure\u00a03j presents the line segment analysis of the three channels (Atto488, Cy3, and Cy5) after 8\u2009min of the Subs-2 addition. These observations corroborate that the Dz, immobilized in the PC core, can be used for multiple catalytic cycles of bond cleavage, which is crucial for a metabolic system.\n\nAfter investigating the catalytic activity of the Dz and the product diffusion in a compartmentalized state, we set out to establish an intra-protocellular downstream adaptation pathway, in which a signal, released via metabolic bond cleavage, triggers a cascade leading to a functional phenotype-like change in the PCs. In this regard, we used a loop-containing substrate (Subs-3), in which a Cy5-n* sequence (black)\u2014 complementary to the shell barcode n of the PC\u2014is concealed using another ssDNA (pink) carrying the RNA linkage at its Loop-1 domain and a BHQ at the 3\u2032 end (Fig.\u00a04a, b). The Cy5 fluorescence is quenched in Subs-3 because the Cy5 of n* and the quencher of Loop-1 are in proximity in the hybridized state (Supplementary Figs.\u00a0S1 and S3). Two mismatches were strategically placed at the duplex domains on either side of the loop to keep the Tm around 39\u2009\u00b0C so that both parts of cleaved Loop-1 melt away as soon as the loop is cleaved by the Dz. The loop of Subs-3 consists of 11 nt with one RNA linkage at the middle and is designed to be recognized by the Dz active site. The time-dependent Cy5 fluorescence upon cleavage of the RNA linkage at the loop domain of Subs-3 was monitored via fluorescence spectroscopy after injecting a solution of Subs-3 in three separate scenarios: (i) Dz encapsulated inside the PC (Dz\u2282PCs), (ii) Dz are in solution hybridized with monomeric barcode, and (iii) in PCs in a buffered solution without the Dz (Fig. 4b, c). Upon addition of Subs-3, the Cy5 fluorescence increases for scenarios (i) and (ii), indicating the DCBC and subsequent bond cleavage driven duplex melting (BCDM). It is evident that the metabolic release of Cy5-n* is 1.5 times higher in the case of Dz\u2282PCs, and occurs at a faster rate than the reaction in solution. This observation corroborates the fact that the catalytic efficiency is higher inside the PCs. The fluorescence intensity increases negligibly in the case of the negative control (no Dz; (iii)), indicating less than 5% of the thermal leakage of Subs-3 at the experimental temperature (37\u2009\u00b0C).\n\na Schematic representation of the Dz-catalyzed RNA linkage cleavage of Subs-3 and subsequent duplex melting, releasing the Cy5-n* strand in situ, which triggers a downstream DSD reaction at the shell of Atto488-nshort*-labeled Dz\u2282PCs, changing the shell-fluorescence from green to magenta. b Schematic representation of two scenarios, where the DCBC and subsequent BCDM were performed (1) in solution where Dz is hybridized with a monomeric m-sequence and (2) in Dz\u2282PCs using Subs-3. c The spectrofluorimetric analysis of DCBC and downstream BCDM in the case of Dz in solution (dark purple trace) and at its encapsulated state (magenta trace). The thermal uncaging of Subs-3 (in the absence of Dz) is shown in a gray trace. d, e Time-dependent cytometric analysis of intra-protocellular DCBC, BCDM, and DSD reaction via monitoring change in PC fluorescence intensity of Atto488 and Cy5, respectively. The gradual decrease of Atto488 fluorescence and rapid increase in Cy5 fluorescence indicates the metabolic phenotype-like change in Dz\u2282PCs. f, g Schematic representation of DCBC, downstream BCDM, and DSD reaction in a mixed-PC system, containing active Atto488-nshort*-labeled (green) Dz\u2282PCs and dormant Atto565-nshort*-labeled (blue) PCs. h Time-dependent CLSM images of metabolic phenotype-like change in the mixed-PC system. Upon Subs-3 addition, a gradual increase of magenta fluorescence is observed at the shell of the active green PCs substituting the green fluorescence, while the blue dormant PCs remain unchanged. i, K The line segment analysis on an active PC before (Line-1) and after (Line-3) the reaction and downstream transformation, respectively. j, l The line segment analysis on a dormant PC before (Line-2) and after (Line-4) the reaction and downstream transformation, respectively. Scale bars: 5\u2009\u03bcm. The error regions in panel c represent the standard deviation of two independent experiments. Condition: for spectroscopic measurements: [Dz\u2282PCs], [Dz in solution]\u2009=\u20092\u2009\u03bcM, [Subs-3]\u2009=\u20096\u2009\u03bcM, for cytometry experiments: [Dz\u2282PCs]\u2009=\u20090.5\u2009\u03bcM, [Subs-3]\u2009=\u20091.5\u2009\u03bcM and for the microscopic experiments: [Dz\u2282PCs]\u2009=\u20097\u2009\u03bcM, [Subs-3]\u2009=\u200916.6\u2009\u03bcM, at 37\u2009\u00b0C, TE buffer at 35\u2009\u00b0C.\n\nTo demonstrate the metabolic signal transduction in the PCs, we combined the two consecutive processes, DCBC and BCDM, to release Cy5-n* from Subs-3 inside the Dz\u2282PCs, which subsequently diffuses towards the shell and triggers a downstream DSD reaction. The DSD reaction leads to a substitution of the Atto488-nshort* that was initially present to label the shell in green. This DSD induces a color change in the PC shell due to tighter anchoring of the Cy5-n* (Fig.\u00a04a). This corresponds to a change in the phenotype of the PC. The DSD is enabled using an Atto488-nshort*, which only features a complementarity of 13 nt to the n barcode domain (n\u2009=\u200921 nt), leaving a toehold domain of 8 nt free for the DSD. Flow cytometry analysis of Atto488-nshort*-labeled Dz\u2282PC shows a rapid increase in Cy5 fluorescence (magenta channel) upon injection of Subs-3 (Fig. 4e), whereas the fluorescence of Atto488 (green channel) gradually decreases over time (Fig.\u00a04d). These observations indicate that (i) the Cy5-n* sequence is catalytically released from the input signal (Subs-3) upon DCBC and BCDM in the PC core, leading to an enhancement of the magenta fluorescence, and (ii) that the DSD reaction at the PC shell occurs via ejection of the Atto488-nshort* from the PC shell, resulting in a decrease of the green fluorescence. It is essential to realize that the product is now removed from any substrate/product binding competition at the Dz in the PC interior by spatial relocalization into the shell. In a control experiment, when a Subs-3 solution is added to a dormant PC flow (without the whole Dz), no change in fluorescence at the Atto488 channel (green) is observed (Supplementary Fig.\u00a08).\n\nNext, we investigated the Dz-catalyzed downstream signal processing in Dz\u2282PCs using in situ CLSM (Fig. 4f\u2013h and Supplementary Fig.\u00a09). To clearly monitor changes, we mixed active PCs (Atto488-nshort*-labeled Dz\u2282PCs; shell in green) with dormant Atto565-nshort*-labeled PCs (without the Dz; shell labeled in blue; Fig.\u00a04f, g). Upon adding Subs-3 into the mixed-PC dispersion, the Cy5 fluorescence (magenta channel) appears exclusively inside the active Dz\u2282PC cores and close to the shell, while the dormant magenta PCs remain dark in the core. Within 5\u2009mins of the substrate addition, the color of the active Dz\u2282PC shells changes from green to magenta, confirming the downstream DSD substitution of Atto488-nshort* in the shell. The Atto488-nshort* is released into the surroundings and increases the background fluorescence. In contrast, the shell color of the dormant PCs remains unaltered after 8\u2009min, indicating the absence of a metabolic reaction network to produce Cy5-n*. The line segment analyses on active Dz\u2282PCs before and after the reaction are shown in Fig. 4i, k (Line-1 and Line-3), representing the decrease of green fluorescence (Atto488-nshort*) at the PC shell and enhancement of magenta fluorescence (Cy5) at the core and mainly at the shell of the active PCs. The intensity of the blue shell-fluorescence of the dormant PCs remains very similar before and after the reaction (Fig.\u00a04j, l; Line-2 and Line-4). This stability of the blue fluorescence in the dormant PCs also underscores hardly any diffusive exchange of the Cy5-n* between active and dormant PCs at this substrate concentration. In a control experiment, when a high concentration Subs-3 solution (10 equivalent to the shell barcode) is added to a dormant PC dispersion, no DSD at the PC shell, hence no decreases in the shell-fluorescence, is observed (Supplementary Fig.\u00a010a).\n\nMoreover, we envisaged a more drastic downstream adaptation scenario by installing communication amongst active PCs via the metabolic presentation of an attractive multivalent interaction between them. In this context, we designed a Subs-4, which is similar to Subs-3 but features an additional palindromic sequence (6 nt\u2009=\u2009CTC GAG) attached to Cy5-n* (Fig.\u00a05a). The Tm of the palindrome (p) is well below room temperature (17\u2009\u00b0C), so Subs-4 does not form homodimers at the experimental temperature (~35\u2009\u00b0C). However, we hypothesized that p could induce inter-PC attraction by multivalent p\u2013p interactions. Indeed, upon the addition of Subs-4 into a dispersion of Atto488-nshort*-labeled Dz\u2282PCs, the shell color first changes over time from green to magenta due to the release of Cy5-n*-p (from the PC core) and ensuing DSD at the shell. Critically, due to the localization of the Cy5-n*-p at the shell, the emerging magenta PCs start forming prototissue-like aggregates via multivalent inter-PC p\u2013p duplexes (Fig. 5b). In a control experiment, when 10 equivalent (to the barcode n concentration) of Subs-4 is added to a dormant PC suspension, where the PCs do not contain any Dz, no substantial PC assembly is observed (Supplementary Fig.\u00a010b). These control experiments confirm that catalysis is a critical aspect of the downstream process.\n\na Schematic representation of a downstream cascade, DCBC\u2009\u2192\u2009BCDM\u2009\u2192\u2009DSD reaction at PC shell\u2192 multivalent palindromic interprotocellular duplex formation, using Subs-4 as an input signal. b The time-dependent CLSM image of Atto488-nshort*-labeled Dz\u2282PCs before and after the addition of Subs-4. At t\u2009=\u200910\u2009min, the CLSM image represents a prototissue (\u223c68 PCs) built upon multivalent p\u2013p* interactions. c Illustration and CLSM images of prototissues from five PC-mixtures, in which the palindromic-density at the PC shell is varied from 0\u2009\u2192\u2009100%. Merged channels represent Atto488 (green) and Cy5 (magenta) fluorescence. d, e statistical distribution of PCprototissue number fraction and size of the prototissue as a function of palindromic-density at PC shell. f Schematic illustration of downstream interprotocellular signal transduction and the growth of sender and receiver prototissues in a mixture containing active Atto488-nshort*-labeled (green) PCs (Dz\u2282PCs), and the dormant Atto565-nshort*-labeled (blue) PCs. g Time-dependent CLSM images of interprotocellular communication and growth of prototissues in a mixed-PC system. A gradual increase of magenta fluorescence is observed at the shell of the active green PCs substituting the green fluorescence leading to the formation of sender prototissue. The shell color of dormant PCs changes to pink following the receiver prototissue formation within 4\u2009min Subs-4 addition. The merged channel represents Atto488 (green), Atto565 (blue), and Cy5 (magenta) fluorescence. h Time-dependent growth of sender and receiver prototissues. i The zoomed-in images of two receiver prototissues (blue and merged channel). BCE represents brightness and contrast enhancement. The error bar in d represents the standard deviation of two different sample means at a particular palindromic-density (N\u2009=\u2009358 PC-counts over two samples). For e, h the mean and the median line over the prototissue population are represented inside the box. The box represents the five-number summary of the PCprototissue date set and is extended from the first quartile to the third quartile. The whiskers represent the standard deviation of ten prototissue counts. The dotted lines are a guide to the eye. The scale bar\u2009=\u20095\u2009\u03bcm. Condition: [Dz\u2282PCs]\u2009=\u20095\u2009\u03bcM, [Subs-4]\u2009=\u200935\u2009\u03bcM in TE buffer at 35\u2009\u00b0C.\n\nTo obtain a quantitative understanding of the downstream prototissue formation, we set out to correlate the size of the prototissues (that is the number of PCs in a prototissue) with the surface density of the palindromic strand at the PC shell. To this end, we varied the palindrome surface density by co-functionalization of the n barcodes in the p(T20-n) shells with the palindromic Cy5-n*-p (magenta) and a dummy Atto488-n* (green). Figure\u00a05c\u2013e display the number fraction PC in prototissue (PCprototissue) and free PC (PCfree), as well as the size of the prototissue as a function of five palindrome densities at the PC surface by statistical image analysis after 1\u2009h reaction time (see also Supplementary Fig.\u00a011). The number of PCs assembled in prototissues, as well as the total number assembled within prototissues, increases with increasing the surface density of the palindromic sequence at the shell (Fig.\u00a05d, e). Prototissue formation is completely absent at 0% surface density, but starts to appear already at 25% degree of functionalization; even though with relatively small aggregates of only ca. 6 PCs. Due to similar reaction time in the metabolic reaction cycle, we can estimate that at least 65% of strand displacement occurs in a metabolic reaction cycle (as presented in Fig.\u00a05a, b), because a similar prototissue formation is obtained therein.\n\nSince the statistical analysis clearly shows that already relatively small degrees of palindrome surface functionalization are sufficient to induce prototissue formation, and since not all of the produced Cy5-n*-p products produced in an active PC are needed for a complete functionalization of a shell, we hypothesized that an excess of those might be used as a chemical messenger to activate otherwise dormant PCs (without Dz in the core) for assembly in a sender/receiver setup. To realize such a sender/receiver setup, we mixed active, DZ-containing PCs (sender, green channel, labeled with Atto488-nshort*) with dormant receiver PCs (blue channel, labeled with Atto565-nshort*, no Dz in the core) and added a high concentration of Subs-4 (~7 equivalent to the Dz at the PC core). Indeed, first, the known rapid color change of the active PC shell (green to magenta) with subsequent prototissue formation of the sender PCs occurs (Fig.\u00a05f, g, and Supplementary Fig.\u00a012). Interestingly, after 4\u2009min of Subs-4 addition, the receiver PCs, however, also start forming prototissue-like structures. The blue fluorescence of the shell decreases, while a slight magenta color appears at the receiver PC shell. Therefore, the shell turns blue to purple and pink in the merged CLSM channel. This observation confirms that some of the product (Cy5-n*-p) generated in the sender PCs is released and triggers the DSD at the catalytically inactive receiver PC shells substituting the original Atto565-nshort* strands hence driving prototissue formation of dormant receiver PCs. Importantly, the sender PCs can be unambiguously localized because they have both a magenta core due to the accumulation of the magenta-fluorescent product from the Dz reaction and a magenta shell from the DSD at the PC surface, while the receiver prototissues have a shell labeled in blue and magenta (originating from inter-PC signal transport and DSD) but without a magenta core (Fig.\u00a05g, after 900\u2009s of Subs-4 addition; sender and receiver prototissue 1 and 2, respectively). Two specifically highlighted areas clearly show these differences for a prototissue formed from sender PCs and one formed from receiver PCs (Fig.\u00a05g, i). We also refer the reader to line segment analysis of the CLSM images of sender and receiver prototissue in Supplementary Fig.\u00a013. Due to the spatial delay in signal transfer from the sender to the receiver PCs, the metabolic growth of prototissues has slower kinetics in the case of the receiver prototissue with respect to the sender prototissue. Interestingly, the delayed activation of the receiver PCs also leads to largely self-sorting structures with clear domains of sender PC prototissues that form more quickly and receiver PC prototissues that assemble preferentially with themselves later due to higher mobility of them as long as they are not assembled. Figure\u00a05h summarizes the corresponding time-dependent analysis of the respective prototissue growths. These results confirm that rationally designed signal transduction cascades\u2014combining catalytic Dz-based conversion, DSD reactions, and multivalent binding scenarios\u2014allow for establishing a metabolic PC system, in which a signal gets processed into an effector to establish phenotype-like changes and communication. Moreover, the metabolic downstream signal transduction from active PCs (sender) to the dormant PCs (receiver), leading to the interprotocellular communication and morphological adaptation, resembles, albeit on a simplistic level, adaptation pathways in living cellular communities.\n\nIn summary, we introduced generic and versatile signal processing routines into communities of PCs by exploiting established DNAzyme and DSD reaction scenarios. The approach has the encapsulation of a DNAzyme inside the crowded macromolecular interior of a highly programmable all-DNA PC at its core. Gratifyingly, we found that DNAzymes have an enhanced activity inside such PCs, and they can be used to cleave RNA linkage-containing DNA signaling molecules to release output strands (metabolites). Those metabolites were shown to induce downstream processes by spatial relocation from the core to the shell and site-selective\u00a0strand displacement reactions. The ensuing metabolic adaptation can be evolved to work on different levels of function and complexity. Simple phenotype-like changes in individual PCs can be evolved to induce attractive interactions between PCs of the same type by presenting multivalent binders, and even communication to a secondary PC population can be established. These metabolic features are reminiscent of the functional behavior of a living cell at simplistic levels.\n\nEven though DNAzymes have been established for several purposes, we believe that our approach to using this DNAzyme in a confined state and establishing a DNA-based downstream reaction cascade based on using the catalytic conversion to lead to PC adaptation provides valuable insight into designing minimalistic life-like abiotic systems that can process, translate, communicate, and relay DNA-based signals in more complex sensory environments. Taking into account recent advances in sensing antibodies55, as well as the widely developed fields of DNA aptamers56 and DNAzymes57, it appears feasible to achieve a broader sensing capability and to ultimately arrive at situations where communication between a natural cell and a PC can be established.",
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+            ]
+        },
+        {
+            "section_name": "Methods",
+            "section_text": "The synthesis of the ssDNA polymers was adapted and slightly modified from our previous report42. The stock solutions of 5\u2032-phosphorylated templates and their corresponding ligation strand (see Supplementary Table\u00a01 and Supplementary Fig.\u00a01) were mixed (in equimolar stoichiometry) to attain a final concentration of 1\u2009\u03bcM in TE buffer (Invitrogen; 10\u2009mM Tris(hydroxymethyl)aminomethane pH\u2009=\u20098 and 1\u2009mM EDTA) containing additionally 100\u2009mM NaCl (total volume 100\u2009\u03bcL). The concentrations of the strands are kept low to prevent inter-strand hybridizations. The buffered mixture was heated up to 85\u2009\u00b0C (for 5\u2009min) at a rate of 3\u2009\u00b0C\u2009s\u25001 and slowly cooled down to 20\u2009\u00b0C at 0.01\u2009\u00b0C\u2009s\u25001. After annealing the strands, 20\u2009\u03bcL of 10 X commercial ligase buffer (Lucigen; 500\u2009mM TRIS-HCI, 100\u2009mM MgCl2, 50\u2009mM dithiothreitol, and 10\u2009mM ATP), 75\u2009\u03bcL of water, and 5\u2009\u03bcL of T4 ligase (4\u2009U\u2009\u03bcL\u25001) were added in the reaction tube containing 100\u2009\u00b5L of the template strand, stirred (10\u2009min, 400 rpm) and left to react for 4\u2009h at 30\u2009\u00b0C. The T4 ligase was then denatured by heating the reaction mixture for 20\u2009min at 70\u2009\u00b0C. Then 10\u2009\u03bcL of exonuclease I (Lucigen; 40\u2009U\u2009\u03bcL\u25001) and 10\u2009\u03bcL of Exonuclease III (Lucigen; 200\u2009U\u2009\u03bcL\u25001) are added, and the mixture was kept overnight at 37\u2009\u00b0C on a thermo-shaker (Eppendorf) with gentle stirring (300 rpm) to digest unreacted ligation strands and non-circularized templates in solution. Then the exonucleases were subsequently deactivated by heating the reaction mixture at 80\u2009\u00b0C for 40\u2009min. The circular templates were purified using the Amicon Ultra-centrifugal filters with a 10\u2009kDa cut-off (Merck Millipore) and washed three times using TE buffer over the same filter. The concentration of circular templates was measured by the use of a ScanDrop (Jena Analytic) spectrophotometer, and the solutions were diluted to 1\u2009\u03bcM using TE buffer. The template synthesis was repeated in multiple batches, and a stock solution of the circular template was prepared to avoid batch-to-batch discrepancy.\n\nTo synthesize multiblock ssDNA polymers, 10\u2009\u03bcL circular template (1\u2009\u03bcM) were mixed with 20\u2009\u03bcL of commercial 10 X polymerase buffer (Lucigen; 500\u2009mM TRIS-HCl, 100\u2009mM (NH4)2SO4, 40\u2009mM Dithiothreitol, 100\u2009mM MgCl2), 2\u2009\u03bcL of exonuclease resistant primer (10\u2009\u03bcM in TE buffer), 5\u2009\u03bcL of \u03a629 Polymerase (Lucigen; 10\u2009U\u2009\u03bcL\u25001), 20\u2009\u03bcL of pyrophosphatase (New England Biolabs; 0.1\u2009U\u2009\u03bcL\u25001), and 10\u2009\u03bcL of an adjusted dNTP mixture (total dNTP concentration of 5\u2009mM, the percentage of each base correspond to the expected sequence composition in the ssDNA polymer), and 134\u2009\u03bcL of ultrapure nuclease-free water. The reaction mixtures were kept at 30\u2009\u00b0C for 60\u2009h on a thermo-shaker with a gentle stirring (300 rpm). The solution containing ultralong ssDNA polymer was subjected to temperature-induced cleavage for 15\u2009min at 95\u2009\u00b0C, and the resulting solution was then washed through Amicon Ultra-centrifugal filters with a 30\u2009kDa cut-off (Merck Millipore) (three to four times) using 350\u2009\u03bcL of TE buffer. The amount and purity of the ssDNA polymers were determined using a ScanDrop (Jena Analytic) spectrophotometer. The pyrophosphatase enzyme was added to prevent the formation of insoluble magnesium pyrophosphate as a side product that hinders the polymerization process and is also accountable for resulting in so-called nanoflowers and might cause misperception during the microscopic investigations.\n\nThe synthesis of the PCs was adapted and slightly modified from our previous report42. The PCs were prepared by mixing the ultralong ssDNA-multiblock polymers to attain the target concentration (for p(A20-m), typically, around 0.16\u2009g\u2009L\u25001, which corresponds to the repeating unit (r.u.) concentration of 10\u2009\u03bcM and for p(T20-n), around 0.03\u2009g\u2009L\u25001, which corresponds to [r.u.]\u2009=\u20091.67\u2009\u03bcM) in TE buffer (pH 8). The stoichiometric ratio of p(A20-m): p(T20-n)\u2009=\u20096: 1 represents an optimized empirical condition in order to obtain well-defined PCs with minimized free p(T20-n) amount in solution. The mixture was heated to 95\u2009\u00b0C for 15\u2009min (heating and cooling rate 3\u2009\u00b0C\u2009s\u25001) for homogenization and thermal cleavage of long ssDNA polymer chains (no phase-separation) using a thermocycler. A solution of MgCl2 (2\u2009M) was added to the mixture to attain the final concentration of 50\u2009mM (for phase-separation of p(A20-m) at a Tcp of ~47\u2009\u00b0C) and subsequently heated to 95\u2009\u00b0C for 12\u2009min with heating and cooling ramps of 3\u2009\u00b0C\u2009min\u25001. After the formation of the PCs, a stoichiometric amount of corresponding fluorescently-labeled barcode* oligomeric sequences (Atto488-m*, Atto565-n* or Atto647-n*) were added to the solution and left the colloidal solution for 2-3\u2009h at room temperature with a constant stirring (500 rpm) to hybridize with the PC-barcodes before monitoring them via CLSM imaging. The thermal reduction of the molecular weight of the RCA polymers is crucial to obtaining spherical PCs instead of unwanted agglomerations. Usually, the PCs are stable for several weeks, even though they slowly sediment at the bottom of the tube. The PCs can be sedimented and redispersed numerous times after sequential post-synthetic functionalization at the interior and the shell.\n\nA stock solution of annealed DNAzyme (Dz, composed of Split-Dz1 and Split-Dz2) (200\u2009\u03bcM) was added to a freshly prepared PC medium (50\u2009\u03bcL, [r.u.] or [barcode-m]\u2009=\u200910\u2009\u03bcM) to functionalize the m-barcodes inside the PCs with Dz entirely. The DNAzyme-loaded protocells (Dz\u2282PC) were left for 2\u2009h at room temperature with continuous stirring (400 rpm). The Dz\u2282PCs were centrifuged (12,000 rpm, ~8\u2009min) and redispersed with TE buffer containing 50\u2009mM MgCl2. The purified DNAzyme-loaded PC solution was used for further experiments.\n\nDz\u2282PC (10\u2009\u03bcM encapsulated Dz) stock solution is diluted five times using a TE buffer solution with 10\u2009mM NaCl on a 384-well plate and kept inside the Tecan plate reader for 5\u2009min to equilibrate at the desired temperature. A stock solution of the substrate was injected into the PC solution (1\u2009\u03bcL, 5\u2009\u03bcM), and the fluorescence intensities were recorded (for Cy5: excitation 629\u2009nm, emission 679\u2009nm, bandwidth interval 10\u2009nm, settle time 0.5\u2009s) every 20\u2009s interval over 1\u2009h period. Before every measurement, the plate was subjected to an orbital shaking (200 rpm, 3\u2009s). The concentration of the uncaged product (hence the % of bond cleavage) throughout the reaction was calculated from a calibration plot of the product Cy5-appended oligomer (at various concentrations). In the case of catalysis in solution, the Dz was hybridized with an m-barcode sequence, and the final concentration was maintained at 2\u2009\u03bcM in TE buffer containing 50\u2009mM MgCl2 and 10\u2009mM NaCl before the substrate addition.\n\nThe shells of the freshly prepared washed Dz\u2282PC (10\u2009\u03bcM encapsulated Dz) were hybridized with Atto488-n*/ Atto488-nshort*in order the visualize (excitation: 488-line, 364-well plate) the protocells before the addition of the substrates (Figs.\u00a02h, 3a, 4h and 5b, 5g). A stock solution of the substrate (0.5\u2009mM) was added to the reaction medium (30\u2009\u03bcL) to a final concentration of 25\u201330\u2009\u03bcM. The Dz\u2282PCs were then visualized by excitation with two lasers: 488\u2009nm (for shell) and 638\u2009nm (for the Cy5 product). In some cases, the area of interest for the CLSM measuring was changed after capturing a few images to prevent the photobleaching of Cy5. During the reaction, the well plate was kept at 30 or 37\u2009\u00b0C using a temperature-controlled microscopic stage. For the mixed-PC (active and dormant) experiment (Figs.\u00a04h and 5g), three laser lines were used to excite the PCs \u2015488, 554, and 638\u2009nm for Atto488-nshort*, Atto565-nshort*, and Cy5 product, respectively\u2014and the images were recorded with minimum crosstalk amongst the detectors.\n\nThe Dz\u2282PCs (shell labeled with Atto488-n*) were first imaged using a low intensity of the corresponding laser in a glass-bottom 364-well plate. A stock solution of Subs-1 (0.5\u2009mM, 1.5\u2009\u03bcL) was added to the PC solution, and the reaction was monitored over 20\u201330\u2009min. The FRAP was done after the completion of the reaction. Photobleaching was attained using 100% intensity on both the 488\u2009nm and 638 lines (\u22640\u2009mW in the focal plane). Seven steps of bleaching (each step 6\u2009s) were performed on the Dz\u2282PCs to deplete the fluorescence fully at the region of interest, and the 20 images were recorded every 10\u2009s of the post-bleach sessions. The images were compared before and after the photobleaching steps. The data were presented in Fig. 3b, c.\n\nThe data were collected on a Gallios flow cytometer (Beckman Coulter). Atto488 and Cy5 were excited with a 488-nm or 638-nm laser and detected using a 525/40-nm or 660/20-nm bandpass filter, respectively. PCs were identified in the FSC/SSC scatter plot. PCs without Atto488 and Cy5 fluorescence were excluded from the analysis (<3% of all PCs, Supplementary Figs.\u00a05d, 8c, d). Approximately 500 PCs were measured per second. Acquired data before and after the addition of the substrate was concatenated and gated using FlowJo (v10.6.1, Becton, Dickinson, and Company). Binned medians were calculated over 4\u2009s of acquisition time, and data were plotted using ggCyto in R 4.1.1. The concentration of encapsulated Dz in the PC is 0.5\u2009\u03bcM for all the cytometry measurements.\n\nThe series of fluorescence images were processed using ImageJ (Fiji) by first applying a background subtraction. Then, the temporal profiles of both the magenta and green channels in the region of interest were extracted. The values plotted correspond to the magenta and green channels with the reaction time after normalizing with respect to the initial magenta and green intensities. The fluorescence intensities for the line segment analysis were presented without normalization.\n\nThe reproducibility of each experiment was confirmed using three independent PC suspensions. No technical replicates were reported. For the fluorescence intensity measurements (Figs.\u00a02c and 4c), three samples were prepared in three wells of a 386-well plate, and the experiments were run parallelly. For the microscopic analysis, corresponding changes over a large area with ~40\u201350 PCs were recorded and analyzed. The reproducibility of these experiments was checked with different PC batches and by imaging them using the same experimental parameters. Different areas were imaged in the kinetics to avoid the influence of photobleaching. For the statistical analysis, ~400 PCs from two samples were imaged and counted both in the free state as well as in the prototissue to prepare the box plots (Fig.\u00a05d, e, h).\n\nFurther information on research design is available in the\u00a0Nature Research Reporting Summary linked to this article.",
+            "section_image": []
+        },
+        {
+            "section_name": "Data availability",
+            "section_text": "The source file also contains the numerical values of the number of protocells involved in flow cytometry kinetics, presented in Figs.\u00a02f\u2013g and 4d\u2013e. Additional supporting data are available from the corresponding author upon request.\u00a0Source data are provided with this paper.",
+            "section_image": []
+        },
+        {
+            "section_name": "References",
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+            "section_image": []
+        },
+        {
+            "section_name": "Acknowledgements",
+            "section_text": "We would like to thank Oliver S. Thomas for help with flow cytometry data analysis and plotting. A.S. acknowledges the support of the Alexander von Humboldt Foundation. We acknowledge the support by the European Research Council Consolidator Grant to A.W. (M3ALI (agreement 677960)). A.W. acknowledges generous support from the Gutenberg Research College in the framework of a Gutenberg Research Professorship. M.H. and W.W. acknowledge support by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany\u2019s Excellence Strategy CIBSS\u2014EXC-2189\u2014Project ID: 390939984.",
+            "section_image": []
+        },
+        {
+            "section_name": "Funding",
+            "section_text": "Open Access funding enabled and organized by Projekt DEAL.",
+            "section_image": []
+        },
+        {
+            "section_name": "Author information",
+            "section_text": "A3BMS Lab, University of Mainz, Department of Chemistry, Duesbergweg 10-14, 55128, Mainz, Germany\n\nAvik Samanta,\u00a0Wei Liu\u00a0&\u00a0Andreas Walther\n\nFaculty of Biology, Cluster of Excellence CIBSS - Centre for Integrative Biological Signalling Studies, University of Freiburg, 79104, Freiburg, Germany\n\nMaximilian H\u00f6rner\u00a0&\u00a0Wilfried Weber\n\nCluster of Excellence livMatS @ FIT \u2013 Freiburg Center for Interactive Materials and Bioinspired Technologies, University of Freiburg, 79110, Freiburg, Germany\n\nAndreas Walther\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nA.S. and A.W. conceived the project and designed the experiments. A.S. and M.H. performed the Cytometric experiments. A.S. performed the other experiments. W.L. optimized the palindromic sequences. A.S. analyzed the data and prepared the draft manuscript. A.W. and W.W. supervised the project. All authors commented on the manuscript.\n\nCorrespondence to\n                Avik Samanta or Andreas Walther.",
+            "section_image": []
+        },
+        {
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+            "section_text": "The authors declare no competing interests.",
+            "section_image": []
+        },
+        {
+            "section_name": "Peer review",
+            "section_text": "Nature Communications thanks the anonymous reviewer(s) for their contribution to the peer review of this work.\u00a0Peer reviewer reports are available.",
+            "section_image": []
+        },
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+            "section_image": []
+        },
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+            "section_image": []
+        },
+        {
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+            "section_text": "Open Access  This article 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. The images or other third party material in this article are included in the article\u2019s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article\u2019s 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/.\n\nReprints and permissions",
+            "section_image": []
+        },
+        {
+            "section_name": "About this article",
+            "section_text": "Samanta, A., H\u00f6rner, M., Liu, W. et al. Signal-processing and adaptive prototissue formation in metabolic DNA protocells.\n                    Nat Commun 13, 3968 (2022). https://doi.org/10.1038/s41467-022-31632-6\n\nDownload citation\n\nReceived: 20 October 2021\n\nAccepted: 28 June 2022\n\nPublished: 08 July 2022\n\nVersion of record: 08 July 2022\n\nDOI: https://doi.org/10.1038/s41467-022-31632-6\n\nAnyone you share the following link with will be able to read this content:\n\nSorry, a shareable link is not currently available for this article.\n\n\n\n\n                            Provided by the Springer Nature SharedIt content-sharing initiative\n                        ",
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+            ]
+        },
+        {
+            "section_name": "This article is cited by",
+            "section_text": "Nature Communications (2025)\n\nNature Communications (2025)\n\nNature Chemical Engineering (2025)\n\nNature Synthesis (2025)\n\nNature Communications (2025)",
+            "section_image": []
+        }
+    ]
+}

204b5195b64c3d61006b27ec770c4dff1032fc98f2d87979a64b6b2c0c0f6e1e/metadata.json

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+{
+    "title": "Incomplete human reference genomes can drive false sex biases and expose patient-identifying information in metagenomic data",
+    "pre_title": "Incomplete human reference genomes can drive false sex biases and expose patient-identifying information in metagenomic data",
+    "journal": "Nature Communications",
+    "published": "18 January 2025",
+    "supplementary_0": [
+        {
+            "label": "Supplementary Information",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-56077-5/MediaObjects/41467_2025_56077_MOESM1_ESM.pdf"
+        },
+        {
+            "label": "Description of Additional Supplementary Files",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-56077-5/MediaObjects/41467_2025_56077_MOESM2_ESM.pdf"
+        },
+        {
+            "label": "Supplementary Data 1",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-56077-5/MediaObjects/41467_2025_56077_MOESM3_ESM.xlsx"
+        },
+        {
+            "label": "Supplementary Data 2",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-56077-5/MediaObjects/41467_2025_56077_MOESM4_ESM.xlsx"
+        },
+        {
+            "label": "Supplementary Data 3",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-56077-5/MediaObjects/41467_2025_56077_MOESM5_ESM.xlsx"
+        },
+        {
+            "label": "Supplementary Data 4",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-56077-5/MediaObjects/41467_2025_56077_MOESM6_ESM.xlsx"
+        },
+        {
+            "label": "Supplementary Data 5",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-56077-5/MediaObjects/41467_2025_56077_MOESM7_ESM.xlsx"
+        },
+        {
+            "label": "Supplementary Data 6",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-56077-5/MediaObjects/41467_2025_56077_MOESM8_ESM.xlsx"
+        },
+        {
+            "label": "Supplementary Data 7",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-56077-5/MediaObjects/41467_2025_56077_MOESM9_ESM.xlsx"
+        },
+        {
+            "label": "Reporting Summary",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-56077-5/MediaObjects/41467_2025_56077_MOESM10_ESM.pdf"
+        },
+        {
+            "label": "Transparent Peer Review file",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-56077-5/MediaObjects/41467_2025_56077_MOESM11_ESM.pdf"
+        }
+    ],
+    "supplementary_1": NaN,
+    "supplementary_2": NaN,
+    "source_data": [
+        "https://hartwigmedical.github.io/documentation/data-access-request-methods.html",
+        "https://argos.igs.umaryland.edu",
+        "https://www.ncbi.nlm.nih.gov/bioproject/231221",
+        "https://www.internationalgenome.org/data",
+        "https://www.ebi.ac.uk/ena/browser/view/PRJEB83637",
+        "https://www.ddbj.nig.ac.jp/jga/index-e.html",
+        "https://ega-archive.org/studies/EGAS00001007027"
+    ],
+    "code": [
+        "https://github.com/cguccione/human_host_filtration",
+        "https://github.com/cguccione/host-filtration-notebooks"
+    ],
+    "subject": [
+        "Data processing",
+        "Medical ethics",
+        "Metagenomics"
+    ],
+    "license": "http://creativecommons.org/licenses/by/4.0/",
+    "preprint_pdf": "https://www.researchsquare.com/article/rs-4721159/v1.pdf?c=1737292036000",
+    "research_square_link": "https://www.researchsquare.com//article/rs-4721159/v1",
+    "nature_pdf": "https://www.nature.com/articles/s41467-025-56077-5.pdf",
+    "preprint_posted": "22 Oct, 2024",
+    "research_square_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "As next-generation sequencing technologies produce deeper genome coverages at lower costs, there is a critical need for reliable computational host DNA removal in metagenomic data. We find that insufficient host filtration using prior human genome references can introduce false sex biases and inadvertently permit flow-through of host-specific DNA during bioinformatic analyses, which could be exploited for individual identification. To address these issues, we introduce and benchmark three host filtration methods of varying throughput, with concomitant applications across low biomass samples such as skin and high microbial biomass datasets including fecal samples. We find that these methods are important for obtaining accurate results in low biomass samples (e.g., tissue, skin). Overall, we demonstrate that rigorous host filtration is a key component of privacy-minded analyses of patient microbiomes and provide computationally efficient pipelines for accomplishing this task on large-scale datasets.Biological sciences/Microbiology/Microbial communities/MetagenomicsBiological sciences/Computational biology and bioinformatics/Data processingHealth sciences/Health care/Medical ethics",
+            "section_image": []
+        },
+        {
+            "section_name": "Figures",
+            "section_text": "Figure 1Figure 2Figure 3Figure 4Figure 5Figure 6",
+            "section_image": [
+                "https://assets-eu.researchsquare.com/files/rs-4721159/v1/854ea99c630cf37a05c11c4c.png",
+                "https://assets-eu.researchsquare.com/files/rs-4721159/v1/a632328cc04d995e02bd0625.png",
+                "https://assets-eu.researchsquare.com/files/rs-4721159/v1/e7e3be2e499584b2c040308d.png",
+                "https://assets-eu.researchsquare.com/files/rs-4721159/v1/07648a4ecfd256de7d9da6f7.png",
+                "https://assets-eu.researchsquare.com/files/rs-4721159/v1/40bbdceeae4338b5e0153929.png",
+                "https://assets-eu.researchsquare.com/files/rs-4721159/v1/d68b00057c5721929f168177.png"
+            ]
+        },
+        {
+            "section_name": "Additional Declarations",
+            "section_text": "Yes there is potential Competing Interest.\nRob Knight is a scientific advisory board member and consultant for BiomeSense, Inc., has equity, and receives income. He is a scientific advisory board member and has equity in GenCirq. He is a consultant and scientific advisory board member for DayTwo and receives income. He has equity in and acts as a consultant for Cybele. He is a co-founder of Biota, Inc., and has equity. He is a cofounder of Micronoma, has equity, and is a scientific advisory board member. The terms of these arrangements have been reviewed and approved by the University of California, San Diego, in accordance with its conflict-of-interest policies. Daniel McDonald is a consultant for BiomeSense, Inc., has equity, and receives income. The terms of these arrangements have been reviewed and approved by the University of California, San Diego, in accordance with its conflict-of-interest policies.",
+            "section_image": []
+        },
+        {
+            "section_name": "Supplementary Files",
+            "section_text": "SupplementalTablesCollated.pdfSupplementalTable1.xlsxSupplemental Table 1SupplementalTable2.xlsxSupplementalTable3.xlsxSupplemental Table 3SupplementalTable4.xlsxSupplementalTable5.xlsxSupplementalTable6.xlsxSupplemental Table 6SupplementalFigure1.pdfSupplementalFigure2.pdfSupplemental Figure 2SupplementalFigure3.pdfSupplemental Figure 3SupplementalFigure4.pdfSupplementalFigure5.pdfNMEDAN134392rsflat.pdf",
+            "section_image": []
+        }
+    ],
+    "nature_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "As next-generation sequencing technologies produce deeper genome coverages at lower costs, there is a critical need for reliable computational host DNA removal in metagenomic data. We find that insufficient host filtration using prior human genome references can introduce false sex biases and inadvertently permit flow-through of host-specific DNA during bioinformatic analyses, which could be exploited for individual identification. To address these issues, we introduce and benchmark three host filtration methods of varying throughput, with concomitant applications across low biomass samples such as skin and high microbial biomass datasets including fecal samples. We find that these methods are important for obtaining accurate results in low biomass samples (e.g., tissue, skin). Overall, we demonstrate that rigorous host filtration is a key component of privacy-minded analyses of patient microbiomes and provide computationally efficient pipelines for accomplishing this task on large-scale datasets.",
+            "section_image": []
+        },
+        {
+            "section_name": "Introduction",
+            "section_text": "Metagenomic next-generation sequencing (mNGS) encompasses various high-throughput DNA profiling techniques that enable environment-agnostic taxonomic profiling of microorganisms, including bacteria, archaea, fungi, and viruses1. mNGS has shown increasing adoption in clinical contexts for diagnosing infectious diseases, surveilling microbial pathogens, and predicting antibiotic efficacy2,3 across fecal, skin, and tissue samples. Utilizing mNGS in these settings is attractive due to its untargeted and high-throughput characteristics; however, its untargeted nature can result in substantial and confounding amounts of non-microbial DNA (e.g., human DNA) when processing low-microbial biomass samples, especially at higher sequencing depths.\n\nTo mitigate the influence of non-microbial DNA on metagenomic studies, diverse host depletion techniques have been developed, ranging from experimental modification of DNA extraction steps (e.g., differential lysis)4 to real-time sorting of reads during sequencing5. Computational host filtration, or simply host filtration, refers to computational approaches for removing host DNA from sequenced samples, regardless of whether prior host depletion steps were performed. Separating host genetic information from microbial counterparts is a crucial step in mNGS workflows, especially in the analysis of low microbial biomass samples, such as those derived from skin, saliva, or tumors6,7. Additionally, these methodologies are imperative to increase the rigor with which debated microbial communities, like putative blood-borne microbiota, can be assayed.\n\nWhen human DNA reads from mNGS are not correctly identified during the host filtration step, they may be incorrectly classified as microbial reads, creating potentially misidentified taxonomic classifications and biased effect sizes (inflation or deflation of mismapped taxa)7. These misclassifications can manifest as false positive taxonomic classifications, and in this work we further demonstrate these false positives can alter biological conclusions. Further, failure to remove human DNA from metagenomic sequencing samples can leak private genetic information about the host into putatively microbial data, enabling re-identification of study participants8.\n\nAlthough host filtration is generally a common preprocessing step9, the algorithmic choice for host filtration and employed human reference database(s) can result in substantially different biological results7. Tools differ between pipelines, but most host filtration approaches map reads to a host reference genome followed by sequence-based computational subtraction of host reads to obtain human-filtered data10.\n\nMost host filtration tools10 and recommended host filtration workflows11,12 exclusively use a single human reference, which fails to capture the diversity of human genomes and cannot remove population-specific variation. Portions of the human genome that are incomplete in these references, such as the Y chromosome in GRCh38 or earlier versions of T2T-CHM13 (v1.0), can permit flow-through of human reads from those regions to microbial mapping steps, leading to the mismapping of taxa during classification and artifactual data distributions (e.g., false sex differences in the low biomass microbial profiles). Moreover, regions of population-specific genome variation or haplotypes not well covered in singular reference genomes can allow leakage of patient-identifying information in microbial reads8. To date, previous work13 has either failed to incorporate pangenome references14 or to provide computationally efficient methods capable of host filtering across dozens of human genomes7, and both are needed to protect patient privacy and improve output quality. Therefore, we were motivated to explore more efficient methods for host filtration using the most comprehensive human references available to protect the privacy of disseminated metagenomics datasets and mitigate artifactual biases associated with missing genome regions.\n\nIn this work, we identify and resolve an artifactual technical effect caused by insufficient host filtration in quantifying the microbial profiles associated with tumor tissue from mNGS. We then implement and benchmark three improved host filtration approaches that leverage two complementary algorithmic approaches and a wide variety of human reference genomes to maximize host read removal. We apply these novel methodologies towards multiple sample types in both low and high biomass conditions. Finally, we show that improved host filtration prevents host re-identification from mNGS datasets with matched genotyping information. These efforts support utilization of comprehensive host filtration preprocessing for current and future mNGS studies to increase data robustness and protect patient privacy.",
+            "section_image": []
+        },
+        {
+            "section_name": "Results",
+            "section_text": "We initially and incidentally discovered detrimental effects from improper host filtration when exploring sequencing data from a cohort of metastatic human tumor tissues (Hartwig Medical Foundation15 hereafter \u201cHMF\u201d). These data were originally processed and published before the release of T2T-CHM13v2.016, which added a complete human Y chromosome, and have since been independently analyzed for microbiomes17. After isolating non-human reads from deep, whole-genome sequenced samples of 4902 metastatic tumors (Supplementary Data\u00a01), we applied quality and length filtering, followed by re-alignment against GRCh38.p7. Surprisingly, our initial analysis of putative metastatic tumor low biomass microbial profiles revealed significant differences between male and female-labeled samples (Fig.\u00a01a; p\u2009=\u20090.00025, RPCA18-PERMANOVA). Subsequent re-analysis of the same data using T2T-CHM13v2.016, which included the first complete Y chromosome, abolished the male-female sex separation in our data (Fig.\u00a01b; p\u2009=\u20090.29, RPCA18-PERMANOVA). These results suggested that missing regions of human reference chromosomes can directly cause related artifactual biases in downstream microbiome data.\n\na RPCA of microbial relative abundance quantification from tumor samples in the Hartwig Medical Foundation Database, which was originally subject to GRCh38.p7 filtration exclusively. Statistically significant differences were found between male and female groups (PERMANOVA; pseudo-F\u2009=\u200965.4, p\u2009=\u20090.00025). b Identical dataset and pre-processing steps done in a but with the addition of the T2T-CHM13v2.0 reference genome in host filtration. Differences were not statistically significant between male and female groups (PERMANOVA; pseudo-F\u2009=\u20091.23, p\u2009=\u20090.29).\n\nTo validate that this result was not unique to RPCA, we re-calculated results with Weighted and Unweighted UniFrac19, Bray-Curtis20 dissimilarity, and Jaccard21 similarity index. We also tested another microbial database, Web of Life release 222, all with and without rarefaction. Notably, neither the choice of rarefaction level nor microbial database affected the identification of artifactual sex differences. The results were less affected by filtration against T2T-CHM13v2.0 when qualitative distance metrics were used (i.e., Unweighted UniFrac and Jaccard similarity index). However, quantitative metrics (i.e., Weighted UniFrac and Bray-Curtis) reproduced our original findings that additional filtration against T2T-CHM13v2.0 abolished sex differences (Supplementary Data\u00a02).\n\nTo investigate why quantitative metrics were affected but qualitative metrics were not, we examined a subset of 100 samples from HMF. We randomly selected metastatic tissue samples across various body sites, all of which had metastasized from a primary colorectal tumor. We isolated reads from these samples that were removed when filtered with T2T-CHM13v2.0 but retained when filtered with GRCh38.p7. We refer to these reads as \u201cT2T-filtered\u201d. Using Woltka and RefSeq release 200, we mapped the T2T-filtered reads to their corresponding operational genomic units (OGUs)23 (Supplementary Data\u00a03). Notably, 99.895% of the reads (5,590,189/5,596,038) matched only four taxa: Toxoplasma gondii (G000006565), Bifidobacterium tibiigranuli (G009371885), Alcanivorax hongdengensis (G000300995), and Tetrasphaera japonica (G001046855). When reads we observed as being mistakenly mapped to microbial taxa are removed with T2T-CHM13v2.0 filtering, the quantitative diversity metrics more accurately reflect the per-sample microbial diversity (Fig.\u00a01b). However, qualitative metrics relying on presence-absence (and not abundance) are less affected, and thereby more robust to, falsely inflated abundances of T.gondii, B. tibiigranuli, A. hongdengensis, and T. japonica. These results demonstrate the importance of validating conclusions with qualitative metagenomic methods when using older or incomplete genome references\u2014although the human references are now essentially complete, the same is not true for other species, so this category of validation will continue to be important into the future.\n\nTo test whether these four taxa shared regions of sequence similarity with the human genome, we took the same T2T-filtered reads from the subset of 100 HMF samples described above, and mapped those sequences against RS210-clean, a version of RefSeq release 210 (2022-01-01) in which regions of microbial genomes shared with human genomes based on Exhaustive1 and Conterminator24 were masked. We found that using a human-scrubbed microbial database eliminated some of the T2T-filtered reads from mapping to microbes (Supplementary Data\u00a04). 5,596,038 T2T-filtered reads mapped to microbes using RefSeq release 200, but only 53 mapped to microbes using RS210-clean. This result suggested that a cleaned microbial database may alone abolish the false male-female sex difference. However, a strong human-filtration pipeline that uses T2T-CHM13v2.0 would have removed all these T2T-filtered reads, so that none of them would map to microbes regardless of which database was used.\n\nTo confirm that a cleaned microbial database would abolish the sex difference without any additional filtration, we then applied RS210-clean on a larger subset of 477 metastatic tissue samples across various body sites, all of which had metastasized from the colon using GRCh38.p7 filtration alone. Importantly, we found that the sex differences were eliminated (p\u2009=\u20090.14, RPCA18-PERMANOVA). These results indeed demonstrate that host filtration of either the reads (prior to mapping) or the microbial database is sufficient to prevent sex biases.\n\nTo verify that the T2T-filtered reads from the subset of 100 HMF samples described above was in fact derived from the human Y chromosome, we aligned the T2T-filtered reads using minimap225 (v. 2.26) and an index based only on the Y chromosome portion of T2T-CHM13v2.0, and observed an overall alignment of 88.99% to the Y chromosome. We speculate that the remaining 11.01% are likely due to additions of regions in other chromosomes with the T2T-CHM13v2.0 release. We spot-checked alignments of a subset of Y chromosome mapped reads using the BLAST26 web portal. For example, a read that aligns with 100% identity to the Y chromosome is also identified as T. gondii at 98.67% identity when using Nucleotide BLAST26. To confirm the T2T-filtered reads were likely mismapped to microbial genomes, we calculated the depth and breadth for the top ten multi-mapped organisms (Supplementary Fig.\u00a01a). We observe a large coverage peak within each genome with low mean coverage depth, suggesting an artifactual signal. We extracted the genomic regions corresponding to the coverage peak for each organism and confirmed they correspond to low complexity regions of each respective microbial reference genome (Supplementary Data\u00a05). Finally we include coverage depth and breadth assessments for these same reads against the Y chromosome from the T2T-CHM13v2.0 and note a more uniform distribution, suggesting the true origin of the reads corresponds to the more complete Y chromosome in T2T-CHM13v2.0 rather than any microbial genome (Supplementary Fig.\u00a01b). Overall, these data suggest that the sex differences identified in the HMF dataset are attributable to human Y chromosome sequences leaking through the GRCh38.p7 filter, which were subsequently mapped to microbial taxa containing genomic regions common to the human genome.\n\nInspired by this resolution to the problem of artifactual sex-specific differences, we sought to create and evaluate pipelines for thorough host filtration in a computationally efficient manner (described below). These pipelines can be conservatively combined with microbial database cleaning/masking approaches, as we and others have described elsewhere7,24. However, we caution that microbial database masking alone may not adequately address patient re-identification concerns, because human reads remain mixed with microbial reads, as addressed later in this work.\n\nWe thus proposed and benchmarked three methods for improved host filtration that utilizes traditional sequence alignment25 and a novel indexing-based approach called Movi27. We evaluate multiple human references, including the most updated versions of GRCh38.p14, T2T-CHM13v2.016, and HPRC-2023 release14, to maximize captured human genomic diversity. Our methods are as follows: 1) Alignment with minimap2 to GRCh38.p14 and T2T-CHM13v2.0, and indexing with Movi to GRCh38.p14, T2T-CHM13v2.0, and HPRC, 2) Alignment with minimap2 to GRCh38.p14, T2T-CHM13v2.0, and HPRC, and indexing with Movi to GRCh38.p14, T2T-CHM13v2.0, and HPRC, 3) Indexing with Movi to GRCh38.p14, T2T-CHM13v2.0, and HPRC (Fig.\u00a02a; see Methods for details). Additionally, we compared our methods to the only other publication using HPRC for host filtration, which used all three human genome reference sets with minimap225 in both paired-end and single-end mode. We also benchmarked our methods against the strict host filtration method described by Sepich-Poore et al.7 (Supplementary Fig.\u00a02a).\n\na Pipeline of host filtration methods. b Using simulated data with a 50/50 mix of human data from HPRC and microbial data from FDA-ARGOS, we applied the 3 host filtration methods with 3 different sample sizes. Runtimes were averaged across 10 runs per sample size. HG38: GRCH38.p14, T2T: T2T-CHM13v2.0, HPRC: Human Pangenome Reference Consortium 2024 release.\n\nTo compare the run time of host filtration methods, we simulated data of 50% human and 50% microbial reads using ten sampled genomes from HPRC and over 800 complete bacterial assemblies from the FDA-ARGOS database28. Using these ten simulated datasets, we subsampled them at ten thousand, 1 million, and 10 million reads, followed by applying all filtration methods on each to assess their scalability (Fig.\u00a02b). Methods 1 and 3 had comparable runtimes: 11.13\u2009min and 11.15\u2009min at 1 million reads, respectively. In comparison, Method 2\u2019s use of HPRC alignment with minimap2 created exponentially increasing run times (46\u2009min, 55\u2009min, and 2.5\u2009h at ten thousand, 1 million, and 10 million reads, respectively) as the dataset size increased. The strict host filtering method described by Sepich-Poore et al.7 also took the longest to complete, or 1.59\u2009h for 1 million reads (Supplementary Fig.\u00a02b).\n\nWe next applied the three host filtration methods to assess sensitivity on the aforementioned ten samples of 1 million reads each, excluding the ten pangenomes we used to simulate the human data during filtration. An ideal host filtration method would result in zero remaining human reads (Fig.\u00a03a, Supplementary Data\u00a06) and a minimal number of lost microbial reads (Fig.\u00a03b, Supplementary Data\u00a06). For the remaining human reads (Fig.\u00a03a), we found significant differences between Method 1 and Method 3, as well as Method 2 and Method 3 (Wilcoxon signed-rank test, p\u2009=\u20090.0020), indicating that the combination of alignment and indexing-based approaches for host filtration outperforms indexing based approaches alone. For microbial reads lost (Fig.\u00a03b), we found significant differences across all three methods (Wilcoxon signed-rank test, p\u2009=\u20090.0020 for all comparisons). We find that the indexing-based host filtration approach alone (Method 3) retains the greatest number of microbial reads, while alignment-based steps, as in the initial steps of Method 1 and Method 2, inadvertently discard an increasing number of microbial reads proportional to the number of human references used for alignment. Although Method 2 was most effective at removing human reads, it also removed 242.5 and 288.5 more microbial reads on average compared with Method 1 and 3, respectively. In contrast, Method 3 maximized the number of microbial reads kept, losing only 43.5 microbial reads on average, but also allowed an average of 4.5 human reads through. Method 1 struck a balance, losing 89.5 microbial reads on average and eliminating all the human reads in 8 out of the 10 cases. We found that the prior Sepich-Poore et al. 7 method performed identically to Method 2 regarding the number of human reads removed (Supplementary Fig.\u00a03a) and unnecessarily removed an additional ten microbial reads (Supplementary Fig.\u00a03b). Because host filtration is used in a wide range of applications, it is crucial to allow users to choose between methods and determine if, for a given application and regulatory environment, it is acceptable to lose more microbial reads while ensuring maximum human read removal; conversely, one may want to maximize the number of microbial reads retained while still removing the majority of host reads. We note that microbial reads may be lost inadvertently due to sequence similarity between microbial input reads and human reference databases when using both alignment and indexing-based approaches (see Fig.\u00a03 and Supplementary Fig.\u00a04).\n\nUsing the 10 simulated datasets of 1 million reads as described in Fig.\u00a02b, we a calculated the number of human reads remaining, and b number of microbial reads remaining, for host filtration Methods 1\u20133 (HPRC host filtration performed excluding the 10 genomes used for data simulation). HG38: GRCH38.p14, T2T: T2T-CHM13v2.0, HPRC: Human Pangenome Reference Consortium 2024 release. Box plots show the median (center line), interquartile range (IQR; Q1\u2013Q3; box), whiskers extending to Q1 \u2212 1.5\u2009\u00d7\u2009IQR and Q3\u2009+\u20091.5\u2009\u00d7\u2009IQR, minimum and maximum values at whisker ends, and points representing individual observations both within and beyond the whisker range.\n\nTo determine the robustness of these three methods across a range of microbial biomasses, we evaluated each method on human exome data as well as tissue, skin, and fecal metagenomic samples. First, we obtained 30 International Genome Sample Resource (IGSR) phase 3 human exome sequencing samples29, which are putatively human. After sampling 1 million reads each, we examined the number of human reads remaining, with an ideal host filtering method having zero reads left. We found Method 2 left the smallest amount of human exome reads followed by Method 1, then Method 3 (average reads remaining; Method 1: 32.66, Method 2: 24, Method 3: 351.53). There were significant differences between Method 1 and Method 2 (Wilcoxon signed-rank test, p\u2009=\u20092.6e\u221205), between Method 2 and Method 3 (Wilcoxon signed-rank test, p\u2009=\u20098.2e\u221206), and between Method 1 and Method 3 (Wilcoxon signed-rank test, p\u2009=\u20093.8e\u221205) (Fig.\u00a04a, Supplementary Data\u00a06). Mirroring the distributions seen in human simulated data benchmarks (Fig.\u00a03a), Method 2 removed the largest number of human sequences, followed by Method 1, then Method 3. Interestingly, we found nearly ten times as many human exome reads remained compared to the simulated human data (Fig.\u00a03a). However, without access to the samples, it is not possible to determine whether the increased number of reads in the human exome data compared to the simulated human data is due to real microbial presence (contamination or biological) in the exome sample, imperfect amplification or selection chemistry, and/or reduced performance of the host filtration procedure.\n\na The number of reads remaining after host-filtering 30 human exomes subset to 1 million reads across methods. b 100 metastatic colorectal cancer tissue samples were selected from HMF and read counts were calculated following application of improved host filtration methods. HG38 GRCH38.p14, T2T T2T-CHM13v2.0, HPRC Human Pangenome Reference Consortium 2024 release. Box plots show the median (center line), interquartile range (IQR; Q1\u2013Q3; box), whiskers extending to Q1\u2009\u2212\u20091.5\u2009\u00d7\u2009IQR and Q3\u2009+\u20091.5\u2009\u00d7\u2009IQR, minimum and maximum values at whisker ends, and points representing individual observations both within and beyond the whisker range.\n\nUsing these three host filtration methods, we re-analyzed the aforementioned 100 colorectal tissue tumor samples from HMF, finding additional human reads removed compared to T2T-CHM13v2.0 alone (Fig.\u00a04b, Supplementary Data\u00a06). For HMF total read count following host filtration, we found significant differences between Method 1 and Method 2 (Wilcoxon signed-rank test, p\u2009=\u20093.9e\u221218), between Method 2 and Method 3 (Wilcoxon signed-rank test, p\u2009=\u20091.2e\u221217), and between Method 1 and Method 3 (Wilcoxon signed-rank test, p\u2009=\u20093.9e\u221218). Again, Method 2 has the least reads followed by Method 1 and then Method 3 (average reads remaining; Method 1: 84,663.12, Method 2: 84,009.03, Method 3: 84,692.71). Although we cannot verify if the remaining reads are all microbial, we can conclude, based on the simulations, that Method 2 likely has lower read counts due to removal of true microbial reads.\n\nNext, we applied our host filtration methods to mNGS data from skin samples, where microbial and human DNA would be expected in varying proportions. Specifically, we analyzed 77 skin swab samples from pediatric healthy controls and subjects with atopic dermatitis (Fig.\u00a05a, Supplementary Fig.\u00a05, Supplementary Data\u00a06). The percentage of non-human reads remaining across skin samples varied, consistent with distinct levels of host background within each sample, with Method 2 providing the lowest percentage of reads remaining, followed by Method 1, then Method 3. For the total percentage of reads remaining of these skin samples following host filtration, we found significant differences across all three methods (Wilcoxon signed-rank p\u2009=\u20092.5e\u221214 for all comparisons).\n\na 87 human skin samples were host-filtered with the improved methods, we then calculated the percentage of reads remaining. b We calculated the percentage of reads remaining on a per-sample basis for each of the 50 human fecal samples examined. HG38: GRCH38.p14, T2T: T2T-CHM13v2.0, HPRC: Human Pangenome Reference Consortium 2024 release. Box plots show the median (center line), interquartile range (IQR; Q1\u2013Q3; box), and whiskers extending to Q1\u2009\u2212\u20091.5\u2009\u00d7\u2009IQR and Q3\u2009+\u20091.5\u2009\u00d7\u2009IQR. Box plots show the median (center line), interquartile range (IQR; Q1\u2013Q3; box), whiskers extending to Q1\u2009\u2212\u20091.5\u2009\u00d7\u2009IQR and Q3\u2009+\u20091.5\u2009\u00d7\u2009IQR, minimum and maximum values at whisker ends, and points representing individual observations both within and beyond the whisker range.\n\nLastly, we evaluated a high microbial biomass dataset of 50 fecal samples from older adults consisting of healthy controls and subjects with Alzheimer\u2019s disease30 (Fig.\u00a05b, Supplementary Data\u00a06). As expected, we observed nominal reductions in the percentage of total reads, although still greater than 1% of reads. For the total percentage of reads remaining in these fecal samples following host filtration, we found significant differences between all three methods (Wilcoxon signed-rank test, p\u2009=\u20097.6e\u221210 for all comparisons), and the same pattern of Method 2 having the lowest percentage of reads remaining followed by Method 1, then Method 3.\n\nImproper host filtration of metagenomic samples can leak sensitive genomic information. In a recent study, Tomofuji et al.8 re-identified patients from human reads that leaked through fecal metagenomic data, matching them to blood-derived genotype data from the same individuals (Supplementary Data\u00a01). Their study initially used host filtration steps derived from traditional filtration methods8. To test the effectiveness of our approaches to disrupt a host re-identification signal, we applied the above methods to the 343 fecal samples from Tomofuji et al.8 re-filtering host data with steps outlined in Methods 1 and 2. Using the 343 paired genotype samples to test whether re-identification (from the fecal samples) was still possible (see Methods for details), we found that filtration with any combination of two human references (GRCh38.p14, T2T-CHM13v2.0, HPRC) was sufficient to prevent patient re-identification, haplotype reconstruction, and phenotype prediction (Fig.\u00a06). These data demonstrate the importance of thorough host filtration prior to public upload of mNGS data while providing computationally efficient tools to do so.\n\nThe 343 fecal samples from Tomofuji et al. Nature Microbiology 2023, with paired genotype data, were re-analyzed with various combinations of updated host filtration methods (GRCh38.p14, T2T-CHM13v2.0, Human Pangenome Reference Consortium 2024 release) resolving host data leakage. The x-axis of the plots indicates the number of bases used for the calculation of the likelihood scores. The y-axis of the plot indicates the two-sided P values calculated using a standard normal distribution based on the standardized likelihood scores. The red and blue dashed lines indicate p\u2009=\u20094.3\u2009\u00d7\u200910\u22127 (0.05/117,649 tests) and p\u2009=\u20091.5\u2009\u00d7\u200910\u22124 (0.05/343 tests), respectively. The results of the 117,649 tests (343 genotype data\u2009\u00d7\u2009343 metagenome data) are indicated as the colors of the points. Some samples could not be used for the re-identification analysis because too few reads remained after filtering, hence the fewer dots shown across host filtration methods. Full description on the calculation of P values can be found in the Methods.",
+            "section_image": [
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+            ]
+        },
+        {
+            "section_name": "Discussion",
+            "section_text": "While host filtration and host depletion are important steps of careful mNGS analyses, only host filtration has relevant use cases for thousands of already-generated human datasets, especially those initially generated without the original intent of microbial analysis. Through processing whole genome sequencing (WGS) data from metastatic tumor samples, we incidentally identified the impact of insufficient host filtration through artifactual sex biases that human DNA introduced in downstream analyses. These biases had larger impacts on abundance-based metrics and can be mitigated by using qualitative approaches. Nonetheless, such biases introduced by insufficient host filtration likely persist for other metagenomic sequencing datasets, particularly those generated prior to the release of the T2T-CHM13v2.0 reference genome containing the full Y chromosome. Thus, it remains prudent to continue developing and refining techniques to easily scrub human DNA from pre-existing and future mNGS datasets.\n\nBeyond biasing microbial data, an additional consequence of insufficient host filtration in human studies is the retention of personally-identifying human DNA sequences in mNGS datasets. Many mNGS data generation and usage agreements dictate that metagenomic applications of whole genome sequencing will be used to generate and analyze microbial DNA, not human DNA: this is particularly relevant in clinical environments where patients may consent to microbial analysis via mNGS of samples derived from a human host but may not consent to their host genomic content analysis31. Moreover, patients are often unaware that untargeted sequencing approaches intended for microbial study will also sequence some amount of host DNA, and failure to comprehensively remove host DNA from metagenomic sequencing data may violate data usage and patient consent agreements by inadvertently enabling deanonymization and reidentification. This is particularly important when depositing microbiome datasets in public repositories, which typically do not require restricted/controlled access8. Even when efforts are devoted to preventing re-identification of individuals (for example, by only sharing summary-level data), others have shown that re-identification of participants from specific GWAS is still possible, or even in DNA mixtures where an individual contributes less than 0.1% of the total genomic material32. Therefore, as sequencing methods continue to provide higher mNGS throughput, it is imperative that computationally efficient techniques countering their unintended privacy consequences are made available.\n\nTo address this need, we have proposed an efficient, customizable, and effective host filtering pipeline that accurately separates human and microbial reads from mNGS datasets, with demonstrated applications across real samples of varying biomass. We recommend using Method 1, which is time efficient (Fig.\u00a02b) while leaving a majority of the microbial reads (Fig.\u00a03b), but removes enough human reads to disrupt subject reidentification. In cases where the maximum amount of human reads must be removed, even at the cost of losing microbial reads, then Method 2 would be more appropriate. Finally, if a user wants to maximize the remaining microbial reads, then Method 3 would be best. Given the scalability of Movi27, we anticipate that additional human references can be easily incorporated as they are released without major impacts on runtime, making the approach future proof.\n\nTomofuji et al. describe the process of performing patient reidentification using relatively few human DNA sequences retained in fecal sequencing data by combining paired genotype data8. Using their data, we demonstrated how our methods can prevent patient reidentification, thereby protecting patient privacy. As interest in metagenomic studies of human biological processes grows, increased emphasis should be placed on applying end-to-end privacy-protecting methodologies, inclusive of computational workflows. Sequencing human DNA is a byproduct of mNGS, even in fecal samples, and may persist despite molecular host depletion protocols. Thus, applying computational host filtration techniques remains imperative when performing (or uploading) human-associated microbiome studies.\n\nAll host filtration methods remain imperfect due to the under-explored genomic diversity of the human population and the concomitant lack of complete and individualized human reference genomes. Our proposed workflows incorporate more genetic diversity than any computational host filtration approach to date while remaining computationally efficient. Since existing reference databases do not account for the complete set of human genetic variation or non-germline sequence variants frequently found in cancer and other diseases, read-based host filtration approaches may leave a small number of human reads in the data while performing a negative selection for human DNA.\n\nAlthough removing human reads is an important part of downstream microbial analysis data, this is just one part of the puzzle in properly detecting the true microbial profiles of low biomass human samples. Many other factors, including various ways the sample may become contaminated from the collection process through sequencing, require other tools and strategies beyond our host filtration pipeline to be accounted for.\n\nIf researchers desire extra protections to ensure no human reads are inadvertently mapped, a positive selection for microbial reads can be performed using reference databases confirmed to be fully microbial. We conducted this type of analysis using a microbial database scrubbed of human reads derived from Sepich-Poore et al.7 and similarly noted a resolution of the artifactual sex-difference effect with the cleaned database alone. Additionally, researchers may choose to use a broader range of microbial reference databases beyond RefSeq, which may have more low-complexity regions masked, potentially eliminating some of the mismapping issues leading to sex differences. Additionally, we provide a list to the community of \u2018false positive taxa\u2019 we identified with the addition of T2T-CHM-13v2.0 filtering across common microbial databases (RefSeq release 200 and 21033, Web of Life version 223, Genome Taxonomy Database release 22034) as a resource to the community (Supplementary Data\u00a07). However, we caution that cleaning microbial reference databases or using alternative microbial databases in principle cannot address the retention of human reads in metagenomics datasets due to bias from incomplete representation of variation in the human genome.\n\nNevertheless, this work highlights the importance of and provides appropriate tools for thorough host filtration to mitigate false alignments and erroneous conclusions. The methods here provide an important starting point for conducting host filtration using state-of-the-art methods while being readily expandable for future improvements and reference databases.",
+            "section_image": []
+        },
+        {
+            "section_name": "Methods",
+            "section_text": "All participants from which fecal and skin samples were derived provided informed consent, and protocols were approved by the Institutional Review Boards at the University of Wisconsin-Madison (#2015-0030) and the University of California San Diego (#200844) respectively.\n\nHuman reference genomes GRCh38.p7, GRCh38.p14, and T2T-CHM-13v2.0 were retrieved from NCBI (Supplementary Data\u00a01). All 94 currently published reference assemblies from the Human Pangenome Reference Consortium website. More information on downloading each reference can be found in Supplementary Data\u00a01.\n\nThe Hartwig Medical Foundation15 (HMF) performed DNA sequencing of tumor tissue (n\u2009=\u20099973 samples) and mapped reads to reference genome GRCh37.p13 using BWA-MEM35 (v. 0.7.x) to create BAM files. Pre-aligned BAM files were downloaded from HMF in October 2021, and unmapped reads were extracted from the BAM files. The files were then filtered through fastp36 (v. 0.20.1) with a length cutoff of 45\u2009bp minimum and default adapter removal, then using minimap2 (v. 2.17) mapped to either GRCh38.p737 or GRCh38.p7\u2009+\u2009T2T-CHM13v2.016 human databases. Finally, samtools38 (v. 1.11) was used to extract reads which did not align to the human reference. The full command used is: fastp -l 45 -i $R1 -I $R2 -w 16 --stdout | minimap2 -ax sr -t 16 $human_database - -a | samtools fastq -@ 16 -f 12 -F 256 -1 $R1_out -2 $R2_out. Following host filtration, reads were aligned to the RefSeq release 200 database using the SHOGUN39 protocol with Woltka23 in the Qiita40 platform. RefSeq33 release 200 includes the NCBI representative and reference microbial genomes corresponding to release date 2020-05-14. Dimensionality reduction of the corresponding BIOM table41 was then performed through Gemelli\u2019s RPCA function (v. 0.0.6)18 to create a distance matrix on which PERMANOVA42 differences across sex and a Robust Aitchison PCA plot were created, both using QIIME243 (v. 2022.2.0).\n\nFor all three methods, raw FASTQ files are quality filtered using fastp36 (v. 0.23.4) with a length cutoff of 45\u2009bp minimum and subject to adapter removal using the full list of adapters hardcoded in fastp (as opposed to relying on fastp\u2019s automated detection which is limited to a subset of sequences).\n\nFor host filtration methods that utilize sequence alignment, we generated individual minimap225 (v. 2.26) indexes using default parameters for each individual human reference genomes. Sequence alignment was then performed with parameters: -2 -ax sr. To host filter, sequences were aligned sequentially to each genome discarding reads which mapped. We used samtools38 (v. 1.19) to reverse unmapped sequences from SAM back into FASTQ format (with arguments -f 12 -F 256 -N for paired-end data and -f 4 -F 256 for single-end data) after each consecutive alignment. Finally, for paired-end data we used fastq-pair44 (v. 0.4) to sort and match filtered read pairs into individual files.\n\nFor host filtration methods that utilize indexing, we generated a full index over all 94 published pangenome references from HPRC release 2023, along with GRCh38.p14 and T2T-CHM-13v2.0 using Movi27 (unversioned; git commit hash 76d5a6da1ec0aeb0121b5ac7c59b295936e23cc1). Movi generates pseudo-matching lengths (PMLs) which are approximations of sequence similarity between the query and the index. We used movi-default to generate PML distributions for each queried read and explored several different mathematical transformations of the resulting PML distributions into singular per-read scores. The PML distributions produced by Movi roughly approximate matching statistics previously validated for sequence classification tasks27. Thus, we reasoned that reads with larger PML distribution values had higher similarity to human genomic regions within the index than those with lower values. We tested several transformations of PML distributions into summative scores and devised approach-specific threshold values based on a theoretical human read of length 150 with a singular contiguous matching run of length 31. First, we utilized the maximum PML score within the distribution as the test value and thus computed the threshold for the maximum approach as 31. Next, we calculated the average PML score within the distribution as the test value and thus computed the threshold for the average approach as 3.306. To maximally distinguish PML distributions that feature discontinuous runs of matching nucleotides, we devised a custom metric that magnifies the summative score for read distributions with long stretches of matches above a minimum run-length threshold (denoted \\(w\\)). In concordance with the previous maximum and average metrics, we computed the threshold for the custom approach as 0.175 with a minimum run-length value of 5. Through experimental validation on mixed human/microbe datasets, we found that our custom metric had the best discriminative performance. To verify this approach, we ran a grid search over various thresholds for the custom metric (thresholds: 0.145 to 0.200 by increments of 0.005; minimum run-length: 2 to 12 by increments of 1) on our simulated data for which we had labeled ground truth (see \u201cSimulated data\u201d). The results showed strong recall for our use cases at the default threshold, but we acknowledge that some users may prefer higher stringency on human DNA removal even at the cost of inadvertent microbial DNA removal. Thus, we implemented both the metric (\u201cmaximum\u201d, \u201caverage\u201d, or \u201ccustom\u201d) and the numerical threshold as configurable options in our host filtration pipeline to meet the needs of all users. The equation for the custom metric is denoted below:\n\nWe benchmarked three methods to compare different combinations of the aforementioned alignment-based and indexing-based host filtration approaches. We use minimap2 for alignment based on its support for this application in prior work11.\n\nStep i (filled circle): aligned reads to human reference GRCh38.p14 with minimap2 (v. 2.26), then used samtools (v. 1.19) to extract reads that did not align to the human reference. Step ii (filled square): aligned remaining reads from step i to human reference T2T-CHM13v2.0 with minimap2 (v. 2.26), then used samtools (v. 1.19) to extract reads that did not align to the human reference. Step iii (star): matched remaining reads from step ii to an aggregated human reference set consisting of GRCh38.p14, T2T-CHM13v2.0, and the 94 HPRC pangenomes using indexing-based filtration with Movi, as described above.\n\nStep i (filled star): aligned reads sequentially to GRCh38.p14, T2T-CHM13v2.0, and the 94 HPRC pangenomes with minimap2 (v. 2.26), then used samtools (v. 1.19) to extract reads that did not align with each iteration. Step ii (star): matched remaining reads from step i to an aggregated human reference set consisting of GRCh38.p14, T2T-CHM13v2.0, and the 94 HPRC pangenomes using indexing-based filtration with Movi, as described above.\n\nStep i (star): matched reads to an aggregated human reference set consisting of GRCh38.p14, T2T-CHM13v2.0, and the 94 HPRC pangenomes using indexing-based filtration with Movi, as described above.\n\nAlthough all Methods use GRCh38.p14, T2T-CHM13v2.0, and HPRC as part of the Movi indexing approach, we want to emphasize that only Method 2 also uses them for minimap2-based alignment. Although minimap2 and Movi are both useful tools for linking short reads to reference genomes, their underlying algorithms are distinct and thus the two tools produce differing results (Fig.\u00a03) and runtimes (Fig.\u00a02b). Minimap2 uses a traditional seed-chain-align approach to identify exact matches to a reference, while Movi uses the Move structure introduced by Nishimoto and Tabei in 2021 to compute pseudo-matching lengths to a reference45. Combining minimap2 and Movi utilizes the respective strengths of each of their implementations, and appears to result in the highest number of reads removed.\n\nWe calculated the number of microbial, bacterial, eukaryota, viral, and archaea genome frequencies listed in Supplementary Data\u00a06 using the SHOGUN39 protocol via the Qiita40 platform with the RefSeq release 210 (2022-01-01) database. We listed forward and reverse read counts separately in Supplementary Data\u00a06 to directly report the number of reads mapped to microbial taxa. Read counts listed throughout all other portions of the manuscript count forward and reverse reads as a single count. Additionally, in the case of the Tissue Samples from Various Metastatic Cancer, the \u2018Before host filtration number\u2019 is following GRCh38.p7 host filtration and not the purely raw reads as in the other cases.\n\nAs a resource to the community, we calculate microbial alignments from reads retained following GRCh38.p14 filtration, but removed with the addition of T2T-CHM-13v2.0 filtration. We do this by tabulating the additional reads removed from the aforementioned 100 colorectal tissue tumor samples from HMF when incorporating T2T-CHM-13v2.0 for host filtration (Method 1 step ii) referred to as \u201cT2T-filtered\u201d reads above. We aligned these removed reads to a diverse set of microbial reference databases \u2013 RefSeq release 20033, RefSeq release 21033, Web of Life release 223, and GTDB release 22022 \u2013 and reported the resulting spurious microbial alignments (Supplementary Data\u00a07).\n\nWe used two-sided Wilcoxon signed-rank tests using SciPy46 (v. 1.8.0) to assess differences in medians between reads retained or removed across differing methods. Because this test involves ranking the absolute differences between pairs, and since reads retained or reads removed tend to either decrease or increase respectively across pairs, the resulting test statistic reported is 0 for all comparisons. For all boxplots, throughout the figures, the box represents the interquartile range (IQR), with the centerline being the median and the top and bottom of the box representing Q1 and Q3. Boxplots were generated using matplotlib47 (v. 3.8.0), and the whiskers of the plot were left at matplotlib defaults, making them +/\u22121.5 from the IQR. Outliers were removed from the boxplots since a scatter plot with all dots was overlaid. To facilitate computationally efficient benchmarking of the host filtration methods, we analyzed a subset of n\u2009=\u2009100 samples from the HMF dataset, and n\u2009=\u200950 samples from the Alzheimer\u2019s disease fecal dataset while using complete datasets for all other sample types. All p values are rounded two decimal places, and all test statistics are reported with three significant figures unless otherwise specified.\n\nData was simulated using ART Illumina46,48 (v. 2.5.8). Human reads were simulated using HPRC genomes, and microbial reads were simulated from FDA-ARGOS28. Supplementary Data\u00a01 further describes simulated dataset accession.\n\nFor the re-identification analysis, we utilized human reads extracted from mNGS data and imputed SNP array data in the previous study8. The main steps in the human read extraction were as follows: (i) trimming of low-quality bases, (ii) identification of candidate human reads, (iii) removal of duplicated reads, and (iv) removal of the potential bacterial reads. We trimmed the raw reads to clip Illumina adapters and cut off low-quality bases using the Trimmomatic49 (v. 0.39; parameters: ILLUMINACLIP:TruSeq3-PE-2.fa:2:30:10:8:true TRAILING:20 MINLEN:60). We discarded reads less than 60\u2009bp in length after trimming. Then, we mapped the trimmed reads to the human reference genome (GRCh37, human_g1k_v37_decoy) using bowtie250 (v. 2.3.5.1) with the \u2018\u2014no-discordant\u2019 option and retained only the properly mapped reads. Next, we performed duplicate removal by Picard MarkDuplicates (v. 2.22.8) with \u2018VALIDATION_STRINGENCY\u2009=\u2009LENIENT\u2019 option. Finally, we mapped the duplicate removed reads to the bacterial reference genome set constructed in Kishikawa et al.51. This reference was composed of the 7881 genomes including those derived from Nishijima et al.52 and those identified in the cultivated human gut bacteria projects53,54,55. We kept only reads of which both paired ends failed to align. The resulting reads were defined as human reads and used in the subsequent analyses. Then, extracted human reads were subjected to the host filtration methods, namely the first steps two steps of Method 1: GRCh38.p14 alignment, and GRCh38.p14/T2T-CHM13v2.0 alignment, along with the first step of Method 2: GRCh38.p14/T2T-CHM13v2.0/HPRC alignment.\n\nFor the re-identification analysis, we utilized likelihood score-based method introduced in the previous study8. We calculated the likelihood that each sample in the genotype dataset produced the observed human reads in the fecal samples from two input data; (i) human reads in the gut-derived mNGS data which were mapped to the human reference genome and (ii) genotype dataset of the multiple samples. We extracted the SNP sites which were covered by at least a read and included in the reference panel by \u2018bcftools mpileup\u201956 with the \u2018-T\u2019 option. To get independent SNP sites, we applied clumping to the list of the SNPs which were covered by at least a read. We used \u2018\u2013indep-pairwise 100 30 0.1\u2019 option in PLINK for clumping at Rsq\u2009=\u20090.1. Then, we calculated the likelihood according to the model proposed in Li et al.57. Suppose an SNP site \\(i\\) was covered by \\({n}_{i}\\) reads in the gut-derived mNGS data, \\({k}_{i}\\) reads were from the reference allele, and \\({n}_{i}-{k}_{i}\\) reads were from the alternative allele. bcftools56 (v. 1.10.2) was used to calculate the read coverage with \u2018-q 40 -Q 20\u2019 options. The error probability of the read bases was \\(\\varepsilon\\) and error independency was assumed. In this study, \\(\\varepsilon\\) was set at 1\u2009\u00d7\u200910\u22126 following the assumption in Li et al.57. At the SNP site \\(i\\), the number of the alternative allele of an individual \\(j\\) (\\({g}_{i,j}\\)) could be 0 (Ref / Ref), 1 (Ref / Alt), or 2 (Alt / Alt). Then, the likelihood that the sample with a \\({g}_{i}\\) alternative alleles at SNP site \\(i\\) produced the observed human reads in the gut-derived mNGS data was expressed as\n\nWhen the clumping procedure retained \\(N\\) independent SNP sites, a log-transformed likelihood (likelihood score; \\({LS}\\)) that a genotype data produced the observed human reads in the gut-derived mNGS data was expressed as\n\nNext, we drew the background distribution of the likelihood score from (i) human reads in the gut-derived mNGS data which were mapped to the human reference genome, and (ii) allele frequency data for the SNP sites used for calculating the likelihood score. In this study, Japanese subjects in the combined reference panel of 1KG Project Phase 358 version 5 genotype (n\u2009=\u2009104) and Japanese WGS data (n\u2009=\u20091037) were used to calculate the allele frequency59. When an alternative allele frequency at SNP site \\(i\\) was \\({p}_{i}\\) and the number of the alternative allele was \\({g}_{i,{pop}}\\) (=0, 1, or 2), theoretical genotype frequencies at SNP site \\(i\\) were expressed as\n\nThen, the expected log transformed likelihood that a genotype data randomly drawn from the specified population produced the observed human reads in the mNGS data was expressed as\n\nGiven that SNP sites were independent, the variance of the likelihood score in a specific population was expressed as\n\nUsing \\(E\\left({{LS}}_{{pop}}\\right)\\) and \\(V\\left({{LS}}_{{pop}}\\right)\\), we calculated the standardized likelihood score of the individual \\(j\\) as \\(\\frac{({{LS}}_{j}-E\\left({{LS}}_{{pop}}\\right))}{\\sqrt{V\\left({{LS}}_{{pop}}\\right)}}\\). We transformed standardized likelihood scores to P values based on the normal distribution. We identified the pair of the gut-derived mNGS and genotype data (imputed SNP array data was used in this study) derived from the same individuals based on the P values.\n\nFurther information on research design is available in the\u00a0Nature Portfolio Reporting Summary linked to this article.",
+            "section_image": []
+        },
+        {
+            "section_name": "Data availability",
+            "section_text": "The raw HMF data used in this study is under the purview of the Hartwig Medical Foundation and contains patient-protected information that cannot be shared publicly (see https://hartwigmedical.github.io/documentation/data-access-request-methods.html for data access guidelines for access request details). The FDA-ARGOS database used in this study is publicly available from the official website (https://argos.igs.umaryland.edu) as well as NCBI BioProject PRJNA231221 (https://www.ncbi.nlm.nih.gov/bioproject/231221). The human exome data used in this study is derived from the IGSR phase 3 data, which is available via the official EMBL-EBI portal (https://www.internationalgenome.org/data). The atopic dermatitis skin sample data and the Alzheimer\u2019s disease fecal sample data used in this study are available from ENA under accession PRJEB83637. The fecal sample data from Tomofuji et al. are publicly available from JGA under accessions JGAS000260, JGAS000316, and JGAS000531 (https://www.ddbj.nig.ac.jp/jga/index-e.html). The blood sample data from Tomofuji et al. are publicly available from EGA under accession EGAS00001007027.",
+            "section_image": []
+        },
+        {
+            "section_name": "Code availability",
+            "section_text": "Code and instructions to implement the methods of host filtration can be found on GitHub (https://github.com/cguccione/human_host_filtration). Code used to create simulated data, run host filtration metrics and create figures can be found on GitHub (https://github.com/cguccione/host-filtration-notebooks).",
+            "section_image": []
+        },
+        {
+            "section_name": "References",
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+            "section_image": []
+        },
+        {
+            "section_name": "Acknowledgements",
+            "section_text": "This work was supported by AGA Research Foundation (AGA Research Scholar Award AGA2022-13-05) and NIH grant R01 CA270235 to K.C. The study was supported in part by the NIDDK-funded San Diego Digestive Diseases Research Center (P30 DK120515) to K.C. Additionally this work was supported by NIH grants (R01 CA241728, P30 CA023100, NIH/NIGMS T32GM007198, NIH Pioneer DP1AT010885), the National Cancer Institute (NCI U24CA248454), and CDC award 75D301-22-C-14717 to R.K. The study was supported in part by R21HG013433 to B.L. This study was supported in part by JSPS KAKENHI (22H00476), and AMED (JP24km0405217, JP24ek0109594, JP24ek0410113, JP24kk0305022, JP243fa627002, JP243fa627010, JP243fa627011, JP24zf0127008, JP24tm0524002, JP24wm0625504, JP24gm1810011), JST Moonshot R&D (JPMJMS2021, JPMJMS2024), to Y.O., with additional support from Takeda Science Foundation, Ono Pharmaceutical Foundation for Oncology, Immunology, and Neurology, Bioinformatics Initiative of Osaka University Graduate School of Medicine, Institute for Open and Transdisciplinary Research Initiatives, Center for Infectious Disease Education and Research (CiDER), and Center for Advanced Modality and DDS (CAMaD), Osaka University. This project was enabled in part by the Alzheimer\u2019s Gut Microbiome Project (AGMP), supported by the National Institute on Aging grants: 1U19AG063744 and 3U19AG063744-04S1, awarded to Dr. Kaddurah-Daouk at Duke University in partnership with multiple academic institutions. As such, the investigators within the AGMP not listed in this publication\u2019s authors\u2019 list, provided analysis-ready data, but did not participate in designing the study, conducting the analyses or writing of this manuscript. A listing of AGMP Investigators can be found at https://alzheimergut.org/meet-the-team/. A complete listing of the AD Metabolomics Consortium (ADMC) investigators can be found at: https://sites.duke.edu/adnimetab/team/. We thank Cameron Martino for his support and advice throughout this project.",
+            "section_image": []
+        },
+        {
+            "section_name": "Author information",
+            "section_text": "These authors contributed equally: Caitlin Guccione, Lucas Patel.\n\nThese authors jointly supervised this work: Kit Curtius, Rob Knight.\n\nDivision of Biomedical Informatics, Department of Medicine, University of California San Diego, La Jolla, CA, USA\n\nCaitlin Guccione\u00a0&\u00a0Kit Curtius\n\nBioinformatics and Systems Biology Program, University of California San Diego, La Jolla, CA, USA\n\nCaitlin Guccione\u00a0&\u00a0Lucas Patel\n\nDepartment of Pediatrics, University of California San Diego, La Jolla, CA, USA\n\nCaitlin Guccione,\u00a0Lucas Patel,\u00a0Daniel McDonald,\u00a0Antonio Gonzalez,\u00a0Yang Chen,\u00a0Amanda Hazel Dilmore\u00a0&\u00a0Rob Knight\n\nMedical Scientist Training Program, University of California, San Diego, La Jolla, CA, USA\n\nLucas Patel\n\nDepartment of Genome Informatics, Graduate School of Medicine, the University of Tokyo, Tokyo, 113-8654, Japan\n\nYoshihiko Tomofuji,\u00a0Kyuto Sonehara\u00a0&\u00a0Yukinori Okada\n\nDepartment of Statistical Genetics, Osaka University Graduate School of Medicine, Suita, 565-0871, Japan\n\nYoshihiko Tomofuji,\u00a0Kyuto Sonehara\u00a0&\u00a0Yukinori Okada\n\nLaboratory for Systems Genetics, RIKEN Center for Integrative Medical Sciences, Yokohama, 230-0045, Japan\n\nYoshihiko Tomofuji,\u00a0Kyuto Sonehara\u00a0&\u00a0Yukinori Okada\n\nShu Chien-Gene Lay Department of Bioengineering, University of California San Diego, La Jolla, CA, USA\n\nGregory D. Sepich-Poore\u00a0&\u00a0Rob Knight\n\nFeinberg School of Medicine, Northwestern University, Chicago, IL, USA\n\nGregory D. Sepich-Poore\n\nDepartment of Computer Science, Johns Hopkins University, Baltimore, MD, USA\n\nMohsen Zakeri\u00a0&\u00a0Ben Langmead\n\nBiomedical Sciences Graduate Program, University of California San Diego, La Jolla, CA, USA\n\nYang Chen\u00a0&\u00a0Amanda Hazel Dilmore\n\nHal\u0131c\u0131o\u011flu Data Science Institute, University of California San Diego, La Jolla, CA, USA\n\nNeil Damle\u00a0&\u00a0Rob Knight\n\nDepartment of Cognitive Science, University of California San Diego, La Jolla, CA, USA\n\nNeil Damle\n\nWeill Institute for Neurosciences. Department of Neurology. University of California, San Francisco (UCSF), San Francisco, CA, USA\n\nSergio E. Baranzini\n\nDepartment of Dermatology, University of California San Diego, La Jolla, CA, USA\n\nYang Chen,\u00a0George Hightower,\u00a0Teruaki Nakatsuji\u00a0&\u00a0Richard L. Gallo\n\nRady Children\u2019s Hospital, San Diego, CA, USA\n\nGeorge Hightower\n\nCenter for Microbiome Innovation, University of California San Diego, La Jolla, CA, USA\n\nRichard L. Gallo\u00a0&\u00a0Rob Knight\n\nLaboratory of Statistical Immunology, Immunology Frontier Research Center (WPI-IFReC), Osaka University, Suita, 565-0871, Japan\n\nYukinori Okada\n\nPremium Research Institute for Human Metaverse Medicine (WPI-PRIMe), Osaka University, Suita, 565-0871, Japan\n\nYukinori Okada\n\nVA San Diego Healthcare System, San Diego, CA, USA\n\nKit Curtius\n\nMoores Cancer Center, University of California San Diego, La Jolla, CA, USA\n\nKit Curtius\n\nDepartment of Computer Science and Engineering, University of California San Diego, La Jolla, CA, USA\n\nRob Knight\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nC.G. and L.P. conceived and designed the study. C.G., L.P., A.G., Y.C., A.H.D., G.H., T.N., and R.L.G. collected and processed the data. C.G., L.P., D.M., and N.D. performed the primary analyses. Y.T., K.S., and Y.O. performed the re-identification analyses. M.Z. and B.L. conceptualized, implemented, and supported application of the pangenome index. C.G. and L.P. performed the statistical analysis. D.M., G.D.S.P., and S.E.B., aided in interpreting the results and drafting the manuscript. C.G. and L.P. wrote the manuscript with input from all authors. K.C. and R.K. supervised the project. All authors reviewed and approved the final manuscript.\n\nCorrespondence to\n                Kit Curtius or Rob Knight.",
+            "section_image": []
+        },
+        {
+            "section_name": "Ethics declarations",
+            "section_text": "D.M. is a consultant for BiomeSense, Inc., has equity and receives income. The terms of these arrangements have been reviewed and approved by the University of California, San Diego in accordance with its conflict of interest policies. G.H. is the recipient of the Robert A. Winn Diversity in Clinical Trials: Career Development Award, which is partly funded by Bristol-Meyer Squibb Foundation. B.L. is the owner of InOrder Labs LLC. K.C. has research grant support from Phathom Pharmaceuticals. R.K. is a scientific advisory board member, and consultant for BiomeSense, Inc., has equity and receives income. He is a scientific advisory board member and has equity in GenCirq. He is a consultant for DayTwo, and receives income. He has equity in and acts as a consultant for Cybele. He is a co-founder of Biota, Inc., and has equity. He is a cofounder of Micronoma, and has equity and is a scientific advisory board member. The terms of these arrangements have been reviewed and approved by the University of California, San Diego in accordance with its conflict of interest policies. The remaining authors declare no competing interests.",
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+            "section_name": "About this article",
+            "section_text": "Guccione, C., Patel, L., Tomofuji, Y. et al. Incomplete human reference genomes can drive false sex biases and expose patient-identifying information in metagenomic data.\n                    Nat Commun 16, 825 (2025). https://doi.org/10.1038/s41467-025-56077-5\n\nDownload citation\n\nReceived: 18 October 2024\n\nAccepted: 07 January 2025\n\nPublished: 18 January 2025\n\nVersion of record: 18 January 2025\n\nDOI: https://doi.org/10.1038/s41467-025-56077-5\n\nAnyone you share the following link with will be able to read this content:\n\nSorry, a shareable link is not currently available for this article.\n\n\n\n\n                            Provided by the Springer Nature SharedIt content-sharing initiative\n                        ",
+            "section_image": [
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+            ]
+        },
+        {
+            "section_name": "This article is cited by",
+            "section_text": "Nature Microbiology (2025)",
+            "section_image": []
+        }
+    ]
+}

25c408184b362d88e4b325539cba6266ed5a074284a0c4b361fcfb1504c30517/metadata.json

@@ -0,0 +1,148 @@
+{
+    "title": "Non-Amontons frictional behaviors of grain boundaries at layered material interfaces",
+    "pre_title": "Non-Amontons Frictional Behaviors of Grain Boundaries at Layered Material Interfaces",
+    "journal": "Nature Communications",
+    "published": "02 November 2024",
+    "supplementary_0": [
+        {
+            "label": "Supplementary Information",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-024-53581-y/MediaObjects/41467_2024_53581_MOESM1_ESM.pdf"
+        },
+        {
+            "label": "Transparent Peer Review file",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-024-53581-y/MediaObjects/41467_2024_53581_MOESM2_ESM.pdf"
+        },
+        {
+            "label": "Description of Additional Supplementary Files",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-024-53581-y/MediaObjects/41467_2024_53581_MOESM3_ESM.pdf"
+        },
+        {
+            "label": "Supplementary Movie 1",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-024-53581-y/MediaObjects/41467_2024_53581_MOESM4_ESM.mp4"
+        },
+        {
+            "label": "Supplementary Movie 2",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-024-53581-y/MediaObjects/41467_2024_53581_MOESM5_ESM.mp4"
+        },
+        {
+            "label": "Supplementary Movie 3",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-024-53581-y/MediaObjects/41467_2024_53581_MOESM6_ESM.mp4"
+        }
+    ],
+    "supplementary_1": [
+        {
+            "label": "Source data",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-024-53581-y/MediaObjects/41467_2024_53581_MOESM7_ESM.xlsx"
+        }
+    ],
+    "supplementary_2": NaN,
+    "source_data": [
+        "https://doi.org/10.5281/zenodo.13768451"
+    ],
+    "code": [],
+    "subject": [
+        "Mechanical and structural properties and devices",
+        "Two-dimensional materials"
+    ],
+    "license": "http://creativecommons.org/licenses/by/4.0/",
+    "preprint_pdf": "https://www.researchsquare.com/article/rs-3436204/v1.pdf?c=1730639194000",
+    "research_square_link": "https://www.researchsquare.com//article/rs-3436204/v1",
+    "nature_pdf": "https://www.nature.com/articles/s41467-024-53581-y.pdf",
+    "preprint_posted": "19 Nov, 2023",
+    "research_square_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Against conventional wisdom, corrugated grain boundaries in polycrystalline graphene, grown on Pt(111) surfaces, are shown to exhibit negative friction coefficients and non-monotonic velocity dependence. Using combined experimental, simulation, and modeling efforts, the underlying energy dissipation mechanism is found to be dominated by dynamic buckling of grain boundary dislocation protrusions. The revealed mechanism is expected to appear in a wide range of polycrystalline two-dimensional material interfaces, thus supporting the design of large-scale dry superlubric contacts.Physical sciences/Materials science/Nanoscale materials/Graphene/Mechanical and structural properties and devicesPhysical sciences/Physics/Condensed-matter physics/Surfaces, interfaces and thin films",
+            "section_image": []
+        },
+        {
+            "section_name": "Additional Declarations",
+            "section_text": "There is NO Competing Interest.",
+            "section_image": []
+        },
+        {
+            "section_name": "Supplementary Files",
+            "section_text": "SupplementaryInformationGBfriction20230921.pdfMovieDescription20230921.pdfSupplymetaryMovie1.mp4Movie 1SupplymetaryMovie2.mp4Movie 2SupplymetaryMovie3.mp4Movie 3",
+            "section_image": []
+        }
+    ],
+    "nature_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Against conventional wisdom, corrugated grain boundaries in polycrystalline graphene, grown on Pt(111) surfaces, are shown to exhibit negative friction coefficients and non-monotonic velocity dependence. Using combined experimental, simulation, and modeling efforts, the underlying energy dissipation mechanism is found to be dominated by dynamic buckling of grain boundary dislocation protrusions. The revealed mechanism is expected to appear in a wide range of polycrystalline two-dimensional material interfaces, thus supporting the design of large-scale dry superlubric contacts.",
+            "section_image": []
+        },
+        {
+            "section_name": "Introduction",
+            "section_text": "Structural superlubricity (SSL), the fascinating phenomenon of ultra-low interfacial friction, originating from effective lateral force cancellation at crystalline interfaces, has evolved over the past two decades from being a purely theoretical concept to the verge of becoming of practical use1. Among various candidates for SSL realization, two-dimensional (2D) material interfaces demonstrate extraordinary potential, benefitting from unique weak van der Waals interlayer interactions accompanied by strong covalent intralayer networks inherent to 2D materials2. Since the 2004 milestone experimental verification of SSL in twisted nanoscale graphitic contacts3, extensive scientific exploration of the scaling-up of SSL has been triggered. Notably, recent experimental studies have pushed the limit up to the micrometer-scale, based on single-crystal 2D material interfaces4,5,6. However, volume preparation of large-scale high-quality single-crystal 2D samples remains a challenging task under standard laboratory conditions7,8. At increasing length-scales, 2D materials, often synthesized via chemical vapor deposition (CVD) or pyrolysis, typically exhibit a polycrystalline structure consisting of misoriented crystal surface patches separated by grain boundaries (GBs)9,10,11,12,13,14,15. The former enhances interfacial incommensurability favoring SSL16, whereas the latter may introduce additional energy dissipation channels that enhance friction, therefore challenging the scaling-up of SSL towards the macroscale.\n\nGBs are typically formed through a chain of dislocations (e.g., pentagon-heptagon pairs in graphene) at the borderline of contacting misoriented grains. For 2D materials, the introduction of GBs leads to substantial modifications in their structural11,13, mechanical17,18,19, chemical20, thermal transport21,22,23, electrical24,25,26,27,28,29,30,31, and ferromagnetic properties32. Recent theoretical and computational studies on the tribological properties of GBs in 2D layered interfaces have predicted unique frictional mechanisms involving a shear-induced GB protrusion (un)buckling mechanism that may lead to negative friction coefficients (NFCs)33,34. Furthermore, intricate moir\u00e9 superstructure stick-slip dynamics and scattering over elongated GBs was predicted to enhance friction at high normal loads35. Going beyond single GB considerations, enhanced interfacial friction at multi-grain contacts was also predicted36,37,38. In accordance, recent experimental evidence indicate the enhancement of both van der Waals39 and Coulombic40 friction over 2D material GBs. This calls for an experimental investigation of the microscopic mechanisms underlying GB friction aiming to identify routes to control, manipulate, and eliminate it.\n\nIn this work, we investigate the mechanisms of 2D GB friction via detailed atomic force microscopy (AFM) experiments, rationalized by fully atomistic simulations and phenomenological modeling. Considering the prototypical polycrystalline graphene (PolyGr) system, we demonstrate that corrugated GBs present NFCs and non-monotonic velocity dependence of friction. Conversely, flat GBs are shown to exhibit linear friction increase with normal load, obeying Amontons\u2019 law, as well as logarithmic velocity dependence, similar to single-crystalline surfaces. Our atomistic simulations indicate that dynamic snap-through GB protrusion (un)buckling mechanism plays a key role, allowing the construction of a phenomenological two-state model that fully rationalizes the experimental results.",
+            "section_image": []
+        },
+        {
+            "section_name": "Results and discussion",
+            "section_text": "To perform the experiments, single layered PolyGr films were grown on Pt(111) surfaces by CVD under ultrahigh vacuum (UHV) conditions. Non-contact (NC) and contact AFM measurements were used to perform in-situ investigations under UHV conditions (base pressure\u2009\u2264\u20091\u2009\u00d7\u200910\u221210 mbar) of the dissipative frictional behavior of elongated GBs formed between adjacent PolyGr grains of different lattice orientations (for a schematic representation see Fig.\u00a01a and for further experimental details see \u201cMethods\u201d and Supplementary Notes\u00a01-2).\n\na Schematic diagram of the experimental set-up to characterize PolyGr grain boundaries (GBs). b Topography and (c) torsional frequency shift \\(\\left(\\Delta {f}_{{{{\\rm{TR}}}}}\\right)\\) maps of a GB of misfit angle \\({\\theta }_{{{{\\rm{GB}}}}}=21.43\\pm 0.66^\\circ\\) over a scan area of 10\u00d710 nm2 obtained at the second flexural frequency shift of \\(-340\\,{{{\\rm{Hz}}}}\\). d-e Vertical and torsional energy dissipation maps corresponding to panels b and c, respectively. The inset of panel e shows a cross-section of the energy dissipation map along the scan-line marked by the dashed blue line. In these measurements, the amplitudes of the second flexural and the torsional modes were \\({A}_{{2}^{{{{\\rm{nd}}}}}}=600\\,{{{\\rm{pm}}}}\\) and \\({A}_{{{{\\rm{TR}}}}}=80\\,{{{\\rm{pm}}}}\\), respectively.\n\nThe in-situ bimodal NC-AFM measurements provide the surface topography and the atomically resolved structure of the grown PolyGr. A typical corrugated GB of misfit angle (i.e., the relative lattice misorientation between two neighboring grains) of \\({\\theta }_{{{{\\rm{GB}}}}}=21.43\\pm 0.66^\\circ\\) is shown in Fig.\u00a01b, c. The misfit angle is determined by fast Fourier transform (FFT) of the atomically resolved structures in Fig.\u00a01c (see Supplementary Note\u00a03 for further details of GB angle determination), which are superimposed on the moir\u00e9 superstructures appearing due to the lattice and orientational mismatch between the graphene grains and the underlying Pt(111) substrate. The chain of GB dislocations clearly appears in the topography (Fig.\u00a01b) and torsional oscillation frequency shift (Fig.\u00a01c) maps as upward protrusions of average height of ~0.7\u2009\u00c5, in agreement with previous theoretical predictions33 and experimental observations13. Notably, this GB defect corrugation is ~3.5 times larger than that of the observed moir\u00e9 superstructures and its lateral extent of ~1\u2009nm covers several carbon rings, making it clearly distinct from its surroundings.\n\nA rough estimation of the spatially resolved energy dissipation map appears in Fig.\u00a01d. This map is obtained from the beam deflection traces recorded during the non-contact topography scan of Fig.\u00a01b (See \u201cMethods\u201d for further details). Already at this resolution, pronounced energy dissipation features are clearly observed above the GB protrusions. Higher resolution results, obtained from the torsional frequency shift map of Fig.\u00a01c, are presented in Fig.\u00a01e. These results demonstrate that energy dissipation is localized around specific GB protrusions, suggesting that these defects are actively undergoing buckling/unbuckling transitions33,34. The double peak structure characterizing the energy dissipation trace (see inset in Fig.\u00a01e) signifies three sliding steps across the GB: (i) first peak\u2014downward buckling of the protrusion as the tip approaches the GB; (ii) region between the peaks\u2014tip sliding over the suppressed protrusion with lower energy dissipation; and (iii) second peak\u2014unbuckling of the protrusion as the tip leaves the GB region. Away from the GB, over the bulk area of the adjacent grains ultralow energy dissipation is observed in line with recent experimental observations41,42.\n\nTo investigate the effect of external load on the frictional properties of GBs, we turned to perform frictional measurements under UHV conditions in the contact AFM mode. Figure\u00a02a, b present lateral force maps of an extended GB having a misfit angle of \\({\\theta }_{{{{\\rm{GB}}}}}=2.35\\pm 0.10^\\circ\\). The latter is extracted using an FFT analysis of the atomic lattice orientations in the bordering grains (see Supplementary Fig.\u00a04) that manifest different moir\u00e9 superstructures. The clear stick-slip features with atomic periodicity measured across the grain regions indicate the pristine nature and degree of cleanness of the grown graphene samples. At the contact mode, the convolution between the AFM tip geometry (radius of curvature <\u20097\u2009nm) and the surface topography results in artificially widened GB features that are imaged with an apparent width of ~\\(6.83\\pm 0.36\\,{{{\\rm{nm}}}}\\). Nonetheless, the lateral force map presents well-defined periodic patterns along the main axis of the GB with a period of \\(D=5.34\\pm 0.23\\) nm (see Fig.\u00a02a, b), which are associated with individual GB dislocations. According to Frank\u2019s equation10,43:\n\nwhere \\({\\vec{b}}_{\\left({{\\mathrm{1,0}}}\\right)}\\) is the Burgers vector of the most common edge-sharing heptagon-pentagon pair dislocation (\\(\\left|{\\vec{b}}_{\\left({1,0}\\right)}\\right|=2.46{{{\\text{\\AA }}}}\\), see Supplementary Fig.\u00a05a), this periodicity corresponds to a misfit angle of \\({\\theta }_{{{{\\rm{GB}}}}}\\approx 2.64^\\circ\\). The good agreement of this value with the independent FFT estimation based on the atomic lattice orientations, validates our GB characterization (see further validation in Supplementary Note\u00a04 and Supplementary Fig.\u00a05b) and confirms that each periodic GB pattern in the force map designates an isolated (1,0) type pentagon-heptagon dislocation, as D matches the theoretical periodicity of (1,0) dislocations along the GB10.\n\na Lateral force map for a GB with a misfit angle of \\({\\theta }_{{{{\\rm{GB}}}}}=2.35\\pm 0.10^\\circ\\), measured under a normal load of 3.1 nN with a sliding velocity of 73.2 \\({{{\\rm{nm}}}}\\cdot {{{{\\rm{s}}}}}^{-1}\\). D denotes the distance between neighboring GB dislocations. b Zoom-in on the area marked by the green dashed square in panel (a) showing atomically resolved lateral force patterns. c-e Lateral force loops taken across the red dashed line appearing in panel (a) under normal loads of (c) \u22120.78 nN, (d) 2.35 nN, and (e) 7.84 nN, where forward and backward traces are marked in black and red, respectively, and the GB region is marked by the light-red background. f Load dependence of the friction force (blue circles) averaged over 3\u20135 independent scans of an area of 30\u2009\u00d7\u200930\u2009nm2 at a sliding velocity of 41.9 \\({{{\\rm{nm}}}}\\cdot {{{{\\rm{s}}}}}^{-1}\\). The error bars represent the corresponding standard deviations. g Velocity dependence of the average friction force (orange rectangles) measured under a normal load of 0.5\u2009nN. The full lines in panels f and g represent the results of the two-state phenomenological model with the following parameters: \\(T=300\\) K, \\({E}_{1}=0.18\\) eV, \\({E}_{2}=0.26\\) eV, \\(\\Delta x=10.8\\) \u00c5, \\(\\alpha=0.2\\) \\({{{\\rm{eV}}}}\\cdot {{{\\rm{GP}}}}{{{{\\rm{a}}}}}^{-1}\\), \\(\\beta=0.2\\), \\({c}_{0}=0.05\\) eV, \\(N=1\\), \\({f}_{0}=16.76\\) kHz, \\({c}_{1}=4.5\\) pN, \\(\\mu=6\\times {10}^{-4}\\). Here, the effective protrusion stiffness is calculated as \\({k}_{0}=\\frac{{E}_{1}+{E}_{2}}{{\\Delta x}^{2}}\\), reflecting the fact that the maximum elastic energy stored by the spring \\(\\left(\\frac{1}{2}{k}_{0}{\\Delta x}^{2}\\right)\\), cannot exceed \\(\\Delta {E}_{\\max }\\).\n\nFigure\u00a02c\u2013e presents three force trace loops taken along the red dashed line appearing in Fig.\u00a02a at increasing normal loads. Regardless of the value of the normal load, the average differences between the trace and retrace curves at the two grain regions are 3.56 and 6.68 pN, respectively, indicating very small energy dissipation due to non-conservative frictional forces. A significantly larger average difference of 42.54 pN is obtained over the GB region at a negative normal load of \u22120.78\u2009nN (transferred via the inherent adhesion), signifying enhanced frictional energy dissipation. Notably, when increasing the external normal load to 2.35 and 7.84\u2009nN, the average differences between the trace and retrace curves at the GB region reduce. Figure\u00a02f presents the friction force as a function of normal load evaluated under a sliding velocity of 41.9 \\({{{\\rm{nm}}}}\\cdot {{{{\\rm{s}}}}}^{-1}\\) by averaging the lateral force traces over a square area of 30\u2009\u00d7\u200930\u2009nm2 around the GB under a given normal load. While this area includes not only the GB itself but also part of the moir\u00e9 superstructures of the adjacent grains, the latter, as shown above, have minor contribution to the overall results (see Supplementary Fig.\u00a011)41,42. Notably, the average friction force (averaged over 3 to 5 independent scans) measured over the GB is found to decrease by up to a factor of 2 with increasing applied load, then it levels off at a normal load of ~4\u2009nN, corresponding to a pressure of 1\u20132\u2009GPa. The system therefore manifests a negative friction coefficient of \u22121.11\u2009\u00d7\u200910\u22123. Above a normal load of 8 nN, the friction force turns to exhibit typical Amontons-like behavior with linear increase of friction with the normal load up to the highest load considered. A similar behavior is found for other corrugated GBs (see Supplementary Note\u00a06).\n\nAs shown in Fig.\u00a02g, at the regime of NFCs, we also found an atypical non-monotonic behavior of the friction with the sliding velocity, where, for example, the friction force peaks at a velocity of ~600 \\({{{\\rm{nm}}}}\\cdot {{{{\\rm{s}}}}}^{-1}\\) under a normal load of 0.5\u2009nN. Overall, a 2-fold enhancement of the friction is found across three decades of the velocity increase. Conversely, in the plateau load regime of Fig.\u00a02f, the friction velocity dependence exhibits a monotonic (logarithmic) increase with sliding velocity (see Supplementary Fig.\u00a015).\n\nThese behaviors are qualitatively different from that previously found over moir\u00e9 superstructures at surface grain regions, where low and nearly constant friction (<\u200910\u2009pN) was observed at low normal loads and sliding velocities, followed by a linear or logarithmic increase, respectively, above a system-dependent threshold41,42. This suggests that different mechanisms underly frictional energy dissipation at GBs and grain moir\u00e9 regions.\n\nA question arises whether the unique frictional behavior exhibited by corrugated GBs characterizes also flat GBs formed by a continuous chain of dislocations10,11,33. To address this question, we repeated our measurements for the flat GB with a misfit angle of \\({\\theta }_{{{{\\rm{GB}}}}}=27.30\\pm 1.07\\)\u02da, shown in the low temperature scanning tunneling microscopy (STM) images of Supplementary Figs.\u00a09, 10. The lateral force map in Fig.\u00a03a demonstrates three distinct regions that exhibit substantially different force traces, including two grains of different moir\u00e9 superstructures and a continuous GB. Notably, the friction force measured over the GB is comparable to that measured over the grain of larger moir\u00e9 supercell, rather than its small moir\u00e9 tile counterpart. This suggests that flat GBs do not introduce additional energy dissipation channels not observed over moir\u00e9 grain regions.\n\na Lateral force map of a flat graphene GB with a misfit angle of \\({\\theta }_{{{{\\rm{GB}}}}}=27.30\\pm 1.07\\)\u02da, measured under a normal load of 5.7 nN and a sliding velocity of 146.5 \\({{{\\rm{nm}}}}\\cdot {{{{\\rm{s}}}}}^{-1}\\). b, c Load dependence of the frictional force measured at sliding velocities of 30.5 and 244.1 \\({{{\\rm{nm}}}}\\cdot {{{{\\rm{s}}}}}^{-1}\\), respectively. d Velocity dependence of the friction force measured under a normal load of 1.0\u2009nN. The green squares represent the friction force. The error bars in panels (b\u2212d) designate the corresponding standard deviations obtained by performing 5 to 6 independent scans. The solid lines are linear fits against the experimental data.\n\nFigure\u00a03b,c present the load dependence of the averaged GB friction measured at sliding velocities of 30.5 and 244.1 \\({{{\\rm{nm}}}}\\cdot {{{{\\rm{s}}}}}^{-1}\\), respectively, showing a linear kinetic friction force increase with normal load up to 14 nN, and kinetic friction coefficients lower than 1\u2009\u00d7\u200910\u22123, well within the superlubric regime. The slight deviation from linearity apparent in Fig.\u00a03c may be attributed to the emergence of moir\u00e9-level friction over the large moir\u00e9 supercell grain41,42. For this flat GB system, the commonly observed monotonic (logarithmic) increase of friction with sliding velocity is also obtained (see Fig.\u00a03d). Recent experiments on flat MoS2 GBs presented similar Amontons\u2019 law type friction force dependence on the applied normal load further supporting our findings40. We note that the values of the friction force measured for the flat GB (Fig.\u00a03) are somewhat higher than those measured for the corrugated counterpart shown in Fig.\u00a02. This comparison, however, is misleading since these two independent measurements have been performed with different AFM tips. Hence, the analysis focuses on the load dependence of friction and not on the absolute friction force values.\n\nTo rationalize the experimental findings regarding the unconventional load dependence of friction at corrugated GBs, we performed fully atomistic simulations of a model system consisting of a diamond tip sliding over a corrugated graphene GB (GB protrusion height of ~2\u2009\u00c5, see Fig.\u00a04a) supported by a Pt(111) substrate. For comparison, we also performed simulations on a flat GB setup (GB protrusion height of <\u20090.2\u2009\u00c5, see Fig.\u00a04b). The left grain of the PolyGr layer was oriented roughly in alignment with the \\(\\left\\langle 1\\bar{1}0\\right\\rangle\\) lattice direction of the Pt(111) surface, leading to a large moir\u00e9 period of ~2.2\u2009nm. To form the corrugated or flat GBs, the right grain was rotated counterclockwise by misfit angles of \\({\\theta }_{{{{\\rm{GB}}}}}\\)\u2009=\u20092\u00b0 and 27.8\u00b0, respectively, yielding moir\u00e9 periods of ~2\u2009nm in the former case and on the order of the atomic lattice period or below for the latter. These model systems aim to mimic the experimental topographies presented in Figs.\u00a02a and 3a. The sliding simulations were performed at zero temperature and at a sliding velocity of 2 \\({{{\\rm{m}}}}\\cdot {{{{\\rm{s}}}}}^{-1}\\) (See \u201cMethods\u201d and Supplementary Note\u00a07 for further details).\n\na, b Simulation setup for sliding over (a) a corrugated GB and (b) a flat GB. The gray and orange spheres represent the diamond tip and the Pt(111) substrate, respectively. The PolyGr atoms are colored according to their height above the average surface (see false color bars to the right of each panel). The lateral dimensions of the Pt(111) substrate are 41.6\u2009\u00d7\u200940.8 nm2. c, d Lateral force trace loops obtained under normal loads of 0 and 12.2 nN for (c) the corrugated and (d) flat GBs. e, f GB atom height and vertical velocity (\\({v}_{z}\\)) trajectories for the (e) corrugated and (f) flat GBs. g The averaged GB friction as a function of normal load for the corrugated (orange) and flat (blue) GBs.\n\nThe sliding simulation results reveal that the GB topography plays a vital role in the frictional behavior. Under zero external normal load, in addition to the atomic scale stick-slip motion, the corrugated GB exhibits significant differences between the forward and backward lateral force traces when the tip crosses a GB protrusion (see Fig.\u00a04a, c). Increasing the normal load to 12\u2009nN significantly diminishes these differences, in qualitative agreement with the experimental results presented in Fig.\u00a02c\u2013e. For the flat GB, only atomic-scale stick-slip motion is observed with no significant trace differences in the GB region (see Fig.\u00a04d). Figure\u00a04e presents the height and vertical velocity variations of a given atom, residing at a corrugated GB protrusion area, as a function of tip displacement. The sharp features characterizing the two traces clearly indicate a shear-induced buckling/unbuckling energy dissipation mechanism, similar to that recently predicted for multi-layered PolyGr interfaces33,34. As the tip approaches an upward protrusion, it gradually presses down on it until a sudden snap-through event occurs, resulting in a downward protruding state. When the tip leaves the GB area, the protrusion buckles back to its upward protruding state (See Supplementary Movie\u00a01). The instantaneous buckling velocity reaches up to ~100 \\({{{\\rm{m}}}}\\cdot {{{{\\rm{s}}}}}^{-1}\\), giving rise to considerable kinetic energy dissipation in the vertical direction. As the normal load increases, the snap-through buckling behavior is suppressed, the features in the height and velocity profiles become smoother, and the overall energy dissipation decreases (See Supplementary Movie\u00a02 and Supplementary Fig.\u00a018).\n\nIn contrast, for the flat GB, where effective cancellation of lateral strain between contacting dislocations results in negligible out-of-plane corrugation, the transition (un)buckling energy barrier is small33. This results in much smoother height and vertical velocity trajectories with out-of-plane velocity variations below 1 \\({{{\\rm{m}}}}\\cdot {{{{\\rm{s}}}}}^{-1}\\) and significantly reduced energy dissipation (see Fig.\u00a04f and Supplementary Movie\u00a03).\n\nThe relations between the averaged friction force and the normal load for the corrugated and the flat GBs are presented in Fig.\u00a04g, showing non-monotonic dependence with NFCs in the low load regime for the corrugated GB, and linear growth with load for the flat GBs, both of which are in good qualitative agreement with the experimental results shown in Figs.\u00a02f, and 3b, c (see Supplementary Note\u00a07 for details regarding the calculation of the average friction force). Our MD simulations reveal a similar qualitative non-Amontons behavior for other scanline directions and substrate thicknesses (see Supplementary Figs.\u00a019, 20).\n\nThe fact that our non-reactive atomistic simulations correctly describe both the force traces and the experimentally observed dependence of friction on the normal load indicates that they capture well the underlying frictional mechanisms, thus providing a microscopic understanding of the involved phenomena. Specifically, this indicates that tip-surface bonding, expected to occur at higher normal loads for pristine surfaces44, has minor effect on friction also in our case despite the expected higher reactivity of GB regions.\n\nNonetheless, due to the computational burden involved, such simulations are limited to sliding velocities considerably higher than those accessible in experiments. To address this issue, we harnessed the understanding gained by the atomistic simulations to devise a simplistic phenomenological model that captures the essential physical ingredients to describe the frictional behavior of corrugated GBs at a wide range of experimental conditions. The key ingredient of the phenomenological model is a shear-induced transition between two (meta-)stable states, representing the upward and downward protruding GB dislocation configurations. A similar model was developed in details in Ref. 34 for a PolyGr contact embedded within a graphitic stack. In what follows, we provide a brief overview of a modified model focusing on its adaptation to the case of an AFM tip sliding over a corrugated layered material GB.\n\nWe mark by \\(\\Delta E\\left(x\\left(t\\right),\\sigma \\right)\\) the transition energy barrier (TEB) between the two states. We assume that it depends mainly on the distance \\(\\left(x\\left(t\\right)\\right)\\) between the tip apex and the GB protrusion and on the normal load \\(\\left(\\sigma \\right)\\). For simplicity, we assume linear spatial interpolation between the bare buckling energy barrier before the tip reaches the protrusion region, \\(\\Delta {E}_{\\max }=\\Delta E\\left(x=0\\right)\\), and the barrier obtained when the tip resides above the center of the protrusion, \\(\\Delta {E}_{\\min }\\left(\\sigma \\right)=\\Delta E\\left(x=\\Delta x,\\sigma \\right)\\). We note that \\(\\Delta {E}_{\\max }\\) is independent of the normal load since the tip does not reside above the protrusion. We further assume the following linear relations between \\(\\Delta {E}_{\\max }\\), \\(\\Delta {E}_{\\min }\\) and \\(\\sigma\\):\n\nwhere \\({{{\\rm{\\alpha }}}}\\), \\(\\beta\\), and \\({c}_{0}\\) are fitting parameters. In accordance with the simulation results, we also assume that the protrusions buckle and unbuckle independently, such that the survival probability of the system at a given state can be described by a first-order transition rate equation of the form:\n\nwhere \\({v}_{0}={{{\\rm{d}}}}x\\left({{{\\rm{t}}}}\\right)/{dt}\\) is the constant sliding velocity of the tip, \\({f}_{0}\\) is the attempt frequency, which formally depends on the structure of the potential energy surface near equilibrium, and the exponential Arrhenius factor introduces the dependence of the transition rate on the barrier height and the thermal energy \\({k}_{B}T\\). Correspondingly, the probability density distribution of the protrusion to buckle at a given tip position is given by \\(f\\left(x,\\sigma,\\Delta {E}_{\\max }\\right)=-{{{\\rm{d}}}}p\\left(x,\\sigma,\\Delta {E}_{\\max }\\right)/{{{\\rm{d}}}}x\\). Given this probability density, we can now evaluate the elastic energy dissipated by a tip sliding induced buckling event of an individual protrusion over the sliding path \\(\\Delta x\\) via:\n\nHere, \\({k}_{0}\\) is an effective stiffness characterizing the elastic deformation at the tip-protrusion contact, such that the integrated term signifies the dissipated elastic energy invested in depressing the dislocation up to the buckling point when the tip is located at point \\(x\\). The Heaviside step function screens unphysical negative TEBs.\n\nTo account for the fact that different GB protrusions can have different bare energy barriers, one should average the individual protrusion energy dissipation over the distribution of barrier heights, \\({P}_{b}\\left({\\Delta E}_{\\max }\\right)\\), yielding the following expression for the friction force:\n\nwhere \\(N\\) is the total number of GB protrusions crossed simultaneously by the tip along a given scanline. For simplicity, we further assume a uniform distribution of the bare energy barriers bound to the energy range \\(\\left[{E}_{1}:{E}_{2}\\right]\\). Finally, to account for baseline friction resulting from, e.g., atomic-scale stick-slip dynamics, an additional friction term, \\({F}_{0}\\), is added:\n\nwhere, per Amonton\u2019s friction law, \\({F}_{0}\\) is assumed to depend linearly on the normal force \\({F}_{{{{\\rm{n}}}}}\\):\n\nWhile a logarithmic dependence of \\({F}_{0}\\) on velocity may be also expected, previous experimental results demonstrated that it remains constant in the low velocity superlubric regimes considered in our experiments41,42. For a direct comparison with experimental results, we further assume that the contact area has a circular shape with a constant radius of 12\u2009\u00c5 (i.e., 4.5\u2009nm2 in area, close to that of the tip in the MD simulations) to convert normal pressure, \\(\\sigma\\), to the normal force, \\({F}_{{{{\\rm{n}}}}}\\). This is in line with previous theoretical predictions45 and supported by our MD simulations (Supplementary Note\u00a07).\n\nThe model parameters are extracted from our MD simulation results (whenever possible) or fitted against the experimental measurements, within reasonable physical bounds33,34,46 (see caption of Fig.\u00a02 and Supplementary Note\u00a08). The resulting parametrized two-state model reproduces well the unique load and velocity dependence of the friction force across corrugated GBs demonstrated in our experiments (see Fig.\u00a02f, g) and atomistic simulations (see Fig.\u00a04g and Supplementary Note\u00a08). The phenomenological model allows us to identify the dominating factors responsible for the observed frictional behavior of corrugated GBs. Specifically, the NFC behavior can be attributed to the lowering of the buckling energy barrier with increasing tip normal load, leading to a decrease in the dissipated energy per buckling event.\n\nThe non-monotonic velocity dependence of the friction force is traced to balancing two competing effects: (i) decrease of thermally assisted buckling probability with increasing velocity due to the reduced time that the tip spends over the GB protrusion; and (ii) increase in the overall dissipated energy per buckling event, resulting from the fact at higher sliding velocities the tip can shift further along the sliding path before overcoming the energy barrier, such that buckling may occur at larger protrusion depressions.\n\nThe observations of unconventional frictional properties of negative differential friction coefficients and non-monotonic velocity dependence are not limited to the corrugated GB considered above and are well reproduced in other corrugated GBs (see Supplementary Figs.\u00a012, 13). This demonstrates the general nature of our findings, which have a significant impact on scaling-up structural superlubricity towards macroscopic contacts that inevitably involve polycrystalline layered material interfaces. Assuming a constant GB density, one might na\u00efvely conclude that overall GB friction contribution would grow linearly with contact area, thus eliminating structural superlubricity at large scales. Our results, however, demonstrate that by harnessing the unconventional frictional properties of GBs (e.g., negative friction coefficients and non-monotonic velocity dependence) together with other unique control schemes, such as gate-tunable behavior40, one may restore and control structural superlubricity in large-scale polycrystalline two-dimensional material interfaces.",
+            "section_image": [
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+            ]
+        },
+        {
+            "section_name": "Methods",
+            "section_text": "The PolyGr layer was grown in a UHV chamber on a freshly prepared Pt(111) surface. Prior to the chemical vapor deposition, the Pt(111) surface was cleaned by cycles of sputtering and high-temperature annealing. PolyGr was synthesized by means of ethylene dosing directly onto the hot surface (see Supplementary Note\u00a01 for a detailed description).\n\nThe homebuilt ultrahigh vacuum atomic force microscope of beam deflection type (base pressure of <\u20091\u2009\u00d7\u200910\u221210 mbar) was operated at room temperature (300\u2009K) with a Nanonis Control System by SPECS GmbH. The bimodal mode was used to characterize the PolyGr surface and detect non-contact friction. Contact mode was used to conduct friction force measurements, where the AFM tip is in direct contact with the PolyGr layer.\n\nThe energy dissipation (in units of eV per oscillation cycle) was calculated according to the following formula47,48:\n\nwhere \\({E}_{0}\\) is the energy loss per oscillation cycle caused by the intrinsic dissipation of the freely oscillating cantilever, \\({V}_{{{{\\rm{exc}}}}}\\) is the voltage needed to maintain a constant excitation amplitude, \\(f\\) is the eigenfrequency of the cantilever, and \\({V}_{{{{\\rm{exc}}}},0}\\) and \\({f}_{0}\\) are the corresponding values for the free cantilever. Here, the fix-ended cantilever is driven by a shaking piezo-element, the exciting voltage of which was modulated to maintain constant oscillation amplitude when interacting with the PolyGr sample.\n\nIn the beam deflection NC-AFM measurements, the second flexural oscillation mode (resonant frequency of \\({f}_{{2}^{{{{\\rm{nd}}}}}}=1.02\\,{{{\\rm{MHz}}}}\\) and amplitude of \\({A}_{{2}^{{{{\\rm{nd}}}}}}=600\\,{{{\\rm{pm}}}}\\)) was used to control the tip-sample distance. The relatively large oscillation amplitude allows us to obtain a consistent value of the average tip-sample distance and thus a clear topographic map, against which the corresponding dissipation map can be compared in the NC mode. This implies that the tip is strongly influenced by long-range dissipative interactions other than those induced by the GB itself. While such interactions reduce the contrast of the NC dissipation map, the high sensitivity of \\({V}_{{{{\\rm{exc}}}}}\\) and \\(f\\) towards the tip-sample distance allows to obtain a meaningful image.\n\nTo analyze the NC-AFM friction signal at the torsional mode, the cantilever was oscillated at the torsional resonant frequency with an excitation amplitude of \\({A}_{{{{\\rm{T}}}}}=80\\,{{{\\rm{pm}}}}\\ll {A}_{2^{{{\\rm{nd}}}}}\\). In such case, the energy loss signal is more sensitive to the local interactions between the tip and the PolyGr surface, thus reducing other long-range interaction effects. Therefore, the energy dissipation map provided by tortional mode measurements (Fig.\u00a01e) shows a much higher contrast compared to the beam deflection map (Fig.\u00a01d).\n\nThe molecular dynamics (MD) simulation model system consisted of a spherical-cap shaped diamond tip (2.3\u2009nm in height, 5\u2009nm in radius at the cut surface) sliding atop a bi-crystalline graphene layer supported by a 1.36\u2009nm thick Pt(111) substrate, as shown in Fig.\u00a04a, b. The PolyGr atomic arrangements were created using a Voronoi tessellation approach developed by Shekhawat et al12,49. The inter-atomic interactions within the diamond tip and the graphene layer were described with the second-generation reactive empirical bond order (REBO) potential50. The inter-atomic interactions within the Pt substrate were described via the embedded-atom-method (EAM) potential51. Due to the lack of dedicated anisotropic force-fields for the PolyGr/Pt(111) and PolyGr/diamond interfaces, we adopted the isotropic Lennard-Jones (LJ) potential to describe these interactions. While being unable to simultaneously capture both binding and sliding energy landscapes, with appropriate parameterization this potential was shown to provide a good qualitative description of frictional processes41,42,52. The LJ parameters for the diamond/graphene carbon atom interactions were taken to be \\({\\sigma }_{{{{\\rm{CC}}}}}=3.4\\) \u00c5 and \\({\\varepsilon }_{{{{\\rm{CC}}}}}=0.00284\\) eV53. For carbon/Pt interactions, we benchmarked the LJ parameters against available DFT and experimental reference values for the binding energy and equilibrium interlayer distance between graphene and Pt(111), yielding \\({\\sigma }_{{{{\\rm{C}}}}-{{{\\rm{Pt}}}}}=3.35\\) \u00c5 and \\({\\varepsilon }_{{{{\\rm{C}}}}-{{{\\rm{Pt}}}}}=0.006\\) eV, which were then used for both the tip-substrate and the graphene-substrate interactions (See Supplementary Note\u00a07).\n\nAll sliding simulations were performed at zero temperature by driving the diamond tip via a spring with stiffness of 10 \\({{\\rm{N}}\\cdot {m}}^{-1}\\) at a constant velocity of 2 \\({{{\\rm{m}}}}\\cdot {{{{\\rm{s}}}}}^{-1}\\) under external normal loads in the range of 0-25 nN. All simulations were carried out using the LAMMPS package54. See Supplementary Note\u00a07 for further simulation details.",
+            "section_image": []
+        },
+        {
+            "section_name": "Data availability",
+            "section_text": "The data that support the findings presented in this paper are available within the paper and its supplementary information. A source data file is provided with this paper and can be downloaded at: https://doi.org/10.5281/zenodo.13768451.",
+            "section_image": []
+        },
+        {
+            "section_name": "References",
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+        },
+        {
+            "section_name": "Acknowledgements",
+            "section_text": "Y.S. acknowledges fruitful discussions with M. Kisiel. The Basel group thank the Swiss Nanoscience Institute (SNI) and the European Research Council (ERC) under the European Union\u2019s Horizon 2020 research and innovation program (ULTRADISS grant agreement No 834402). E.M., T.G., and R.P. acknowledge the Swiss National Science Foundation (grant no. 200021_228403 and 200021L_219983). X.G. acknowledges the postdoctoral fellowships of the Sackler Center for Computational Molecular and Materials Science and Ratner Center for Single Molecule Science at Tel Aviv University. M.U. acknowledges the financial support of the Israel Science Foundation, grant No. 1141/18 and the ISF-NSFC joint grant 3191/19. O.H. is grateful for the generous financial support of the Israel Science Foundation under grant No. 1586/17, the Heinemann Chair in Physical Chemistry, Tel Aviv University Center for Nanoscience and Nanotechnology, and the Naomi Foundation for generous financial support via the 2017 Kadar Award.",
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+            "section_name": "Author information",
+            "section_text": "These authors contributed equally: Yiming Song, Xiang Gao.\n\nDepartment of Physics, University of Basel, Basel, Switzerland\n\nYiming Song,\u00a0R\u00e9my Pawlak,\u00a0Shuyu Huang,\u00a0Antoine Hinaut,\u00a0Thilo Glatzel\u00a0&\u00a0Ernst Meyer\n\nDepartment of Physical Chemistry, School of Chemistry, The Raymond and Beverly Sackler Faculty of Exact Sciences and The Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv, Israel\n\nXiang Gao,\u00a0Oded Hod\u00a0&\u00a0Michael Urbakh\n\nKey Laboratory for Design and Manufacture of Micro-Nano Biomedical Instruments, School of Mechanical Engineering, Southeast University, Nanjing, China\n\nShuyu Huang\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nE.M., M.U., and O.H. conceived the original idea behind this study. Y.S. and E.M. designed the experimental aspects of the study, and Y.S. performed the experiments and analyzed the experimental data. S.H. and T.G. assisted with the friction measurements. R.P. and A.H. assisted with the LT-STM characterizations. M.U., O.H., and X.G. designed the simulations and analyzed their results. X.G. conducted the simulations and theoretical calculations. E.M., M.U., O.H., X.G., and Y.S. wrote the manuscript. All the authors commented on the manuscript.\n\nCorrespondence to\n                Oded Hod, Michael Urbakh or Ernst Meyer.",
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+            "section_text": "Song, Y., Gao, X., Pawlak, R. et al. Non-Amontons frictional behaviors of grain boundaries at layered material interfaces.\n                    Nat Commun 15, 9487 (2024). https://doi.org/10.1038/s41467-024-53581-y\n\nDownload citation\n\nReceived: 31 October 2023\n\nAccepted: 14 October 2024\n\nPublished: 02 November 2024\n\nVersion of record: 02 November 2024\n\nDOI: https://doi.org/10.1038/s41467-024-53581-y\n\nAnyone you share the following link with will be able to read this content:\n\nSorry, a shareable link is not currently available for this article.\n\n\n\n\n                            Provided by the Springer Nature SharedIt content-sharing initiative\n                        ",
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2669d87695ed810730ad4b1dbb8f435931321c0605b14080576f6ae386246072/metadata.json

@@ -0,0 +1,161 @@
+{
+    "title": "Main-group element-boosted oxygen electrocatalysis of Cu-N-C sites for zinc-air battery with cycling over 5000\u2009h",
+    "pre_title": "Durable oxygen reduction catalysis of Cu-N-C sites boosted by adjacent main-group element for rechargeable Zn-air batteries with cycling over 5000 h",
+    "journal": "Nature Communications",
+    "published": "27 September 2024",
+    "supplementary_0": [
+        {
+            "label": "Supplementary Information",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-024-52494-0/MediaObjects/41467_2024_52494_MOESM1_ESM.pdf"
+        },
+        {
+            "label": "Peer Review File",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-024-52494-0/MediaObjects/41467_2024_52494_MOESM2_ESM.pdf"
+        },
+        {
+            "label": "Description of Additional Supplementary Files",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-024-52494-0/MediaObjects/41467_2024_52494_MOESM3_ESM.pdf"
+        },
+        {
+            "label": "Supplementary Data 1",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-024-52494-0/MediaObjects/41467_2024_52494_MOESM4_ESM.xlsx"
+        },
+        {
+            "label": "Supplementary Data 2",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-024-52494-0/MediaObjects/41467_2024_52494_MOESM5_ESM.xlsx"
+        },
+        {
+            "label": "Supplementary Data 3",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-024-52494-0/MediaObjects/41467_2024_52494_MOESM6_ESM.xlsx"
+        }
+    ],
+    "supplementary_1": [
+        {
+            "label": "Source Data",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-024-52494-0/MediaObjects/41467_2024_52494_MOESM7_ESM.xlsx"
+        }
+    ],
+    "supplementary_2": NaN,
+    "source_data": [
+        "/articles/s41467-024-52494-0#Sec19"
+    ],
+    "code": [],
+    "subject": [
+        "Batteries",
+        "Electrocatalysis",
+        "Fuel cells"
+    ],
+    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
+    "preprint_pdf": "https://www.researchsquare.com/article/rs-3582926/v1.pdf?c=1727521866000",
+    "research_square_link": "https://www.researchsquare.com//article/rs-3582926/v1",
+    "nature_pdf": "https://www.nature.com/articles/s41467-024-52494-0.pdf",
+    "preprint_posted": "17 Dec, 2023",
+    "research_square_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Developing highly active and durable air cathode catalyst is crucial but challenging for rechargeable zinc-air batteries (ZABs). Herein, a large-area, flexible, self-standing carbon membrane encapsulating adjacent Cu/Na dual-atom-sites catalyst is prepared by a scalable solution blow spinning combined pyrolysis strategy. The Cu-N-C site is inspired by the neighboring Na-containing functional group, which enhances O2 adsorption and optimizes the rate-determining step of O2 activation (*O2\u2192*OOH) during the oxygen reduction reaction (ORR) process. Meanwhile, the Cu-N4 sites are encapsulated inside the carbon nanofibers and anchored by the carbon matrix to form a C2-Cu-N4 configuration, reinforcing the stability of the Cu centers. Moreover, the C matrix, anchored with a Na-containing functional group endows its outer shell C with negative charge, rendering the carbon skeletons less susceptible to corrosion by oxygen species and further preventing the dissolution of Cu centers. Under this multi-type regulations, ZAB with CuNa-CF catalyst as the air cathode demonstrates an unprecedentedly long charging/discharging stability for more than 5000 h with no noticeable decay. This remarkable stability improvement represents a critical step in developing Na-inspired Cu-N-C sites to overcome the durability barriers of ZABs for their future practical applications.Physical sciences/Chemistry/Catalysis/ElectrocatalysisPhysical sciences/Energy science and technology/Energy storage/BatteriesPhysical sciences/Materials science/Materials for energy and catalysis/Fuel cellsPhysical sciences/Nanoscience and technology/Nanoscale materials/Synthesis and processingPhysical sciences/Chemistry/Catalysis/Catalyst synthesis",
+            "section_image": []
+        },
+        {
+            "section_name": "Additional Declarations",
+            "section_text": "There is NO Competing Interest.",
+            "section_image": []
+        },
+        {
+            "section_name": "Supplementary Files",
+            "section_text": "SupplementaryInformation.docxSupplementary Information",
+            "section_image": []
+        }
+    ],
+    "nature_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Developing highly active and durable air cathode catalysts is crucial yet challenging for rechargeable zinc-air batteries. Herein, a size-adjustable, flexible, and self-standing carbon membrane catalyst encapsulating adjacent Cu/Na dual-atom sites is prepared using a solution blow spinning technique combined with a pyrolysis strategy. The intrinsic activity of the Cu-N4 site is boosted by the neighboring Na-containing functional group, which enhances O2 adsorption and optimizes the rate-determining step of O2 activation (*O2\u2009\u2192\u2009*OOH) during the oxygen reduction reaction process. Meanwhile, the Cu-N4 sites are encapsulated within carbon nanofibers and anchored by the carbon matrix to form a C2-Cu-N4 configuration, thereby reinforcing the stability of the Cu centers. Moreover, the introduction of Na-containing functional groups on the carbon atoms significantly reduces the positive charge on their outer shell C atoms, rendering the carbon skeletons less susceptible to corrosion by oxygen species and further preventing the dissolution of Cu centers. Under these multi-type regulations, the zinc-air battery with Cu/Na-carbon membrane catalyst as the air cathode demonstrates long-term discharge/charge cycle stability of over 5000\u2009h. This considerable stability improvement represents a critical step towards developing Cu-N4 active sites modified with the neighboring main-group metal-containing functional groups to overcome the durability barriers of zinc-air batteries for future practical applications.",
+            "section_image": []
+        },
+        {
+            "section_name": "Introduction",
+            "section_text": "The excessive consumption of fossil fuels and their environmental impact drive researchers to explore alternative energy carriers or devices for energy storage and conversion1,2,3. In recent years, rechargeable zinc-air batteries (ZABs) have emerged as one of the most promising technologies due to their low cost, high safety, high theoretical energy density, and environmental friendliness4. However, unsatisfactory energy conversion efficiency and limited durability are the main bottlenecks restricting the widespread application of ZABs5,6,7. These shortcomings predominantly originate from the sluggish kinetics of oxygen reduction/evolution reactions (ORR/OER) and the low stability of catalysts in air cathodes8,9,10. Although satisfactory catalytic activity can be achieved with precious metal-based catalysts (Pt, Ir, Ru, etc.), their high cost and poor durability force researchers to explore non-precious metal alternatives11. Recently, atomically dispersed M-N-C (M = non-precious metal) catalysts have attracted increasing interest as promising ORR electrocatalysts. In particular, Fe-N-C catalysts exhibit remarkable ORR activity even comparable to that of commercial Pt/C catalyst12,13,14. However, due to the Fenton effect, the Fe sites will inevitably react with the H2O2 formed during the ORR process and resulting in relatively low ORR/ZABs stability15. Thus, achieving a balance between the activity and durability of ORR catalysts is crucial for advancing the practical application of ZABs.\n\nInspired by nature, cytochrome c oxidase is commonly employed in animal cells to convert oxygen to water, which is composed of heme a3/CuB (heme-copper oxidases)16. This suggests that copper-based materials could serve as potential ORR catalysts. Notably, compared with Fe-N-C catalysts, Cu-N-C catalysts can effectively prevent the occurrence of the Fenton reaction. However, Cu-N-C catalysts featuring the Cu-N4 configuration usually demonstrate inferior oxygen adsorption energy and poor ORR catalytic performance due to the less accessible d-orbitals in the central Cu sites17. How to modify the Cu-N-C sites to ensure their high catalytic activity while maintaining good stability has become a bottleneck in the development of efficient ORR catalysts. In recent years, main-group metal catalysts, including Mg, Ca, Sn, and Sb, have been widely explored as an emerging class of catalysts for hydrosilylation, hydroamination, and electrochemical reactions18,19,20,21. However, due to the lack of the combination of empty and filled host orbitals, the majority of main-group metal-based catalysts encounter challenges in accelerating electron transfer processes during ORR22. Indeed, some main-group metals exhibit a suitable affinity for oxygenated species, particularly Na. It can be reasonably proposed that rationally optimizing the electronic structure of the Cu-N4 active site by introducing oxyphilic Na may improve the conversion of oxygenated species and accelerate the kinetics of the ORR. However, seldom research has been reported to study the activity effects of main-group metals on transition metal catalysts towards ORR/ZABs up to now.\n\nWhile considerable attention has been directed towards developing highly active catalysts for ORR and rechargeable ZABs, the stability of these catalysts has often been overlooked. Some studies have indicated that the decline in catalyst stability may be attributed to the poisoning of active sites by intermediates or by-products generated during electrochemical reactions23. Based on this, Bao and co-workers synthesized a catalyst with Fe nanoparticles confined inside pea-pod-like carbon nanotubes. They utilized the graphitic wall to protect the active centers, and achieved an improved stability of polymer electrolyte membrane fuel cell in 201324. Since then, the concept of carbon encapsulation has emerged as an important strategy to enhance the stability of metal-based catalysts. Additionally, forming coordination bonds between the metal active sites and the substrate atoms is another effective method to improve the stability of electrocatalysts, which can also enhance the conductivity of the active sites25. In addition to the poisoning and deactivation of active sites, the stability of the carbon support is also crucial for the stability of catalysts. Carbon corrosion at high potentials represents the main cause of the migration, dissolution, and aggregation of metal active centers, and is also an important factor leading to the deterioration of catalyst stability26. Notably, when the C atoms adjacent to the metal active site become less positively charged, it will alleviate the attack by negatively charged oxygen intermediates, thereby reducing the leaching of active sites from the carbon matrix caused by the corrosion of neighboring C atoms. Therefore, modifying the C atoms around the metal active sites with functional groups to make them less positively charged is a rational strategy to prevent carbon corrosion and further enhance the stability of metal active centers. Unfortunately, limited effort has been devoted to mitigating carbon corrosion in M-N-C catalysts. In this regard, it is reasonable to expect that if one can thoroughly analyze the effects of main-group Na-containing functional groups on the Cu-N-C site and synthesize an electrocatalyst with an appropriate coordination environment for Cu atoms, combined with carbon encapsulation and substrate catalytic site fixation strategies, highly active and durable ZABs could be achieved. Nevertheless, it is undoubtedly a great challenge to obtain such a rationally designed Cu/Na dual-atom sites catalysts to meet these multi-type regulations.\n\nHerein, we report a rationally designed dual-metal site catalyst with transition Cu atoms and main-group Na-containing functional groups encapsulated in carbon nanofibers (CuNa-CF) by using a pyrolysis-followed solution blow spinning strategy (SBS). The intrinsic activity of the Cu-N4 site in the CuNa-CF catalyst is boosted by the adjacent Na-containing functional group, which addresses the problem that the traditional Cu-N4-C catalysts have inferior oxygen adsorption energy and are not suitable for serving as ORR catalysts. Thus, our CuNa-CF catalyst exhibits an excellent ORR half-wave potential as high as 0.89\u2009V. Meanwhile, thanks to the neighboring main-group metal-ligand effect, carbon encapsulation, and support anchoring effect, the electrocatalytic stability of the CuNa-CF catalyst is further improved, and it can maintain 97.85% relative current after 48\u2009h of long-term ORR catalytic stability measurement. The ZAB with CuNa-CF catalyst as the air cathode demonstrates remarkable discharge/charge cycle stability for more than 5000\u2009h without noticeable decay at the current density of 1\u2009mA\u2009cm\u22122. Additionally, the CuNa-CF air cathode can even operate stably for over 950\u2009h at a higher current density of 50\u2009mA\u2009cm\u22122. The as-assembled flexible solid-state ZAB and button-type all-solid-state ZAB also show satisfactory cycling stabilities, offering new perspectives for powering wearable devices and microelectronic devices.",
+            "section_image": []
+        },
+        {
+            "section_name": "Results",
+            "section_text": "As illustrated in Fig.\u00a01, the CuNa-CF catalyst was synthesized by using SBS technology followed by a temperature-programmed pyrolysis process. Firstly, chlorophyllin sodium copper complex (CSCC) was used as the heteroatom metal precursor, in which, the Cu atom coordinates with four N atoms and there are three Na atoms bonded to three branches through carboxylate bonds. Polyacrylonitrile (PAN) was selected as the carbon precursor due to its high stability of carbon skeleton structure at high temperatures27. By using SBS technology, a PAN nanofiber membrane with uniform CSCC dispersion (CSCC-PAN) was first prepared. After pre-oxidation in air, the linear PAN chains in the CSCC-PAN converted into heat-resistant aromatic ladder structures, and this unique aromatic structure could stabilize CSCC by forming \u03c0-\u03c0 interactions with aromatic-like structures in CSCC28. In order to protect the loading of Na atoms and the coordinating N atoms adjacent to the Cu atom, the annealing conditions during the pyrolysis process were carefully optimized. Finally, a flexible CuNa-CF catalyst membrane was successfully obtained (Supplementary Fig.\u00a01). As shown in Supplementary Fig.\u00a02a, the Brunauer-Emmett-Teller (BET) specific surface area of the as-prepared CuNa-CF catalyst membrane is 597.31\u2009m\u00b2/g, and the catalyst mainly possesses micropores and mesopores. Thermogravimetric analysis (TGA) is a powerful technique for determining the formation of catalysts during the pyrolysis of catalyst precursors. The overall weight loss of CSCC was approximately 65%, indicating that apart from the loss caused by physically adsorbed water, CSCC partially decomposed during the pyrolysis process (Supplementary Fig.\u00a02b). The pre-oxidized pure PAN membrane began to decompose at about 300\u2009\u00b0C and maintained a mass ratio of 37.6% at 900\u2009\u00b0C. During the carbonization process from 300\u2009\u00b0C to 900\u2009\u00b0C, the pre-oxidized pure PAN membrane underwent significant degradation and weight loss. Non-carbon elements such as H, O, and N in the oxidized PAN fiber were partially removed in the form of small molecular gases or liquid tar, and taking away a large amount of carbon atoms29. The pre-oxidized CSCC-PAN membrane exhibited a TGA curve similar to that of the pre-oxidized PAN membrane, which is attributed to the partial decomposition of CSCC and the partially removal of non-carbon elements generated after the pre-oxidation step. The metal contents of Cu and Na in CuNa-CF catalyst are 1.89\u2009wt% and 0.711\u2009wt% (the atom ratio of Cu to Na is close to 1:1) as determined by inductively coupled plasma mass spectrometry (ICP-MS, Supplementary Table\u00a01), respectively. In order to confirm the significance of Na in the CuNa-CF catalyst, the CuPc-CF catalyst (Na-free) was prepared by using copper phthalocyanine (CuPc) as the metal precursor through the same strategy, and the loading amount of Cu in CuPc-CF catalyst is 2.60\u2009wt% (Supplementary Fig.\u00a03 and Supplementary Table\u00a01).\n\nThe dual metal site catalyst with transition Cu atom and main-group Na-containing functional group encapsulated in the flexible carbon nanofibers (CuNa-CF) was synthesized by using pyrolysis followed solution blow spinning technology. Uniformly dispersed chlorophyllin sodium copper complex-polyacrylonitrile (CSCC-PAN) membrane can be scalable produced by using solution blow spinning strategy.\n\nThe scanning electron microscope (SEM) and transmission electron microscopy (TEM) were used to examine the morphology of the CuNa-CF catalyst. As shown in Fig.\u00a02a, the fluffy and aligned carbon nanofibers of CuNa-CF intricately interlace with each other, forming an interconnected 3D network structure. The TEM image of CuNa-CF reveals a smooth surface, and the average diameter of the nanofibers is approximately 220\u2009nm, also no obvious metal nanoparticles can be observed (Supplementary Fig.\u00a04a). This agrees well with the results from X-ray diffraction (XRD) analysis, in that there are no obvious diffraction peaks corresponding to Cu or CSCC, and it only displays a broad peak and a tiny peak at 24.1\u00b0 and 44.2\u00b0 assigned to the (002) and (101) crystal planes of carbon (Supplementary Fig.\u00a04b), indicating that Cu atoms are uniformly dispersed in carbon fibers without agglomeration during the pyrolysis step30. The dispersion of Cu atoms was directly monitored by aberration-corrected high-angle annular dark-field scanning transmission electron microscopy (AC-HAADF-STEM) in sub-angstrom resolution (Fig.\u00a02b). Due to the sensitive Z-contrast of heavy elements, the homogeneously and densely dispersed bright dots (tagged by red circles) corresponding to Cu atoms could be easily observed, revealing that Cu atoms were dispersed at the atomic level in CuNa-CF31. It is worth noting that the Cu atoms are situated on the carbon lattice, further confirming that CSCC enters into the aromatic structure formed by PAN during the pyrolysis process. As shown in Fig.\u00a02c, the AC-HAADF-STEM image and the corresponding EDS elemental mapping images illustrate the well distributions of C, N, O, Cu, and Na elements in CuNa-CF. Notably, the CuPc-CF (Na-free) catalyst synthesized with CuPc as the metal precursor also exhibits a similar Cu single-atom site on the carbon lattice as observed in the CuNa-CF catalyst (Supplementary Fig.\u00a05). To further confirm the neighboring relationship between Cu and Na atoms in the CuNa-CF catalyst, the HADDF-STEM image and the corresponding EELS spectrum of a selected small area (0.5\u2009nm\u2009\u00d7\u20090.5\u2009nm) are shown in Fig.\u00a02d\u2013f, in which the signals of Cu and Na atoms were both detected, which provided strong evidence for the presence of neighboring Cu and Na atoms. Raman spectroscopy and X-ray photoelectron spectroscopy (XPS) were also conducted to investigate the structural transformations during the pre-oxidation/pyrolysis processes, and the chemical composition of CuNa-CF and CuPc-CF catalysts. These analyses indicated that the structure and composition of the Cu complex (CSCC or CuPc) were partially retained in their final catalyst (Supplementary Note\u00a01, Supplementary Figs.\u00a06\u20139, and Supplementary Table\u00a02). After that, the presence of the -COONa functional group in the CuNa-CF catalyst was further revealed by Fourier transform infrared spectroscopy (FT-IR) analysis. As shown in Supplementary Fig.\u00a010, the FT-IR spectra of CSCC and CuNa-CF catalyst both exhibit an obvious peak at 1567\u2009cm\u22121, which can be attributed to the -COO\u207b asymmetric vibration band32. Combined with the XPS results, the existence of the -COONa functional group in the CuNa-CF catalyst was confirmed.\n\na Scanning electron microscope image of the CuNa-CF membrane. b Aberration-corrected high-angle annular dark-field scanning transmission electron microscopy (AC-HAADF-STEM) image, some of Cu atoms are marked by red circles. c HAADF-STEM image of the CuNa-CF catalyst and the corresponding energy dispersive X-ray spectroscopy elemental mapping images for C, N, O, Cu, and Na. d HAADF-STEM image of the CuNa-CF catalyst and the corresponding scanning transmission electron microscopy-electron energy loss spectroscopy (STEM-EELS) mapping (e) taken from the orange boxed area in (d). f the corresponding EELS spectrum of the 0.5\u2009nm\u2009\u00d7\u20090.5\u2009nm selected small area in (e).\n\nTo further confirm the electronic structure and coordination environment of Cu atoms in CuNa-CF and CuPc-CF catalysts, X-ray absorption spectroscopy (XAS) measurements were performed33. As shown in the X-ray absorption near-edge structure (XANES), the absorption edges of CuNa-CF and CuPc-CF partially overlap, indicating that the oxidation states of Cu atoms in these two catalysts are similar (Fig.\u00a03a and Supplementary Fig.\u00a011). By comparing with other reference samples, the absorption-edge positions for CuNa-CF and CuPc-CF catalysts are both located between Cu foil and CuO, implying that the Cu atoms in these two catalysts are positively charged with an oxidation state between 0 and +2 (Supplementary Fig.\u00a012). The Fourier transform (FT) extended X-ray absorption fine structure (EXAFS) spectra in the R space verify the absence of Cu aggregation in both CuNa-CF and CuPc-CF catalysts, and the Cu atoms remain in an isolated state due to the absence of Cu-Cu coordination path when compared to Cu foil (Fig.\u00a03b and Supplementary Fig.\u00a013). The FT-EXAFS curves of CuNa-CF and CuPc-CF display main peaks at approximately 1.44\u2009\u00c5 and 1.50\u2009\u00c5, corresponding to the Cu-N bond. Also, a tiny peak at ~2.3\u2009\u00c5 can be detected in the both two catalysts, which is attributed to the interaction between the Cu atom and the C atoms in the underlying carbon lattice. For the high resolution in R-space and k-space, the wavelet transform (WT)-EXAFS analysis was performed to justify the atomic dispersion of Cu atoms in these two catalysts. As shown in Fig.\u00a03c, the main intensity maximum can be observed at k\u2009~\u20093.85\u2009\u00c5\u22121 in CuNa-CF and CuPc-CF catalysts responding to the Cu-N bonds, which is consistent with CSCC and CuPc complexes. By comparing with the Cu foil and CuO, no Cu-Cu signals can be detected in these two catalysts (white dashed line), confirming that the Cu atoms in CuNa-CF and CuPc-CF are atomically dispersed and coordinated with N atoms. Interestingly, both CuNa-CF and CuPc-CF show a slight intensity maximum at k\u2009~\u20096.55\u2009\u00c5\u22121 (white dot line), which differs from the Cu-C coordination at the second shell in CSCC and CuPc complexes, indicating that the Cu-C coordination in CuNa-CF and CuPc-CF is distinct from that in metal precursors. In order to gain more detailed structural understanding of CuNa-CF and CuPc-CF, the Cu quantitative coordination configurations were constructed, and Fourier-transformed EXAFS fitting curves were calculated (Fig.\u00a03d, e and Supplementary Table\u00a03). Based on the fitting results, the Cu atoms in both CuNa-CF and CuPc-CF catalysts are coordinated with four N atoms, which is consistent with the structures of CSCC and CuPc complexes. Additionally, two Cu-C coordination bonds are present in both catalysts, indicating that the Cu-N4 sites are embedded in the carbon matrix and there have some strong interactions between Cu atoms and the C atoms in the underlying carbon lattice matrix. These findings support the formation of the C2-Cu-N4 site in these two catalysts. Combined with the XPS and FT-IR results, the dominant active sites in CuNa-CF and CuPc-CF catalysts can be postulated as C2-Cu-N4-COONa and C2-Cu-N4, respectively (Supplementary Note\u00a01). In order to get a specific schematic model, density functional theory (DFT) calculations were carried out (Supplementary Fig.\u00a014 and 15)34,35,36. The ortho-C atoms in the underlying carbon lattice matrix served as anchors to stabilize the Cu atom in both CuNa-CF and CuPc-CF catalysts, and the para-C atom of Cu in the carbon matrix was used to anchor the -COONa functional group in the CuNa-CF catalyst because of the existence of the strong coordination interaction (vide infra). The corresponding schematic modularizations of CuPc-CF catalyst and CuNa-CF catalyst are illustrated in the insets of Fig.\u00a03d, e.\n\na Cu K-edge X-ray absorption near-edge structure spectra. b Fourier transformed extended X-ray absorption fine structure (EXAFS) spectra in R space. c Wavelet transformed EXAFS spectra for Cu foil, CuPc-CF, CuNa-CF, CuO, CuPc, and CSCC. d, e Fourier transformed EXAFS fitting curves for CuPc-CF and CuNa-CF, respectively. Insets in d and e show schematic models of the CuPc-CF catalyst and CuNa-CF catalyst, respectively (Cu atom is green, Na atom is purple, O atoms are pink, N atoms are blue, C atoms in the layer where the Cu site is located are dark gray, and C atoms in the layer below Cu site are light gray).\n\nTo further validate that the distinctive electrocatalytic performance of the C2-Cu-N4 site is inspired by the neighboring Na atom in the CuNa-CF catalyst, the CuPc+NaCl-CF catalyst was prepared by introducing NaCl during the synthesis of the CuPc-CF catalyst. NaCl-CF (Cu-free) and CF (Cu, Na-free) were also synthesized by using the same methods, except for the different metal precursors (Supplementary Note\u00a02, Supplementary Figs.\u00a016\u201321, and Supplementary Tables\u00a01 and 2). The electrocatalytic ORR performance of the as-prepared catalysts was evaluated in an O2-saturated 0.1\u2009M KOH electrolyte37. The CuNa-CF catalyst exhibited the highest activity with the most positive half-wave potential (E1/2, 0.89\u2009V) among the as-prepared catalysts and the commercial 20\u2009wt% Pt/C catalyst (Fig.\u00a04a). It is worth noting that the CuNa-CF catalyst has a similar Cu coordination environment to that of CuPc-CF in the first coordination shell. The enhanced ORR performance of the CuNa-CF catalyst compared to the CuPc-CF catalyst can be attributed to the presence of Na-containing functional groups adjacent to C2-Cu-N4 sites in the CuNa-CF catalyst, which modulate the ORR catalytic activity of the C2-Cu-N4 sites. The half-wave potential of the CuPc+NaCl-CF catalyst is between that of CuNa-CF and CuPc-CF, providing further experimental evidence for the effect of the neighboring Na-containing functional group and confirming the significant role of the C2-Cu-N4-COONa site in the ORR process. During the synthesis of the CuPc+NaCl-CF catalyst, NaCl was randomly distributed in the PAN fibers, resulting in an uncontrolled coordination relationship between the Cu and Na atoms, which led to the difference in catalytic performance between the CuNa-CF and CuPc+NaCl-CF catalysts. Specifically, the ORR polarization curve of the CuNa-CF catalyst also exhibits an onset potential of 1.04\u2009V, which is 20\u2009mV and 30\u2009mV higher than those of the CuPc+NaCl-CF and Pt/C catalysts, respectively, suggesting that less energy is required to generate ORR intermediates and drive the ORR on the CuNa-CF electrode. Notably, CuNa-CF catalyst displayed the highest kinetic current density (Jk\u2009=\u200910.64\u2009mA\u2009cm\u22122) at 0.85\u2009V, surpassing other studied catalysts and the commercial Pt/C catalyst (Fig.\u00a04b, and the detailed data are listed in Supplementary Table\u00a04). Moreover, the CuNa-CF catalyst also exhibited a high kinetic current density of 4.51\u2009mA\u2009cm\u22122 at its half-wave potential (0.89\u2009V), representing its high intrinsic ORR electrocatalytic activity (Supplementary Fig.\u00a022). The Tafel slopes calculated from polarization curves are commonly used to analyze the ORR kinetics on different catalysts. The CuNa-CF catalyst displayed a lower Tafel slope compared to other catalysts, indicating reduced oxygen binding energy and accelerated ORR kinetics at the C2-Cu-N4-COONa site (Supplementary Fig.\u00a023 and Supplementary Table\u00a05). To further understand the catalytic processes of the CuNa-CF catalyst, linear sweep voltammetry (LSV) tests on a rotating disk at varying speeds from 400 to 1600\u2009rpm were carried out (Fig.\u00a04c). The limiting current density increased with the promotion of rotating speed, confirming that the ORR performance of CuNa-CF is highly dependent on the rate of oxygen diffusion, which conforms to the first-order kinetics model. By using the Koutecky-Levich equation, the electron transfer numbers at various potentials were calculated to be ~ 4 (Fig.\u00a04d), indicating that the ORR on the CuNa-CF catalyst follows a four-electron transfer pathway from O2 to OH\u2212. As shown in Fig.\u00a04e, a nearly complete four-electron transfer pathway for the ORR was also observed on both the CuNa-CF and Pt/C catalysts by operating rotating ring disk electrode measurement over a wide potential range, which is consistent with the findings calculated by Koutecky-Levich equation38. Notably, the yield of H2O2 with the CuNa-CF catalyst is less than 5% in a wide potential range from 0.2\u2009V to 0.9\u2009V, certifying that the ORR followed a highly selective and efficient four-electron transfer pathway.\n\na Oxygen reduction reaction polarization curves without iR correction for CuNa-CF, CuPc+NaCl-CF, CuPc-CF, NaCl-CF, CF, and commercial 20% Pt/C catalysts in O2-saturated 0.1\u2009M KOH solution at 1600\u2009rpm with a scan rate of 5\u2009mV\u2009s\u22121 (the resistance of the solution was 40\u2009\u00b1\u20095 \u03a9). b Comparison of onset potential (Eonset), half-wave potential (E1/2), and kinetic current density (Jk, at 0.85\u2009V, V versus RHE) for different catalysts. c Linear sweep voltammetry (LSV) curves of the CuNa-CF catalyst at different rotation speeds (400, 625, 900, 1225, and 1600\u2009rpm). d Koutecky-Levich plots and corresponding electron transfer numbers for the CuNa-CF catalyst at different potentials (0.2\u2009V, 0.3\u2009V, 0.4\u2009V, 0.5\u2009V, 0.6\u2009V, and 0.7\u2009V, V versus RHE). e H2O2 yield and electron transfer number of the CuNa-CF catalyst and Pt/C catalyst measured by the rotating ring-disk electrode (RRDE). f Long-term electrochemical stability of the CuNa-CF catalyst and Pt/C catalyst.\n\nApart from the ORR catalytic selectivity and activity, methanol tolerance and catalytic durability are also important in evaluating ORR catalysts39. As displayed in Supplementary Fig.\u00a024, a negligible attenuation in current density was recorded of the CuNa-CF catalyst during the methanol tolerance ability tests. In sharp contrast, the current density of Pt/C catalyst suffered from a sharp drop, highlighting the outstanding methanol tolerance ability of CuNa-CF. During the long-term stability test, the ORR current density of the commercial Pt/C catalyst decreased rapidly. In contrast, no significant decrement was observed with the CuNa-CF catalyst, and its final relative current remained at 97.85% even after 48\u2009h of the ORR electrocatalytic stability test (Fig.\u00a04f). As compared, the CuPc-CF (Na-free) catalyst showed poor ORR stability with only 63.27% relative current retained after a 10-hour chronoamperometry test (Supplementary Fig.\u00a025). The HAADF-STEM image reveals the aggregation of the Cu atoms after the long-term stability test (Supplementary Fig.\u00a026). Based on the above results, it is a promising way to enhance the stability of atomically dispersed Cu catalysts by constructing a Na-containing functional group adjacent to the C2-Cu-N4 active site, which could prevent the corrosion of carbon atoms around the active site by reducing the positive charge of the carbon atoms near the copper active site, and further avoid the migration, dissolution, and aggregation of the metal active center (Supplementary Note\u00a03 and Supplementary Figs.\u00a027 and 28). In addition, the Cu-N4-COONa sites embedded in the carbon matrix and the strong Cu-C coordination interaction can stabilize the Cu/Na site and enhance its ORR stability. Due to the rational design of the catalytic site, the CuNa-CF catalyst is comparable to or even surpasses other reported precious metal/non-precious metal catalysts (Supplementary Table\u00a06). To evaluate the practical application potential of this catalyst in batteries, we also examined its oxygen evolution reaction (OER) performance (including the OER catalytic activity and stability of the as-prepared catalysts). Surprisingly, this rationally designed catalytic site in the CuNa-CF catalyst also has significant facilitating effect on OER (Supplementary Note\u00a04, Supplementary Figs.\u00a029\u201332, and Supplementary Table\u00a07).\n\nEncouraged by the remarkable ORR/OER electrocatalytic activity and stability of the CuNa-CF catalyst, we assembled various types of Zn-air batteries by using CuNa-CF as the air cathode to demonstrate its potential applications in practical energy devices. Supplementary Figs.\u00a033 and 34 reveal that the CuNa-CF air cathode liquid-state ZAB delivers a high specific capacity of 621.55\u2009mAh\u2009g\u22121, corresponding to an energy density of 715.15\u2009Wh\u2009kg\u22121, which surpasses that of the battery with the commercial Pt/C catalyst as the air cathode (specific capacity of 612.23\u2009mAh\u2009g\u22121 and energy density of 645.73\u2009Wh\u2009kg\u22121). The CuNa-CF catalyst also achieved a peak power density of 264.18\u2009mW\u2009cm\u22122, which is obviously higher than that of the Pt/C cathode ZAB (Supplementary Fig.\u00a035), illustrating its considerable potential as an alternative to precious metal cathodes. Besides, the long-term discharge/charge cycle stability of ZAB is regarded as a critical judging indicator for practical applications. For liquid-state ZABs, the cycling stabilities of CuNa-CF and Pt/C\u2009+\u2009RuO2 air cathodes were evaluated by continuous discharge and charge tests at a constant current density (Supplementary Fig.\u00a036). As shown in Fig.\u00a05a, the CuNa-CF cathode ZAB demonstrates remarkable stability for more than 5000\u2009h with negligible changes in discharge/charge voltage at a constant current density of 1\u2009mA\u2009cm\u22122. Such high stability has rarely been reported to date (Supplementary Table\u00a08). After over 5000\u2009h of ZAB operational stability testing, the CuNa-CF catalyst was characterized again (Supplementary Fig.\u00a037a), and HAADF-STEM analysis confirmed that the Cu atoms remained homogeneously and densely dispersed in the carbon fibers without forming nanoclusters. Furthermore, in order to reveal the presence of neighboring Cu and Na atoms in the CuNa-CF catalyst after long-term discharge/charge cycle stability testing, HAADF-STEM imaging combined with corresponding EELS spectrum analysis were further conducted. A selection of 0.5\u2009nm\u2009\u00d7\u20090.5\u2009nm small area HAADF-STEM image and the corresponding EELS spectrum are shown in Supplementary Fig.\u00a037b\u2013d, the signals for Cu and Na atoms were both detected and provided strong evidence for the presence of neighboring Cu and Na atoms. Surprisingly, the ZAB with the CuNa-CF air cathode can also tolerate high current density discharge/charge cycles, and deliver a smooth discharge and charge cycling curve for more than 1200\u2009h at the current density of 10\u2009mA\u2009cm\u20132, indicating its outstanding rechargeable ability, which undoubtedly exceeds the performance of the commercial Pt/C\u2009+\u2009RuO2 cathode ZAB (Supplementary Figs.\u00a038 and 39). Inspired by the high discharge/charge cycle stability of ZABs with the CuNa-CF air cathode, we further conducted the discharge/charge cycle stability test of ZAB at a higher current density of 50\u2009mA\u2009cm\u22122. The catalyst loading was optimized first and the initial discharge voltage of ZAB reached its optimal value with a CuNa-CF catalyst loading of 1.0\u2009mg\u2009cm\u22122 (Supplementary Fig.\u00a040). Then, a ZAB with this optimal CuNa-CF catalyst loading on the air cathode was assembled and its discharge/charge cycle stability at a high current density of 50\u2009mA\u2009cm\u22122 was tested. As shown in Supplementary Fig.\u00a041, the ZAB with the CuNa-CF air cathode is still able to exhibit good discharge/charge cycle stability for over 950\u2009h even at a high constant current density of 50\u2009mA\u2009cm\u22122, further confirming the high electrocatalytic stability of the CuNa-CF catalyst and its application potential in rechargeable ZABs. As the CuNa-CF catalyst is a flexible membrane material, it can be directly used as the air cathode of both flexible solid-state ZAB and button-type all-solid-state ZAB. The schematic illustration of the flexible solid-state ZAB is shown in Fig.\u00a05b, in which the CuNa-CF membrane is employed as the air cathode and a home-made flexible hydrogel serves as the electrolyte. During the stability test at a constant current density of 1\u2009mA\u2009cm\u20132, although the flexible solid-state ZAB experienced folding and revert flattening states, it presented a highly stable discharge and charge profile (Fig.\u00a05c), indicating its practical application potential in flexible energy storage devices. In response to the development of small or micro appliances and the growing demand for button-type batteries, a button-type all-solid-state ZAB with CuNa-CF membrane air cathode was also assembled (Fig.\u00a05d). It is gratifying that the button-type all-solid-state ZAB held on a stable running for more than 1000\u2009min at a constant current density of 1\u2009mA\u2009cm\u20132 (Fig.\u00a05e). It was also capable of powering a series of LED lights on a wristband using just two series-connected batteries (Supplementary Fig.\u00a042), indicating the application ability of CuNa-CF membrane in miniature electrical devices.\n\na Discharge/charge cycling curves of CuNa-CF air cathode liquid-state zinc-air battery (ZAB). b Schematic illustration of the flexible solid-state ZAB. c Cycling stability of flexible solid-state ZAB with CuNa-CF membrane as the air cathode, and the insets are digital photos of the flexible solid-state ZAB in various states (flat/bent/revert flat). d Simplified schematic of the button-type all-solid-state ZAB. e Operating stability of button-type all-solid-state ZAB using CuNa-CF membrane as the air cathode.\n\nTo gain a deeper insight into the enhanced ORR electrocatalytic performance of the CuNa-CF catalyst, density functional theory (DFT) calculations were carried out40. Based on the HAADF-STEM, XAS and XPS results, the main active site in the CuNa-CF catalyst is identified as the Cu-N4-COONa site, also the ortho-C atoms in the underlying carbon lattice matrix serve as anchors for stabilizing the Cu active site. At first, the interactions between the Cu-N4-COONa active sites and the graphite adsorbates (C) were studied by analyzing the projected density of state (PDOS, Supplementary Fig.\u00a043), and we found that the graphene substrate barely influences the electronic structure of the Cu-N4-COONa site, except that the conductivity of the Cu-N4-COONa sites is significantly enhanced thanks to the \u03c0\u2013\u03c0 stacking. Due to the longer bond length between Cu and C (already exceeds 3 angstroms from EXAFS and DFT results) for CuNa-CF and CuPc-CF, the impact on the electronic structure for axially adjacent C atoms is minimal. Further PDOS analysis reveals that the combination with graphene has almost no effect on the position of the d-band center of the Cu 3d orbitals (Supplementary Fig.\u00a044). Thus, we primarily focus on the role of major active Cu-N4-COONa sites in CuNa-CF catalyst, and consider different atomistic configurations in further DFT calculations. As shown in Supplementary Figs.\u00a045 and 46, with -COONa adsorption on the S1 site of Cu-N4 monolayer, the Cu-N4-COONa shows the lowest total energy and is regarded as the most stable structure. After modification with the neighboring -COONa functional group, charge transfer and more charge accumulation can be observed at the Cu-N4 site (Fig.\u00a06a\u2013c), forming a unique electronic structure. As shown in Supplementary Fig.\u00a047, the introduction of the -COONa functional group increases the distribution of electronic states near the Fermi level in Cu-N4 site, and thus enhancing its conductivity. As a result, the introduction of the coordination environment (-COONa functional group) could modify the electronic states of the Cu-N4 active site, which in turn modulates its conductivity and further enhances its ORR electrocatalytic activity41,42,43,44. To further analyze the effect of the coordination environment on the catalytic activity, we further investigated the ORR catalytic process on the pure Cu-N4 site and the Cu-N4 site which modified with the -COONa functional group (Supplementary data\u00a01 and 2). For 4e\u2212 transfer ORR process, the metal active sites will adsorb oxygen molecules in the first step and the nearly positive adsorption energies of O2 on Cu-N4 sites (\u22120.08\u2009eV, Fig.\u00a06d) reveal its inertness. By contrast, the much more negative adsorption energies after the \u2013COONa coordination (\u22120.58\u2009eV) indicate that the Cu-N4-COONa site can spontaneously activate O2 molecules and ensure the subsequent ORR process. Moreover, the ORR free energy diagrams for pure Cu-N4 and Cu-N4-COONa are investigated in Fig.\u00a06e, f. Due to the weak protonation ability of O2 (*O2\u2009\u2192\u2009*OOH step), the Cu-N4 site shows a high ORR overpotential of 1.21\u2009V. After the -COONa modification, the ORR overpotential of Cu site in the Cu-N4-COONa configuration declines to 0.83\u2009V, suggesting that the adjacent ligand effect of -COONa is beneficial for optimizing the adsorption energies of ORR intermediates and improving the catalytic activity of Cu sites, in good agreement with our experimental results. Subsequently, according to the Bader charge transfer results (Fig.\u00a06g), the Cu-N4-COONa site (0.57 e) can accept more charge from *OOH than the pure Cu-N4 site (0.40 e), indicating the strong anchoring of OOH* on the Cu-N4-COONa site. The PDOS analysis also corroborates that the Cu-3d orbital are more overlapped with *OOH intermediates after the -COONa functional group modification, demonstrating the better activation for O2 molecules on the Cu-N4-COONa site. In order to quantify the bonding strength in electronic state, the crystal orbital Hamilton population (COHP) analysis was conducted (Fig.\u00a06h), in which the interaction between Cu and O atoms of adsorbed *OOH species is described by the product of their corresponding Hamiltonian matrix element and the densities of states matrix. From the COHP analysis, it can be seen that the absolute values of integrated COHP of Cu\u2013O bonds from adsorbed *OOH hybridization up to the Fermi level on Cu-N4-COONa site is larger than that of the pure Cu-N4 site, suggesting the stronger binding strength, and thus also further optimize the binding strength of ORR intermediates and guaranteeing better electrochemical catalytic performance. After that, considering the potential ion exchange of the Na ions in the CuNa-CF catalyst and the K ions in the electrolyte, ICP-MS and DFT calculations were further conducted. It was found that even the Cu-N4 site modified with the -COOK functional group, it can also exhibit an improvement in its ORR catalytic activity (Supplementary Note\u00a05, Supplementary Fig.\u00a048, and Supplementary data\u00a03). Combining the experimental and theoretical results, we believe this provides an efficient strategy and successful case for enhancing electrocatalytic activity through coordination with main-group metals containing functional groups.\n\nAtomistic structures of (a) Cu-N4 and (b) Cu-N4-COONa configurations. c Charge density differences of Cu-N4-COONa, the isosurface levels are set to 0.002 e \u00c5\u22123, where charge depletion and accumulation were depicted by cyan and yellow, respectively. It can be seen that there is charge accumulation on the C around COONa. d Adsorption energies for O2 on Cu-N4 and Cu-N4-COONa sites. The calculated Gibbs free energy evolution diagrams for ORR through a 4e\u2212 pathway on active sites of (e) Cu-N4 and (f) Cu-N4-COONa under electrode potential of U\u2009=\u2009\u20090\u2009V, where the elementary reaction in red dotted line represents the potential limiting step. g Projected density of state (PDOS) analysis of Cu-3d orbital with OOH intermediates on Cu-N4 and Cu-N4-COONa. Charge density differences and Bader charge transfer are illustrated inside. h The crystal orbital Hamilton population (COHP) analysis of Cu active sites and O atoms of OOH intermediates, the integrated crystal orbital Hamilton population (ICOHP) values (in eV per bond) are listed.",
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+            ]
+        },
+        {
+            "section_name": "Discussion",
+            "section_text": "Balancing the activity and stability of oxygen electrocatalysts is crucial for their practical applications, which has driven the exploration of non-Fe-based atomically dispersed M-N-C catalysts. Drawing inspiration from nature, we have synthesized a kind of atomically dispersed Cu-N-C catalyst via a facile solution blow spinning followed by pyrolysis strategy. To enhance the intrinsic activity of the Cu-N-C catalyst, a Na-containing functional group was introduced in proximity to the Cu-N4 active centers. The results revealed that the introduction of Na-containing functional group facilitated the adsorption/activation of O2 at the Cu-N4 site, thereby enhancing its intrinsic activity. Simultaneously, the introduction of Na-containing functional group can mitigate the carbon corrosion and stabilize the Cu-N4 sites, thereby improving its stability. Consequently, the obtained CuNa-CF catalyst exhibited remarkable ORR performance, particularly demonstrating a discharge/charge cycle stability of more than 5000\u2009h when used as the air cathode catalyst of ZAB. We believe that the concept and strategy of modulating Cu-N-C catalysts with the main-group element functional groups proposed in this work not only expand and enrich the research of main-group elements in electrocatalysis applications, but also provide guidance for the future design of non-Fe-based M-N-C oxygen electrocatalysts that balance activity and stability. Furthermore, it offers a reliable methodology for the development of high-performance non-precious metal-based air cathode catalysts for ZABs.",
+            "section_image": []
+        },
+        {
+            "section_name": "Methods",
+            "section_text": "Polyacrylonitrile (PAN, M.W.,150,000, Sigma Aldrich Co.), N,N-Dimethylformamide (DMF, 99.8%, Damas Beta Co., Ltd.), Chlorophyllin Sodium Copper Salt (95%, Meryer Shanghai Chemical Technology Co., Ltd.), Copper (II) Phthalocyanine (CuPc, 95%, Alfa Aesar Co., Ltd.), Sodium Chloride (NaCl, 99.5% Sigma Aldrich Co.), Methanol (99.8%, Sinopharm Chemical Reagent Co. Ltd), Potassium Hydroxide (KOH, 85%, General-Reagent Co., Ltd.), Zinc Acetate (Zn(CH3COO)2, 99.99%, Aladdin), Polyvinyl Alcohol (PVA, 99%, Shanghai Aladdin Bio-Chem Technology Co., Ltd.), Commercial Pt/C (Pt, 20\u2009wt%, Suzhou Sinero Technology Co., Ltd.), Ruthenium (IV) oxide (RuO2, 99.9% trace metals basis, Sigma-Aldrich), Nafion D-521 Dispersion (5%, Alda Aesar), and Isopropanol (99.7%, Sinopharm Chemical Reagent Co., Ltd.) were used as received. The ultrapure water was obtained from the Milli-Q System.\n\nIn a typical synthesis of the CuNa-CF catalyst, 0.1709\u2009g of chlorophyllin sodium copper salt was added to 10.0\u2009mL of DMF solution under vigorous agitation. The mixture was ultrasonicated for 30\u2009min and stirred for 24\u2009h to form a homogeneous solution. Then, 1.00\u2009g of PAN was added to the above solution under vigorous agitation and stirred for 48\u2009h to obtain a homogeneous and viscous solution. Subsequently, the solution was transferred into a 3\u2009mL syringe with a 30\u2009G needle and delivered at a constant flow rate of 1.00\u2009mL/h to the surrounding high-speed air jet flow (45.00\u2009L/min) for solution blow spinning process. The distance between the tip of nozzle and the non-woven collector was 35\u2009cm. The obtained chlorophyllin sodium copper-PAN membrane was dried in the vacuum oven at 60\u2009\u00b0C overnight. Then, the chlorophyllin sodium copper-PAN membrane was pre-oxidized in air at 260\u2009\u00b0C for 3\u2009h with a heating rate of 1\u2009\u00b0C/min. Finally, the pre-oxidized chlorophyllin sodium copper-PAN membrane was annealed at 900\u2009\u00b0C for 2\u2009h under a gas flow of 100 sccm Ar with a heating rate of 5\u2009\u00b0C/min. After cooling to 25\u2009\u00b0C, the CuNa-CF catalyst was obtained. By replacing the chlorophyll sodium precursor with copper phthalocyanine, copper phthalocyanine and sodium chloride, sodium chloride, and no metal precursor, we also synthesized CuPc-CF catalyst, CuPc+NaCl-CF catalyst, NaCl-CF catalyst, CF catalyst, respectively.\n\nTransmission electron microscopy (TEM) images of the as-synthesized catalysts were obtained using a JEM-2100F. Field emission scanning electron microscope (FE-SEM) images were acquired with a JEOL JSM-7001F. Aberration-corrected high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) images and energy dispersive X-ray spectroscopy (EDS) mapping images were attained on a FEI Titan 80\u2013300 (acceleration voltage, 300\u2009kV). Powder X-ray diffraction (XRD) patterns were collected with a D/max-2500/PC powder diffractometer using monochromatized Cu-K\u03b1 radiation (\u03bb\u2009=\u20090.15418\u2009nm, 9\u2009kW). X-ray photoelectron spectroscopy (XPS) was performed with a Thermo Fisher ESCALAB 250Xi. Quantitative analysis of the metal loading in different catalysts was conducted using an Agilent ICP-MS 8800. The Raman spectra were collected with a Horiba LabRAM HR Evolution Raman microscope using 532\u2009nm laser excitation. The specific surface area and porosity were measured by isothermal nitrogen adsorption-desorption analysis on an Autosorb-iQ1-MP. The specific surface areas were calculated using the multi-point Brunaure-Emmert-Teller (BET) method. The thermogravimetric analysis (TGA) was performed on a NETZSCH-TGA-X70 over the temperature range from 25\u2009\u00b0C to 900\u2009\u00b0C in an argon atmosphere. Fourier transform infrared spectroscopy (FT-IR) spectra were recorded using a Spotlight 400 Perkin-Elmer infrared spectrum microscope. The absorption spectra of the Cu K-edge were measured by 1W1B beamline of Beijing Synchrotron Radiation Facility (BSRF, China) in fluorescence mode. The X-ray absorption spectroscopy (XAS) data were analyzed using Athena software and the Fourier-transformed EXAFS fitting curves in R-space were obtained using Artemis module of IFEFFIT software packages. All spectra were collected under ambient conditions.\n\n1\u2009mg of the as-prepared catalyst was dispersed in 200\u2009\u03bcL of a mixture solution containing 95\u2009\u03bcL of isopropanol, 95\u2009\u03bcL of ultrapure water and 10\u2009\u03bcL of Nafion solution. The mixture was ultrasonicated for 3\u2009h to form a homogeneous catalyst ink. Then 8\u2009\u03bcL of the catalyst ink was dropped onto the surface of a polished glassy carbon rotating disk electrode (RDE, Pine Research Instrumentation) or a rotating ring-disk electrode (RRDE, Pine Research Instrumentation) followed by drying in the air. The resulting electrode was used as the working electrode for the oxygen reduction reaction (ORR) with a catalyst loading of approximately 0.2\u2009mg\u2009cm\u22122. For oxygen evolution reaction (OER), 10\u2009\u03bcL of the catalyst ink was loaded onto the surface of the carbon cloth (0.25 cm2) and used as the working electrode, with a catalyst loading of 0.2\u2009mg\u2009cm\u22122. The commercial Pt/C catalyst and RuO2 catalyst-modified electrodes were prepared in the same way.\n\nAll electrochemical tests were conducted in a conventional three-electrode system at a temperature of 25\u2009\u00b1\u20091\u2009\u00b0C by employing a CHI 760E electrochemical station (Shanghai Chenhua Instruments Company) equipped with a Pine Modulated Speed Rotator. A graphite rod (Shanghai Chenhua Instruments Company) and an Ag/AgCl electrode (3.5\u2009M KCl, Shanghai Chenhua Instruments Company) were used as the counter electrode and reference electrode, respectively. The obtained potentials were normalized to the reversible hydrogen electrode (RHE) according to Nernst equation (\\({E}_{{RHE}}={E}_{{Ag}/{AgCl}}+0.0591\\times {pH}+0.205\\)). For ORR, a rotating disk electrode or rotating ring-disk electrode coated with the as-prepared catalyst were served as the working electrodes. The electrolyte was 0.1\u2009M KOH solution (pH = 13.0\u2009\u00b1\u20090.2), and the resistance of the solution was 40\u2009\u00b1\u20095 \u03a9. Prior to measurement, the O2 was purged in the electrolyte for about 30\u2009min to keep saturated O2 in the electrolyte. The linear sweep voltammetry (LSV) experiments were performed with a scan rate of 5\u2009mV\u2009s\u22121 at various disk rotation speeds of 400, 625, 900, 1225, and 1600\u2009rpm. The number of electrons transferred (n) at different potentials were calculated by using Koutecky-Levich Eqs. (1)-(3):\n\nHere J is the measured current density (mA cm\u22122), JL and JK are the diffusion-limiting current density (mA cm\u22122) and kinetic current density (mA cm\u22122), \u0277 is the angular velocity of the disk (rpm), n represents the electron transfer number, F is the Faraday constant (96485\u2009C\u2009mol\u22121), Co is the saturated O2 concentration (1.2\u00d710\u22126\u2009mol\u2009cm\u22123), Do is the diffusion coefficient of O2 in the electrolyte (1.9\u00d710\u22125 cm2 s\u22121), V is the kinematic viscosity (0.01 cm2 s\u22121). RRDE test is the most effective way to test and calculate the electron transfer number and the yield of hydrogen peroxide (Eqs.\u00a04\u20135):\n\nHere Id is the disk current and Ir is the ring current, N is the H2O2 collection coefficient at the ring. Long term stability tests were carried out by measuring the current changes under an operation potential of 0.66\u2009V (vs. RHE) for 48\u2009h.\n\nFor OER, the electrolyte was 1.0\u2009M KOH solution (pH = 13.8\u2009\u00b1\u20090.2), and the resistance of the solution was 6\u2009\u00b1\u20091 \u03a9. The OER performance of the as-prepared catalysts were obtained from LSV with a scan rate of 10\u2009mV\u2009s\u22121. The long-term stability tests were carried out by conducting chronopotentiometry (V-t) test for 48\u2009h under a constant current density of 10\u2009mA\u2009cm\u22122 for each catalyst.\n\nA homemade liquid-state zinc-air cell was assembled to evaluate the catalytic activity of the as-prepared catalyst in practical applications. A polished zinc foil (1.5\u2009cm\u00d71\u2009cm) was used as the anode, a gas diffusion layer coated with the catalyst (1\u2009cm\u00d71\u2009cm) served as the air cathode. The electrolyte was a mixture solution of 6.0\u2009M KOH and 0.2\u2009M zinc acetate. The specific capacity and energy density were collected by galvanostatic discharge testing at a current density of 10\u2009mA\u2009cm\u22122 until the zinc foil in contact with the electrolyte was fully reacted, and then normalized to the consumed mass of the Zn foil (Eq.\u00a06).\n\nHere, Idischarge is the discharge current density (10\u2009mA\u2009cm\u22122), T is the time when reaction stops, mZn1 and mZn2 are the weights of the Zn foil before and after discharge process, respectively. The discharge/charge cycle stability tests were held at constant current densities of 1\u2009mA\u2009cm\u22122, 10\u2009mA\u2009cm\u22122 and 50\u2009mA\u2009cm\u22122 (catalyst loading: 0.2\u2009mg\u2009cm\u22122 for 1\u2009mA\u2009cm\u22122 and 10\u2009mA\u2009cm\u22122, 1.0\u2009mg\u2009cm\u22122 for 50\u2009mA\u2009cm\u22122). All tests were operated in ambient environment with the LAND testing system (LAND Electronics Ltd.).\n\nFor the flexible solid-state zinc-air battery, a PVA-KOH-Zn(CH3COO)2 hydrogel polymer was used as the electrolyte. The hydrogel was prepared by dissolving 2.00\u2009g of polyvinyl alcohol (PVA) in 20\u2009ml of deionized water and stirring for 2\u2009h at 90\u2009\u00b0C. Then, 2\u2009ml of 6.0\u2009M KOH solution with 0.2\u2009M Zn(CH3COO)2 was added to the above mixture and stirred for 0.5\u2009h to form a homogeneous solution. Finally, the gel was poured onto a plate and the PVA-KOH-Zn(CH3COO)2 hydrogel polymer was obtained after cooling in a freezer. The catalyst membrane (5\u00d710\u2009mm) and a polished zinc foil were used as the air cathode and anode, respectively. The battery testing method followed the procedure used for the liquid-state zinc-air battery (the stability test was hold at a constant current density of 1\u2009mA\u2009cm\u22122).\n\nA button-type all-solid-state zinc-air battery is also composed of an air cathode (catalyst membrane), a zinc foil anode (0.1\u2009mm thickness) and an electrolyte hydrogel polymer (PVA-KOH-Zn(CH3COO)2 hydrogel polymer prepared using the same method as for the flexible solid-state zinc-air battery). The battery testing method followed the procedure used for the liquid-state zinc-air battery (the stability test was hold at a constant current density of 1\u2009mA\u2009cm\u22122).\n\nAll of the calculations were performed by means of spin polarized density functional theory (DFT) methods using the Vienna Ab initio Simulation Package (VASP)45. The projector augmented wave (PAW) method was adopted to describe electron-ion interaction45. The Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional within a generalized gradient approximation (GGA) was employed, while a 520\u2009eV cut off energy for the plane-wave basis set was used for the valence electrons. Moreover, the DFT-D3 scheme of dispersion correction was used to describe the van der Waals (vdW) interactions in molecule adsorption46. The self-consistent filed (SCF) calculations were performed with an energy and force convergence criterion of 10\u22125\u2009eV and 0.02\u2009eV\u2009\u00c5\u22121, respectively. To avoid the interactions between two adjacent periodic images, the vacuum thickness was set to be 15\u2009\u00c5. The atomic structures were analyzed by using the VESTA code47. The free energy correction in ORR was obtained similarly by including the ZPE and entropic contributions from vibrational degrees of freedom calculated with the substrate fixed.\n\n(1) Computational details of the Gibbs free energy for 4e\u2212 ORR. The reaction steps considered for the electrochemical reduction of 4e\u2212 ORR under base condition are generally reported to proceed as follow (Eqs.\u00a07\u221211):\n\nHere * represents either the catalytic active sites of vacant surface, or intermediate species adsorbed on the active sites. By considering the zero-point energy (ZPE) and entropy corrections, the Gibbs free energy for ORR can be calculated with the following Eq.\u00a01248:\n\nHere \u0394E indicates the adsorption energy difference for each species adsorbed on the catalyst, \u0394ZPE and \u0394S are the zone point energy and entropy difference between the adsorbed state and corresponding free-standing state, respectively. The calculated values of \u0394ZPE and \u0394S are listed as follows:\n\nSpecies\n\nPressure (bar)\n\nTemperature (K)\n\nEnergy (eV)\n\nZPE (eV)\n\nTS (eV)\n\nH2O\n\n0.035\n\n298.15\n\n\u221214.23\n\n0.57\n\n0.58\n\nH2\n\n1\n\n298.15\n\n\u22126.77\n\n0.27\n\n0.40\n\nO2\n\n1\n\n298.15\n\n\u22129.86\n\nHere \\(\\hslash\\) is the reduced Planck constant and \\({\\omega }_{j}\\) is the frequency associated with the harmonic mode in the gamma point. The same values for the adsorbed species are used throughout the entire text, as vibrational frequencies have been found to depend much less on the catalyst surface. The contributions (TS) values of the free molecules are taken from the NIST database50, For water, the entropy is calculated at 0.035\u2009bar through S=S0\u2009+\u2009kBTln(P/P0) to derive the chemical potential of liquid water, because at this pressure gas-phase water is in equilibrium with liquid water at 298.15\u2009K.\n\n(2) Electronic Structure Analysis. Crystal orbital Hamilton population (COHP) analysis was performed with the LOBSTER 3.2.0 package, which reconstructs the orbital-resolved wave functions via projection of the delocalized PAW to localized atomic-like basis sets51,52. Basis sets given by Koga with additional functions fitted to atomic VASP-PBE wave functions were used53,54. Atomic charges were computed using the atom-in-molecule (AIM) scheme proposed by Bader55. The electron density differences were evaluated using the formula \u0394\u03c1\u2009=\u2009\u03c1(AB) - \u03c1(A) - \u03c1(B), then analyzed by using the VESTA code.",
+            "section_image": []
+        },
+        {
+            "section_name": "Data availability",
+            "section_text": "All data needed to evaluate the conclusions in the paper are present in the paper and/or the Supplementary Information.\u00a0Source data are provided with this paper.",
+            "section_image": []
+        },
+        {
+            "section_name": "References",
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+        },
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+            "section_name": "Acknowledgements",
+            "section_text": "We acknowledge the support from the National Natural Science Foundation of China (Grant Nos. 52371228, 51972191 of Ruitao Lv), the National Key Research and Development Program of China (Grant Nos. 2021YFA1200800, 2021YFC2902900, 2021YFF0500503 of Ruitao Lv and Chen Chen), the National Natural Science Foundation of China (Grant Nos. 21925202, U22B2071 of Chen Chen), Yunnan Provincial Science and Technology Project at Southwest United Graduate School (Grant No. 202302AO370017 of Chen Chen), and International Joint Mission on Climate Change and Carbon Neutrality (Chen Chen).",
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+            "section_name": "Author information",
+            "section_text": "Yifan Li\n\nPresent address: Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Canada\n\nAijian Huang\n\nPresent address: Department of Chemistry and Biochemistry, University of California, Los Angeles, Los Angeles, CA, USA\n\nThese authors contributed equally: Yifan Li, Aijian Huang.\n\nState Key Laboratory of New Ceramics and Fine Processing, School of Materials Science and Engineering, Tsinghua University, Beijing, China\n\nYifan Li,\u00a0Lingxi Zhou,\u00a0Bohan Li,\u00a0Muyun Zheng\u00a0&\u00a0Ruitao Lv\n\nEngineering Research Center of Advanced Rare Earth Materials, Department of Chemistry, Tsinghua University, Beijing, China\n\nAijian Huang,\u00a0Chang Chen\u00a0&\u00a0Chen Chen\n\nCollege of Materials Science and Engineering, Fuzhou University, Fuzhou, China\n\nZewen Zhuang\n\nKey Laboratory of Advanced Materials (MOE), School of Materials Science and Engineering, Tsinghua University, Beijing, China\n\nFeiyu Kang\u00a0&\u00a0Ruitao Lv\n\nGuangdong Provincial Key Laboratory of Thermal Management Engineering and Materials and Institute of Materials Research, Tsinghua Shenzhen International Graduate School, Tsinghua University, Shenzhen, China\n\nFeiyu Kang\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nRuitao Lv and Yifan Li conceived and designed the project. Yifan Li carried out the sample synthesis, characterizations, electrochemical measurements, and manuscript writing. Chang Chen contributed to the zinc-air batteries tests and manuscript writing. Aijian Huang and Chen Chen carried out the computational investigation and provided the analyses. Zewen Zhuang contributed to the analysis of the XAS results. Feiyu Kang contributed to the discussion and revision of the manuscript. Lingxi Zhou, Bohan Li, and Muyun Zheng helped to discuss the experimental data. Ruitao Lv is responsible for the overall supervision of the project. All the authors participated in preparing the manuscript and contributed to the discussion.\n\nCorrespondence to\n                Chang Chen, Chen Chen or Ruitao Lv.",
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+            "section_text": "Nature Communications thanks Xiao-Chun Wang, Yuan-Yao Li, and Ramendra Sundar Dey for their contribution to the peer review of this work. A peer review file is available.",
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+            "section_image": []
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+            "section_text": "Li, Y., Huang, A., Zhou, L. et al. Main-group element-boosted oxygen electrocatalysis of Cu-N-C sites for zinc-air battery with cycling over 5000\u2009h.\n                    Nat Commun 15, 8365 (2024). https://doi.org/10.1038/s41467-024-52494-0\n\nDownload citation\n\nReceived: 06 December 2023\n\nAccepted: 10 September 2024\n\nPublished: 27 September 2024\n\nVersion of record: 27 September 2024\n\nDOI: https://doi.org/10.1038/s41467-024-52494-0\n\nAnyone you share the following link with will be able to read this content:\n\nSorry, a shareable link is not currently available for this article.\n\n\n\n\n                            Provided by the Springer Nature SharedIt content-sharing initiative\n                        ",
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+            "section_name": "This article is cited by",
+            "section_text": "Nature Communications (2025)\n\nRare Metals (2025)",
+            "section_image": []
+        }
+    ]
+}

26d52d823145ea21a1a607520d91858a4edffd9242234a28dbea7be9bba9acc3/metadata.json

@@ -0,0 +1,146 @@
+{
+    "title": "Giant electric field-induced second harmonic generation in polar skyrmions",
+    "pre_title": "Giant electric field-induced second harmonic generation in polar skyrmions",
+    "journal": "Nature Communications",
+    "published": "14 February 2024",
+    "supplementary_0": [
+        {
+            "label": "Supplementary Information",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-024-45755-5/MediaObjects/41467_2024_45755_MOESM1_ESM.pdf"
+        },
+        {
+            "label": "Peer Review File",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-024-45755-5/MediaObjects/41467_2024_45755_MOESM2_ESM.pdf"
+        },
+        {
+            "label": "Description of Additional Supplementary Files",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-024-45755-5/MediaObjects/41467_2024_45755_MOESM3_ESM.pdf"
+        },
+        {
+            "label": "Supplementary Movie 1",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-024-45755-5/MediaObjects/41467_2024_45755_MOESM4_ESM.gif"
+        },
+        {
+            "label": "Supplementary Movie 2",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-024-45755-5/MediaObjects/41467_2024_45755_MOESM5_ESM.gif"
+        },
+        {
+            "label": "Reporting Summary",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-024-45755-5/MediaObjects/41467_2024_45755_MOESM6_ESM.pdf"
+        }
+    ],
+    "supplementary_1": NaN,
+    "supplementary_2": NaN,
+    "source_data": [],
+    "code": [],
+    "subject": [
+        "Nonlinear optics"
+    ],
+    "license": "http://creativecommons.org/licenses/by/4.0/",
+    "preprint_pdf": "https://www.researchsquare.com/article/rs-3457550/v1.pdf?c=1708002897000",
+    "research_square_link": "https://www.researchsquare.com//article/rs-3457550/v1",
+    "nature_pdf": "https://www.nature.com/articles/s41467-024-45755-5.pdf",
+    "preprint_posted": "21 Nov, 2023",
+    "research_square_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Electric field-induced second harmonic generation (EFISH) allows electrically controlling nonlinear light-matter interactions crucial for emerging integrated photonics applications. Despite its wide presence in materials, the figures-of-merit of EFISH are yet to be elevated to enable novel device functionalities. Here, we show that the polar skyrmions, a topological phase spontaneously formed in PbTiO3/SrTiO3 ferroelectric superlattices, exhibit an outstanding comprehensive EFISH performance. The second-order nonlinear susceptibility and modulation depth, measured under non-resonant 800 nm excitation, reach ~54.2 pm V-1 and ~664% V-1, respectively, and high response bandwidth (at gigahertz scales), wide operating temperature range (up to ~400 K) and good fatigue resistance (>1010 cycles) are also demonstrated. Through combined in-situ experiments and phase-field simulations, we establish the microscopic links between the exotic polarization configuration and field-induced transition paths of the skyrmions and their EFISH response. Our study not only presents a highly competitive thin-film material platform ready for constructing on-chip devices, but opens up new avenues of utilizing topological polar structures in the fields of photonics and optoelectronics.Physical sciences/Materials science/Materials for optics/Nonlinear opticsPhysical sciences/Optics and photonics/Optical physics/Nonlinear optics",
+            "section_image": []
+        },
+        {
+            "section_name": "Additional Declarations",
+            "section_text": "There is NO Competing Interest.",
+            "section_image": []
+        },
+        {
+            "section_name": "Supplementary Files",
+            "section_text": "EFISHSI231017.pdfMovieS1Pip2.gifMovie S1MovieS2Pxz2.gifMovie S2",
+            "section_image": []
+        }
+    ],
+    "nature_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Electric field-induced second harmonic generation allows electrically controlling nonlinear light-matter interactions crucial for emerging integrated photonics applications. Despite its wide presence in materials, the figures-of-merit of electric field-induced second harmonic generation are yet to be elevated to enable novel device functionalities. Here, we show that the polar skyrmions, a topological phase spontaneously formed in PbTiO3/SrTiO3 ferroelectric superlattices, exhibit a high comprehensive electric field-induced second harmonic generation performance. The second-order nonlinear susceptibility and modulation depth, measured under non-resonant 800\u2009nm excitation, reach ~54.2\u2009pm\u2009V\u22121 and ~664% V\u22121, respectively, and high response bandwidth (higher than 10\u2009MHz), wide operating temperature range (up to ~400\u2009K) and good fatigue resistance (>1010 cycles) are also demonstrated. Through combined in-situ experiments and phase-field simulations, we establish the microscopic links between the exotic polarization configuration and field-induced transition paths of the skyrmions and their electric field-induced second harmonic generation response. Our study not only presents a highly competitive thin-film material ready for constructing on-chip devices, but opens up new avenues of utilizing topological polar structures in the fields of photonics and optoelectronics.",
+            "section_image": []
+        },
+        {
+            "section_name": "Introduction",
+            "section_text": "Second-harmonic generation (SHG) is a second-order nonlinear optical (\u03c7(2)) process in which two photons with \u03c9 frequency combine into one frequency-doubled (2\u03c9) photon. Since its discovery in 1961, SHG has been widely employed in the realm of lasers and optoelectronic devices as well as in materials and biomedical sciences as the fundamental basis of powerful characterization methods1,2,3. More recently, the advent of integrated photonic platforms has fostered emerging on-chip devices such as all-optical switches, frequency combs, and quantum light sources4,5,6. Emerging SHG devices demand integratable materials in which nonlinear optical properties can preferably be tuned by an applied electric field to enable electrical modulation and/or reconfiguration functionalities. As mediated by a third-order nonlinear optical (\u03c7(3)) process which imposes no restraints on crystal symmetries, electric field-induced second-harmonic generation (EFISH) has been studied for various materials, including optical crystals7,8, polymers9, (strain-free) silicon10,11, layered metal chalcogenides12,13,14,15,16 and artificial photonic structures17,18. However, these materials in general exhibit weak effective \u03c7(2) susceptibilities (which is the product of the \u03c7(3) susceptibility and electric field) and low modulation depths (mostly a few percent per volt), limiting their applications. Alternatively, tunable SHG can be realized in polar, \u03c7(2)-active materials by altering their crystallographic structures or domain microstructures. The switching of ferroelectric domains is accompanied by modulation of SHG responses due to an interference effect between the opposite domains, which can be appreciable depending on specific domain configurations within the illuminated material volumes19,20. Large SHG modulation can also be generated through an electrically induced transition between polar and nonpolar phases, as exemplified by BiFeO3/TbScO3 superlattices21 and MoTe2 monolayers15. However, such processes typically occur at mesoscopic scales and are determined by the phase front or domain wall propagation kinetics, invariably resulting in hysteretic and sluggish modulation responses further to be plagued by fatigue phenomena. The combination of hysteresis and slow modulation significantly reduces the utility of the high SHG modulation depths exhibited by conventional polar materials.\n\nRecent observations of topological polar structures bring new opportunities for discovering and designing optoelectronic functionalities. These polar structures include, for instance, vortices, skyrmions and merons hosted in PbTiO3/SrTiO3 superlattices or multilayers22,23,24,25,26,27,28,29. The polarization configurations commonly feature a nanosized periodic unit with swirling electric dipoles and long-range in-plane ordering of the polar units. Local regions with highly frustrated polarization are stabilized in these polar structures, resembling N\u00e9el or Bloch types of domain walls. Emergent properties result from the rich structural characteristics, including negative permittivity30, SHG circular dichroism31 and sub-terahertz collective dynamics32. Several studies have also examined the in situ polarization evolution of polar vortices and skyrmions, indicating their responsiveness to external stimuli with large alterations of the polarization magnitude33,34,35,36. These results thus hint at the potential of topological polar structures for SHG modulation.\n\nHere, we introduce a polar-skyrmionic EFISH effect, shown schematically in Fig.\u00a01a. In the ground state, the skyrmions collectively are \u03c7(2)-inactive due to the pseudo-centrosymmetry exhibited by the dipoles of each skyrmion and the interfacial c-domain region surrounding it. Symmetry breaking results from applying an electric bias to tip the balance of the dipoles and engenders a strong SHG response. This process does not involve the nucleation or motion of domain walls and thus can be tuned rapidly and reversibly with electric bias, yielding giant SHG modulation depths that are not available in spatially simpler polarization configurations. Other advantages of the exotic polarization configuration of the skyrmions, described below, also contribute to a highly appealing overall EFISH performance. PbTiO3/SrTiO3 superlattices (and similar ferroelectric/dielectric systems of other materials) can be readily adopted for constructing on-chip optoelectronic devices, either by direct epitaxial growth or through the transfer and integration of released oxide membranes. Our study advances the understanding of nonlinear optical properties of topological polar structures and may lead to new directions in integrated photonics.\n\na Phase-field model-adapted schematic of an electric field-induced transition (1\u2009MV\u2009cm\u22121 for the right part) in the polarization vector (arrows) configuration of polar skyrmions that engenders an enhanced second-harmonic generation response. b H0L-slice (at Qy\u2009=\u20090\u2009\u00c5\u22121) X-ray reciprocal space map around the LSAT 002 reflection for a [(PbTiO3)14/(SrTiO3)16]8 superlattice, with the arrow denoting the superlattice (SL) periodicity along the Qz direction. Inset: HK0-slice (at Qz\u2009=\u20093.097\u2009\u00c5\u22121) reciprocal space map showing the in-plane skyrmion periodicity with four strong lobes along the H00/0K0 directions. c Cross-sectional HAADF-STEM image of [(PbTiO3)14/(SrTiO3)16]8 superlattices, displaying distinct intensity contrast for the constituent layers as marked. Scale bar\u2009=\u200920\u2009nm. d, Energy-dispersive X-ray spectroscopy mapping for Pb, Sr and Ti. e\u2013g High-resolution HAADF image (e) and corresponding polar displacement (f) and electric field (g) distribution maps for a PbTiO3 layer region containing a skyrmion. The phase-field simulated Pz distribution is overlaid in (f). g is extracted from the measured DPC images. Scale bar\u2009=\u20092\u2009nm.",
+            "section_image": [
+                "https:////media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41467-024-45755-5/MediaObjects/41467_2024_45755_Fig1_HTML.png"
+            ]
+        },
+        {
+            "section_name": "Results",
+            "section_text": "As a model system, we focus on ~96\u2009nm [(PbTiO3)14/(SrTiO3)16]8 superlattices epitaxially grown on (001)-cut (LaAlO3)0.3-(SrAl0.5Ta0.5O3)0.7 (LSAT) substrates buffered with a conducting 5\u2009nm SrRuO3 layer. In comparison with the polar skyrmion-hosting superlattices previously realized on SrTiO3 substrates, we select LSAT substrate as it exhibits much lower absorptivity at terahertz frequencies and larger contrast in the refractive indices with PbTiO3 and SrTiO337,38, facilitating the guided propagation of light in the superlattices. We have controlled the growth conditions such that the substrate misfit strain is partially (by about 1%, biaxially) relaxed within the SrRuO3 buffer layers via a low-concentration array of edge dislocations at the SrRuO3/LSAT interface, as confirmed by cross-section scanning transmission electron microscopy (STEM) imaging and X-ray reciprocal space mapping (RSM) about the LSAT 013 and 103 in-plane reflections (Supplementary Fig.\u00a0S1). Relaxing of the epitaxial mismatch within the SrRuO3 layer is critical to achieving a sufficiently low defect density and strain gradient in the subsequent growth of the superlattice. A three-dimensional (3D) RSM about the LSAT 002 reflection (Fig.\u00a01b), together with the two in-plane RSMs, reveals excellent crystallinity of the resultant superlattices. Well-defined thickness fringes are observed along the out-of-plane direction in agreement with the designed layer periodicity of ~12\u2009nm (that is, 30 unit cells). Along the in-plane directions, diffraction satellites appear at wavevectors separated from the 00L rod by ~0.083\u2009\u00c5\u22121, which equates to a real-space periodicity of ~7.6\u2009nm, with a fourfold lobe pattern of the satellites. These features are apparent in the HK0 RSM (Fig.\u00a01b, inset). The diffraction features indicate the occurrence of well-populated polar skyrmions with a large extent of in-plane ordering along the [100] and [010] directions.\n\nThe real-space configuration of the skyrmions was probed using cross-section STEM acquired in both high-angle annular dark-field (HAADF) and differential phase contrast (DPC) modes, as presented in Fig.\u00a01c\u2013g. Large-scale HAADF images (Fig.\u00a01c) show uniform layers of PbTiO3 and SrTiO3 with clear interfaces. Elemental mapping results confirm no interdiffusion between the two constituent layers (Fig.\u00a01d), again attesting to the high growth quality. The HAADF intensity contrast reflects the locations of cation columns, from which polar displacement vectors can be derived. Local electric field information can be semi-quantitatively extracted from the vectorial DPC signals. Correlative distribution maps of local polar displacement and electric field vectors are illustrated for a region of a single PbTiO3 layer within the superlattice in which there is a skyrmion with two interfacial c-domains (Fig.\u00a01e\u2013g). Line profiles of the z components Pz and Ez are depicted around the center of the skyrmion in Supplementary Fig.\u00a0S1e. The polarization and electric field alternate with opposite directions across the skyrmion walls. In the imaged region, the polarization vectors form clockwise/anti-clockwise swirling patterns and have greatly suppressed polarization magnitude, reminiscent of N\u00e9el-type domain walls. Altogether, these structural characteristics are consistent with the previous accounts of polar skyrmions25,28,30, suggesting an optimal testbed of our PbTiO3/SrTiO3 superlattices for exploring their nonlinear optical properties.\n\nThe EFISH effect of the skyrmions was measured at a macroscopic device level using thin-film capacitor devices. The test devices consisted of all-oxide, symmetric SrRuO3/superlattice/SrRuO3 capacitors with a diameter of 100 \u03bcm fabricated by chemical etching lithography (see details in \u201cMethods\u201d). The top SrRuO3 layer serves both as an electrode and a semi-transparent optical window for SHG measurements. The normal incidence geometry allows in-focus imaging via laser scanning39, as shown in Supplementary Fig.\u00a0S2 and the SHG intensity map inset of Fig.\u00a02a. The EFISH response of the capacitors has a distinct and uniform (except for the electrode boundaries) SHG intensity contrast for the biased region and a constant background signal for the outside region. Focusing at a single spot on the capacitor, the SHG intensity as a function of bias voltage and angles of the input/output light polarization (that is, SHG polarimetry) can be acquired, as shown in Supplementary Fig.\u00a0S2. These measurements yield systematic evolution trends that are well reproducible among a few tens of capacitors tested in this study, signifying the robustness of the EFISH effect. Nevertheless, we have determined that the polar skyrmions can be more effectively probed in the 45\u00b0 incidence geometry (see Fig.\u00a02a, inset), as opposed to the normal incidence one, because their dominant, out-of-plane polarization vectors can couple with a non-zero z-component of the light electric field in the former case, and thus shifted the emphasis to addressing the former results.\n\na Measured SHG intensity as a function of applied voltage for different polarization states (p-, parallel and s-, perpendicular to the plane of incidence) of the input fundamental light. The bias voltage sequence in each cycle was from 0 to 20\u2009V, then to \u221220\u2009V and back to 0\u2009V. Insets: schematic of the 45\u00b0 measurement geometry of in situ SHG on a SrRuO3/superlattice/SrRuO3 (SRO/SL/SRO) capacitor device, and a SHG image near the electrode boundary measured in the normal incidence geometry. Scale bar\u2009=\u200910\u2009\u03bcm. b, c Polar plots of the input polarization angle-dependent SHG intensity measured under (b) 0\u00b0 (p-out) and (c) 90\u00b0 (s-out) output polarization conditions. Lines are model-fitting results to the measured data points. An average laser power of ~200\u2009mW was delivered onto the samples in these measurements.\n\nFigure\u00a02a presents typical bias voltage-induced evolution trends of the SHG response. Under the p-in/p-out (light polarization) conditions, the SHG intensity in Fig.\u00a02a increases from the background level (that is, weak to no definite response at 0\u2009V) rapidly until an inflection point at ~10\u2009V, after which the increasing trend slows down with gradual saturation and mild signs of decline set in at ~15\u2009V. For negative biases (from 0 to \u221220\u2009V), a similar trend is observed albeit with a lower enhancement factor (~0.3 times) of the maximum SHG intensity. Such evolution trends are found to be fully reversible and almost hysteresis-free during each cycle (especially within the \u00b110\u2009V range); applying larger voltages could quickly result in irreversible degradations of the capacitors due to elevated leakage currents.\n\nThe results in Fig.\u00a02 highlight that the PbTiO3/SrTiO3 superlattices with polar skyrmions have a giant EFISH modulation depth. The modulation depth, defined as \u0394I2\u03c9(Vbias)/I2\u03c9(Vbias=0), reaches a peak value of ~664%\u2009V\u22121 at 7\u2009V. Such a giant modulation effect is entirely absent in single-layer PbTiO3 (c-domain structure) and SrTiO3 epitaxial films measured using the same methods (Supplementary Fig.\u00a0S3) and thus is a result of the polarization configuration of the PbTiO3/SrTiO3 superlattices rather than a consequence of the individual properties of the component layers.\n\nThe polar-skyrmionic EFISH effect also exhibits rich anisotropic behaviors, as is evident in the dramatic difference between the p-in and s-in conditions at positive biases in Fig.\u00a02a. Systematic insight into the anisotropy was obtained from the SHG polarimetry analysis. Figure 2b, c presents input polarization-dependent polar plots measured under p-out and s-out conditions, respectively. The p-out results (Fig.\u00a02b) have distinct pattern symmetries for positive (fourfold) and negative (twofold with missing 90\u00b0-oriented lobes) voltages. The magnitude of the p-out response is also different between positive and negative voltages, with a larger magnitude at positive bias. The s-out results (Fig.\u00a02c) have similar fourfold patterns with 45\u00b0-oriented lobes for both polarities. For each bias polarity, these pattern symmetries appear to be invariant with the magnitude of the voltage, and thus can be fitted using a second-order \u03c7(2) susceptibility tensor with fixed ratios between the coefficients (Supplementary Note\u00a01). Through simultaneous fitting of the p-out and s-out polarimetry patterns, we have established that the \u03c7(2) tensors for the positive and negative polarities are:\n\nrespectively. The ratios between the \u03c731(2), \u03c733(2), and \u03c715(2) for the negative polarity are very close to those of PbTiO3 bulk crystals (4mm point group)40,41. The positive polarity, however, is associated with a markedly enhanced \u03c733(2) and diminished \u03c731(2). This suggests that the emergence of SHG contributors in the latter is more complex than a single c-domain scenario. Furthermore, we have quantified these nonlinear optical coefficients using a reference LiNbO3 sample (see Supplementary Fig.\u00a0S4 and Supplementary Note\u00a02). The largest induced \u03c733(2) in the PbTiO3 layers and the global SHG efficiency (occurring at ~14\u2009V) are about 54.2\u2009pm\u2009V\u22121 and 9.3\u2009\u00d7\u200910\u221211\u2009W\u22121, respectively. This \u03c733(2) is larger than the bulk value (~17\u2009pm\u2009V\u22121) and primarily accounts for the giant modulation depth under the p-in/p-out conditions.\n\nSynchrotron-based in situ RSM measurements, in conjunction with phase-field simulations, reveal the microscopic processes underlying the EFISH modulation. The fact that we used a large X-ray beam footprint (see \u201cMethods\u201d) causes diffraction signals to include contribution from the unbiased regions and introduces uncertainties in the quantitative analysis of the bias-induced behavior, but offers a macroscopic view of it with good statistics. From the reconstructed 3D-RSMs (Fig.\u00a03a), we extract the profiles of the first-order 00L superlattice diffraction peak and the intensities of the H00 and 0K0 skyrmion satellites. Figure\u00a03b illustrates the splitting of the superlattice peak at \u00b115\u2009V due to the occurrence of a new peak at the lower Qz side, which corresponds to an out-of-plane lattice expansion by ~0.25%. This signifies a process of the polarization vectors rotating towards the applied field direction, that is, a transition from the skyrmions to a single c-domain state with an upward or downward Pz. Accordingly, the satellite intensities decrease gradually with increasing bias and indistinguishably between the H- and K-directions (Fig.\u00a03c); meanwhile, no shifts of the satellite wavevectors nor new satellites are observed, suggesting that the superlattice preserves the average in-plane ordering of the pristine state with 4mm macroscopic symmetry. These diffraction results qualitatively corroborate the SHG polarimetry analysis but notably, display no obvious difference between negative and positive biases as would be expected from Fig.\u00a02b.\n\na 3D reciprocal space maps near the 002 reflection of the [(PbTiO3)14/(SrTiO3)16]8 superlattice, denoting the orientations of applied electric field and crystallographic axes for in situ RSM studies. b 00L diffraction patterns around the first-order superlattice peak extracted from the 3D-RSMs and corresponding peak-fitting results for different applied voltages. c Evolution of the volume-summed diffraction intensities of the skyrmion satellites along the H00/0K0 directions as a function of applied voltage. The light yellow line serves as a guide for the eye. d Pontryagin density maps for \u22129.4\u2009V (left), 0\u2009V (middle) and 9.4\u2009V (right) extracted from the phase-field models, highlighting the domain wall regions of the skyrmions. Scale bar\u2009=\u200910\u2009nm. e Illustrations for the origin and breaking manner of the pseudo-centrosymmetry in the polar skyrmions under (left) zero and (right) positive biases, respectively. The red circle delineates a centrosymmetric unit, and the yellow dot marks the inversion center. f Fourier transform amplitudes of the autocorrelation function of the Pontryagin density, F{R(q, t)}, at the ~0.103\u2009nm\u22121 and 0.190\u2009nm\u22121 spatial frequencies as a function of bias voltage, obtained from the phase-field models. Inset: the spatial frequency spectra of the Fourier amplitudes for selected biases.\n\nThe real-space configuration of the skyrmions, however, takes different transition paths between the two polarities, even if they can ultimately be converted into single c-domains at a high electric field along either direction. Figure\u00a03d presents the phase-field results at \u00b19.4\u2009V for comparison (see also Supplementary Movie\u00a0S1 and S2); here we show the distributions of the Pontryagin density q, the surface integral of which is the topological number (= \u00b11) of the skyrmion. Upon application of negative bias, the skyrmions expand and coalesce, leading to a continuous c-domain matrix randomly embedded with much elongated, stripe-like (and reduced in quantity) skyrmions. By contrast, the configuration of the skyrmions is better protected against positive biases by shrinking on-site individually (thus maintaining their quantity) and more coherently until reaching a high voltage (>14\u2009V). Such difference stems from the upward Pz direction of the skyrmion center in the pristine state, which is due to the epitaxial growth conditions42. We further speculate that the initial state can be selected by modifying the growth conditions. This built-in asymmetry of the superlattices determines the asymmetric-in-bias transition paths at the nanoscale. Note that, over larger length scales, the simulation box-averaged values of the three polarization components follow similar evolution trends for the two polarities (Supplementary Fig.\u00a0S5), consistent with the diffraction results. Note also that, the field induced skyrmion evolution path in this study agrees qualitatively well with several previous studies with indirect measurements and theoretical calculations30,43, as well as direct in situ TEM observations36.\n\nBased on the microscopic processes observed using X-ray diffraction and through phase-field simulations, we find that polar skyrmions cause the EFISH effect through a delicate, skyrmion wall-involved mechanism. As depicted in Fig.\u00a03e, the pristine-state configuration exhibits pseudo-centrosymmetry due to a balance between the skyrmions and interfacial regions (near-zero net Pz), and thus is SHG inactive, consistent with the experimental results. The applied out-of-plane electric field directly couples with the PbTiO3 lattice and causes switching of its electric dipoles to form larger portion of c-domains. Therefore, the skyrmions constituted by those dipoles expand or shrink according to the field direction, displacing their wall positions at which the inversion centers are located (non-zero net Pz). This process breaks the centrosymmetry and activates the SHG response. To account for the process statistically from the simulated configurations, we calculate the Fourier transform of the autocorrelation function of the Pontryagin densities (Fig.\u00a03f, Supplementary Fig.\u00a0S6, and Supplementary Note\u00a03). The spatial frequency spectra of the Pontryagin densities exhibit correlation peaks at ~ 0.190\u2009nm\u22121 and 0.103\u2009nm\u22121, corresponding to the real-space distance between the two opposite walls of each skyrmion (the intra-skyrmion correlation) and that between the closest pair of skyrmions (the inter-skyrmion correlation), respectively. The intra-skyrmion correlation is suppressed by electric fields, in line with the wall displacement manner of symmetry breaking. The bias-dependence of the inter-skyrmion correlation exhibits a trend highly resembling the observed EFISH trends (cf. Fig.\u00a02a, the p-in/p-out curve), and thus represents a previously hidden order parameter associated with the EFISH modulation.\n\nTo relate the measured \u03c7(2) to the above structural mechanisms, we have developed a minimal model containing two separate contributors to the SHG process: interfacial c-domains and skyrmion walls. At negative biases, due to the weak correlation and the reduced quantity of the skyrmions, the contribution of the skyrmion walls to the global \u03c7(2) is incoherent and insignificant compared to the c-domains, as is indeed evidenced by the SHG polarimetry results. By contrast, the inter-skyrmion correlation is strong and the skyrmion walls are ordered at positive biases; therefore, their contribution to the global \u03c7(2) can coherently build up to compete with the c-domains. The \u03c7(2) tensor for a circular skyrmion can be derived in a closed form based on that of N\u00e9el-type domain walls44,45, which also conforms to a 4mm point-group symmetry with non-vanishing \u03c731(2), \u03c733(2), and \u03c715(2) (Supplementary Note\u00a04). The skyrmion walls thus should have an anomalously large \u03c733(2), in addition to a negative \u03c731(2) that cancels with that of the c-domains. Note that at the atomistic level, the SHG susceptibility is rooted in the anharmonicity of electronic structure, the calculation of which for the present system is beyond our phase-field framework and yet prohibitive using first-principle methods46. We postulate that the frustrated polarization at the skyrmion walls modulates the electronic structure with large anharmonicity along the out-of-plane direction. As a counterpart to the skyrmion walls, the polar vortex cores were found to exhibit partial reduction of Ti4+ to Ti3+ ions34, and qualitatively dissimilar \u03c7(2) tensors for the a1/a2-domain and vortex phases were also confirmed47. We further point out that other extrinsic mechanisms, such as light interference and reflection by the skyrmion walls48,49 and superlattice interfacial effects50, might also influence the EFISH response here, but given the large difference between the skyrmion size and probing wavelength, an effective approach is currently lacking to substantiate these subwavelength effects.\n\nWe next address several key characteristics of the polar-skyrmionic EFISH effect closely pertaining to its application in optoelectronic devices. These measurements also provide further microscopic insights. Figure\u00a04a presents the temperature evolution trend of the SHG intensities measured at d.c. voltages of \u00b110\u2009V. For both bias polarities, the SHG intensity decreases as temperature rises and approaches to the zero-field level above ~450\u2009K, then followed by a full recovery after cooling down. This trend indicates a reversible phase transition behavior and sets an upper temperature limit for applications51. Note that the same polarization dependencies during heating are observed from the polarimetry results (Fig.\u00a04a, inset) and suggest that the electrically induced transition paths of the skyrmions are maintained. This is corroborated by phase-field simulations which reveal an onset of thermal destabilization of the skyrmions above ~500\u2009K (Supplementary Fig.\u00a0S5).\n\na Temperature dependent SHG intensities measured at applied voltages of 10/\u221210\u2009V under the p-in/p-out conditions. The SHG intensity after cooling from 470\u2009K is shown as hollow dots. Inset: Polar plots of the input polarization angle-dependent SHG intensity for selected temperatures, measured at 10\u2009V under the p-out condition. The intensities are normalized to the same value scale. b SHG intensity as a function of a.c. frequency of sinusoidal (0\u2009V to\u2009\u00b1\u200910\u2009V peak-peak) voltage waveforms. For both polarities, the SHG intensity is normalized against its d.c. value. c SHG intensity as a function of voltage cycle number measured using 10\u2009MHz, 0 to \u00b1\u200920\u2009V square voltage waveforms, under the p-in/p-out polarization conditions. d Comparison of the modulation depth and nonlinear susceptivity \u03c7(2) of (PbTiO3)14/(SrTiO3)16 superlattices with other materials from literatures. Part of the data points were estimated values as marked. e Schematic of a Fresnel-lens type device that can focus EFISH signal. f Simulated SHG intensity distribution in the incidence plane of the Fresnel-lens device (shown as the 45\u00b0 line on the left) excited by a fundamental light along the -y direction. The output light propagates along the +x direction, showing a concentrated intensity at the designed focal length of ~60\u2009\u03bcm. Scale bar = 10\u2009\u03bcm. g SHG intensity at the focal point of the Fresnel-lens device as a function of bias voltage (the same value for both polarity of electrodes), in comparison with the single capacitor device.\n\nFigure\u00a04b presents the frequency dependence of the a.c. EFISH response, measured using sinusoidal voltage waveforms within the 103\u2212107\u2009Hz range. The effective SHG intensities counted over a fixed period are close to half the d.c. intensities at \u00b110\u2009V (as can be derived by integrations of the results in Fig.\u00a02a) and show a marginal decline up to 107\u2009Hz. This implies that the underlying microscopic processes of the skyrmions are faster than a time scale of at least 50\u2009ns. Higher frequency measurements are not available at present but in light of the flat trends for the measured range, an operating bandwidth in the gigahertz scales can arguably be inferred. Furthermore, the cycling fatigue properties are evaluated at high voltages of \u00b120\u2009V using 10\u2009MHz square waveforms (that is, on/off switching), as presented in Fig.\u00a04c. During a typical duration of 1010 cycles, the SHG intensity variations are found to be within the range of \u00b110% of the initial intensity (even with the sample drifts uncorrected), indicating a remarkable stability. Intuitively, both the observed fast and fatigue-resistant EFISH response of the skyrmions can be associated with the small length scale (few-unit cell), cooperative manners of ion motion in their polarization transition processes, akin to the emergence of sub-terahertz collective vibration modes in polar vortices32.\n\nThe above measurements feature a relatively wide working temperature range, high dynamical response bandwidth and long cycling life of the polar-skyrmionic EFISH effect, all desirable for device applications such as high-performance nonlinear electro-optic modulators. In Fig.\u00a04d, we compare (PbTiO3)14/(SrTiO3)16 superlattices with multiple other types of materials or devices as regards the nonlinear susceptibility \u03c7(2) and EFISH modulation depth. The PbTiO3/SrTiO3 superlattice system exhibits the highest level of modulation depth combined with a strong \u03c7(2). The \u03c7(2) value is especially competitive among thin-film materials and surpasses the LNOI (LiNbO3-on-insulator) platform. Note that some of the materials or devices included here realize large figure of merits by exploiting intrinsic or extrinsic resonance enhancement mechanisms which however are constrained to narrow wavelength ranges, for example, the electronic interband transitions in WSe2 and the PFO conjugate polymer, and the plasmonic resonance in Au nanoslit cavities9,12,18. As to the skyrmions, the EFISH response is expected to be broadband from mid-infrared frequencies (above the phonon bands) to the optical bandgap (~3.3\u2009eV), and those resonance mechanisms may also be incorporated to augment the response for a particular wavelength range.\n\nTo illustrate the SHG modulator applications, we propose a Fresnel-lens type device with electrically tunable focusing function. As shown in Fig.\u00a04e, the device operates in the 45\u00b0 incidence geometry and consists of 4 pairs of concentric SrRuO3 ring electrodes with varying widths and alternately biased by positive and negative voltages. We then predict the device output performance using the measured bias-dependent \u03c7(2) as an input for the finite-element modeling. From the simulated intensity distribution profile (Fig.\u00a04f), the SHG signals form a focal point at a length of ~60\u2009\u03bcm due to an interference between the oppositely biased areas of the superlattice. The SHG intensity is enhanced at the focal point by a factor of 4 compared to the single capacitor device (Fig.\u00a04g), and the in-between modulation levels can be reached through different combinations of bias voltages. The focal length and enhancement factor of Fresnel-lens devices can be adjusted by varying the geometric parameters. Furthermore, we envisage that an in-plane waveguide type device can be fabricated on the superlattice films with a periodic electrode pattern for biasing alternately or a metasurface structure, thereby potentially achieving high conversion efficiencies through quasi-phase matching10,52.",
+            "section_image": [
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+            ]
+        },
+        {
+            "section_name": "Discussion",
+            "section_text": "Here, we point up that the observed EFISH phenomena reflect the topological protection attribute of skyrmions in ferroelectric/dielectric superlattices. Under applied electric fields, the skyrmions deform and/or shift continuously, yet remain topologically equivalent, until the input electrostatic energy surpasses an energy barrier to break the topological protection. This embodies a general strategy to manipulate the nonlinear optical properties of topological polar structures. Furthermore, PbTiO3/SrTiO3 superlattices can be re-engineered to tune the quasiparticle interaction energies and ordering states of the skyrmions through the misfit strain and layer makeup53,54,55. For instance, using a more tensile substrate of SrTiO3 may stiffen the skyrmionic interaction and decline the EFISH modulation slope; reducing the SrTiO3 component layer thickness may directly boost the global efficiency due to increased PbTiO3 volume fraction. Other topological phases such as polar vortices, dipole waves and other structures should also be explored for electrically tunable SHG properties, though the likely phase coexistence (e.g., with a1/a2-domains on DyScO3 substrates) can play an adverse role by involving the hysteretic phase transition processes33. More radically, new superlattice or multilayer ferroelectric systems can be designed to stabilize polar skyrmions with engineered electronic anharmonicity (e.g., through ion doping), fusing an intrinsically enhanced \u03c7(2) with the agile tunability of the skyrmionic configurations.\n\nIn conclusion, we have demonstrated the electric field induced second-harmonic generation of the polar skyrmions based on (PbTiO3)14/(SrTiO3)16 superlattices, and elucidated the microscopic mechanisms through a combination of in situ experiments and phase-field simulations. The fabricated capacitor EFISH devices yield a remarkable comprehensive performance: a modulation depth of ~664%\u2009V\u22121, \u03c7(2) of ~54.2\u2009pm\u2009V\u22121 and SHG efficiency of ~9.3\u2009\u00d7\u200910\u221211\u2009W\u22121 under 800-nm excitation, reinforced by the other merits such as large response bandwidth, good cycling fatigue resistance and wide operating temperature range. The form of thin-film superlattices presents multiple degrees of freedom for further tuning of the EFISH properties, in addition to an integratable material. All these place the polar skyrmions a technologically competitive system, and may revive the long-lasting interest of ferroelectrics in the fields of integrated photonics, metamaterials and optoelectronics.",
+            "section_image": []
+        },
+        {
+            "section_name": "Methods",
+            "section_text": "[(PbTiO3)14/(SrTiO3)16]8 superlattices were grown on (001)-cut (LaAlO3)0.3-(SrAl0.5Ta0.5O3)0.7 (LSAT) single crystal substrates by pulsed laser deposition (PLD), with a 5-nm buffer layer of SrRuO3 serving as the bottom electrode. A 248\u2009nm KrF excimer laser (COMPex205, Coherent) was used to ablate ceramic targets of PbTiO3, SrTiO3, and SrRuO3 with the laser fluence and repetition rate as: 1.3\u2009J\u2009cm\u22122/5\u2009Hz, 1.7\u2009J\u2009cm\u22122/3\u2009Hz and 1.5\u2009J\u2009cm\u22122/10\u2009Hz, respectively. The SrRuO3 and superlattice layers were grown in an oxygen pressure of 25\u2009Pa and 10\u2009Pa, respectively, and the growth temperature for all layers was 650\u2009\u00b0C. After deposition, the superlattice films were annealed for 10\u2009min at 650\u2009\u00b0C followed by cooling to room temperature under an oxygen pressure of 20\u2009kPa. To fabricate capacitor test structures, a SrRuO3 capping layer of ~20-nm thickness was deposited with the same conditions as the bottom SrRuO3 layer onto the superlattice films. These SrRuO3-capped films were then subjected to ultraviolet optical lithography with the extra SrRuO3 layer removed by dissolving in ~15\u2009g\u2009L\u22121 NaIO4 water solution.\n\nCross-sectional thin specimens of the superlattice were prepared using a focused ion beam on a dual-beam microscope (Scios2, Thermo Fisher Scientific) or ion milling (PIPS II, Model 695, Gatan) after mechanical polishing. STEM observations were performed on a double-aberration-corrected transmission electron microscope (Spectra 300, Thermo Fisher Scientific), equipped with a field-emission electron source and operated at an accelerating voltage of 300\u2009kV. Energy-dispersive X-ray spectroscopy (EDX) data was collected using a Super-X detector equipped on the microscope. High-angle annular dark-field (HAADF)-STEM and differential phase contrast (DPC) images were collected with a probe convergence angle of 26.0\u2009mrad. HAADF images were collected with an inner collection angle of 31\u2009mrad, and DPC imaging was performed using a segmented detector with a collection angle of 7\u201329\u2009mrad. The local electrical field distribution was approximately evaluated from the DPC data, based on quantification of electron beam deflection56,57. Positions for all atomic columns in the HAADF images were obtained by 2D Gaussian fits using Matlab codes58. Displacement vectors of B-site columns (DB) were calculated based on local offsets of their sublattice relative to the A-site sublattice. The direction of spontaneous polarization (Ps) in each unit cell is opposite to the direction of B-site displacement. Values of Ps can be evaluated based on an empirical linear relation between Ps and B-site vector DB, i.e. Ps\u2009\u2009=\u2009\u2009\u03ba*DB, where \u03ba is a constant of 2.50\u2009\u03bcC cm\u22122\u2009pm\u22121 for the PbTiO3 systems59.\n\nThree-dimensional reciprocal space mapping (3D RSM) and in situ electric field dependent RSM were performed at the BL02U2 beamline of the Shanghai Synchrotron Radiation Facility. A monochromated X-ray beam with a photon energy of 10\u2009keV (bandwidth <2\u2009\u00d7\u200910\u22124) was used. The beam size was cut to ~70 (horizontal)\u2009\u00d7\u2009200 (vertical)\u2009\u03bcm2 using a pair of motorized slits, leading to a footprint of ~225\u2009\u00d7\u2009200\u2009\u03bcm2 on the sample surface for the Bragg angle (~18.7\u00b0) of LSAT 002 reflection. This beam footprint fully covered the capacitor test structures with a diameter of 100\u2009\u03bcm. The superlattices were mounted in the vertical scattering geometry on a four-circle diffractometer, and a tungsten probe station was attached on the latter to bias the samples. A 2D photon-counting area detector (Eiger 500\u2009K, Dectris) was used to record the diffraction intensity. The 3D RSM results were reconstructed from raw measured data using custom Matlab and Python codes.\n\nSHG measurements were performed on a home-developed laser-scanning microscope system39. A Ti:sapphire femtosecond laser (MaiTai, Spectra-Physics) was employed as the 1\u03c9 excitation source, emitting at 35\u2009fs pulse width, 800\u2009nm center wavelength, and an average power of 50\u2013200\u2009mW. For the normal incidence geometry, the 1\u03c9 laser beam was focused using an objective lens (numerical aperture = 0.55), which also collected the backscattered 2\u03c9 light signals. The excitation light polarization was controlled with a zero-order half waveplate, and the 2\u03c9 light polarization was analyzed using a Glan\u2013Taylor prism polarizer. The 2\u03c9 light signals were band-pass filtered and recorded with a photomultiplier tube detector. For the 45\u00b0 incidence geometry, the 1\u03c9 laser beam was directed on the sample surface with a convex lens (numerical aperture ~0.5) via another optical path, and the samples were 45\u00b0 tilted so that the upright reflected 2\u03c9 light signals could be collected and detected using the same path as the backscattering geometry. In both cases, sharp tungsten probes were used to bias the 100-\u03bcm diameter capacitors in situ under SHG measurement. Electrical test signals were supplied by a functional generator (Rigol DG2052) or a source meter (Keithley 2470) which could measure the leakage current simultaneously. A heating stage was used to heat the samples in open air up to 450\u2009K.\n\nPhase-field simulations were employed to investigate the polar structure of the (PbTiO3)14/(SrTiO3)16 (PTO/STO) superlattice on a LSAT substrate. The polarization evolution processes were obtained by solving the time-dependent Ginzburg\u2013Landau equations:\n\nwhere P, t, L are the spontaneous polarization vector, evolution timestep and kinetic coefficient, respectively. The total energy F can be written as the volume integration of the Landau, mechanical, electrostatic, and polarization gradient energy densities, i.e.,\n\nDetailed expressions for the individual energy density functionals60 and the materials parameters of PTO and STO43,52 can be found in previous reports.\n\nA three-dimensional mesh of 192\u2009\u00d7\u2009192\u2009\u00d7\u2009350 was used, with each grid representing 1 unit cell. The periodic boundary condition was applied along the x and y dimensions, while a superposition method was used in the out-of-plane direction61. Along the latter direction, the thicknesses of the substrate, thin film, and air were set as 30, 300, and 20, respectively. To account for the elastic inhomogeneity while solving the elastic equilibrium equation, an iterative perturbation method was used. Thin-film mechanical boundary conditions were adopted, where the out-of-plane stress components were fixed to zero on the top film surface, while on the substrate bottom sufficiently far away from the electrode/superlattice film interface, the out-of-plane displacement was set to be zero.\n\nFurther information on research design is available in the\u00a0Nature Portfolio Reporting Summary linked to this article.",
+            "section_image": []
+        },
+        {
+            "section_name": "Data availability",
+            "section_text": "The experimental and modeling data that support the findings of this study are available from the corresponding authors upon request.",
+            "section_image": []
+        },
+        {
+            "section_name": "References",
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+            "section_image": []
+        },
+        {
+            "section_name": "Acknowledgements",
+            "section_text": "The authors thank Lingfei Wang and Jingdi Lu for providing the NaIO4 etchant recipe and Jingbo Sun for useful discussion. This work was financially supported by Basic Science Center Project of the National Natural Science Foundation of China (NSFC) under grant No. 52388201 (Q.L., J.-F.L. and C.-W.N.), NSFC grant No. 52150092 (Q.L.), No. 52073155 (Q.L.), No. 92166104 (Z.H.), the Joint Funds of the NSFC grant No. U21A2067 (Z.H.), and by National Key R&D Program of China under Grant No. 2020YFA0309100 (Q.L.) and 2021YFA1202801 (Q.Z.), Beijing Municipal Natural Science Foundation under Grant No. 1212016 (Q.Z.). The in situ RSM experiment was carried out at the beamline BL02U2, Shanghai Synchrotron Radiation Facility (SSRF). The phase-field simulations are performed using the Mu-PRO software package (https://muprosoftware.com), on the MoFang III cluster on Shanghai Supercomputing Center (SSC).",
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+        },
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+            "section_name": "Author information",
+            "section_text": "These authors contributed equally: Sixu Wang, Wei Li.\n\nState Key Laboratory of New Ceramics and Fine Processing, School of Materials Science and Engineering, Tsinghua University, 100084, Beijing, China\n\nSixu Wang,\u00a0Wei Li,\u00a0Chenguang Deng,\u00a0Jing-Feng Li,\u00a0Ce-Wen Nan\u00a0&\u00a0Qian Li\n\nSchool of Materials Science and Engineering, Zhejiang University, 310027, Hangzhou, China\n\nZijian Hong\u00a0&\u00a0Yongjun Wu\n\nResearch Institute of Zhejiang University-Taizhou, 318000, Taizhou, Zhejiang, China\n\nZijian Hong\n\nCAS Key Laboratory of Standardization and Measurement for Nanotechnology, CAS Center for Excellence in Nanoscience, National Center for Nanoscience and Technology, 100190, Beijing, China\n\nHan-Bin Gao\u00a0&\u00a0Qiang Zheng\n\nShanghai Synchrotron Radiation Facility, Shanghai Advanced Research Institute, Chinese Academy of Sciences, 201204, Shanghai, China\n\nXiaolong Li\u00a0&\u00a0Yueliang Gu\n\nDepartment of Materials Science and Engineering, University of Wisconsin-Madison, Madison, WI, 53706, USA\n\nPaul G. Evans\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nQ.L. conceived and designed the project. S.W. performed film growth and device fabrication. S.W., W.L. and C.D. performed SHG studies. S.W., W.L., Y.G. and X.L. performed in situ synchrotron XRD. H.G. and Q.Z. performed STEM imaging. Z.H. and Y.W. performed phase-field simulations. S.W., Z.H. and Q.L. analyzed the phase-field results. W.L. performed finite-element device modeling. P.G.E., J.-F.L. and C.-W.N. discussed the results. S.W. and Q.L. wrote the manuscript with input from all the authors.\n\nCorrespondence to\n                Zijian Hong, Qiang Zheng or Qian Li.",
+            "section_image": []
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+            "section_image": []
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+            "section_text": "Nature Communications thanks Jimin Zhao and the other anonymous reviewer(s) for their contribution to the peer review of this work. A peer review file is available.",
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+            "section_text": "Wang, S., Li, W., Deng, C. et al. Giant electric field-induced second harmonic generation in polar skyrmions.\n                    Nat Commun 15, 1374 (2024). https://doi.org/10.1038/s41467-024-45755-5\n\nDownload citation\n\nReceived: 17 October 2023\n\nAccepted: 04 February 2024\n\nPublished: 14 February 2024\n\nVersion of record: 14 February 2024\n\nDOI: https://doi.org/10.1038/s41467-024-45755-5\n\nAnyone you share the following link with will be able to read this content:\n\nSorry, a shareable link is not currently available for this article.\n\n\n\n\n                            Provided by the Springer Nature SharedIt content-sharing initiative\n                        ",
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+            ]
+        },
+        {
+            "section_name": "This article is cited by",
+            "section_text": "Nature Physics (2025)\n\nNature Nanotechnology (2025)\n\nNature Materials (2025)\n\nNature Communications (2025)\n\nNature Communications (2024)",
+            "section_image": []
+        }
+    ]
+}

26f7c5dac8d891bdf1c6f4d2a03dfa6663bdf562aea9984920d5a6957eae9024/metadata.json

@@ -0,0 +1,146 @@
+{
+    "title": "Forest fragmentation impacts the seasonality of Amazonian evergreen canopies",
+    "pre_title": "Fragmentation disrupts the seasonality of Amazonian evergreen forests",
+    "journal": "Nature Communications",
+    "published": "17 February 2022",
+    "supplementary_0": [
+        {
+            "label": "Supplementary Information",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-022-28490-7/MediaObjects/41467_2022_28490_MOESM1_ESM.pdf"
+        },
+        {
+            "label": "Peer Review File",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-022-28490-7/MediaObjects/41467_2022_28490_MOESM2_ESM.pdf"
+        },
+        {
+            "label": "Reporting Summary",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-022-28490-7/MediaObjects/41467_2022_28490_MOESM3_ESM.pdf"
+        }
+    ],
+    "supplementary_1": NaN,
+    "supplementary_2": NaN,
+    "source_data": [
+        "https://etsin.fairdata.fi/dataset/e488f81b-b927-4bbd-a6f7-2f532f434b2b",
+        "https://lpdaac.usgs.gov/products/mcd18a2v006/",
+        "https://gmao.gsfc.nasa.gov/reanalysis/MERRA/"
+    ],
+    "code": [],
+    "subject": [
+        "Ecological modelling",
+        "Ecosystem ecology",
+        "Phenology",
+        "Tropical ecology"
+    ],
+    "license": "http://creativecommons.org/licenses/by/4.0/",
+    "preprint_pdf": "https://www.researchsquare.com/article/rs-722038/v1.pdf?c=1646868932000",
+    "research_square_link": "https://www.researchsquare.com//article/rs-722038/v1",
+    "nature_pdf": "https://www.nature.com/articles/s41467-022-28490-7.pdf",
+    "preprint_posted": "29 Jul, 2021",
+    "research_square_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Predictions of the magnitude and timing of leaf phenology in Amazonian forests remain highly controversial, which limits our understanding of future ecosystem function with a changing environment. Here, we use biweekly terrestrial LiDAR surveys spanning wet and dry seasons in Central Amazonia to show that plant phenology of old-growth forests varies strongly across strata but that this seasonality is sensitive to disturbances arising from forest fragmentation. In combination with continuous microclimate measurements, we found that when maximum daily temperatures reached 35 \u00b0C in the latter part of the dry season, the upper canopy of large trees in undisturbed forests shed their leaves and branches. By contrast, the understory greens-up with increased light availability driven by the upper canopy loss alongside more sunlight radiation, even during periods of drier soil and atmospheric conditions. However, persistently high temperatures on forest edges exacerbated the upper canopy losses of large trees throughout the dry season, and the understory seasonality in these light-rich environments was disrupted as a result of the altered canopy structure. These findings demonstrate the plant-climate interactions controlling the seasonality of wet Amazonian forests and show that forest fragmentation will aggravate forest loss under a hotter and drier future scenario.Environmental EngineeringEnvironmental PolicyTerrestrial EcologyClimatologyClimate Analysis and Modelingleaf phenologyforestsAmazonian forestsforest fragmentation and loss",
+            "section_image": []
+        },
+        {
+            "section_name": "Additional Declarations",
+            "section_text": "There is NO Competing Interest.",
+            "section_image": []
+        },
+        {
+            "section_name": "Supplementary Files",
+            "section_text": "SupplementaryInformation.pdfSupplementary Information",
+            "section_image": []
+        }
+    ],
+    "nature_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Predictions of the magnitude and timing of leaf phenology in Amazonian forests remain highly controversial. Here, we use terrestrial LiDAR surveys every two weeks spanning wet and dry seasons in Central Amazonia to show that plant phenology varies strongly across vertical strata in old-growth forests, but is sensitive to disturbances arising from forest fragmentation. In combination with continuous microclimate measurements, we find that when maximum daily temperatures reached 35\u2009\u00b0C in the latter part of the dry season, the upper canopy of large trees in undisturbed forests lost plant material. In contrast, the understory greened up with increased light availability driven by the upper canopy loss, alongside increases in solar radiation, even during periods of drier soil and atmospheric conditions. However, persistently high temperatures in forest edges exacerbated the upper canopy losses of large trees throughout the dry season, whereas the understory in these light-rich environments was less dependent on the altered upper canopy structure. Our findings reveal a strong influence of edge effects on phenological controls in wet forests of Central Amazonia.",
+            "section_image": []
+        },
+        {
+            "section_name": "Introduction",
+            "section_text": "Leaf phenology of Amazonian forests is a key component controlling the exchange of energy and trace gases\u2014water vapour, carbon dioxide and volatile organic compounds\u2014with influences on vegetation feedbacks on regional and global climates1,2,3,4,5. In the past decade, several studies have demonstrated from field data and remote sensing that a majority of Amazonian forests respond to climatic variations2,6. There is also mounting evidence that evergreen canopies exhibit seasonal variations7,8,9,10,11 with changes in leaf demography and canopy structure12. Long-term studies have shown that 60\u201370% of species of humid Amazonian forests flush new leaves in the dry months12,13 linked to higher solar radiation4,14, which leads to increases in gross primary productivity as a result of new young leaves with higher photosynthetic capacity and water-use efficiency4,15,16. However, when some Amazonian forests are impacted by water stress, leaf development is reduced17\u00a0and trees shed their leaves10,18, with significant effects on leaf area dynamics19. To complicate matters further, leaf phenology also responds to multiple genetic factors, which have evolved to maximise photosynthetic and water-use efficiency during the dry season, reduce plant competition for light and water, and minimise herbivore pressure7,16,20,21,22.\n\nThe impacts of climatic variations on leaf phenology can also be exacerbated by forest fragmentation23. Forest edges contain a large abundance of early successional species with resource-acquisitive strategies that maximise new leaf production and growth24,25, but may be more vulnerable to climatic\u00a0variations26. Forest fragmentation can increase the evaporative demand due to higher temperatures and wind exposure, and soil moisture can be lower at fragment edges27, which may cause leaves to drop and lead to higher branch turnover12,23. However, ground observations of litterfall in Amazonian forests have shown only mild seasonality near edges28. Indeed, substantial uncertainty remains regarding the responses of fragmented forests to climatic seasonality, particularly because drought resistance varies among species29,30,31 and surviving trees may acclimate or be adapted to the drier, hotter conditions near edges32. As the number of contiguously forested areas is significantly decreasing in the Amazon33, understanding the effects of forest fragmentation on phenology is crucial for predicting alterations to canopy function in fragmented forests.\n\nSeasonal variations in leaf quantity and leaf area across evergreen Amazonian forests have frequently been considered negligible or small4,12,21,34. However, these studies are based on passive optical remote sensing approaches, which cannot detect potential differences between canopy strata. These approaches tend to detect only upper canopy trees with deeper roots and water access30, and that are likely adapted to more stressful conditions such as high solar radiation, high temperatures and low air humidity35. Active remote sensing observations from LiDAR may provide new insights into the interacting biophysical factors controlling phenology since LiDAR pulses penetrate the vertical canopy. Repeated terrestrial laser scanning (TLS, or \u2018terrestrial LiDAR\u2019) measurements can monitor subtle changes in forest structure36, and provide observations of the balance between new leaf development (flush of new leaves, plant growth) and loss to abscission (leaf and branch fall) that can be separated across forest strata. Furthermore, the detailed and precise structural measurements offered by this system can help answer fundamental questions about the three-dimensional (3D) ecology of trees37 without suffering from potentially confounding artefacts present in passive optical satellite images11,34. Recently, LiDAR-based studies have shown that leaf phenology in Amazonian forests is stratified over canopy positions, with understory growth occurring when abscission in the upper canopy contributes to increased light penetration in the lower canopy layers19,38.\n\nHere, we investigate the phenology of forests within the Biological Dynamics of Forest Fragments Project (BDFFP) in Central Amazonia, the world\u2019s longest\u2010running experimental study of habitat fragmentation39. We use terrestrial laser scanning (TLS, or \u2018terrestrial LiDAR\u2019) surveys collected every 15\u2009days spanning the wet and dry seasons to investigate how forest fragmentation and microclimatic seasonality interact to affect plant area of the understory and the upper canopy. Using a combination of 11 repeat TLS surveys, as well as continuous air temperature and soil moisture measurements in undisturbed old-growth forests and fragmented forests under edge effects, we hypothesised that: (1) vertically stratified plant phenology in undisturbed forests varies with seasonal microclimatic conditions; (2) the understory phenology is dependent on seasonal variations in the upper layers of the canopy; and (3) plant phenology is sensitive to disturbances arising from forest fragmentation, with the hotter and drier conditions of edges exacerbating leaf and branch losses during the dry season. To our knowledge, the work presented in this paper is the first to analyse tropical forest phenology with high spatial resolution 3D measurements (Fig.\u00a01) and the first to experimentally demonstrate the effects of forest fragmentation on the seasonal variation of leaf area, and its vertical stratification, combined with microclimate measurements.\n\nColours depict plants within distinct vertical strata. The high-speed terrestrial laser scanning (TLS) data acquisition of 500,000 measurements per second provides detailed measurements capable of detecting fine-scale changes in vegetation structure. We used a scan resolution of 40\u2009mdeg in both azimuth and zenith directions, which results in a point spacing of 1.4\u2009cm at a 20\u2009m distance from the scanner. The laser pulse repetition rate used was 600\u2009kHz, allowing a measurement range of up to 350\u2009m and up to eight returns per pulse.",
+            "section_image": [
+                "https:////media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41467-022-28490-7/MediaObjects/41467_2022_28490_Fig1_HTML.png"
+            ]
+        },
+        {
+            "section_name": "Results",
+            "section_text": "Daily precipitation estimates indicate the occurrence of a 4-month period of accumulated rainfall below 200\u2009mm\u2009month\u22121, and significant reductions in soil moisture between July and September in Central Amazonia (hereinafter referred to as \u201cdry season\u201d). The term \u201cdry season\u201d indicates a period of lower water availability and does not necessarily indicate that forests were water-limited. This dry season was coincident with a period of high MODIS-estimated Photosynthetic Active Radiation (PAR, Fig.\u00a02a) and with significant increases in the locally measured understory temperature of interior forests and fragment edges (Fig.\u00a02b, c). Forest fragmentation led to higher local temperatures in the edges, while water moisture in the soil remained unaffected by edge effects.\n\na Estimated diffuse, direct and total (diffuse\u2009+\u2009direct) Photosynthetic Active Radiation (PAR, in red) estimated from MODIS and accumulated 30\u2009days (monthly) rainfall from NASA POWER (grey area). Each red point represents the monthly average calculated from daily estimates with error bars representing the 95% confidence intervals. b Maximum daily temperatures in the edge understory (red) and interior (dark grey) and c mean daily soil moisture (as volumetric water soil content: cm3 water/cm3 soil) measured continuously every 15\u2009min in the edges (red) and in the interior of fragments (dark grey). Fifth order polynomial models were fit to the microclimate data for visualisation purposes. The shaded area corresponds to the dry season, defined as the period with accumulated monthly precipitation\u2009<200\u2009mm\u2009month\u22121.\n\nRepeated TLS data acquired in two transects of 100\u2009\u00d7\u200910\u2009m and one transect of 30\u2009\u00d7\u200910\u2009m between April and October 2019 every 15\u2009days (except between the end of April and early June when the duration between measurements was 40\u2009days) were used to calculate Plant Area Density (PAD, one-sided area of plant material per unit of volume in m2\u2009m\u22123). PAD is a combination of the leaf area and the surface area of woody components, including branches and trunks. An analysis of the vertical profile of the vegetation revealed the existence of only two vertical axes of variation during the dry season, with positive PAD changes below the height of 15\u2009m above the ground (referred to as understory) and negative PAD changes above 15\u2009m height (referred to as upper canopy) (Supplementary Fig.\u00a03). The sum of PADs for each 1\u2009m2 vertical column (X-, Y-coordinate) was then calculated to obtain PAI, one-sided area of plant material per unit of ground surface in m2\u2009m\u22122 (Fig.\u00a03a). Nonlinear mixed models demonstrated that distance from forest edges has significant effects on PAI within 35\u201340\u2009m of forest margins (Supplementary Fig.\u00a02), and we, therefore, considered edge in this study categorically as the forests within 40\u2009m of the forest fragment margins and interior as the forests at least 40\u2009m distant from the fragment margins. These results demonstrate the existence of vertical and horizontal within-season trends in phenology that should be considered when analysing across-season trends.\n\na Forest phenology acquired using a Terrestrial Laser Scanner (TLS) within the Biological Dynamics of Forest Fragments Project (BDFFP) was vertically stratified, with the understory (<15\u2009m aboveground) and upper canopy (\u226515\u2009m aboveground) presenting different trajectories of growth during the dry season. However, the vegetation structure and phenology were both significantly altered by edge effects up to 40\u2009m from the forest fragment margins. PAI predictions from linear mixed modelling used measurement date (time), a categorical variable that indicates whether plots were near an edge (edge effects) and an interaction term time\u2009\u00d7\u2009edge effects as fixed variables. Edge effects nested within transect identity were included as random variables (Eqs.\u00a01 and 2). Predicted relative PAI of the understory, upper canopy and total PAI (that combined both vertical strata) in b forest edges and c undisturbed interior forests was calculated as the PAI at any time divided by initial PAI (PAIi) collected in April 2019. Each point (and lines corresponding to linear interpolations between points) represents the mean relative PAI obtained by fitting 200 randomised permutations of subsets split into 80/20 for calibration and validation, respectively. The shaded areas represent 95% confidence intervals based on uncertainty in those parameter estimates. While transects exhibited similar phenological trends, PAI differed significantly between transects\u2014thereby we here show the predicted values. See Supplementary Fig.\u00a04 for measured PAI and Supplementary Fig.\u00a05 for absolute predicted PAI values and model uncertainty. The shaded area represents the dry season between mid-June and mid-October.\n\nThe TLS time-series revealed a strong vertical variability in the timing and magnitude of seasonal changes in the PAI of both\u00a0structurally undisturbed forests and forests under edge effects. While transects exhibited similar phenological trends, PAI differed significantly between them (Supplementary Fig.\u00a04). We then used linear mixed models to detect the effects of edges on the seasonality of understory PAI, upper canopy PAI, and total PAI (understory\u2009+\u2009upper canopy PAI), whilst controlling for spatial effects caused by transect differences by including edge effects nested within transect identity as random effects. The most parsimonious model (based on AIC; see Supplementary Table\u00a01) to predict PAI for both the understory and total PAI was Eq. (1) which includes the additive effects of season and edge effects on PAI, both as categorical variables, and their interactive effects. Eq. (2) was selected for upper canopy PAI, which includes the effects of edge and an interaction term between edge effects and season. (Supplementary Table\u00a01; Fig.\u00a03; Supplementary Fig.\u00a05).\n\nwhere PAIi is the plant area index in transect i, \u03b20 and \u03b21-3 are the fixed effect parameters, ui is the random intercept for edge effects nested within transect i (1\u2009|\u2009Transects/Edge effects), and \u2107i is residual error. Both time and edge effects (edges versus interior) were treated as categorical variables.\n\nIn forest interiors, losses in the understory preceded the dry season, while significant losses in the upper canopy occurred at the end of the dry season (Fig.\u00a03c, Supplementary Fig.\u00a05b and 5d). More specifically, the PAI of the understory declined rapidly between April and early June (t\u2009=\u2009\u22123.4; P-value\u2009<\u20090.001) and reached a 5.3% (\u22120.43\u2009m2\u2009m\u22122) decline by late July (t\u2009=\u2009\u22124.2; P-value\u2009<\u20090.001). The PAI then increased to a full recovery (+0.43\u2009m2\u2009m\u22122) in September (t\u2009=\u2009\u22121.2; P-value\u2009=\u20090.21). By contrast, the upper canopy layer showed an inverse seasonal pattern to the understory; the upper canopy PAI remained relatively stable from April\u2013September, but experienced a 7.6% (\u22120.25\u2009m2\u2009m\u22122) decrease in late September (t\u2009=\u2009\u22123.9; P-value\u2009<\u20090.001).\n\nThe PAI time-series of forest edges (Fig.\u00a03b, Supplementary Fig.\u00a05a and 5c) showed significantly distinct patterns in comparison with those observed in forests distant from edges (indicated by the significant time\u2009\u00d7\u2009edge effects interaction term; Supplementary Table\u00a01). Despite a subtle decline in PAI between April and July of 3.4% (\u22120.08\u2009m2\u2009m\u22122) (Fig.\u00a03b), the PAI in the edge understory did not show significant seasonal changes (t\u2009=\u2009\u22121.7; P-value\u2009=\u20090.07). However, the upper canopy of edges had significant PAI losses of 6% (\u22120.25\u2009m2\u2009m\u22122) by mid-July (t\u2009=\u20092.2; P-value\u2009<\u20090.05), nearly 3\u2009months before the upper canopy of interior forests was significantly affected (Fig.\u00a03c).\n\nThe temporal patterns of total PAI in forest edges and forest interior had patterns that reflected the combination of the stratified phenological trends. In the forest interior, a decrease of 2.7% (\u22120.34\u2009m2\u2009m\u22122) was observed between April and early July (t\u2009=\u2009\u22122.8; P-value\u2009<\u20090.005), and remained relatively stable throughout the dry season. The phenology of forest edges showed very similar trends to forest interior when distinct strata were not considered; the total PAI decreased by 3.2% (\u22120.25\u2009m2\u2009m\u22122) between April and early July (t\u2009=\u2009\u22122.2; P-value\u2009=\u20090.03), and also\u00a0remained relatively\u00a0stable throughout the dry season. These results show that when the seasonal patterns are not vertically stratified, the PAI trends for the edges versus interiors are strikingly similar and mainly driven by the understory PAI, where the majority of the plant area is.\n\nWe also illustrate the significant seasonal variations in PAI against the microclimatic conditions measured in the edges of the fragment and in the forest interior (Supplementary Fig.\u00a06 and 7). Losses in PAI of canopies in edges and forest interior occurred when temperatures were elevated (above 35\u2009\u00b0C; Supplementary Fig.\u00a06d). Losses in PAI of upper canopies in the forest edges preceded canopy losses in the interior by 3\u2009months, which coincided with temperatures 3\u20135\u2009\u00b0C hotter in edges throughout the dry season than interior environments (Supplementary Fig.\u00a06c); this strongly supports the idea that the seasonal dynamics of Amazonian forests at the upper canopy level is dependent on temperature, and that fragmentation exacerbates these effects. On the other hand, the understory of interior forests had sharp decreases in PAI between April and June, a period when soil moisture was still high, and maximum temperatures were relatively low (27.8\u2009\u00b1\u20090.6\u2009\u00b0C, Supplementary Fig.\u00a07b and 7d). However, the understory PAI of these forests increased with losses in the upper canopy PAI, even with increases in temperature and high solar radiation (Fig.\u00a02a), and a full recovery in plant area occurring when the temperatures peaked in September. These findings support the idea that light is a more important control of the forest understory than temperature and water availability.\n\nWe then investigate whether decreasing leaf area in the understory of forest edges and in the forest interior was synchronised with variation in upper canopy plant area. We found a strongly negative linear correlation between variations in PAI of the upper canopy and understory in the forest interior only (F-value\u2009=\u200954.4; P-value\u2009<\u20090.001; R2\u2009=\u20090.84; Fig.\u00a04). There was no relationship in edges (F-value\u2009=\u20091.2; P-value\u2009=\u20090.29; R2\u2009=\u20090.02), which aligns with our hypothesis that fragmentation changes phenological patterns; in this case, affecting the seasonal pattern of understory dependency on upper canopy plant area.\n\nLiDAR-based PAI data measured between April and October 2019 in Central Amazonian forests were classified as a forest edges, situated within 40\u2009m from the forest fragment margins, and as b forest interior, situated at least 40\u2009m from the fragment margins. Black dots represent the mean value of each Terrestrial Laser Scanning (TLS) survey based on 3480 understory and 3480 upper canopy PAI values in the forest interior and 1653 understory and 1653 upper canopy PAI values in the forest edges. Model\u2019s R2 and P-value were calculated from simple linear regression (Understory PAI\u2009=\u2009\u03b20\u2009+\u2009\u03b21 Upper canopy PAI). The red line in panel b represents predicted values by the model, with the shaded grey area corresponding to the two-sided 95% confidence intervals. The highlighted point in red in panel (a) denotes the first TLS measurement made in April 2019. We excluded this point to further investigate the covariance between strata but found no significant relationship (Supplementary Fig.\u00a08).",
+            "section_image": [
+                "https:////media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41467-022-28490-7/MediaObjects/41467_2022_28490_Fig2_HTML.png",
+                "https:////media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41467-022-28490-7/MediaObjects/41467_2022_28490_Fig3_HTML.png",
+                "https:////media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41467-022-28490-7/MediaObjects/41467_2022_28490_Fig4_HTML.png"
+            ]
+        },
+        {
+            "section_name": "Discussion",
+            "section_text": "Repeat high density terrestrial LiDAR combined with microclimate measurements of a Central Amazonian forest provided a unique perspective on the seasonal dynamics of vegetation and the interaction with fragmentation. PAI\u2014as leaf area index (LAI) and the surface area of woody components\u2014showed inverse patterns in the understory versus upper canopy. In the structurally undisturbed interior of a large forest fragment, plant area in the understory decreased by ~5% before the start of the dry season and fully recovered by mid dry season in September. Conversely, the upper canopy (>15\u2009m aboveground) of interior forest maintained its canopy structure throughout most of the dry season, with the greatest losses (~8%) in upper canopy PAI occurring from September to mid-October, when the microclimate reaches its lowest soil moisture and maximum temperatures are high (above 35\u2009\u00b0C). Variations in plant area in the understory were strongly coordinated with upper canopy changes in PAI (R2\u2009=\u200984%, Fig.\u00a04), which suggests that leaf flush in the understory follows increasing light availability as plant area is lost in the upper canopy. Edge effects, however, changed the phenological patterns observed in interior forests; while edge effects exacerbated upper canopy loss throughout the dry season, the understory was less seasonal. The pattern of higher leaf loss in the upper canopy, where large trees dominate, is consistent with edge effects enhancing leaf stress and creating periods of high evaporative demand\u2014indeed, temperatures were consistently 3\u20135\u2009\u00b0C higher and soil moisture levels lower in the dry season in the forest edges. This study demonstrates the value of repeated terrestrial LiDAR surveys, which allow the detection of fine-scale changes in forests without potential artefacts of passive remote sensing studies36, and provide a perspective on forest dynamics and its spatial variability that is difficult to achieve with lower resolution remote sensing approaches.\n\nOur PAI time-series of interior forests indicated upper canopy losses that are sensitive to elevated temperatures, whereas the understory maintains high leaf production under high light availability mediated by upper canopy dynamics, even during periods of drier soil and atmospheric conditions during non-El Ni\u00f1o years. Passive remote sensing and field observations have demonstrated that Central Amazonian forests \u201cgreen up\u201d during the dry season9,11, but with negligible increases in PAI4,12. Our findings demonstrate, instead, stratified canopy responses to seasonally mediated environmental conditions and suggest that large trees may mediate a green up in the lower canopy. We show that if phenological patterns are not vertically stratified, total canopy PAI (the combined understory and upper canopy PAI) tends to reflect the understory PAI (where most of the PAI is). These results suggest that if differences between strata are not considered alongside changes in LAI, litterfall production and leaf demography, predictions of the climatic influences on vegetation may be undermined or misleading.\n\nVertical differences in phenology may arise from a direct response to changing light availability in the understory and from contrasting functional and hydraulic properties between canopy and understory trees. Recent studies in Amazonian forests have shown that leaf area increases in the understory occur under maximal irradiance conditions when the upper canopy layer is partially deciduous during the dry season38,40, as diffuse and direct solar radiation in the understory can increase linearly with decreasing upper canopy plant area41. The dominant species in the understory of Amazonian forests are distinct from upper canopy dominants and are differentiated and more complex in functional strategies35,42. Understory trees have xylem that is more embolism resistant and can tolerate more negative water potentials in the dry season without risking hydraulic failure compared to upper canopy trees, which tend to be more vulnerable to drought-induced embolism30. High embolism resistance of understory trees allows an anisohydric stomatal behaviour (low degree of regulation) and the maintenance of high stomatal conductance at the peak of the dry season30. The high drought tolerance of understory trees is also likely to be a key trait allowing them to flush new leaves during periods of water stress. In contrast, canopy trees exhibit lower embolism resistance, high stomatal sensitivity and significant declines in photosynthesis during periods of high atmospheric demand and low soil water availability43. The loss of upper canopy leaves in Amazonian forests at the end of the dry season is consistent with the importance of water availability for leaf development38, and suggests that canopy trees in these forests may be vulnerable to periods of high evaporative demand2,22. These results challenge the paradigm of Amazonian large trees being necessarily\u00a0capable of accessing deep water and hence being primarily light-limited44,45.\n\nThis study presents a dataset of fine-scale, high-frequency LiDAR, elucidating the magnitude and timing of forest phenology and impact of fragmentation from one of the most important experiments on tropical forest fragmentation (BDFFP). However, the generality of our findings across years and sites, particularly across large-scale Amazonian gradients in seasonality, edaphic properties, and soil moisture, remains to be tested. At a site in the eastern central Amazon with trees attaining a maximum size ~10\u2009m taller (Tapaj\u00f3s National Forest, Par\u00e146), Smith and colleagues found more complex vertically and horizontally stratified dynamics19. Here, in contrast to our study, the upper canopy above 20\u2009m increased in plant area towards the end of the dry season. On the other hand, the sunlit canopy surface zone below 20\u2009m\u2014common in this vertically heterogeneous site with a large amount of canopy gaps\u2014decreased through the late dry season, consistent with our upper canopy results. The shaded understory layer below 20\u2009m increased as the mid-canopy decreased, displaying a strong anticorrelation pattern that could be analogous to the forest interior understory vs upper canopy relationship that we observed. The canopy surface near 20\u2009m in the Tapaj\u00f3s could be more functionally analogous to the upper canopy of the BDFFP where, indeed, much of the dry season decrease in plant area occurred between 15 and 25\u2009m height (Supplementary Fig.\u00a03). However, what explains the contrast in the \u2018above 20\u2009m\u2019 Tapaj\u00f3s upper canopy? These sites differ in fertility, mean rainfall, length of dry season, and other factors47. Upper canopy trees in the Tapaj\u00f3s access deep soil water30, while more typically wet forests near Manaus may not root as deeply, potentially because of smaller tree sizes48 or functional selection49. Overall, these results suggest that there may be environmental (including belowground factors) and species-specific trait-linked controls on canopy structure and phenological climate responses. Better understanding these controls can help us predict variation in climate response across the Amazon.\n\nGround measurements are preferred to study subtle changes in canopy density in comparison to scans from above the canopy. Ground measurements are immune to seasonal changes in vegetation-ground reflectance ratios that may affect the transmittance estimated from airborne and spaceborne LiDAR systems, and which may otherwise negatively affect LAI estimates10. Such artefacts may have contributed to the negative correlations between upper canopy and understory LAI from the Amazonian-scale IceSat-based estimates presented in Tang and Dubayah38,40. Although our sampling effort attempted to minimise uncertainties in the PAI estimates, we did not account for (i) changes in leaf orientation and light transmittance caused by leaf age and changes in plant water content50,51, or (ii) a potential bias induced by not separating wood from leaves in the estimation of PAI, as leaf turnover rates can be different from branch turnover rates52. However, both (i) and (ii) require an automated separation of leaves from woody materials, which may contribute to additional uncertainties that can vary through space and time53.\n\nWe observed strong edge effects that changed the phenological patterns observed in the interior forests. Upper canopy PAI losses were significantly affected by the dry season in forest edges, occurring nearly 3\u2009months before upper canopy losses in the interior forests. Dry season temperatures in forest edges were 3\u20135\u2009\u00b0C higher than in the interior of the fragment, while changes in soil moisture were small. These higher temperatures may lead to an increase in vapour pressure deficit (VPD), inducing stomatal closure and leaf loss23,43,54,55, as shedding leaves may help to avoid the desiccating effects of water and heat stress56. On the other hand, plant area in the understory of forest edges was unaffected by the seasonal microclimatic changes or losses in upper canopy leaf area. The aseasonality of plant area in the understory of edges indicates that leaf production rates were similar to leaf loss rates during wet and dry seasons. These edges are dominated by pioneer species25 that thrive under the light-rich environment caused by lateral light penetration and by the formation of gaps associated with the mortality of large trees57. These conditions may disrupt the between strata light-mediated anticorrelation of leaf area dynamics since edge understories are less affected by variations in the upper canopy structure.\n\nThis study sheds light on the seasonal trends in the plant areas of Amazonian forests and highlights complex interacting effects of climate and human disturbance on forest phenology. The total leaf quantity (LAI) is a key component modulating tree growth58 and net primary productivity59. The consistently higher and aseasonal understory PAI in these fragment edges may explain the increased growth rates of understory tree species in these edges in comparison to the same tree species in interior forests60. However, the dry season losses in upper canopy plant area near the edges 3\u2009months earlier compared with interior forests likely represent a shortening of the photosynthetic-active period of large trees, potentially reducing photosynthetic carbon fixation (gross primary productivity; GPP). If CO2 uptake of the upper canopy is suppressed, this may have negative consequences for investment in tissue maintenance and defence61, which may, in turn, increase the mortality of large trees that dominate upper canopies and contribute to a large reduction in the aboveground biomass of these forests62. Carbon losses from forest degradation already exceed those from deforestation in the Amazon63, and fragmentation is a large contributor to degradation-associated carbon emissions64. Given the drier and warmer future projected for the Central and Eastern regions of the Amazon, and extended dry-season length65, our findings suggest that fragmentation will exacerbate the negative effects of high temperatures on the upper canopy of these forests. Considering that fragment edges cover a total area of 176,555\u2009km2 of Amazonian forests66, the thermal sensitivity of canopies on the edges of fragmented forests could translate into a large component of edge-related carbon losses.\n\nPredicting changes in phenology is particularly challenging, given that the timing of biological events results from an interaction of organism functional traits, genetic background and environmental factors67. Much progress has been made to understand the seasonality of Amazonian tree species and communities at local and regional levels4,7,9,11,14,31,38. Nonetheless, our results show that the variability in phenology that arises from canopy stratification and edge effects has large impacts on plant area seasonality. The lack of edge effects on the seasonal variance of total plant area highlights the challenge faced by passive sensors onboard satellite platforms; these systems may suffer from a flattened perspective with data strongly influenced by canopy layers with a denser plant area and little ability to detect significant height-stratified forest canopy responses to climate. Efforts to separate plants occupying different strata and habitats are needed to address this challenge, which is aligned with recent debates on the effects of strata on regional patterns of species dominance and composition in Amazonian forests35. Unoccupied aerial vehicle-borne laser scanning should be instrumental in this respect. These systems have the capacity to collect high density point clouds at a high temporal frequency over relatively large areas (up to tens of ha) and offers the opportunity to characterise leafing patterns at the scale of individual crowns68. At landscape and regional scales, airborne and satellite-based active LiDAR sensors can also provide a crucial height-stratified perspective (e.g., NASA\u2019s new GEDI mission)69,70.\n\nDespite our progress characterizing height and environmentally stratified canopy phenology, the mechanisms that control phenology at the species level remain elusive. Changes in PAI may not capture the leaf exchange dynamics as it is unknown what proportion of species and trees shed their leaves completely prior to flushing new leaves, and those that go through a more progressive leaf exchange. A mixture of the above strategies can produce a stable PAI even in case of strong seasonality in leaf exchange patterns. We propose that future research on phenology should continue to untangle the interactions of the environment with functional and phylogenetic diversity both within and among species. TLS can be particularly useful in this context; tree segmentation allows for 3D architectural reconstruction and the calculation of structural metrics37,71. TLS-based phenological data at the tree and species levels can help elucidate mechanisms controlling phenology in the Amazon such as (i) the specific environmental factors determining phenology, (ii) the molecular and physiological processes regulating phenology, and (iii) whether variation in phenology reflects genetic differences (high interspecific variation) or plastic responses to environmental heterogeneity (high within-species variation). This may help resolve outstanding debates concerning the mechanisms by which species respond to seasonal climatic variations and improve predictions of plant responses to global changes.",
+            "section_image": []
+        },
+        {
+            "section_name": "Methods",
+            "section_text": "The study was conducted in Central Amazonian forests (2\u00b020 30 \u2032S, 60\u00b0 05 37\u2009W) within the Biological Dynamics of Forest Fragments Project (BDFFP), the world\u2019s longest\u2010running experimental study of habitat fragmentation39. The region has seen notable carbon and biodiversity losses due to forest fragmentation effects25,66 and is predicted to be markedly impacted by climatic changes72. The pioneering BDFFP project sites are composed of forest fragments originally isolated in 1980 by converting mature forest into cattle pastures. Currently, the \u2018matrix\u2019 between the forest fragments is dominated by secondary growth forests, but a 100\u2009m strip surrounding the forest fragments is cleaned regularly by cutting vegetation regrowth to maintain their isolation (Supplementary Fig.\u00a01a). As an experimental control that minimises additional anthropogenic influences such as illegal logging, hunting, fire penetration and pollution, the project offers insights into ecological and environmental changes in fragmented forests. We selected a 100-ha forest fragment to investigate phenological responses within transects varying in distance from the fragment edges (0\u2013500\u2009m). At the community level, the forest edges of our study are dominated by a high density of early successional, fast-growth species, because of the elevated tree mortality near forest edges and seed dispersion from degraded neighbouring habitats, while the centre of the fragment comprises undisturbed primary forest25,39.\n\nThe TLS data were acquired using a RIEGL VZ-400i system between April and October 2019 every 15\u2009days, except between the end of April and early June when the duration between measurements was 40\u2009days (we clarify in the analysis section how we addressed artefacts attributed to sampling effort). We used a scan resolution of 40\u2009mdeg in both azimuth and zenith directions, which results in a point spacing of 34\u2009mm at 50\u2009m distance from the scanner. The laser pulse repetition rate used was 600\u2009kHz, allowing a measurement range of up to 350\u2009m and up to eight returns per pulse. The scans covered two transects of 100\u2009\u00d7\u200910\u2009m near the fragment edges and perpendicular to the forest fragment margins measured 11 times and one transect of 30\u2009\u00d7\u200910\u2009m length in the centre of the forest fragment measured ten times. The transect in the centre lies 500\u2009m from any fragment margin to ensure sampling of forest interior in the absence of edge effects on the canopy structure (~40\u2009m73). This sampling strategy covered a total area of 0.52\u2009ha, which included 274 trees with diameter at breast height (DBH)\u2009\u2265\u200910\u2009cm, lianas, shrubs, saplings, seedlings and acaulescent palms that were repeatedly measured 11 times.\n\nTo ensure a full 3D representation of the upper canopy (35\u2009m in height), each transect consisted of three scan lines parallel to each other with scans spaced at 5\u2009m intervals within and between lines (Supplementary Fig.\u00a01b). The distance between scanning positions was smaller than the 10\u201340\u2009m usually applied in previous studies to minimise data uncertainties due to occlusion in dense tropical forests and maximise data acquisition in the upper canopy74. Given that the RIEGL VZ-400i has a zenith angle range of 30\u2013130\u00b0, an additional scan was acquired at each sampling location with the scanner tilted at 90\u00b0 from the vertical position. A total of 276 scans across all transects each time resulted in a complete sampling of the full hemisphere in each scan location (Supplementary Fig.\u00a01c). All scans were later co-registered into a single point cloud per transect using the RiSCAN PRO software version 2.9, provided by RIEGL. Given that the RIEGL VZ-400i uses onboard sensor data with an algorithm to align scans without the use of reflectors, automatic registration was done before a final adjustment of scans.\n\nWe used the LAStools (rapidlasso, GmbH; Gilching, Germany) suite of computational tools to process the data. To minimise errors in the fusion of the repeated scans, we first created a common digital terrain model (DTM) at 0.5\u2009m resolution using a combination of ground returns from the first survey. Using an inverse distance weighting algorithm in the function grid_terrain from the \u201clidR\u201d package in R, a common DTM was constructed from LiDAR ground returns. Plant area density (PAD) for all transects was then calculated using a voxel-based approach (with a 5\u2009m buffer around each transect to maximise the PAD data). The volume occupied by vegetation within each transect was divided into 1\u2009m3 voxels, and the PAD calculated for each of these voxels (Supplementary Fig.\u00a01d). This procedure was done in the LiDAR data voxelization software AMAPVox75,76. AMAPvox tracks every laser pulse through a 3D grid (voxelised space) to the last recorded hit. The effective sampling area of each laser pulse (or fraction of pulse in case of multiple hits) is computed from the theoretical beam section (a function of distance to laser and divergence of laser beam) and the remaining beam fraction entering a voxel. In case more than one hit is recorded for a given pulse, the beam section is equally distributed between the different hits of the pulse. This information is combined with the optical path length of each pulse entering a voxel to compute the local transmittance or equivalently the local attenuation per voxel. Different estimation procedures are provided in the AMAPVox software. We used the Free Path Length estimator first developed for single return TLS in Pimont and colleagues76 and later extended to the multiple return case77. The common assumption made for all estimation procedures in AMAPvox is to consider vegetation elements as randomly distributed within a voxel (thereby neglecting within voxel clumping) and to express the directional gap probability (or directional transmittance) as a function of the optical path length of laser pulse through a voxel and the local extinction coefficient78. The extinction coefficient is the product of the Plant Area Density and the projection function G(\u03b8), which is the ratio of plant area projected in direction \u03b8 to actual area:\n\nwhere P(\u03b8,l) is the probability of non-interception of a light beam of zenith angle \u03b8 (i.e. directional gap probability) along a path of length l, \u03bb\u03b8 (m\u22121) is the directional attenuation coefficient, and l is the optical path length (m).\n\nThe PAD (m2\u2009m\u22123) is related to \u03bb as follows:\n\nG(\u03b8), the plant projection function, is taken equal to 0.5, assuming a spherical distribution of leaf inclination angles79. This function is likely to be spatially variable in complex forest canopies.\n\nIn total, the number of voxels was 230,609, which were monitored 11 times during seasonal changes. We then calculated the sum of PADs for each 1\u2009m2 vertical column (X-, Y-coordinate) to obtain the PAI, which is a combination of the leaf area index and the area of wood components, including branches and trunks.\n\nAlbeit restricted in their spatial extent, our densely sampled repeated terrestrial laser scans likely provide more accurate and robust measures of PAI than any other method previously used to monitor seasonal changes in plant areas of Amazonian forests. Measurement accuracy is enhanced by the extremely high sampling density and multiple return capacity of the laser system, and multiple view angles reducing the area occluded to the sensor36; fast-to-operate single return laser profilers such as portable ground LiDAR as used by Smith and colleagues19 while having high pulse density may have more limited accuracy80.\n\nTo test the hypotheses that (1) fragmentation has significant effects on the structure of the vegetation in the BDFFP experiment\u2014following Almeida and colleagues73\u2014and (2) that edge effects impact phenology, we related PAI collected during the 11 TLS campaigns with distance from the edge using a nonlinear mixed model. The Eq. (5) included the term exp(\u2212x), as an asymptotic component that represents the saturation of PAI with distance from the edge, denoted by x in the model, and transect as a random variable, allowing us to include any idiosyncratic differences between transects.\n\nwhere \u03b20 to \u03b22 are the model parameters, ui is the random intercept for transect i, and \u03b5i is the normally distributed residual error.\n\nThis approach has been used to investigate edge effects on forest structure and dynamics23,81. The model was fitted using the function nlme in R. The results from this model indicates that the effects of transect account for 6.5% of the total PAI variability only, and that most of the variance (93.5%) is explained by the within-transect variability, including the distance from edge and seasonal variations (Supplementary Fig.\u00a02). A hockey-stick model consisting of two linear segments was also implemented with the R package \u201cSiZer\u201d using the function piecewise linear. This model identified a \u201cdistance from edge\u201d threshold, dividing voxels from the two transects near the fragment margins into edge and interior groups. We demonstrate the edge effects on PAI within 37\u2009m of forest margins (Supplementary Fig.\u00a02). These results corroborate a previous study in the same forest fragments showing edge effects of up to 40\u2009m on canopy height73. Therefore, we considered edge in this study as the forests within 40\u2009m of the forest fragment margins, which resulted in two edge transects (2\u2009\u00d7\u200940\u2009m) and three interior transects (2\u2009\u00d7\u200960\u2009m\u2009+\u20091\u2009\u00d7\u200930\u2009m).\n\nWe also tested the hypothesis suggested by Smith and colleagues19 that the lower and upper strata of the vegetation have asynchronous changes in plant area during the dry season by comparing PAD on October 16th with PAD on June 24th in these strata. Species, functional and phylogenetic composition of the understory are distinct from the upper canopy in Central Amazonian forests30,35. While the understory is comprised of lower branches, seedlings, shade-tolerant and embolism resistant trees and shrubs, lianas, acaulescent palms and saplings of young adult trees, the upper canopy is made up of adult predominantly shade-tolerant species, including tall and emergent trees and lianas. We then calculated the changes in PAD during the dry season to investigate shifts in the vertical profile of vegetation to elucidate the seasonal responses of specific strata (Supplementary Fig.\u00a03a, 3b).\n\nWe observed consistent positive PAD changes below the height of 15\u2009m above the ground and negative PAD changes above 15\u2009m height (Supplementary Fig.\u00a03b). Thus, given the existence of only two axes of variation along the vertical profile of the vegetation, we utilized this height to define understory (<15\u2009m aboveground) and upper canopy (\u226515\u2009m aboveground) in this study. This is consistent with a prior study in the Amazonian forest, which also demonstrated distinct seasonal responses in leaf area above and below a height of 15\u2009m19. The sum of all the understory PADs and the upper canopy PADs are referred to as understory PAI and upper canopy PAI, respectively. Our analysis comprises 5133 PAI values for the understory and 5133 PAI values for the upper canopy, each monitored 11 times during the seasonal climatic variations. The understory accounts for 62\u2009+\u20091.1% of the total PAI in the forest interior and 68\u2009+\u20090.4% of the total PAI of forest edges throughout the period of measurement (Supplementary Fig.\u00a03a).\n\nPAI changes may be controlled by changes in micro and macroclimatic conditions19,38,40. We demonstrate below how we estimated solar radiation and accumulated rainfall at the landscape level, and continuously measured air temperature and soil moisture in the understory of forest edges and interior of forest fragments to examine the synchrony between these factors and the PAI time-series in the understory and canopy.\n\nLeaf flushing in Central Amazonian forests coincides with peaks in PAR (W/m2) during periods of low rainfall4,14,38. PAR varies significantly within forest canopies and changes over time due to variations in the incident solar flux density and solar direction41. Incident solar PAR contains two components: direct PAR and diffuse PAR\u2014and the latter is mostly controlled by scattering of particles and cloud cover in the atmosphere82. The photosynthetic efficiencies of direct and diffuse PAR are different in forests, with positive effects of diffuse light on photosynthetic rates83 and atmospheric CO2 assimilation84 in comparison to plants under direct light conditions. To examine the synchrony between PAR and seasonal PAI changes, we derived solar radiation from the product MCD18A2 V6 (https://lpdaac.usgs.gov/products/mcd18a2v006/). This product uses the bands of the visible spectrum (400\u2013700\u2009nm) of both sensors (Terra and Aqua) from the Moderate Resolution Imaging Spectroradiometer (MODIS) to estimate daily PAR at a 5-km pixel resolution85. Daily mean rainfall estimates were also derived from NASA\u2019s POWER (Prediction of Worldwide Energy Resources) data with a spatial resolution of 0.5\u00b0 latitude by 0.5\u00b0 longitude (55\u2009\u00d7\u200955\u2009km). Meteorological parameters are derived from NASA\u2019s GMAO MERRA-2 assimilation model (https://gmao.gsfc.nasa.gov/reanalysis/MERRA/) and GEOS FP-IT (https://gmao.gsfc.nasa.gov/news/geos_system_news/2016/FP-IT_NRT_G5.12.4.php). We then integrated the daily rainfall estimates to accumulated monthly (30\u2009day period) rainfall and classified dry season as the period with running 30-day rainfall below 200\u2009mm as in Maeda and colleagues86.\n\nSoil moisture and maximum temperatures are key drivers of species\u2019 distributions and affect how species respond to climatic variations87,88. We measured air temperature (\u00b0C) and electrical conductivity of soil moisture (time-domain transmission; TDT) across a network of 22 data loggers varying in distance from the forest fragment margins (0 and 520\u2009m). Temperature-Moisture-Sensor (TMS) data loggers measured air temperature at 15\u2009cm above the ground and TDT at 8\u2009cm below ground, and all the data retrieved using TMS Lolly manager software (Tomst, Czech Republic)89. TDT values were transformed into volumetric soil moisture following calibration curves in Wild and colleagues89 using as input data soil texture (50% clay, 25% sand and 25% silt contents) and mean soil density of 1100\u2009kg/m3 measured by Camargo and Kapos90 in the same forest fragments of our study. Data loggers were shielded from direct solar radiation and recorded data every 15\u2009min. Microclimate data were recorded between 27th April 2019 and 16th October 2019, resulting in a total of 435,798 coupled temperature and volumetric soil moisture readings. TMS device measures microclimate variables affecting many ecological processes, including those related to water and energy balance. We calculated mean daily soil moisture and maximum daily soil moisture to investigate their synchrony with the PAI time series.\n\nWe used a linear mixed-effects (LME) model of understory PAI, upper canopy PAI and a combination of both strata (total PAI) measured from TLS in each transect as a function of time of measurement (time). We also included an interaction term with the plot category of location near an edge or in the forest fragment interior (edge effects) following Qie and colleagues81. The time\u2009\u00d7\u2009edge effects interaction represents how edge effects caused by forest fragmentation influence the seasonal variation in PAI. We compared this LME model with other LME models that contained the variables time and edge effects as additive terms to examine the significance of seasonality and fragmentation on PAI variation. Model explanatory power was assessed in terms of AIC (Supplementary Table\u00a01). The LME model was fitted using the lme function in the \u201cnlme\u201d R package. Variations in transect area and monitoring period can influence PAI trends, and thus we used varIdent weights function to account for the noise attributed to sampling effort91. Performance of the final models was evaluated using an 80/20 split of the data for calibration and validation, respectively, over 200 randomised permutations of the dataset. These analyses generated a distribution of model coefficients and allowed an assessment of model stability and uncertainty of predictions. We calculated 95% confidence intervals from the 2.5% and 97.5% quantiles of the distribution of model coefficients.\n\nIf increasing upper canopy PAI contributes to lower light interception in the lower stratum of the vegetation, we may expect a decreasing leaf development in the understory of forests in the interior of fragments38,41. However, we may also expect that such an effect on understory PAI by increasing upper canopy PAI is reduced or absent near fragment edges, with the loss of tall trees and lateral light from forest edges exposing the understory to more direct sunlight92. We tested this by averaging the community-level PAI in understory and upper canopy strata for each census, and then using linear models (lm function in R) to examine the relationships of PAI between the understory and upper canopy.\n\nFurther information on research design is available in the\u00a0Nature Research Reporting Summary linked to this article.",
+            "section_image": []
+        },
+        {
+            "section_name": "Data availability",
+            "section_text": "The repeated PAI data collected in Central Amazonia using a terrestrial laser scanner (TLS) between April and October 2019 and generated in this study have been deposited in the national Finnish Fairdata services database under accession code https://etsin.fairdata.fi/dataset/e488f81b-b927-4bbd-a6f7-2f532f434b2b. PAR estimates were obtained from https://lpdaac.usgs.gov/products/mcd18a2v006/ and meteorological data from https://gmao.gsfc.nasa.gov/reanalysis/MERRA/. Microclimate measurements collected in the field during the current study are available from the corresponding author on reasonable request within 10\u2009days.",
+            "section_image": []
+        },
+        {
+            "section_name": "Code availability",
+            "section_text": "There is no particular code or mathematical algorithm that is considered crucial to the conclusions. All relevant R-functions that were used are referred to in the Method section (see package vignettes for details).",
+            "section_image": []
+        },
+        {
+            "section_name": "References",
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+            "section_image": []
+        },
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+            "section_name": "Acknowledgements",
+            "section_text": "This study was funded by the Academy of Finland (decision numbers 318252, 319905 and 345472). This publication is number 831 of the Technical Series of the Biological Dynamics of Forest Fragment Forest (BDFFP\u2014INPA / STRI). We thank the Biological Dynamics of Forest Fragment Project team for the thorough logistical support in the field. We are grateful to Renann Henrique Paiva Dias Silva, Juliane Menezes and Vinicius Bertin for the great and thorough\u00a0assistance in the field. G.V. received support from Laboratoire d\u2019Excellence CEBA (ANR-10-LABX-25). K.C. was funded by the European Union\u2019s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 835398. R.S.O. receives a CNPq productivity scholarship and is supported by a NERC-FAPESP grant 2019/07773-1.\u00a0Y.M.d.M. was supported by the Royal Society under the Newton International Fellowship funding (NF170036) and HPC-Europa-3 (HPC17TA3RL), supported by the H2020-European Commission. S.C.S. received support from the US NSF (DEB-1950080 and 1754357) and USDA NIFA.",
+            "section_image": []
+        },
+        {
+            "section_name": "Author information",
+            "section_text": "Department of Geosciences and Geography, University of Helsinki, Helsinki, 00014, Finland\n\nMatheus Henrique Nunes\u00a0&\u00a0Eduardo Eiji Maeda\n\nBiological Dynamics of Forest Fragment Project, National Institute for Amazonian Research, Manaus, AM, 69067-375, Brazil\n\nJos\u00e9 Lu\u00eds Campana Camargo\n\nAMAP, Univ Montpellier, IRD, CIRAD, CNRS, INRAE, Montpellier, France\n\nGr\u00e9goire Vincent\n\nCAVElab\u2014Computational and Applied Vegetation Ecology, Department of Environment, Faculty of Bioscience Engineering, Ghent University, Ghent, Belgium\n\nKim Calders\n\nDepartment of Plant Biology, Institute of Biology, University of Campinas, Campinas, Brazil\n\nRafael S. Oliveira\n\nSchool of Life Sciences, Faculty of Science, University of Technology Sydney, Sydney, NSW, 2007, Australia\n\nAlfredo Huete\n\nInstitute of Geography and Geoecology, Karlsruhe Institute of Technology (KIT), Kaiserstr. 12, 76131, Karlsruhe, Germany\n\nYhasmin Mendes de Moura\n\nCentre for Landscape and Climate Research, School of Geography, Geology and the Environment, University of Leicester, Leicester, LE17RH, UK\n\nYhasmin Mendes de Moura\n\nNational Institute of Amazonian Research, Manaus, Brazil\n\nBruce Nelson\n\nDepartment of Forestry, Michigan State University, East Lansing, MI, USA\n\nMarielle N. Smith\u00a0&\u00a0Scott C. Stark\n\nArea of Ecology and Biodiversity, School of Biological Sciences, Faculty of Science, The University of Hong Kong, Hong Kong, Hong Kong SAR\n\nEduardo Eiji Maeda\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nM.H.N. and E.E.M. conceived the study. M.H.N. and E.E.M. led data collection in the field. M.H.N., G.V. and E.E.M. processed the LiDAR data. M.H.N. performed data analyses and wrote the manuscript. M.H.N., J.L.C.C., G.V., K.C., R.S.O., A.H., Y.M.d.M., B.N., M.N.S., S.C.S. and E.E.M. contributed to the revision of the paper.\n\nCorrespondence to\n                Matheus Henrique Nunes.",
+            "section_image": []
+        },
+        {
+            "section_name": "Ethics declarations",
+            "section_text": "The authors declare no competing interests.",
+            "section_image": []
+        },
+        {
+            "section_name": "Peer review",
+            "section_text": "Nature Communications thanks Lee Vierling and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.",
+            "section_image": []
+        },
+        {
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+            "section_text": "Open Access  This article 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. The images or other third party material in this article are included in the article\u2019s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article\u2019s 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/.\n\nReprints and permissions",
+            "section_image": []
+        },
+        {
+            "section_name": "About this article",
+            "section_text": "Nunes, M.H., Camargo, J.L.C., Vincent, G. et al. Forest fragmentation impacts the seasonality of Amazonian evergreen canopies.\n                    Nat Commun 13, 917 (2022). https://doi.org/10.1038/s41467-022-28490-7\n\nDownload citation\n\nReceived: 02 August 2021\n\nAccepted: 27 January 2022\n\nPublished: 17 February 2022\n\nVersion of record: 17 February 2022\n\nDOI: https://doi.org/10.1038/s41467-022-28490-7\n\nAnyone you share the following link with will be able to read this content:\n\nSorry, a shareable link is not currently available for this article.\n\n\n\n\n                            Provided by the Springer Nature SharedIt content-sharing initiative\n                        ",
+            "section_image": [
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+            ]
+        },
+        {
+            "section_name": "This article is cited by",
+            "section_text": "Nature Communications (2025)\n\nDiscover Sustainability (2025)\n\nNature Ecology & Evolution (2025)\n\nNature (2024)\n\nNature Communications (2023)",
+            "section_image": []
+        }
+    ]
+}

2ae36470298dc21812c2daf83a1347cd8d7520177c40d85a6ff8aa616b82b269/metadata.json

@@ -0,0 +1,126 @@
+{
+    "title": "Universal non-Hermitian skin effect in two and higher dimensions",
+    "pre_title": "Universal non-Hermitian skin effect in two and higher dimensions",
+    "journal": "Nature Communications",
+    "published": "06 May 2022",
+    "supplementary_0": [
+        {
+            "label": "Supplementary Information",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-022-30161-6/MediaObjects/41467_2022_30161_MOESM1_ESM.pdf"
+        },
+        {
+            "label": "Peer Review File",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-022-30161-6/MediaObjects/41467_2022_30161_MOESM2_ESM.pdf"
+        }
+    ],
+    "supplementary_1": NaN,
+    "supplementary_2": NaN,
+    "source_data": [],
+    "code": [],
+    "subject": [
+        "Electronic properties and materials",
+        "Topological insulators"
+    ],
+    "license": "http://creativecommons.org/licenses/by/4.0/",
+    "preprint_pdf": "https://www.researchsquare.com/article/rs-757556/v1.pdf?c=1651921612000",
+    "research_square_link": "https://www.researchsquare.com//article/rs-757556/v1",
+    "nature_pdf": "https://www.nature.com/articles/s41467-022-30161-6.pdf",
+    "preprint_posted": "18 Aug, 2021",
+    "research_square_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Skin effect, experimentally discovered in one dimension, describes the physical phenomenon that on an open chain, an extensive number of eigenstates of a non-Hermitian hamiltonian are localized at the end(s) of the chain. Here in two and higher dimensions, we establish a theorem that the skin effect exists, if and only if periodic-boundary spectrum of the hamiltonian covers a finite area on the complex plane. This theorem establishes the universality of the effect, because the above condition is satisfied in almost every generic non-Hermitian hamiltonian, and, unlike in one dimension, is compatible with all spatial symmetries. We propose two new types of skin effect in two and higher dimensions: the corner-skin effect where all eigenstates are localized at one corner of the system, and the geometry-dependent-skin effect where skin modes disappear for systems of a particular shape, but appear on generic polygons. An immediate corollary of our theorem is that any non-Hermitian system having exceptional points (lines) in two (three) dimensions exhibits skin effect, making this phenomenon accessible to experiments in photonic crystals, Weyl semimetals, and Kondo insulators.Atomic and Molecular PhysicsSoft Condensed-matter Physicsskin effectdimensionsnon-Hermitian hamiltonian",
+            "section_image": []
+        },
+        {
+            "section_name": "Additional Declarations",
+            "section_text": "There is NO Competing Interest.",
+            "section_image": []
+        }
+    ],
+    "nature_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Skin effect, experimentally discovered in one dimension, describes the physical phenomenon that on an open chain, an extensive number of eigenstates of a non-Hermitian Hamiltonian are localized at the end(s) of the chain. Here in two and higher dimensions, we establish a theorem that the skin effect exists, if and only if periodic-boundary spectrum of the Hamiltonian covers a finite area on the complex plane. This theorem establishes the universality of the effect, because the above condition is satisfied in almost every generic non-Hermitian Hamiltonian, and, unlike in one dimension, is compatible with all point-group symmetries. We propose two new types of skin effect in two and higher dimensions: the corner-skin effect where all eigenstates are localized at corners of the system, and the geometry-dependent-skin effect where skin modes disappear for systems of a particular shape, but appear on generic polygons. An immediate corollary of our theorem is that any non-Hermitian system having exceptional points (lines) in two (three) dimensions exhibits skin effect, making this phenomenon accessible to experiments in photonic crystals, Weyl semimetals, and Kondo insulators.",
+            "section_image": []
+        },
+        {
+            "section_name": "Introduction",
+            "section_text": "The study of non-Hermitian Hamiltonians, which can be regarded as the effective description of dissipative processes, can be traced back to the investigation of alpha decay, where real and imaginary parts of the complex energy are related to the experimentally observed energy level and decay rate1. When a lattice system is coupled with environments and has dissipations, e.g. photonic crystals having radiational loss2,3,4 and electronic systems having finite quasiparticle lifetime5,6, the non-Hermitian band theory becomes a conceptually simple and efficient approach7,8,9,10,11,12.\n\nSkin effect13,14,15,16,17,18,19,20,21,22,23, a phenomenon unique to the non-Hermitian band theory, refers to the localization of eigenstates at the boundary, the number of which scales with the volume of the system. For example, in one dimension, all eigenstates of a non-Hermitian Hamiltonian can be localized at the ends of a chain13. This suggests the failure of Bloch\u2019s theorem24,25, which states that eigenstates in the bulk are modulated plane waves. As Bloch\u2019s theorem plays a fundamental role in the development of condensed-matter physics26, the emergence of skin effect indicates a new and possibly revolutionary direction. Especially, the skin effect has been observed experimentally in one-dimensional classical systems27,28,29, inspiring further studies on their higher dimensional generalizations14,30,31,32,33,34,35,36,37. However, a general theory for the higher-dimensional skin effect has not been established.\n\nApart from the skin effect, another focus topic in non-Hermitian band systems is the exceptional point (or line)38,39,40,41,42,43,44,45,46,47 that refers to stable point-type (or line-type) non-Hermitian band degeneracy in the Brillouin zone. At the exceptional point, not only eigenvalues but also eigenstates of the Bloch Hamiltonian coalesce39. Many a novel phenomenon related to exceptional points has been predicted and observed47,48,49,50,51,52, such as the emergence of bulk-Fermi arc terminated at the exceptional points5,45. Since the bulk-boundary correspondence plays a central role in the development of topological phases53, it is natural to ask if there exists a non-Hermitian bulk-boundary correspondence in bands having exceptional points, analogous to the surface Fermi arc in the Weyl semimetals in the Hermitian counterpart54.\n\nIn this paper, we establish a theorem that reveals a universal bulk-boundary correspondence in two and higher dimensional non-Hermitian bands, as shown in Fig.\u00a01. The \u201cbulk\u201d refers to the area of the spectrum of the Hamiltonian on the complex plane with periodic boundary condition, and \u201cboundary\u201d means the presence (absence) of the skin effect for open-boundary system of a generic shape. The theorem states that the skin effect appears if and only if the spectral area is nonzero. This skin effect is \u201cuniversal\u201d for three reasons: (i) a randomly generated local non-Hermitian Hamiltonian has the skin effect with probability one; (ii) the skin effect is, unlike in one dimension, compatible with all point-group symmetries and time-reversal symmetry, including complex-conjugate-type and transpose-type time-reversal symmetry in ref. 11; and (iii) it does not require any special geometry of the open-boundary system. We classify the universal skin effect into non-reciprocal skin effect and generalized reciprocal skin effect according to nonzero and zero current functional, respectively, and also propose the corner-skin effect and geometry-dependent-skin effect as representative phenomena of these two categories.\n\na represents the Brillouin zone. b, d shows that if the spectral area of \\({{{{{{{\\mathcal{H}}}}}}}}({{{{{{{\\bf{k}}}}}}}})\\) is nonzero, the skin effect will appear on some generic open-boundary geometries. c, e shows that when the spectral area of \\({{{{{{{\\mathcal{H}}}}}}}}({{{{{{{\\bf{k}}}}}}}})\\) is zero, or forming one or several arcs on the complex plane, there is no skin effect under any geometry.\n\nA surprising corollary of our theorem is that the stable exceptional points8,41,43 imply the presence of skin effect. Because exceptional points have been either observed or proposed in meta-materials as well as in condensed matter, this corollary makes skin effect observable in known systems. We predict the geometry-dependent skin effect in the two-dimensional photonic crystal studied in ref. 45, and propose to observe this effect in the anomalous dynamics of wave packets.",
+            "section_image": [
+                "https:////media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41467-022-30161-6/MediaObjects/41467_2022_30161_Fig1_HTML.png"
+            ]
+        },
+        {
+            "section_name": "Results",
+            "section_text": "For generic one-dimensional non-Hermitian systems, the correspondence between the spectral shape and the skin effect has been derived17,18, i.e., when the Bloch spectrum is a loop-type (an arc-type), the skin effect appears (disappears).\n\nGeneralizing the correspondence to two dimensions, we note two main differences. One difference is in the periodic-boundary spectrum, Ei(k), where i is the band index and k the crystal momentum in the first Brillouin zone (BZ). Generally speaking, Ei(k) is a mapping from the d-dimensional torus to the complex plane, \\({\\mathbb{C}}\\). When d\u2009=\u20091, the image of Ei(k) forms a loop; but when d\u2009>\u20091, the image is generically a continuum on \\({\\mathbb{C}}\\), denoted by Ei(BZ). The area covered by Ei(BZ) on the complex plane is called the spectral area, denoted by Ai. Another difference is in the variety of open-boundary condition. There is only one geometry for an open system in one dimension, i.e., an open chain; but there are an infinite number of geometries in two dimensions such as triangle, rectangle and pentagon.\n\nNow we are ready to state the theorem of universal skin effect: in the thermodynamic limit, the skin effect is present in a Hamiltonian having open boundary of generic geometry, if the spectral area is nonzero (Ai\u2009\u2260\u20090); vice versa, the skin effect is absent for all possible geometries, if the spectral area is zero (Ai\u2009=\u20090). The open boundary in the theorem refers to the fully open boundary condition in all\u00a0spatial directions. As the periodic-boundary Hamiltonian describes the dynamics in the bulk, the theorem relates a bulk property (spectral area) to a boundary one (existence of skin modes). Fig.\u00a01 shows some schematic examples. The complete proof of the theorem is provided in the Supplementary Note\u00a01.\n\nA brief outline of the proof is illustrated in Fig.\u00a02. The theorem is obtained in three steps: step I establishes the equivalence relation between spectral area and spectral winding number of straight lines in the BZ; step II connects these nonzero spectral winding numbers with skin effect on the stripe geometry \u2014 the geometry with open boundary in only one direction and periodic boundary in other directions; step III illustrates that skin effect on stripe geometry implies skin effect on fully open-boundary geometry (i.e., the universal skin effect), which relies on a conjecture. The justification of this conjecture is discussed in the Supplementary Note\u00a01.\n\nThe first step connects the nonzero spectral area and nonzero spectral winding number along some direction in the BZ. The latter means the Hamiltonian exhibits the skin effect under the corresponding stripe geometry, which is proved in the second step. The skin effect on stripe geometry further reveals the universal skin effect, relying on a conjecture in the third step.\n\nThe above theorem has implied the universality of skin effect in two and higher dimensions. As Ei(BZ) is the image of the d\u2009\u2265\u20092-dimensional torus on the complex plane, it takes fine tuning of parameters to make Ai\u2009=\u20090 for every i. In fact, for single-band Hamiltonian, we can prove that A\u2009=\u20090 if and only if \\({{{{{{{\\mathcal{H}}}}}}}}({{{{{{{\\bf{k}}}}}}}})=P[h({{{{{{{\\bf{k}}}}}}}})]\\), where h(k) is a Hermitian Hamiltonian and P is a complex polynomial (see Supplementary Note\u00a01). In other words, a randomly generated non-Hermitian Hamiltonian \\({{{{{{{\\mathcal{H}}}}}}}}({{{{{{{\\bf{k}}}}}}}})\\) has skin effect: the first meaning of universality. In previous studies, other types of skin effect, such as the line-skin and the high-order-skin effect, in two and higher dimensions have been proposed30,34. These types all require the open-boundary system take a special geometry (usually a rectangle) and are hence considered special and non-generic. Additionally, the number of skin modes in the universal skin effect follows a volume law, which differentiates from the higher-order-skin effect. The skin effect when Ai\u2009\u2260\u20090 assumes a completely generic geometry of boundary: the second meaning of universality. The third meaning of universality lies in the fact that the higher-dimensional skin effect is compatible with all point-group symmetries, i.e., the universal skin effect can appear if and only if the spectral area is nonzero, regardless of the point-group symmetry of the bulk Hamiltonian. While in one dimension, if the bulk Hamiltonian only respects, for example, the inversion symmetry, the periodic-boundary energy spectrum has an arc-form on the complex plane, which means the absence of non-Hermitian skin effect11,23. A standing wave explanation for the theorem is provided in the Supplementary Note\u00a02.\n\nWhile the theorem shows that the skin effect is universal, it does not specify what skin modes look like in higher dimensions. Here, we define the current functional, which partitions the universal skin effect into non-reciprocal skin effect and generalized reciprocal skin effect. Then we report the representative phenomena in these two types, i.e., the corner-skin effect (CSE) and the geometry-dependent skin effect (GDSE), respectively.\n\nThe current functional is defined as\n\nunder the periodic-boundary condition, where i is the energy band index and \u2207\u03b1 indicates the directional derivative along certain direction \u03b1 in d-dimensional momentum space. Here, n(E,\u2009E*) represents a distribution function when the system reaches to a steady state and only depends explicitly on the energy of the system state17. The nonzero current functional (labeled by J\u2009\u2260\u20090) is defined as:\u2009\u2203\u2009\u03b1,\u2009n,\u2009\u2009\u2009J\u03b1[n]\u2009\u2260\u20090; and as a complementary set, the zero current functional (labeled by J\u2009=\u20090) is defined as:\u2009\u2200\u2009\u03b1,\u2009n,\u2009\u2009\u2009J\u03b1[n]\u2009=\u20090. By definition, the nonzero current functional and zero current functional are complete and mutually exclusive mathematically. Therefore, we can classify the universal skin effect (nonzero spectral area) into two types according to the current functional, i.e., the non-reciprocal skin effect (J\u2009\u2260\u20090) and generalized reciprocal skin effect (J\u2009=\u20090), as illustrated in Fig.\u00a03. Note that this classification of skin effect according to the current functional is different from the classification of intrinsic point-gap topology for symmetry class11,18 (see Supplementary Note\u00a03). The current functional is shown to vanish in two and three dimensions under point groups Ci, D2,3,4,6, C2h,3h,4h,6h, D2d,3d,2h,3h,4h,6h, T, Td,h, O and Oh. Therefore, the non-reciprocal skin effect is only compatible with point groups Cm and C2,3,4,6,2v,3v,4v,6v. As a comparison, the generalized reciprocal skin effect is compatible with all point-group symmetries (see also Supplementary Note\u00a03).\n\nThe universal skin effect can be further classified into two types by the current functional, that is, non-reciprocal skin effect (\u2009\u2203\u2009\u03b1,\u2009n,\u2009\u2009\u2009J\u03b1[n]\u2009\u2260\u20090) and generalized reciprocal skin effect (\u2009\u2200\u2009\u03b1,\u2009n,\u2009\u2009\u2009J\u03b1[n]\u2009=\u20090). CSE (a)\u2013(d) and GDSE (e)-(h) are representatives of these two types of\u00a0skin effects, respectively. In (a, b, e, f), the light blue regions represent the spectrum under periodic boundary, where 200*200 k-grid is used, and the red points represent the eigenvalues under different open-boundary geometries. The system size under square geometry in (c, g) is Lx\u2009\u00d7\u2009Ly\u2009=\u200960\u2009\u00d7\u200960, and each triangle geometry in (d, h) has the same right-angled side length Lx\u2009=\u2009Ly\u2009=\u200960. The spatial distributions of eigenstates W(x) are plotted in (c, d, g, h) with the color bars. In the system with GDSE, the skin effect disappears under square geometry (geometry 1) in (g), and reappears under triangle geometry (geometry 2) in (h).\n\nWe define the CSE as a type of the non-reciprocal skin effect (J\u2009\u2260\u20090) that exhibits the particular phenomenon that almost all eigenstates are localized at corners of the open-boundary geometry. The Hamiltonian of the example for CSE is\n\nof which the spectral area under square geometry and triangle geometry is shown in Fig.\u00a03(a, b) with light blue color. Because of the nonzero spectral area, the theorem tells us that the Hamiltonian must have the universal skin effect. This is verified in Fig.\u00a03(c, d), where the spatial distributions of all eigenstates \\(W({{{{{{{\\bf{x}}}}}}}})=\\frac{1}{N}{\\sum }_{n}{\\left|{\\psi }_{n}({{{{{{{\\bf{x}}}}}}}})\\right|}^{2}\\) under different open boundaries are plotted. Here \u03c8n(x) is a normalized right eigenstate and N is the number of these eigenstates. It is found that the wave functions are always localized at the corner of the boundary in Fig.\u00a03(c), even if the open-boundary geometry is changed in Fig.\u00a03(d). We elaborate on the localization of eigenstates for this example in the Supplementary Note\u00a04. We also plot the corresponding eigenvalue spectra under different open boundaries, as shown in Fig.\u00a03(a, b) with red color. One can notice that the spectral areas under periodic and open boundaries do not equal. The CSE is a representative one of non-reciprocal skin effect and inherits its features, including nonzero current functional and incompatibility with certain point-group symmetries.\n\nSimilar to the definition of CSE, the GDSE is one type of generalized reciprocal skin effect (J\u2009=\u20090) showing the unique phenomenon that there is at least one fully open boundary geometry under which the skin effect does not appear. The Hamiltonian of the example for GDSE reads\n\nSince the spectral area is nonzero, our theorem tells us that the system must have skin effect for certain open-boundary geometry, such as a random polygon. However, an interesting phenomenon in this example is that the skin effect disappears under the square geometry due to the existence of two mirror symmetries shown in Fig.\u00a03(g). Once we choose other types of boundaries where mirror symmetries are broken, the skin effect reappears as shown in Fig.\u00a03(h). Since the appearance of the skin effect and the localization\u00a0position depend on the geometry, it is called the GDSE. In one dimension, an open chain does not exhibit skin effect when its spectrum coincides with the corresponding periodic-boundary spectrum on the complex plane. Unlike in one dimension, even if the region covered by the energy spectrum under some open-boundary geometry (such as the triangle geometry in Fig.\u00a03(h)) seems to be the same as the region covered by the periodic-boundary spectrum, the system can still show a skin effect due to the different density of states on the complex plane. It is also a unique feature in two- and higher-dimensional skin effects. In the Supplementary Note\u00a04, we provide some numerical results to illuminate this new type of skin effect and discuss the localization of eigenstates on the open-boundary geometry. In addition, we show that GDSE follows the volume law, i.e., the increase in the number of skin modes is proportional to the increase in the system volume. For GDSE, there is at least one spatial geometry such that skin modes vanish, and as such is mutually exclusive with CSE. Additionally, GDSE is compatible with all point groups, in contrast to CSE.\n\nAn immediate corollary of our theorem is that all lattice Hamiltonians with stable exceptional points have universal skin effect, connecting two unique phenomena in the non-Hermitian band theory. This connection has also been discussed in ref. 31, where the bands around the stable exceptional point form a point gap with nonzero spectral winding number, consequently, exhibiting the skin effect under an open-boundary geometry. Consider a stable exceptional point k0 in two dimensions. Due to the branch point structure of exceptional point, the dispersion around k0 can be expressed as8\\({E}_{\\pm }({{{{{{{\\bf{k}}}}}}}})=\\pm {c}_{0}\\sqrt{{q}_{x}+{c}_{1}{q}_{y}}+O(| {{{{{{{\\bf{k}}}}}}}}-{{{{{{{{\\bf{k}}}}}}}}}_{0}| )\\), where qi=x,y denotes a small derivation from exceptional point in x or y direction, that is, qi\u2009=\u2009ki\u2009\u2212\u2009k0i. Here c0,\u2009c1 are nonzero complex numbers and the stable exceptional point ensures the nonzero imaginary part of c1. Suppose the range of the expansion is r0, then it is clear that \\({A}_{\\pm }\\ge | {c}_{0}| \\pi {{r}_{0}}^{2}/2\\,\\ne\\, 0\\). By the theorem, the system must have universal skin effect (see Supplementary Note\u00a05).\n\nNow we use the photonic crystal model that has been experimentally realized in ref. 45 to demonstrate our corollary. The tight-binding model Hamiltonian with periodic boundary can be written as\n\nwhere \u03c3\u2009=\u2009(\u03c30,\u2009\u03c3x,\u2009\u03c3y,\u2009\u03c3z) is a vector of the Pauli matrices and d(k) is a vector with four components, that is, \\({{{{{{{\\bf{d}}}}}}}}({{{{{{{\\bf{k}}}}}}}})=\\{{\\mu }_{0}-({t}_{2}+{t}_{3})(\\cos {k}_{x}+\\cos {k}_{y}),{t}_{1}[1-\\cos {k}_{x}-\\cos {k}_{y}+\\cos ({k}_{x}-{k}_{y})],{t}_{1}[\\sin {k}_{x}-\\sin {k}_{y}-\\sin ({k}_{x}-{k}_{y})],{\\mu }_{z}+({t}_{2}-{t}_{3})(\\cos {k}_{x}-\\cos {k}_{y})\\}\\). The parameters are chosen as follows, (t1,\u2009t2,\u2009t3,\u2009\u03bc0,\u2009\u03bcz)\u2009=\u2009(0.4,\u2009\u2212\u20090.1,\u20090.5,\u20091.35,\u2009\u2212\u20090.02). As shown in Fig.\u00a04(a), in the Hermitian limit, i.e. \u03b3\u2009=\u20090, the system has two Dirac points along the x-axis. When external dissipation or radiational loss is added, i.e., \u03b3\u2009\u2260\u20090, each Dirac point splits into two exceptional points shown in Fig.\u00a04(b), connected by the bulk Fermi arc. According to our theorem, the system must have the universal skin effect, more precisely, the GDSE. Specifically, the skin effect disappears under square geometry but reappears under diamond geometry, which is verified in the Supplementary Note\u00a06.\n\nTwo Dirac points (a) of a two-dimensional photonic crystal model are split into four exceptional points (b) upon adding non-Hermitian term, such as radiational loss. Correspondingly, the evolution of Gaussian wave packet with initial velocity at the center of a diamond geometry for each ten time intervals is shown in (c) with \u03b3\u2009=\u20090 (Hermitian) and (d) with \u03b3\u2009=\u20091/4 (GDSE). Two Weyl points (e) of a three-dimensional Weyl semimetal are expanded into two exceptional rings (f) after the addition of non-Hermitian perturbations. The spatial distribution of eigenstates, i.e. W(x), is plotted in (g). The modulus square of the propagator from i to oPio(\u03c9) and that from o to iPoi(\u03c9), as functions of \u03c9, are plotted with red color and dark cyan color in (h), respectively.\n\nSo far, we have shown the features of the energy spectrum and wave function in the system with GDSE. We expect some observable phenomena from the skin effect, which motivates us to examine the dynamical properties for the photonic crystal model in Eq.(4). In order to show this, we simulate the time evolution of the wave packet starting at the center of the diamond geometry with an initial velocity perpendicular to one edge. Here the initial state is chosen to be Gaussian form \\(\\left|{\\psi }_{0}\\right\\rangle ={{{{{{{\\mathcal{N}}}}}}}}\\exp [-{\\left(x-{x}_{0}\\right)}^{2}/10-{\\left(y-{y}_{0}\\right)}^{2}/10-i2x-i2y]{\\left(1,1\\right)}^{T}\\), where \\({{{{{{{\\mathcal{N}}}}}}}}\\) is the normalization factor and x0\u2009=\u2009y0\u2009=\u200921 is the center coordinate of the diamond geometry. We plot the corresponding spatial distribution of normalized final states \\(\\left|\\psi ({t}_{f})\\right\\rangle ={{{{{{{\\mathcal{N}}}}}}}}({t}_{f}){e}^{-i{{{{{{{{\\mathcal{H}}}}}}}}}_{{{{{{{{\\rm{OBC}}}}}}}}}{t}_{f}}\\left|{\\psi }_{0}\\right\\rangle\\) for every ten time intervals, where \\({{{{{{{{\\mathcal{H}}}}}}}}}_{{{{{{{{\\rm{OBC}}}}}}}}}\\) represents the open-boundary Hamiltonian on the diamond geometry. As shown in Fig.\u00a04(c), in the Hermitian case, the center of the wave packets obeys the simple law of reflection: the center of the wave packet just bounces between the two edges while slowly dispersing with time. However, in the non-Hermitian case (\u03b3\u2009=\u20091/4) with GDSE, after several oscillations between two edges, the wave packet makes a side jump into the upper left corner as shown in Fig.\u00a04(d). The transverse motion of the wave packet induced by skin effect is explained in more detail in the Supplementary Note\u00a06. This anomalous dynamical behavior is an experimental signature of GDSE.\n\nWe also propose the realization for CSE in a three-dimensional system with exceptional lines. Consider a Weyl semimetal with non-Hermitian term as a perturbation, of which the periodic-boundary Hamiltonian reads\n\nwhere dr(k) and di(k) are vectors with four components, that is, \\({{{{{{{{\\bf{d}}}}}}}}}_{r}({{{{{{{\\bf{k}}}}}}}})=(0,\\sin {k}_{x},\\sin {k}_{y},2-\\cos {k}_{x}-\\cos {k}_{y}+\\sin {k}_{z})\\) and \\({{{{{{{{\\bf{d}}}}}}}}}_{i}({{{{{{{\\bf{k}}}}}}}})=(-\\sqrt{5},1+\\cos {k}_{z},1-\\cos {k}_{z},\\cos {k}_{z})\\). The Hermitian part dr\u2009\u22c5\u2009\u03c3 is a Weyl semimetal possessing two Weyl points, the red cone at (0,\u20090,\u20090) and blue cone at (0,\u20090,\u2009\u03c0) shown in Fig.\u00a04(e). Upon turning on the non-Hermitian term, the Weyl points evolve into two exceptional rings in Fig.\u00a04(f). Consequently, the system exhibits the CSE with \u03b4\u2009=\u20091/6 shown in Fig.\u00a04(g), as a numerical verification of our corollary.\n\nExperimentally, the non-reciprocity of the CSE can be detected by the two-point Green\u2019s function. The modulus square of the propagator from i\u2009=\u2009(1,\u20091,\u20091) to o\u2009=\u2009(16,\u200916,\u200916) is expressed as \\({P}_{oi}(\\omega )={\\sum }_{\\alpha ,\\beta }{|\\langle o,\\beta |\\frac{1}{\\omega -\\hat{H}}|i,\\alpha \\rangle |}^{2}\\), where \u03b1,\u2009\u03b2 label the orbitals of the unit cell. We calculate Poi(\u03c9) and\u00a0Pio(\u03c9) in Fig.\u00a04(h), where a significant difference between them demonstrates the non-reciprocity of CSE.",
+            "section_image": [
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+            ]
+        },
+        {
+            "section_name": "Discussion",
+            "section_text": "Our work has built a bridge between two distinct phenomena that only exist in non-Hermitian systems, i.e., the exceptional points (lines) and the non-Hermitian skin effect, by establishing the correspondence between bulk (spectral area) and boundary (universal skin effect). We prove that the skin effect is universal and compatible with all point-group symmetries and time-reversal symmetry in two and higher dimensions. Due to the universality, it is expected that the skin effect is observable in a wide range of platforms, such as photonic crystals with natural radiational loss, acoustic meta-materials and circuit networks with lossy components such as resistors. Beyond these classical systems, the skin effect can also be realized in condensed matter, e.g., the heavy-fermion material with finite quasiparticle lifetime and the Weyl-exceptional-ring semimetal. The latter is realizable in Weyl semimetals made from inverting bands that have disparate effective masses, such as d- and f-bands.\n\nOne should be reminded, however, that the results in this paper assume the coherent dynamics of the constituent degrees of freedom, which is unlikely the case in macroscopic condensed-matter systems where the coherence length is shorter than the system size. On the contrary, for the systems where the system size and the coherent length are comparable, as in mesoscopic systems, we believe that the universal skin effect has a significant contribution to the transport properties, a subject for future exploration.",
+            "section_image": []
+        },
+        {
+            "section_name": "Data availability",
+            "section_text": "Raw numerical data from the plots presented are available from the authors upon request.",
+            "section_image": []
+        },
+        {
+            "section_name": "Code availability",
+            "section_text": "The code used to generate the figures are available from the authors upon reasonable request.",
+            "section_image": []
+        },
+        {
+            "section_name": "References",
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+        },
+        {
+            "section_name": "Acknowledgements",
+            "section_text": "C.F. acknowledges funding support by the Ministry of Science and Technology of China under grant number 2016YFA0302400, and the Chinese Academy of Sciences under grant number XDB33000000. Z.Y. acknowledges funding support by the National Science Foundation of China (Grant No. NSFC-12104450) and the fellowship of China National Postdoctoral Program for Innovative Talents (Grant No. BX2021300).",
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+        },
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+            "section_text": "Beijing National Laboratory for Condensed Matter Physics, and Institute of Physics, Chinese Academy of Sciences, 100190, Beijing, China\n\nKai Zhang\u00a0&\u00a0Chen Fang\n\nUniversity of Chinese Academy of Sciences, 100049, Beijing, China\n\nKai Zhang\n\nKavli Institute for Theoretical Sciences, Chinese Academy of Sciences, 100190, Beijing, China\n\nZhesen Yang\u00a0&\u00a0Chen Fang\n\nSongshan Lake Materials Laboratory, Dongguan, Guangdong, 523808, China\n\nChen Fang\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nC.F. conceived the work; K.Z. did the major part of the theoretical derivation and numerical calculation; Z.Y. wrote and analyzed the tight-binding Hamiltonian of the photonic crystal model; All authors discussed the results and participated in the writing of the manuscript.\n\nCorrespondence to\n                Zhesen Yang or Chen Fang.",
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+            "section_text": "Zhang, K., Yang, Z. & Fang, C. Universal non-Hermitian skin effect in two and higher dimensions.\n                    Nat Commun 13, 2496 (2022). https://doi.org/10.1038/s41467-022-30161-6\n\nDownload citation\n\nReceived: 28 July 2021\n\nAccepted: 19 April 2022\n\nPublished: 06 May 2022\n\nVersion of record: 06 May 2022\n\nDOI: https://doi.org/10.1038/s41467-022-30161-6\n\nAnyone you share the following link with will be able to read this content:\n\nSorry, a shareable link is not currently available for this article.\n\n\n\n\n                            Provided by the Springer Nature SharedIt content-sharing initiative\n                        ",
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+            ]
+        },
+        {
+            "section_name": "This article is cited by",
+            "section_text": "Communications Physics (2025)\n\nCommunications Physics (2025)\n\nCommunications Physics (2025)\n\nLight: Science & Applications (2025)\n\nNature (2025)",
+            "section_image": []
+        }
+    ]
+}

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+{
+    "title": "Precise solid-phase synthesis of CoFe@FeOx nanoparticles for efficient polysulfide regulation in lithium/sodium-sulfur batteries",
+    "pre_title": "Precision solid synthesis of CoFe@FeOx nanoparticles for regulating Li/Na\u2013S batteries",
+    "journal": "Nature Communications",
+    "published": "18 November 2023",
+    "supplementary_0": [
+        {
+            "label": "Supplementary Information",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-023-42941-9/MediaObjects/41467_2023_42941_MOESM1_ESM.pdf"
+        },
+        {
+            "label": "Peer Review File",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-023-42941-9/MediaObjects/41467_2023_42941_MOESM2_ESM.pdf"
+        }
+    ],
+    "supplementary_1": NaN,
+    "supplementary_2": NaN,
+    "source_data": [
+        "https://doi.org/10.6084/m9.figshare.24426877"
+    ],
+    "code": [],
+    "subject": [
+        "Materials for energy and catalysis",
+        "Nanoparticle synthesis",
+        "Nanoparticles"
+    ],
+    "license": "http://creativecommons.org/licenses/by/4.0/",
+    "preprint_pdf": "https://www.researchsquare.com/article/rs-2863707/v1.pdf?c=1700400095000",
+    "research_square_link": "https://www.researchsquare.com//article/rs-2863707/v1",
+    "nature_pdf": "https://www.nature.com/articles/s41467-023-42941-9.pdf",
+    "preprint_posted": "14 Jun, 2023",
+    "research_square_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Complex metal nanoparticles (NPs) distributed uniformly on supports demonstrate distinctive physicochemical properties and thus attract a wide attention for applications. The commonly used synthesis approaches are the wet chemistry methods, yet they display limitations to achieve the NPs structure design and uniform dispersion simultaneously. Solid synthesis serves as an interesting strategy which can achieve the fabrication of complex metal NPs on supports. Herein, the solid synthesis strategy is developed to precisely synthesize uniformly distributed CoFe@FeOx core@shell NPs via thermal syngas treatment. Fe atoms are preferentially exsolved from CoFe alloy bulk to the surface and then be carburized into a FexC shell under thermal syngas atmosphere, subsequently the formed FexC shell is passivated by air, obtaining CoFe@FeOx with a CoFe alloy core and a FeOx shell. This strategy is universal for the synthesis of MFe@FeOx (M=Co, Ni, Mn). The CoFe@FeOx exhibits bifunctional effect on regulating polysulfides as the separator coating layer for both Li/Na-S batteries. This method could be developed into solid synthetic systems to construct well distributed complex metal NPs.Physical sciences/Materials science/Nanoscale materials/NanoparticlesPhysical sciences/Chemistry/Inorganic chemistry/Solid-state chemistryPhysical sciences/Materials science/Materials for energy and catalysis/BatteriesPhysical sciences/Materials science/Nanoscale materials/Synthesis and processingPrecision synthesisMetal nanoparticlesSolid chemistryCore@shell structureLi/Na-S batteries",
+            "section_image": []
+        },
+        {
+            "section_name": "Additional Declarations",
+            "section_text": "There is NO Competing Interest.",
+            "section_image": []
+        },
+        {
+            "section_name": "Supplementary Files",
+            "section_text": "SI2023.04.26.pdf",
+            "section_image": []
+        }
+    ],
+    "nature_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Complex metal nanoparticles distributed uniformly on supports demonstrate distinctive physicochemical properties and thus attract a wide attention for applications. The commonly used wet chemistry methods display limitations to achieve the nanoparticle structure design and uniform dispersion simultaneously. Solid-phase synthesis serves as an interesting strategy which can achieve the fabrication of complex metal nanoparticles on supports. Herein, the solid-phase synthesis strategy is developed to precisely synthesize uniformly distributed CoFe@FeOx core@shell nanoparticles. Fe atoms are preferentially exsolved from CoFe alloy bulk to the surface and then be carburized into a FexC shell under thermal syngas atmosphere, subsequently the formed FexC shell is passivated by air, obtaining CoFe@FeOx with a CoFe alloy core and a FeOx shell. This strategy is universal for the synthesis of MFe@FeOx (M = Co, Ni, Mn). The CoFe@FeOx exhibits bifunctional effect on regulating polysulfides as the separator coating layer for Li-S and Na-S batteries. This method could be developed into solid-phase synthetic systems to construct well distributed complex metal nanoparticles.",
+            "section_image": []
+        },
+        {
+            "section_name": "Introduction",
+            "section_text": "Metal nanoparticles (NPs) with complex structure and uniform distribution demonstrate distinctive physicochemical properties and are widely applied in many fields. The development of their synthesis strategies benefit the exploration of more applications1,2. The commonly used synthesis approaches of metal NPs are the traditional wet chemistry methods, such as thermal decomposition, precipitation, hydrothermal/solvothermal, microemulsion, and sol-gel methods1,3,4,5. Metal NPs with controlled structure have been successfully synthesized by the thermal decomposition method, such as Co nanorods6, hollow CoS NPs7,8, In2O3 nanoflowers9, MnFe2O4 nanocubes10, FePt Nanocubes11, and FeCo NPs12. The precipitation methods are applied to synthesis Pd-Pt nanodendrites13, Co3O4 nanorods14, and PdPt nanocages15. Meanwhile, several synthesis mechanisms are proposed to investigate the structure modulation of metal NPs, including focusing of size distribution16, Kirkendall effect7, galvanic replacement15, cation exchange17, and limited ligand protection theory9.\n\nAlthough the wet chemical methods control the metal NPs structure well, yet their liquid-phase operation environment leads to the wastage of solvent or water. The construction of a complicated structure needs multistep operation, such as the core@shell structure is realized through coating a shell outside the pre-prepared core3. It is hard to both achieve the structure design and uniform dispersion of metal NPs simultaneously6,11,18. Metal NPs with complex structure can be synthesized via solid-phase synthesis with thermal gas treatment. The Fe3C and Co3C nanocrystalline confined in graphitic shells are synthesized through a chemical vapor deposition method under a mixture of H2, H2O, and CH4 at 850\u2009\u00b0C19. CoFe alloy NPs were formed by exsolution under a thermal reduction atmosphere20. The hollow Co-rich CoCu alloy structure was obtained through exposing the hollow CuCo alloy NPs to thermal syngas21. This thermal gas treatment process is operated under various gas at high temperatures without involving liquid-phase environment, displaying some attractive features, such as elimination of water or solvent wastage, facile operation, and simple synthesis parameters22,23. However, construction of metal NPs under thermal gas atmosphere sometimes is only considered as postprocessing means and has seldom been applied as an effective method to synthesize complex metal NPs. Therefore, constructing metal NPs with specific structure and exploring synthesis mechanism may promote the development of this thermal gas treatment method into a general synthesis strategy.\n\nHerein, the CoFe@FeOx core@shell NPs are successfully prepared through the solid-phase synthesis strategy which is operated under thermal syngas (H2/CO). The obtained CoFe@FeOx NPs are uniformly distributed on carbon matrix and demonstrate a CoFe alloy core and a FeOx shell. This strategy simultaneously realizes the synthesis of core@shell metal NPs and their uniform distribution on supports, serving as a potential synthetic strategy. The as-prepared core@shell NPs is expected to deliver great application prospect for energy storage field. CoFe@FeOx NPs could serve as the modifying layer of commercial separators for high-performance lithium-sulfur (Li-S) and sodium sulfur (Na-S) batteries, which is beneficial for solving the current challenge of commercial separators that can hardly suppress the polysulfide dissolution and shuttle issues24,25. The polar FeOx shell possesses strong adsorption ability to anchor polysulfides and the conductive CoFe core can facilitate the conversion process of polysulfides. As a result, the sulfur utilization and the cycling stability of Li-S and Na-S batteries are significantly enhanced due to the bifunctional effect of CoFe@FeOx NPs on regulating polysulfides. In particular, the Na-S battery with CoFe@FeOx modified separator delivers a high reversible capacity of 320 mAh g\u22121 after 1200 cycles with nearly 100% Coulombic efficiency at 2\u2009A\u2009g\u22121.",
+            "section_image": []
+        },
+        {
+            "section_name": "Results",
+            "section_text": "The experimental synthesis of the CoFe@FeOx starts from the pyrolysis of Co-Fe Prussian blue analogue (PBA). Co-Fe PBA is a kind of coordination polymer with Fe3+ and Co2+ bridged by the CN\u2212 groups. As shown in Fig.\u00a01a, the CoFe@C with a CoFe alloy core and a carbon shell are obtained after the pyrolysis, which are well distributed on carbon matrix. The formed CoFe@C experience carbon shell falling off, Fe shell formation by exsolution, and FexC shell formation by carburization, producing the CoFe@FexC intermediate. The carburization occurs under syngas atmosphere at 240\u2009\u00b0C. The final CoFe@FeOx are obtained through the passivation of FexC shell in air at room temperature. Scanning electron microscope (SEM) image of Co-Fe PBA displays uniformly distributed nanocubes morphology with \u223c200\u2009nm of particle size (Fig. 1b). The diffraction peaks of Co-Fe PBA become disappearing and that of CoFe alloy emerge as the pyrolysis temperature increases from 25 to 700\u2009\u00b0C (Fig.\u00a0S1a). The high-resolution transmission electron microscopy (HRTEM) images demonstrate the formed CoFe@C nanoparticle consists of a CoFe alloy core and a carbon shell (Fig.\u00a01c), with \u223c60\u2009nm of particle size (Fig. S1b). The core shows 2.01\u2009\u00c5 of lattice distance, ascribing to the (110) planes of CoFe alloy (PDF#49-1568). The Raman spectra of CoFe@C exhibits two distinct peaks with ID/IG of 1.00, indicating the shell presents a mixture of amorphous and graphitized carbon (Fig.\u00a0S2). The formed CoFe@FeOx NPs show a core@shell structure, with \u223c5\u2009nm of shell thickness (Fig. 1d). The Fast Fourier Transform (FFT) analysis displays three diffraction facets of the core and two diffraction facets of the shell, ascribing to CoFe alloy and Fe3O4 (PDF#79-0416) respectively.\n\na Schematic diagram of the formation process of the CoFe@FeOx. b SEM, TEM (inner) images, and scheme of Co-Fe PBA. c HRTEM image and the corresponding lattice fringes of the CoFe@C. d The STEM image, the FFT pattern, and e the corresponding elemental mapping images of the CoFe@FeOx.\n\nThe high-angle annular dark-field scanning transmission electron microscope (HAADF-STEM) and electron energy loss spectroscopy (EELS) elemental mapping images of CoFe@FeOx demonstrate that the core is mainly composed of Co and Fe elements and the shell mainly of Fe and O (Fig.\u00a01e, S3, S4). It is noteworthy that, a passivating surface oxide formed at room temperature is often amorphous, beam-induced heating during TEM analysis transforms it into crystalline magnetite (Fe3O4)26. All CoFe@FeOx NPs are distributed uniformly on the carbon matrix, with particle size around 50\u2009nm (Fig.\u00a0S5). The CoFe@FeOx core@shell structure remains unchanged with the carburization temperature increasing from 240 to 500\u2009\u00b0C (Fig.\u00a0S6 and S7). The CoFe@C mainly contains Co, Fe, K, C, O, and N elements with Co and Fe account for 32.4% and 23.0% respectively (Fig.\u00a0S8). The surface of CoFe@C and CoFe@FeOx are both dominated by C due to the carbon matrix and the surface iron state of CoFe@FeOx confirm the existence of FeOx shell. (Fig.\u00a0S9).\n\nThe Fe and Co K-edge X-ray absorption near-edge structure (XANES) spectra of CoFe@FeOx lays in the middle of Fe foil, Fe3O4, and FexC references (Fig.\u00a02a) and Co foil, Co2C, and CoO references (Fig.\u00a02b), indicating a mixture of CoFe alloy, iron/cobalt carbide and oxide phases. The Fourier transformation of Fe and Co k-edge extended X-ray absorption fine structure (EXAFS) spectrum exhibit distinct scattering peaks of Fe/Co\u2212O, Fe/Co-C, and Fe-Co (Figs.\u00a02c, d). Strong peaks of Fe-Co and weak ones of Fe/Co\u2212O and Fe/Co-C suggest a large contribution from CoFe alloy. The experimental data of Fe and Co K-edge XANES and EXAFS spectra are in excellent agreement with the fitted data (Figure\u00a0S10 and S11). Fe K edge wavelet transform extended X-ray absorption fine structure (WTEXAFS) present peaks of Fe-O, Fe-C, and Fe-Co, while that of Co K edge exhibits a main peak of Fe-Co (Figs.\u00a02e, f, and S12). The coordination numbers (CNs) confirm the CoFe@FeOx NPs with a CoFe alloy core and a FeOx shell (Table\u00a0S2).\n\na Fe and b Co K edge XANES spectra, c Fe and d Co K edge EXAFS spectra of CoFe@FeOx, as well as the Fe and Co references. e Fe and f Co K edge WTEXAFS of CoFe@FeOx.\n\nThe M\u00f6ssbauer spectra of CoFe@C confirms the coexistence of CoFe alloy and FeOx species, with CoFe alloy and FeOx accounting for 96% and 4% respectively (Fig.\u00a03a, Table\u00a0S1). The M\u00f6ssbauer spectra of CoFe@FeOx demonstrates a mixture of CoFe alloy, FeOx, and FexC phases, with their content of 72%, 21%, and 7%, respectively (Fig.\u00a03b). FexC denotes a special iron carbide with Bhf of 11.92\u2009T. The phase composition of CoFe@C and CoFe@FeOx is also confirmed by X-ray diffraction (XRD) patterns (Fig.\u00a0S13). The M\u00f6ssbauer spectra of FeOx displays doublet peak and the fitted data of IS (0.26), QS (0.86), and Bhf (0.00) can be assigned to a type of iron oxide with superparamagnetic property and NP size below 10\u2009nm. Combining with the HRTEM, XANES, and XRD of CoFe@FeOx, 72% of CoFe alloy is ascribed to the core, 21% of FeOx to the shell, and 7% of FexC to the unoxidized shell of CoFe@FexC intermediate. The intermediate of CoFe@FexC is hard to be characterized directly due to its instability in air. The experimental evidence of this intermediate is the GC results of the exhaust during carburization. The exhaust contains methane, ethylene, ethane, propylene, propane, butene, butane, pentene, and pentane (Fig.\u00a0S14), indicating the occurrence of catalysis and further indicating the existence of exposed FexC phase. FexC are considered as the active phases in Fischer-Tropsch synthesis (FTS). The carburization process is also a catalytic process of FTS26. The formed FexC shell can be passivated to form an outside FeOx shell27,28. An amorphous surface iron oxide layer has been noticed in the spent iron catalyst after reaction in thermal syngas, confirming the passivation of FexC29,30,31,32.\n\nThe M\u00f6ssbauer spectra of the a CoFe@C and b CoFe@FeOx. c HRTEM image, d the corresponding lattice fringes, as well as e STEM image and the corresponding elemental mapping images of the MnFe@FeOx. f HRTEM image, g the corresponding lattice fringes, as well as h STEM image and the corresponding elemental mapping images of the NiFe@FeOx.\n\nThis solid-phase synthesis strategy via thermal syngas treatment can be generalized to synthesize the MnFe@FeOx and NiFe@FeOx. The precursors of Mn-Fe PBA and Ni-Fe PBA are applied, which are obtained through substituting the cobalt ion of Co-Fe PBA by nickel and manganese ions (Fig.\u00a0S15). The synthesized MnFe@FeOx NPs demonstrate a core@shell structure with 2.10\u2009\u00c5 of lattice distance in the core and 2.40\u2009\u00c5 of that in the shell, ascribing to the (101) and (311) planes of MnFe (PDF#03-0970) and Fe3O4 respectively (Figs.\u00a03c, and d). The STEM and elemental mapping images also confirm the MnFe@FeOx core@shell structure (Fig.\u00a03e). The NiFe@FeOx NPs exhibit a core@shell structure with 1.00\u2009\u00c5 of lattice distance in the core and 1.50\u2009\u00c5 of that in the shell, ascribing to the (311) and (440) planes of NiFe (PDF#38-0419) and Fe3O4 respectively (Figs.\u00a03f, g, and h).\n\nThe FeOx shell thickness of CoFe@FeOx and NiFe@FeOx are 5 and 2\u2009nm respectively. CoFe and NiFe alloy present body-centred cubic and face-centred cubic structure, respectively, and the segregation energy may be influenced by the crystal structure. The thinner shell thickness of NiFe@FeOx may come from the less difference of the segregation energy between Fe and Ni than that between Fe and Co, leading to less Fe atoms exsolved from NiFe alloy to the surface than from CoFe alloy. This solid-phase synthesis strategy via thermal syngas treatment is universal and precise for the synthesis of the MFe@FeOx (M\u2009=\u2009Co, Mn, Ni). Furthermore, this strategy is supposed to be extended to the synthesis of more iron-based bimetallic NPs with excellent distribution, such as, CuFe, ZnFe, etc. The most important factor of this strategy is the exsolution of iron from iron-based alloy and the subsequent carburization. The facile operation and the abundant syngas indicate this solid-phase synthesis strategy is suitable for producing well-designed iron-based NPs in large scale.\n\nUnder a thermal syngas atmosphere, Fe atoms tend to exsolve from the bulk of CoFe alloy NPs to their surface, forming a Fe shell outside the CoFe alloy core. The formed Fe shell is further carburized into a FexC shell by CO, constructing a CoFe@FexC core@shell structure with CoFe alloy as the core and FexC as the shell. FexC presents a special iron carbide. The structural evolution is atomically shown in Fig.\u00a04a. The exsolution and carburization processes may occur simultaneously.\n\na Scheme of the atomic transformation from CoFe alloy to CoFe@FexC. b The energy profile for the segregation pathway of Fe (red ball) and Co atom (blue ball) in the CoFe alloy with the Co vacancy (yellow circle) located in the 2nd layer in the presence of CO adsorption, and the blue and purple color balls are Co and Fe atoms, respectively. c The exsolution of Fe from CoFe alloy based on segregation energy. d CoFe@FexC formed through the carburization of Fe shell by CO.\n\nIt is interesting to observe that cobalt of CoFe@FeOx remains as alloy phase in the core rather than converts into cobalt carbides, since Co2C phase is commonly observed in the syngas-treated CoMn materials33. This can be explained by the exsolution of Fe from CoFe alloy due to the different segregation energy of Co and Fe. In order to theoretically understand the exsolution process of Fe atoms from CoFe alloy, density functional theory (DFT) calculations are applied to investigate the Fe/Co atom segregation energy and segregation pathway in the CoFe alloy (see details in the Supplementary Information). For Fe/Co atoms segregation energy in the CoFe alloy, the Co atom segregation from the bulk to the surface in the CoFe alloy is easier compared to the Fe atom segregation in the absence of CO adsorption (Fig.\u00a0S16, S17, S18), however, in the presence of CO adsorption, the segregation of Fe atom becomes easy, and the segregation of Co atom is suppressed. Thus, Fe atom segregation in the CoFe alloy is preferred instead of Co atom segregation under the CO-rich atmosphere. Meanwhile, for Fe/Co atoms segregation pathway in the CoFe alloy with the presence of CO adsorption, as presented in Fig.\u00a0S19 and S20, the reaction energies of step 1, step 2, step 3 and step 4 for Co atom segregation pathway are 1.79, \u22126.29, 14.00 and \u22127.04\u2009eV, respectively. Hence the step 3 is strongly endothermic, and it is the rate-determining step. However, those of step 1, step 2, step 3, step 4 and step 5 for Fe atom segregation pathway are 1.99, 2.75, \u22124.65, 4.18 and \u22124.06\u2009eV, respectively, thus, the step 4 is the rate-determining step, which is much lower than that of step 3 for Co atom segregation pathway (4.18 vs. 14.00\u2009eV) (Fig.\u00a04b), suggesting that Fe atom segregation pathway is more energetically favorable than Co atom segregation pathway. The similar situation also occurs in the CoFe alloy with the absence of CO adsorption. Furthermore, CO adsorption inhibits Co atom segregation in the CoFe alloy compared with the absence of CO adsorption (14.00 vs. 4.87\u2009eV). More importantly, Fe atom segregation with CO adsorption is more preferred to that without CO adsorption (4.18 vs. 4.53\u2009eV). Moreover, the metal Fe could be rapidly carburized to iron carbides under the FTS conditions (150-350\u2009\u00b0C, 2-3\u2009MPa)34,35,36, which is attributed to CO adsorption. Thus, the easy segregation of Fe atom from the bulk to the surface results in the formation of FexC shell outside the CoFe alloy core.\n\nThe driving force of the exsolution is the different segregation energy between Fe and Co in CoFe alloy (Fig.\u00a04c). The segregation energy of Fe (Eseg-Fe) is lower than that of Co (Eseg-Co) under thermal syngas atmosphere, leading to the exsolution of Fe atoms and the formation of CoFe@Fe core@shell structure. The formed Fe shell can be carburized by CO and convert to FexC shell, while the CoFe alloy core remains, due to the carburization ability of Fe (\u03b8Fe) is much higher than that of CoFe alloy (\u03b8CoFe) (Fig.\u00a04d).\n\nThe universal and facile synthesis of unique core@shell structure endows CoFe@FeOx material good application prospects in energy storage fields, e.g. as advanced modifying material of separators for Li-S batteries and Na-S batteries. Generally, traditional polypropylene (PP) separator has very limited effect for adsorbing the lithium polysulfides (LiPSs) in Li-S batteries, which may lead to the low utilization of S and poor electrochemical performance. Various conducting polymers and covalent\u2013organic frameworks with strong chemical adsorptivity, or carbon matrices like carbon nanotubes or graphene with high conductivity have been employed as the modifying layer of commercial separators, and improving the utilization of S to some extent. However, most of these reported modifying layers hardly simultaneously possess strong adsorbability and high conductivity. The as-prepared CoFe@FeOx exhibits a bifunctional effect on regulating polysulfides as the separator coating layer for Li-S and Na-S batteries. In detail, the polar FeOx shell could effectively adsorb polysulfides in the surface, and the conductive CoFe core facilitates the conversion process of polysulfides, thus significantly suppressing the polysulfide shuttling effect. Commercial multiwalled carbon nanotubes (CNTs) and S powder composite is employed as cathode (Fig.\u00a0S21) and the optical photographs of the modified PP separator (CoFe@FeOx/PP) are shown in Fig.\u00a0S22.\n\nSystematic electrochemical tests for Li-S batteries are carried out in an environmental chamber with the temperature of 25 \u00b0C. The charge/discharge curves and cyclic voltammogram (CV) of Li-S batteries are shown in Fig.\u00a0S23. Detailed performance comparisons of Li-S batteries with traditional PP, CoFe@C modified separator (CoFe@C/PP) and CoFe@FeOx/PP are exhibited in Fig.\u00a0S24. Moreover, the high areal S loading electrode (6.8\u2009mg\u2009cm\u22122) is fabricated (Fig.\u00a0S25), indicating good application prospect of CoFe@FeOx for boosting high energy density practical Li-S batteries. CV curves comparison with different scan rates are shown in Fig.\u00a0S26. To directly compare the anchoring effect of LiPSs between the CoFe@FeOx and the CoFe@C, the shuttle current measurement is performed as shown in Fig.\u00a0S27. The CoFe@FeOx-based battery presents a lower shuttle current than that of the CoFe@C-modified one, indicating the stronger anchoring effect of the CoFe@FeOx for adsorbing LiPSs. The ability to accelerate the conversion process of LiPSs is tested by the Li2S precipitation experiment (Fig.\u00a0S28). The larger precipitation capacity with the CoFe@FeOx/PP (122 mAh g\u22121) demonstrates the good catalytic activity of the CoFe@FeOx to promote the conversion process of LiPSs. In addition, both the MnFe@FeOx and NiFe@FeOx-based Li-S batteries exhibit good cycling stability as show in Fig.\u00a0S29, suggesting MnFe@FeOx and NiFe@FeOx could also effectively restrain the shuttle of LiPSs.\n\nIn order to expand the application of the CoFe@FeOx, the CoFe@FeOx modified commercial glass fiber (GF) separator (CoFe@FeOx/GF) is further designed to regulate Na-S system, as shown in Fig.\u00a05a. And all electrochemical tests for Na-S batteries are also performed in an environmental chamber with the temperature of 25 \u00b0C. The optical photographs and CNTs and S composite cathode are presented in Fig.\u00a0S30. The CV curves of the CoFe@FeOx-based Na-S battery with the scanning rate of 0.2\u2009mV\u2009s-1 (vs Na/Na+) are exhibited in Fig.\u00a0S31, which present typical oxidation peak (1.88\u2009V) and reduction peak (1.16\u2009V)22. The comparison of charge density differences is presented in Figs.\u00a05b and c, which further demonstrates the strong interaction between Na2S4 and FeOx. The optimized adsorption configuration between Na2S4 and FeOx or graphite were displayed in Figs.\u00a0S32 and S33. The binding energy of Na2S4 with FeOx and graphite is -3.95 and -0.75\u2009eV, respectively, indicating the CoFe@FeOx possesses more superior anchoring ability for polysulfides compared to the CoFe@C. The mechanism schematic of CoFe@FeOx enhancing the performance of Na-S batteries is illuminated in Fig.\u00a05d. The core-shell CoFe@FeOx possesses a bifunctional effect on regulating sodium polysulfide (NaPSs), because the polar FeOx shell could effectively anchoring polysulfides in the surface and the conductive CoFe core further catalyzes the transformation process of NaPSs, thus significantly enhancing the utilization of S and electrochemical performance of Na-S batteries. The cycle performances comparison at 0.2\u2009A\u2009g-1 are displayed in Fig.\u00a05e. After 150 cycles, the battery with CoFe@FeOx/GF can maintain a higher capacity of 772 mAh g-1 than those with the CoFe@C/GF (396 mAh g-1) and pure GF (49 mAh g\u22121), indicating the CoFe@FeOx can effectively inhibit the shuttle of NaPSs and promote the conversion process. The rate performances are measured as shown in Fig.\u00a05f and g. The Na-S battery with CoFe@FeOx/GF could deliver the highest specific capacities than that of the CoFe@C modified one. Besides, the CoFe@FeOx-based battery could maintain a high reversible capacity of 320 mAh g-1 after 1200 cycles with nearly 100% Coulombic efficiency at 2\u2009A\u2009g-1 (Fig.\u00a05h). More impressively, the Na-S battery with CoFe@FeOx/GF can deliver a high reversible capacity of 935 mAh g-1 with high S content (70\u2009wt%) and keep a high capacity retention of 635 mAh g-1 after 150 cycles at 0.2\u2009A\u2009g-1 (Fig.\u00a05i). Even at a high current density of 2\u2009A\u2009g-1 (Fig.\u00a0S34), the CoFe@FeOx/GF based Na-S battery can display high reversible capacity of 306 mAh g-1after 600 cycles. The result indicates that CoFe@FeOx possess superior ability for suppressing the shuttle of NaPSs and facilitating their fast conversion process. The morphologies of Na anodes with commercial GF separator and CoFe@FeOx/GF after three cycles at 0.2\u2009A\u2009g-1 are displayed in Fig.\u00a0S35, demonstrating the CoFe@FeOx/GF could inhibit the shuttle effect and protect the Na anode. Moreover, the MnFe@FeOx/GF and NiFe@FeOx/GF-based Na-S batteries could also deliver high capacities of 717 and 666 mAh g-1 after 70 cycles at 0.2\u2009A\u2009g-1, respectively, indicating both the MnFe@FeOx and NiFe@FeOx can also suppress the shuttle effect of NaPSs and improve the utilization of S (Fig.\u00a0S36). Thus, it can be concluded that the core-shell MFe@FeOx (M\u2009=\u2009Co, Mn, Ni) can effectively enhance the performances of Li-S and Na-S batteries because of their unique bifunctional effect on regulating polysulfides.\n\na The optical photographs of the commercial Glass Fiber (GF) separator and CoFe@FeOx/GF separator. The charge density differences of Na2S4 on the surface of b graphite and c Fe3O4. Cyan and yellow regions represent the decreased and increased electron density, respectively. The value of the isosurface is 0.002 electron bohr-3. d The mechanism schematic diagram of the CoFe@FeOx catalyst in Na-S batteries. e Cycling performance comparison at 0.2\u2009A\u2009g-1. f Rate capability comparison at various current densities. g Typical charge/discharge curves at different current densities and h long-term cycling performance of CoFe@FeOx/GF based Na-S battery at 2\u2009A\u2009g\u22121. i Cycling performance of CoFe@FeOx/GF based battery at 0.2\u2009A\u2009g-1. The batteries in Fig.\u00a05e-h are composed of Na metal anode and CNTs and S composite cathode with 50\u2009wt% of sulfur loading. The battery in Fig.\u00a05i is composed of Na metal anode and CNTs and S composite cathode with 70\u2009wt% of sulfur loading. All electrochemical tests are performed in an environmental chamber with the temperature of 25 \u00b0C.\n\nThe electrochemical reaction mechanism of Na-S battery with CoFe@FeOx/GF were further investigated by the ex-situ X-ray photoelectron spectroscopy (XPS). The peaks of S p1/2 and S p3/2 were captured in the original state as shown in Fig.\u00a0S37a. When the battery was discharged to 1.6\u2009V (Fig.\u00a0S37b), soluble long-chain polysulfides (163.65\u2009eV), thiosulfate and polythionate were detected22. And the peaks of short-chain Na2S2 species increased when discharged to 1.2\u2009V (Fig.\u00a0S37c). The peaks of Na2S2 and Na2S obviously increased when the voltage was down to 0.8\u2009V, indicating the complete conversion from S to Na2S2 and Na2S (Fig.\u00a0S37d). The S species exhibited reversible electrochemical behaviors during the charge process as shown in Fig.\u00a0S37e. The S p1/2 and S p3/2 peaks were detected when charged to 3.0\u2009V (Fig.\u00a0S37f), suggesting the polysulfides were transformed into the original S8 molecule23.",
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+            ]
+        },
+        {
+            "section_name": "Discussion",
+            "section_text": "A solid-phase synthetic strategy has been developed to precisely synthesize the well-dispersed CoFe@FeOx core@shell NPs via thermal syngas treatment. The CoFe@FeOx demonstrates a CoFe alloy core and a FeOx shell. According to DFT calculations, Fe atoms are preferentially exsolved from CoFe alloy bulk to the surface due to the lower Fe segregation energy than that of Co, and then the exsolved Fe shell is carburized into FexC shell by CO, forming CoFe@FexC structure, which is verified by the experimental results. The synthesis of the CoFe@FeOx starts from the pyrolysis of Co-Fe PBA. The CoFe@C with a CoFe alloy core and a carbon shell is obtained after the pyrolysis, which is well distributed on carbon matrix. The CoFe@FexC intermediate is produced through treating CoFe@C under syngas atmosphere at 240\u2009\u00b0C for 24\u2009h, whose surface FexC shell is prone to be passivated into FeOx by air at room temperature, generating the final CoFe@FeOx core@shell structure. The synthesized CoFe@FeOx NPs are uniformly distributed on the carbon matrix with \u223c50\u2009nm of CoFe alloy core and 5\u2009nm of FeOx shell. Analogously, the NiFe@FeOx and MnFe@FeOx are obtained through this strategy, demonstrating a universal strategy for the synthesis of MFe@FeOx (M\u2009=\u2009Co, Ni, Mn). The synthesized CoFe@FeOx demonstrate high performance as the modifying layer of commercial separators in Li-S and Na-S batteries. Benefiting from the adsorptive FeOx shell and conductive CoFe alloy core of CoFe@FeOx, the polysulfides shuttling is well restrained and the conversion process of polysulfides is significantly enhanced. The Na-S battery can display a long cycle life of 1200 cycles with nearly 100% Coulombic efficiency. This strategy realizes the precise construction of complex core@shell metal NPs and their uniform distribution on supports simultaneously. The segregation energy and carburization ability of metals are applied to precisely control the spatial location of various iron-based phases at the nanoscale. Moreover, it also manifests interesting features of facile operation and solvent-free synthesis. This solid-phase synthesis strategy is not limited to synthesize iron-based NPs under thermal syngas, but could be developed into solid-phase synthetic systems to construct complex metal NPs.\n\nAny methods, additional references, Nature Research reporting summaries, source data, extended data, supplementary information, acknowledgements, peer review information; details of author contributions and competing interests; and statements of data and code availability are available at",
+            "section_image": []
+        },
+        {
+            "section_name": "Methods",
+            "section_text": "Cobalt nitrate hexahydrate (Co(NO3)2\u00b76H2O), Nickel nitrate hexahydrate (Ni(NO3)2\u00b76H2O), Manganese nitrate tetrahydrate (Mn(NO3)2\u00b74H2O), potassium hexacyanoferrate (III) (K3Fe(CN)6), trisodium citrate dihydrate (Na3C6H5O7\u2009\u2219\u20092H2O) and sulfur powder were purchased from Sinopharm Chemical Reagent Co., Ltd. The commercial multiwalled carbon nanotubes (CNTs) and Li2S powder were purchased from Tokyo Chemical Industry (TCI) Shanghai. All chemical reagents were analytical grade and used without any treatment. Deionized water (DI) was used in all the above experiments. Washing was done with deionized water and reagent-grade ethanol.\n\nCo-Fe PBA precursor was prepared by a simple precipitation method, as reported by previous literatures37. Firstly, the solution A was obtained by dissolving 0.6\u2009mmol of Co(NO3)2\u00b76H2O and 0.9\u2009mmol of Na3C6H5O7\u2009\u2219\u20092H2O into 20\u2009ml of deionized water. Secondly, the solution B was obtained by adding 0.4\u2009mmol of K3Fe(CN)6 into 20\u2009ml of deionized water. Thirdly, the solution B was added slowly into the solution A under vigorously stirring. After continuously stirring for 2\u2009min, the obtained precipitate was aged at room temperature for 24\u2009h. Finally, the Co-Fe PBA precursor was obtained after centrifugation, washing with water and ethanol, and dry at 60\u2009\u00b0C for overnight.\n\nThe CoFe@C material was prepared by pyrolysis of Co-Fe PBA powder at 500\u2009\u00b0C for 4\u2009h with a heating rate of 3\u2009\u00b0C min-1 under a flow of N2 atmosphere.\n\nThe obtained CoFe@C (0.3\u2009g, 20-40 mesh) was loaded into a fixed-bed reactor with an inner diameter of 10\u2009mm and a bed length of 53\u2009cm. The syngas treatment was carried out at 240\u2009\u00b0C for 24\u2009h, with the flowrate of H2 and CO as 10 and 5\u2009ml\u2009min-1, respectively. The exhaust gas composition was analyzed by an online gas chromatograph (GC) equipped with a thermal conductivity detector (TCD) and a flame ionization detector (FID). Products of methane, ethylene, ethane, propylene, propane, butene, butane, pentene, and pentane are detected by GC in the exhaust gas. After the syngas treatment, the temperature was decreased to 25\u2009\u00b0C under syngas atmosphere, and then the syngas was changed to air for 1\u2009h at 25\u2009\u00b0C, with the flow rate of 10\u2009ml\u2009min-1. Finally, the CoFe@FeOx sample was obtained.\n\nThe preparation of Ni-Fe PBA and Mn-Fe PBA is similar with that of Co-Fe PBA, except replacing the cobalt nitrate by nickel and manganese nitrate, respectively. The synthesis process of NiFe@FeOx and MnFe@FeOx are analogous to that of CoFe@FeOx, which undergoes the pyrolysis of PBA, thermal syngas treatment, and air passivation.\n\nThe commercial multiwalled CNTs and S powder composite was prepared by a melt-diffusion method. Typically, 30\u2009mg of CNTs was mixed with 70\u2009mg of sulfur powder with heat treatment at 155\u2009\u00b0C for 24\u2009h in an Ar-filled autoclave to gain the composite cathode with S content of 70\u2009wt%. Similarly, 50\u2009mg of CNTs was mixed with 50\u2009mg of sulfur powder with heat treatment at 155\u2009\u00b0C for 24\u2009h in an Ar-filled autoclave to gain the composite cathode with S content of 50\u2009wt%.\n\nThe CoFe@FeOx/PP (CoFe@C/PP, MnFe@FeOx/PP or NiFe@FeOx/PP) separator was prepared by mixing 95\u2009wt% of CoFe@FeOx (CoFe@C, MnFe@FeOx or NiFe@FeOx) with 5\u2009wt% Sodium Carboxymethyl Cellulose (CMC) binder in deionized water to cast on one side of commercial PP separator (Celgard 2400). The CoFe@FeOx/PP (CoFe@C/PP, MnFe@FeOx/PP or NiFe@FeOx/PP) separator was obtained after vacuum-dried at 70\u2009\u00b0C for all night, followed by cutting into disks with 16\u2009mm in diameter. Similarly, the CoFe@FeOx/GF (CoFe@C/GF, MnFe@FeOx/GF or NiFe@FeOx/GF) separator was prepared with the same process except that replacing PP separator with commercial glass fiber separator (Whatman GF/A 1823-070).\n\nThe Li2S precipitation experiment was tested on the 2032-type coin cells assembled with the tested electrode, lithium foil and PP separator on the Autolab PGSTAT 302\u2009N workstation. Li2S8 electrolyte (0.2\u2009mol\u2009L-1) was prepared by mixing sulfur with Li2S at a molar ratio of 7: 1 in tetraglyme followed by vigorous mixing for all night. Commercial carbon papers (Guangdong Canrd New Energy Technology Co. Ltd.) were used as current collectors to load the well-mixed slurry composed of 70\u2009wt% CoFe@FeOx (or CoFe@C), 20\u2009wt% Super P and 10\u2009wt% CMC. The tested electrodes (loading mass: ~1.5\u2009mg\u2009cm-2) were obtained after drying at 80\u2009\u00b0C for 12\u2009h. 30\u2009mL Li2S8 was dropped onto the tested electrodes during the cell assembly process. Cells were first discharged galvanostatically at 0.112\u2009mA to 2.09\u2009V and then discharged potentiostatically at 2.05\u2009V for Li2S nucleation and growth. The potentiostatic discharge was terminated when the current was below 10-5\u2009A. Based on Faraday\u2019s law, the energy was collected to evaluate the nucleation/growth rate of Li2S on the tested electrodes.\n\nXRD was performed on a Rigaku D/Max2500PC diffractometer with 2\u03b8 range of 5-80 \u00b0. The Cu K\u03b1 radiation was used with the voltage of 40\u2009kV. TEM images were obtained on FEI Tecnai G2 Spirit microscope with 120\u2009kV. HRTEM images were operated on a FEI Tecnai G2 F30S-Twin microscope with 300\u2009kV. HAADF-STEM and EELS were operated on a JEM-ARM200F thermal-field emission microscope. SEM images were measured on a FEI Quanta 200F device. XPS was performed on a KRATOS Axis UltraDLD spectrometer. An Al K\u03b1 X-ray radiation source (1486.6\u2009eV) and charge compensation gun were used. The C 1\u2009s peak (284.60\u2009eV) was used to perform the charge correction. Inductively coupled plasma optical emission spectrometry (ICP-OES) was measured on an ICPS-8100. For sample preparation, calcination treatment was performed at 600\u2009\u00b0C in air (carbon species removement), and then the obtained sample was dissolved in an acidic mixture of HNO3 and HCl. The element content of O, N, and H was determined by an element analyzer of EMGA-930. The element content of C was determined by an element analyzer of EMIA-8100.\n\nThe RT 57Fe M\u00f6ssbauer spectra were acquired from a proportional counter and a Topologic 500\u2009A spectrometer. A 57Co (Rh), moving with a constant acceleration mode, was applied as the \u03b3-ray radioactive source. A standard \u03b1-Fe foil was used as a reference. The spectra were fitted on the base of Lorentzian adsorption curves using MossWinn 3.0i computer program. The derived hyperfine parameters of isomer shift (IS), quadruple splitting (QS), and magnetic hyperfine filed (H), were applied for component identification. The phase content was confirmed on the base of the areas of the adsorption peaks, assuming the iron nuclei for all samples possess the same probability of adsorption of \u03b3 photons. The X-ray absorption spectra including XANES and EXAFS of the samples at K-edge were collected at the Beamline of TLS07A1 in National Synchrotron Radiation Research Center (NSRRC), Taiwan, where 1.5\u2009GeV a pair of channel-cut Si (111) crystals was used in the monochromator.\n\nAll spin-polarized DFT calculations were implemented in the Vienna Ab initio Simulation Package (VASP) software38. The generalized gradient approximation (GGA)39 together with the Perdew-Burke-Ernzerhof (PBE) functional40 was performed to describe the electronic exchange-correlation functions. The electronic wave functions were expanded using a kinetic energy cutoff of 400\u2009eV. The projector-augmented plane wave (PAW) was carried out to perform the electron\u2013ion interactions41,42. Surface Brillouin-zone corresponds to a 3\u00d73\u00d71 k-point grid. The optimization convergence accuracy of the force and energy was less than 0.03\u2009eV\u2009\u00c5\u22121 and 1\u00d710\u22125 eV, respectively.\n\nCoFe alloy was modeled using atomic layers oriented along the (110) plane. For CoFe(110) surface, a five-layer p(3\u00d72) supercell is constructed, the Fe and Co atoms of top four layers and the adsorbates are allowed to relax.\n\nPrevious studies showed that the adsorption of CO can alter the surface segregation of metal materials43, so the segregation behaviors of Fe and Co atoms for the CoFe alloy in the absence and presence of CO were examined. Meanwhile, the segregation energy (Eseg) is defined as the energy required for a single Fe or Co atom to move from the bulk to the surface layer, which can be calculated using the following equation44,45,46:\n\nWhere Esurf n(n=1-3) represents the energy of Fe or Co atom located into the nth layer of CoFe alloy; Esurf 4 represents the energy of Fe or Co atom located into the 4th layer of CoFe alloy. Eseg-n(n=1-3) represents the segregation energy, namely, the energy of Fe or Co atom located into the 4th layer of CoFe alloy being transferred to the nth layer. The more negative value of Esurf n(n=1-3) means that a Fe or Co atom is easier to move from the bulk to the surface layer.\n\nUsually, the alloy segregation occurs with the exchanges between the metal atom and surface/subsurface vacancies43,47,48, for example, DFT studies by Zhang et al.37. fully researched the segregation pathway of Ni atom in Au catalyst, specifically, an Au vacancy was set initially at the second atomic layer and then possible segregation pathway including Ni atom near the vacancy to alter its atomic position with a surface Au atom through a series Au/Ni-vacancy exchange are considered. In this study, the similar Co/Fe segregation pathway in the CoFe alloy is examined using DFT calculations; meanwhile, the same alloy surface used in the segregation energy calculation was adopted as the model surface. A Co or Fe vacancy was initially set in the 2nd layer. Further, a possible pathway is proposed for the 3rd layer Fe or Co atom near the vacancy to change the atomic position with a surface Fe or Co atom through a series of Fe/Co-vacancy exchange steps (see details in the Supplementary Information).\n\n2032-type coin cells are assembled to evaluate the electrochemical performances of Li-S batteries and Na-S batteries in an Ar-filled glove box (O2\u2009<\u20090.01 ppm, H2O\u2009<\u20090.01 ppm). The cathode materials are prepared by blending 80\u2009wt% active materials, 10\u2009wt% carbon black and 10\u2009wt% polyvinylidenedifluoride (PVDF) and pasted onto an aluminum foil (thickness: 50 \u03bcm). A Na foil (the diameter is 10\u2009mm, the thickness is 300-400 \u03bcm) is used as the counter electrode. The areal S loading of the common cathode is 1.5\u2009mg\u2009cm-2. The average mass loading of CoFe@FeOx or CoFe@C on the PP separator (thickness: 25 \u03bcm) is controlled to be around 0.25\u2009mg\u2009cm-2. And the average mass loading of CoFe@FeOx or CoFe@C on glass fiber separator (thickness: 300 \u03bcm) is controlled to be around 0.4\u2009mg\u2009cm-2. The diameter of PP separator or glass fiber separator is 16\u2009mm. 20\u2009\u03bcL of electrolyte is used in Li-S batteries, which is composed of 1\u2009M lithium bis(trifluoromethanesulfonyl)imide (LiTFSI) in a solvent mixture of 1,3-dioxolane (DOL) and dimethoxymethane (DME) (1:1 by volume) with 1\u2009wt% LiNO3. And a solution of 1\u2009M sodium bis(trifluoromethylsulfonyl)imide (NaTFSI) in propylene carbonate (PC) /fluoroethylene carbonate (FEC) (1:1 by volume, 60\u2009\u03bcL) is utilized as the electrolyte for Na-S cells. The galvanostatic charge-discharge tests were conducted on the Neware BTS-610 instrument. The cyclic voltammetry measurements and electrochemical impedance spectrum (EIS) measurements were obtained on the CHI 660D workstation. All tests of cells are carried out in an environmental chamber with the temperature of 25 \u00b0C.",
+            "section_image": []
+        },
+        {
+            "section_name": "Data availability",
+            "section_text": "The main data supporting the findings of this study are available within the main text, the Supplementary Information file, and the Source Data files. Additional raw data are available at https://doi.org/10.6084/m9.figshare.24426877. Source data are provided with this paper.",
+            "section_image": []
+        },
+        {
+            "section_name": "References",
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+        },
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+            "section_name": "Acknowledgements",
+            "section_text": "This work was supported by the National Key R&D Program of China (2021YFA1501900, 2022YFA1504100, 2022YFA1504500), National Natural Science Foundation of China (Nos. 51925207, 52372239, U1910210, 52161145101, 52102322, 62227815, and 22108270), the National Synchrotron Radiation Laboratory (KY2060000173), the Joint Fund of the Yulin University and the Dalian National Laboratory for Clean Energy (Grant. YLU-DNL Fund 2021002), the Fundamental Research Funds for the Central Universities (WK2060000055, WK2400000004). We acknowledge Q. Jiang, W. Liu, Y. Zhao, and R. Han (Dalian Institute of Chemical Physics, Chinese Academy of Sciences) for valuable discussions on the HRTEM images.",
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+        },
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+            "section_name": "Author information",
+            "section_text": "These authors contributed equally: Yanping Chen, Yu Yao.\n\nState Key Laboratory of Catalysis, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian, Liaoning, 116023, China\n\nYanping Chen,\u00a0Haitao Li\u00a0&\u00a0Jian Liu\n\nHefei National Research Center for Physical Sciences at the Microscale, Department of Materials Science and Engineering, National Synchrotron Radiation Laboratory, CAS Key Laboratory of Materials for Energy Conversion, University of Science and Technology of China, Hefei, Anhui, 230026, China\n\nYu Yao,\u00a0Lifeng Wang\u00a0&\u00a0Yan Yu\n\nState Key Laboratory of Clean and Efficient Coal Utilization, College of Chemical Engineering and Technology, Taiyuan University of Technology, Taiyuan, Shanxi, 030024, China\n\nWantong Zhao,\u00a0Baojun Wang\u00a0&\u00a0Riguang Zhang\n\nScience Center of Energy Material and Chemistry, College of Chemistry and Chemical Engineering, Inner Mongolia University, Hohhot, 010021, China\n\nJiangwei Zhang\u00a0&\u00a0Jian Liu\n\nDepartment of Applied Chemistry and Zhejiang Carbon Neutral Innovation Institute, Zhejiang University of Technology, Hangzhou, 310032, China\n\nYi Jia\n\nDICP-Surrey Joint Centre for Future Materials, Department of Chemical and Process Engineering, and Advanced Technology Institute, University of Surrey, Guildford, Surrey, GU2 7XH, UK\n\nJian Liu\n\nCenter of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing, 100049, China\n\nJian Liu\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nJ.L., Y.Yu, and R.Z. conceived the idea for the project and supervised the project. Y.C. and H.L. performed the material synthesis and characterization. Y.Yao, Y.J., and L.W. performed the electrochemical test. W.Z., B.W., and R.Z. performed the theoretical calculations. J.Z. performed X-ray absorption spectra experiments. Y.C. and Y.Yao wrote the manuscript. All authors discussed and commented on the manuscript.\n\nCorrespondence to\n                Riguang Zhang, Yan Yu or Jian Liu.",
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+            "section_text": "Nature Communications thanks Sundara Ramaprabhu, Bin-Wei Zhang and the other anonymous reviewer(s) for their contribution to the peer review of this work. A peer review file is available.",
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+            "section_text": "Chen, Y., Yao, Y., Zhao, W. et al. Precise solid-phase synthesis of CoFe@FeOx nanoparticles for efficient polysulfide regulation in lithium/sodium-sulfur batteries.\n                    Nat Commun 14, 7487 (2023). https://doi.org/10.1038/s41467-023-42941-9\n\nDownload citation\n\nReceived: 09 May 2023\n\nAccepted: 26 October 2023\n\nPublished: 18 November 2023\n\nVersion of record: 18 November 2023\n\nDOI: https://doi.org/10.1038/s41467-023-42941-9\n\nAnyone you share the following link with will be able to read this content:\n\nSorry, a shareable link is not currently available for this article.\n\n\n\n\n                            Provided by the Springer Nature SharedIt content-sharing initiative\n                        ",
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+            ]
+        },
+        {
+            "section_name": "This article is cited by",
+            "section_text": "Nature Communications (2025)\n\nRare Metals (2025)\n\nScience China Chemistry (2025)\n\nRare Metals (2025)",
+            "section_image": []
+        }
+    ]
+}

38c26dbbdb8a0893582e3d008a4b6167c44aff42a31a2ba29c754d75fc356f09/metadata.json

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+{
+    "title": "Inequalities in global residential cooling energy use to 2050",
+    "pre_title": "Inequalities in global residential cooling energy use to 2050",
+    "journal": "Nature Communications",
+    "published": "16 September 2024",
+    "supplementary_0": [
+        {
+            "label": "Supplementary Information",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-024-52028-8/MediaObjects/41467_2024_52028_MOESM1_ESM.pdf"
+        },
+        {
+            "label": "Peer Review File",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-024-52028-8/MediaObjects/41467_2024_52028_MOESM2_ESM.pdf"
+        },
+        {
+            "label": "Reporting Summary",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-024-52028-8/MediaObjects/41467_2024_52028_MOESM3_ESM.pdf"
+        }
+    ],
+    "supplementary_1": [
+        {
+            "label": "Source Data",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-024-52028-8/MediaObjects/41467_2024_52028_MOESM4_ESM.zip"
+        }
+    ],
+    "supplementary_2": NaN,
+    "source_data": [
+        "https://doi.org/10.5281/zenodo.12697821",
+        "/articles/s41467-024-52028-8#ref-CR57",
+        "/articles/s41467-024-52028-8#Sec18"
+    ],
+    "code": [
+        "https://doi.org/10.5281/zenodo.12671063"
+    ],
+    "subject": [
+        "Energy modelling",
+        "Energy supply and demand"
+    ],
+    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
+    "preprint_pdf": "https://www.researchsquare.com/article/rs-3441530/v1.pdf?c=1727211479000",
+    "research_square_link": "https://www.researchsquare.com//article/rs-3441530/v1",
+    "nature_pdf": "https://www.nature.com/articles/s41467-024-52028-8.pdf",
+    "preprint_posted": "24 Oct, 2023",
+    "research_square_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "The interplay of a warming climate and socio-demographic transformations will increase global heat exposure. Assessing future use and impacts of energy-intensive appliances for indoor thermal adaptation is therefore a crucial policy goal. Here we train statistical models on multi-country household survey data (n = 480,555) to generate global gridded projections of residential air-conditioning (AC) uptake and use. Our results indicate that the share of households owning AC could grow from 26% to a scenario median of 38% by 2050, implying a doubling of residential AC electricity consumption, to 925 TWh/yr. This growth will be highly unequal both within and across countries and income groups, with significant regressive impacts. Up to 4.5 billion heat-exposed people may lack AC access in 2050. Outcomes will largely depend on socio-economic development and climate change pathways. Our gridded projections can support the modelling of the impacts of residential AC on decarbonization pathways and health outcomes.Scientific community and society/Energy and society/Energy supply and demandScientific community and society/Social sciences/Climate change/Climate-change impactsScientific community and society/Energy and society/Energy economicsClimate change adaptationair conditioningelectricity consumptionshared socioeconomic pathwaysgridded datasetinequality",
+            "section_image": []
+        },
+        {
+            "section_name": "Additional Declarations",
+            "section_text": "There is NO Competing Interest.",
+            "section_image": []
+        },
+        {
+            "section_name": "Supplementary Files",
+            "section_text": "si.pdf",
+            "section_image": []
+        }
+    ],
+    "nature_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Intersecting socio-demographic transformations and warming climates portend increasing worldwide heat exposures and health sequelae. Cooling adaptation via air conditioning (AC) is effective, but energy-intensive and constrained by household-level differences in income and adaptive capacity. Using statistical models trained on a large multi-country household survey dataset (n = 673,215), we project AC adoption and energy use to mid-century at fine spatial resolution worldwide. Globally, the share of households with residential AC could grow from 27% to 41% (range of scenarios assessed: 33-48%), implying up to a doubling of residential cooling electricity consumption, from 1220 to 1940 (scenarios range: 1590-2377) terawatt-hours yr.\u22121, emitting between 590 and 1,365 million tons of carbon dioxide equivalent (MtCO2e). AC access and utilization will remain highly unequal within and across countries and income groups, with significant regressive impacts. Up to 4 billion people may lack air-conditioning in 2050. Our global gridded projections facilitate incorporation of AC\u2019s vulnerability, health, and decarbonization effects into integrated assessments of climate change.",
+            "section_image": []
+        },
+        {
+            "section_name": "Introduction",
+            "section_text": "Climate change impacts are increasingly being felt1,2, with increased heat exposures being a ubiquitous outcome3,4, leading to serious negative health consequences5,6,7,8,9. Adoption of cooling, in particular air conditioning (AC), as an adaptation to heat is rapidly expanding10,11,12,13, but it is characterized by stark inequalities\u2014across countries and regions14 as well as among households that differ in their capacity to adapt15. While AC\u2019s shielding effects confer potentially large health benefits16,17, its use can increase the demand for energy in ways that can adversely affect electricity systems stability and planning18,19, environmental pollution\u2014including feedback emission of greenhouse gases and climate policy20,21,22, and households\u2019 energy burdens and economic well-being23. These challenges are projected to become increasingly significant as the climate warms. Cooling appliances already account for nearly 20% of global electricity use by buildings12. In turn, the operations of the building sector represents 30% of global final energy consumption and cause 26% of global energy sector carbon dioxide (CO2) emissions24. About two thirds of the 1.6 billion AC units installed globally are in residential buildings, accounting for about half of the total 1,200 terawatt (TW) of installed cooling capacity.\n\nA growing literature investigates AC adoption as a heat adaptation strategy. Prior studies differ in their methodology (e.g., empirical models10,25,26,27,28 or bottom-up engineering simulations22,29,30), context and spatial scale (e.g. city-31,32 or country-level33,34,35) and/or geographic scope (e.g. multi-country10,14,26,36 or global25,27 analysis, see Supplementary Table\u00a01 for key features of globally-relevant projection studies on AC and utilization). Nevertheless, a comprehensive global picture of the potential inequalities in the future expansion of AC, and attendant energy poverty implications of increased cooling electricity use, remains elusive37,38,39. Because income constraints may limit households\u2019 operation of available residential AC40,41,42, it is critical to elucidate the intensive margin of adaptation (i.e., utilization), and its conditional dependence on technology adoption on the extensive margin33,43. Additionally, local climates, community-level institutions and infrastructures, and households\u2019 demographic and socioeconomic characteristics influence these joint adaptation decisions, but in ways that could potentially be context-specific. The latter possibility points to the need to account for heterogeneity in household responses as a driver of inequality in future access to space cooling, energy demand consequences and environmental implications within and across countries and world regions.\n\nHere, we rise to this challenge by assembling and analyzing a multi-country database of household-level microdata covering more than 500 sub-national administrative units in 25 countries (see Supplementary Fig.\u00a01 and Supplementary Table\u00a02). These countries represent 62% of the world\u2019s population and account for 73% of the global electricity consumption. The dataset describes a rich set of characteristics (see Supplementary Table\u00a03 for a complete list of variables) of 673,215 households. We augment the microdata with country- or sub-national-level external data on electricity prices and use external gridded data on urbanization to characterize the degree of urbanization of the region in which a household lives, as well as historical meteorological reanalysis data to construct climate variables (see Methods). We use the resulting dataset to train two-stage classification and regression models of AC adoption and AC impact on residential electricity use (Fig.\u00a01a). We evaluate different model specifications (Supplementary Tables\u00a06-7) to show why our preferred prediction framework is a random forests (RF) machine learning (ML) model, which uses regression tree algorithms to implement flexible non-parametric estimations which capture non-linear relations among variables (see Methods). The estimated non-linear conditional probabilities of AC ownership (1st stage model) and expected values of electricity consumption (2nd stage) are illustrated by examining partial dependence and elasticities (Fig.\u00a01d-e; see Methods), with the aim of connecting econometric estimation goals and ML prediction methods44. We demonstrate the ability of the trained models to assess the probability of AC ownership and the level of AC electricity use in unsampled locations conditional on local household and geographical characteristics. We then use the validated models (Supplementary Figs.\u00a04 and 5) to generate global gridded predictions and projections of current and future AC uptake and use under an array of socio-economic and climate change scenarios (see Supplementary Table\u00a05 for a description of the assumed future evolution of socio-economic, demographic, and climate drivers in each scenario) based on the validated models (Fig.\u00a01c). We leverage the global coverage and high granularity of our estimates to study the current and projected inequalities in the distribution of AC and its usage and identify critical areas of vulnerability in need of actions to increase adaptive capacity. We also draw implications for energy use and carbon dioxide equivalent emissions. Our results can support decision makers at the intersection of public health, infrastructure planning, and energy and climate policy. The resulting datasets are publicly available45 and can be the basis for more informed heat vulnerability and impact assessments.\n\na Flowchart of the residential air-conditioning (AC) analysis. b Countries covered in the household survey global pool database. c Representative example of output gridded projections. d, e Partial dependence plots (conditional probabilities for the 1st stage AC ownership model; expected values for the 2nd stage electricity consumption model, by AC ownership probability bins). f, g Box plots of the distribution of the estimated partial elasticities derived from the models' partial dependences.",
+            "section_image": [
+                "https:////media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41467-024-52028-8/MediaObjects/41467_2024_52028_Fig1_HTML.png"
+            ]
+        },
+        {
+            "section_name": "Results",
+            "section_text": "Our model-based validated (Supplementary Figs.\u00a04 and 5) predictions for 2020 for the world show a high heterogeneity in the distribution of AC across and within regions and countries based on sub-national units defined over a regular global grid with a spatial resolution of 0.5 arc-degrees (Fig.\u00a02a), reflecting the interaction of different climatic conditions and the distribution of population and its socio-economic attributes (Supplementary Figs.\u00a03,8). Existing areas of high concentration of household AC ownership (>50%) are clearly visible in North America, Southern Europe and North Africa, the Middle East, South Africa, Southern Latin America, Japan, Eastern China, and Australia. Looking at 2050 (Fig.\u00a02b displaying Shared Socioeconomic Pathway (SSP) 2(45) scenario; refer to Supplementary Fig.\u00a011 for SSP1(26), SSP3(70), and SSP5(85) scenarios), areas with high AC ownership rates will expand as a result of a warmer climate, rising affluence levels and socio-demographic change (see Supplementary Table\u00a05). Such growth is particularly strong in areas with currently low levels of AC penetration, such as South-East Asia (+96 million households, scenario mean), e.g. Indonesia, and Eastern Asia (+41 millions), e.g. Northern India, sub-Saharan Africa Africa (+72 millions), while it will grow more slowly in Central Europe (+30 millions), North Africa and the Middle East (+24 millions) and portions of Latin America (+33 millions) because of already higher current AC prevalence rates (North America), climate heterogeneity and low propensity to use AC (Europe).\n\nMaps and bar charts of AC ownership (% and count of households) (a, b) and (c, d) household AC electricity consumption (gigawatt-hours yr\u22121 and terawatt-hours yr\u22121), historical (2020 and 2050 for Shared Socioeconomic Pathway (SSP) scenario 2(45). Coupled Model Intercomparison Project Phase 6 (CMIP6) Global Climate Models (GCM) enemble median (exluding 'hot models'62). Supplementary Figs.\u00a011\u201313 in the Supplementary Information provide similar maps and bar charts for SSP scenarios 1(26), 3(70) and 5(85).\n\nIn terms of electricity consumption for AC use, the maps in Fig.\u00a02c, d suggest that the total electricity use for AC tends to be strongly correlated with population density only in areas of high AC penetration, such as the United States, Eastern Asia, and Mediterranean countries. In the rest of the world, AC electricity use tends to be more concentrated in the proximity of larger urban centers. By 2050, new areas with high concentration of demand of are projected to emerge in India, Mexico, and East and South-East Asia. In per-household (HH) terms, we estimate that in 2020 families owning AC consumed an average of 2000 kilowatt-hours HH\u22121 yr\u22121 for cooling, noting that such figure has very large differences across regions: for instance, in North America it stands at 5,445 kilowatt-hours HH\u22121 yr\u22121, while in sub-Saharan Africa at 985 kilowatt-hours HH\u22121 yr\u22121. By 2050, we project the average consumption to range between 1,967 - 2289 kilowatt-hours HH\u22121 yr\u22121, depending on the scenario considered. Supplementary Fig.\u00a014 provides a summary of regional trajectories, while Supplementary Tables\u00a08, 9 report country-level statistics for the projected AC ownership and AC electricity consumption, as well as the corresponding Gini indexes of within-country inequality.\n\nZooming in and looking at within-region and within-country patterns, we observe that growing inequalities will affect the African continent, where AC gains prominence in North African countries and areas of Southern Africa, while it will remain less available to the majority of the population of the sub-Saharan African region. A similar pattern is projected in India, Indonesia and South East Asia: irrespective of a considerable growth in the national AC penetrations, large fractions of the population will remain vulnerable to acute heat. In China, AC use will also soar, with a very strong growth in the intensive margin. Looking at Central and Latin America, strong inequalities are found irrespective of similar heat exposure. For instance, the highest AC penetration rates are projected in Argentina and coastal areas of central Brazil, while populations in the highly exposed northern part of South America will reach significantly lower AC access. Conversely, AC penetration and use are projected to grow more homogeneously across Southern European and Mediterranean countries, another key hotspot of chronic heat exposure. Penetration in the United States, Australia, and Japan, being already close to saturation, will grow more moderately.\n\nWhile these inequalities may also derive from differences in local climates, our analysis shows that within each region and country AC prevalence is and will persistently be unequally distributed across income groups in SSP2(45), as seen in Fig.\u00a03a (see Supplementary Figs.\u00a015\u201317 for additional scenarios). This income-stratified assessment reveals inequalities are observed in all regions: such differences are explained both by income availability inequalities, and by geographical correlations between income levels and heat exposure (noting that both globally and within each of the seven macro-regions considered, countries with highly different income levels exist). Globally, the lowest quintile of income AC penetration is expected to grow from a mean of about 17% to 21\u201339% by 2050, whilst in the highest our projections suggest a growth in the mean value from 52% to about 56\u201360%. It is worth noting, as seen from Supplementary Fig.\u00a019, that the AC availability gap between the top and lowest income quintiles is projected to enlarge in sub-Saharan Africa and South Asia, where we observe the largest increase in AC adoption among the richest households belonging to the fourth and fifth quintile of the income distribution, while in the other regions it is expected to shrink or remain similar.\n\na ranges\u00a0of air-conditioning penetration; b\u00a0ranges\u00a0of AC electricity consumption.\u00a0Note that income quintiles are defined based on each specific region\u2019s income distribution in year 2020, and therefore the global pool panel pools together households belonging to each quintile of different regions. The range of values in each boxplot are based on the projections calculated with the Coupled Model Intercomparison Project Phase 6 (CMIP6) Global Climate Models (GCMs) enemble median (exluding \u2019hot models\u201962). Note: facets have specific y-axis ranges to better emphasize differences among scenarios. Supplementary Figs.\u00a015\u201317 report quintile-level projections for additional scenarios.\n\nFigure\u00a03 b reveals that also household AC electricity consumption is also unequally distributed across income quintiles both globally and within most regions. Interestingly, both at a global scale and within a number of regions (and mostly Middle East & North Africa, Europe & Central Asia and Latin America & Caribbean) we find electricity consumption to have a regressive distribution. Families in low-income quintiles - largely because of their geographical distribution with respect to heat exposure - are consuming similar or higher quantities of electricity to families in higher quintiles within that specific region (for reference, Supplementary Fig.\u00a03 provides a bivariate global map of historical Cooling Degree Days (CDD) exposure and income distribution). Due to lower incomes, this has a significant regressive effect on household energy expenditure. Future socio-economic transformations and growing heat exposure as a result of climate change are found to worsen this energy poverty implication (see Supplementary Fig.\u00a020 for a comparison of the distributions in the AC electricity change between the top and lowest income quintiles). For instance, families in the second income quintile of Middle East & North Africa are projected to consume more than families in any other quintile.\n\nExamining within-region and within-country heterogeneity across quintiles, a decision-relevant scale mirroring the jurisdictions in which policy makers act, we observe that the regressive impact of AC electricity consumption growth is largely a result of income inequality and heat exposure differences within regions. For instance, in the Middle East and North Africa (MENA) region, some of the hottest areas (e.g. regions of the Arabic peninsula or southern Egypt) overlap with the areas with the lowest income levels in the region. A similar pattern can be traced in North America, where the Southern part of the United States and several regions of Mexico are found to be both very hot and poorer than the average; a similar dynamic is found in South Asia, with large areas of Bangladesh and Pakistan being both low-income and heat exposed. Finally, in sub-Saharan Africa - where the highest income difference between the first and the last quintile is found - few countries represent the bulk of the households in the highest income quintile (e.g. South Africa, parts of Angola and the Republic of Congo). Within-country, the Gini indexes of electricity consumption (Supplementary Table\u00a09) reveal that the strongest inequality is found in several low-income countries (we refer to the World Bank 2024 income level country classification46), mostly located in sub-Saharan Africa (Kenya, Tanzania, Ethiopia), in a set of upper-middle income countries (e.g. Fiji, Brazil), but also in some high-income countries (Netherlands, Italy). In most countries, within-country inequalities in AC utilization are expected to decline by 2050, although with large differences across scenarios.\n\nAn a consequence of AC ownership inequality, a large number of individuals are projected to remain without AC by year 2050 (mainly due to income constraints) despite living in climates with considerable heat exposure. To analyze this deprivation dimension of cooling poverty26,47, we leverage the high spatial granularity of our global projections to estimate that, globally, the number of heat-exposed vulnerable people (defined as people without AC exposed to more CDDs yr\u22121 than the regional historical average value) will change from around 2.5 billion today to 3.2 billion by 2050 in SSP2(45), see Fig.\u00a04. We find that higher exposure will be observed in the low AC and high warming future of SSP3(70), with 4.1 billion exposed people. These numbers are consistent with the cooling gap estimates of ref. 25, who estimate a range of 2-5 billion people in 2050.\n\na Cumulative share of the population (pop.) without air-conditioning (AC) in 2050 as a function of Cooling Degree Days yr\u22121 (CDDs/yr) exposure, by global region and scenario. Vertical dashed lines highlight the population-weighted average CDDs yr\u22121 in each region under historical climate (1995\u20132014). b Count of people exposed to more CDDs yr\u22121 than the regional historical average value and living without AC, by global region and scenario. The numbers refer to projections calculated with the Coupled Model Intercomparison Project Phase 6 (CMIP6) Global Climate Models (GCMs) enemble median (excluding 'hot models'62).\n\nInterestingly, we observe that SSP5(85), the scenario with the warmest climate, is projected to be the future with the smallest global adaptation cooling deficit, at 2.4 billion. While this is the result of high economic growth, it also implies the starkest heat exposure for those not gaining access to AC, as seen in Fig.\u00a04a. The figure visualizes\u2014globally and for each major world region - the cumulative fraction of people exposed to a certain cumulative heat exposure (quantified in CDDs yr\u22121) who are estimated not to have AC by year 2050 in the four scenarios considered. In addition, the increases or only moderate decreases in the gap figure is explained by the expected global demographic growth in highly exposed but adaptation capacity-constrained areas, which may partially or more than counterbalance the projected growth in the global AC penetration rates. As a consequence, the deprivation is and will increasingly be concentrated in Africa and in South Asia. In relative terms, this implies that in 2050 36% [scenarios range: 30\u201351%] of the global population living in areas experiencing higher CDD exposure than their regional population-weighted mean is projected to remain without AC, compared to the current estimate of 2.5 billion people (35% of the global population). Hence, while the share of people affected by the global adaptation cooling deficit will remain more or less constant (in the scenario-mean pathway), in absolute terms it will increase by 500 million people [\u2212100 +1600 million].\n\nWhen aggregated to the global level (Supplementary Fig.\u00a014), gridded projections (weighted by the number of households per grid cell) for the middle-of-the-road scenario result in a global projected AC penetration rising from the current 27% to a scenario-median of 41%. Households equipped with an AC unit would increase from 620 millions to an estimated median of 900 millions by 2050. Greater AC availability growth translates into a surge in the use of energy and the related environmental impacts. We project global residential AC electricity consumption (Fig.\u00a05a) to grow from the estimated 1220 terawatt-hours yr\u22121 in 2020 to 1940 (1590\u20132377) terawatt-hours yr\u22121 in 2050. While on a global scale the trajectories are mostly linear (see Supplementary Fig.\u00a018, comparing the projected growth rates in adoption and use of AC), in specific regions, such as East Asia & Pacific, we witness a very rapid growth of AC prevalence and use already in the 2020s, while in other regions, and mainly sub-Saharan Africa and South Asia, such surge is delayed to the decades closer to 2050. This is likely the result of a turning point in the level of available income to access AC. Indeed, a decomposition analysis of the drivers of future AC uptake and utilization growth (Supplementary Fig.\u00a021; see Methods for details and Supplementary Table\u00a05 for the evolution of drivers) reveals that\u2014albeit with some scenario heterogeneity - expenditure growth has the largest relative importance, followed by socio-demographic drivers (including urbanization). The role of climate change, while relevant, is more marginal, consistent with previous evidence14.\n\na Projected global residential AC electricity consumption in 2020-2050 in terawatt-hours yr\u22121 (TWh/yr), Shared Socioeconomic Pathway (SSP) scenario 1(26), 2(45), 3(70), and 5(85). b Projected global residential AC greenhouse gas emissions in 2020 and 2050 in million tons CO2 equivalent (MtCO2e), SSP 1(26), 2(45), 3(70), and 5(85). The ribbon represents the Coupled Model Intercomparison Project Phase 6 (CMIP6) Global Climate Models (GCMs) interquantile range, whilst the solid line depicts the model ensemble median (excluding 'hot models'62). Note: facets have specific y-axis ranges to better emphasize differences among scenarios.\n\nBesides geographical heterogeneity, our results also demonstrate how scenario differences significantly affect AC uptake and energy use projections. Scenarios SSP1(26) and SSP2(45) lead to similar results in most regions, demonstrating how different climate change and socio-economic growth interactions can generate similar impact scenarios. On the other hand, SSP3(70) and SSP5(85) show radically different outcomes irrespective of similar implied radiative forcing. Being SSP3(70) a scenario of regional rivalry, economic stagnation, and high population growth, it results in low AC uptake in the developing world, while SSP5(85) implies strong, fossil-fuel driven economic growth resulting in very high warming and also high cooling energy consumption.\n\nFuture changes in the use of AC electricity will feedback on the global warming dynamics through the additional greenhouse gas emissions in a way that will be influenced by degree of decarbonization of world countries. Fig.\u00a05b shows regional CO2e electricity emissions from the residential use of AC (see Methods for details on the estimation approach), totaling 797 million tons (Mt) in 2020 and - according to our projections\u2014ranging between 590\u20131365 Mt in 2050, with the lion\u2019s share taken by the Americas and Asia (see Supplementary Tables\u00a010, 11 for AC use emission implications by region and by country). For reference, 2021 United States emissions from electric power sector were 1551 Mt. Our estimates hence suggest that future global AC electricity could emit between over one third and almost the equivalent of the current total electricity emissions by the United States48. Interestingly, we observe that in regions where the power sector is projected to rapidly decarbonize, rising AC utilization can decouple from emissions in a scenario of deep decarbonization (SSP1(26)).",
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+            ]
+        },
+        {
+            "section_name": "Discussion",
+            "section_text": "Our analysis indicates that the interaction of anthropogenic climate change and changing socio-economic factors will determine a steep growth in the global uptake and utilization of air-conditioning to cope with heat. We estimate that the share of households owning air-conditioning could grow from 27% to 41% (33\u201348%) by 2050, implying a surge in global residential AC electricity consumption from about 1220 terawatt-hours yr\u22121 in 2020 to 1940 (1590\u20132377) terawatt-hours/yr in 2050. The growth in residential cooling energy demand could increase CO2e emissions up to 590\u20131365 Mt CO2e by 2050, unless the electricity sector undergo a deep decarbonization as described in SSP1(26). Our projections are in general agreement with the International Energy Agency (IEA)\u2019s The Future of Cooling report12, though slightly more conservative. The IEA estimates that globally, the share of households with at least one AC will be about 65% in 2050, while our projections reach a maximum of almost 47% of households in SSP5(85), i.e. from the current 1.8 billion individuals to about 3.8 billion. Yet, other scenarios modeled in our study, like the SSP3(70), which is characterized by low economic growth and convergence and high population growth in low income and lower-middle income countries, lead to a significantly slower pace in the global uptake of AC. In addition, in its baseline scenario, the IEA estimates a more than three-fold increase in residential energy use for cooling by 2050, reaching nearly 4000 terawatt-hours yr\u22121. In the IEA\u2019s efficient cooling scenario, this growth is reduced by about 45%, bringing IEA\u2019s numbers in line with our residential AC electricity consumption projections range. Emission projections are also comparable. IEA\u2019s estimate of current CO2 emissions associated with the global cooling sector stand at 1130 million tons CO2 yr\u22121. This estimate also considers cooling in the commercial and services sectors, which account for about half of the global cooling capacity. Our estimates for 2020 residential AC use carbon dioxide emissions are thus in line, at 797 Mt.\n\nThese global aggregate figures have important policy implications for global, regional, and national energy planning as well as for meeting emission reduction targets. Not by chance, during the United Nations Framework Convention on Climate Change (UNFCCC) 28th Conference of the Parties (COP28), sixty-four countries - with some notable exceptions among highly heat-exposed nations - signed the Global Cooling Pledge49 with the ambition to reduce cooling-related emissions by 68% by 2050, increase access to sustainable cooling by 2030, and increase the global average efficiency of new air conditioners by half. Despite these ambitious global targets, our analysis demonstrates the importance of considering more granular information if cooling and energy poverty and inequalities are to be tackled. Our sub-national projections show that in the absence of dedicated policies, future growth in AC ownership and use will be highly unequally distributed across regions and income groups. The granularity of our projections is an important contribution that yields new evidence at the scale that matters for policy implementation. For instance, we show that in highly exposed regions, such as South Asia and sub-Saharan Africa, by 2050, AC will only be extensively available (AC availability >50%) to people belonging to the highest income groups, while the vast majority of poorer households will be remaining without access. The high spatial resolution and the global coverage of our projections is of crucial importance to reveal future geographical hotspots of climate adaptation inequalities in different world regions and population sub-groups. Gross Domestic Product (GDP) per-capita is identified as the major driver of growing AC uptake and use (Supplementary Fig.\u00a021), highlighting the large relevance of income as an enabler of autonomous adaptation, as well as the necessity for local regulation of cooling solutions. This is also crucial in relation with energy poverty\u2014which connects with adaptive capacity to climate change50 - as adapting to higher temperatures would increase the energy burden of less affluent individuals, who are already spending high shares of their income for energy services51,52. In relation to these issues, the granular evidence presented in our study can enable the promotion of more equitable planning of cooling solutions to cope with heat through public subsidies, international donors, building and city planning, and passive cooling solutions. Indeed, emerging evidence is pointing at the framing of access to cooling as a systemic, multi-dimensional issue47 that tightly connects to climate change adaptation justice discussions recently at the center of global climate conferences53.\n\nThe study is not without caveats. First, the projected electricity demand and ownership rates only refer to residential cooling demand, and therefore they can be considered as lower-bound estimates, not including cooling energy from commercial, industry, and transport. Second, the empirical approach adopted in this paper is not able to explicitly characterize technological change such as future improvements in the efficiency of appliances, building stock insulation, or other low-energy cooling solutions, as well as the heterogeneous cost of purchasing AC units across world regions. These transformations are partially accounted for by the model non-linearities, which determine highly heterogeneous responses of electricity consumption to AC ownership and utilization, with such responses being mediated by income, education, and geography. These variables and their projected transformations in different areas of the world implicitly encapsulate these technological and efficiency transformations. Third, our projections do not take into account future expansion of electricity access, which in sub-Saharan Africa still stands at less than 50% (more than half a billion people), with important repercussions connecting cooling demand and energy use54. Future research could explicitly look at these transformations to assess their potential for reducing future cooling energy demand at a local and global level.\n\nOverall, our dataset contributes to providing the missing input to the modeling community that makes it possible to better assess vulnerability and adaptation assessments when combined with information on the spatial distribution of vulnerable individuals (e.g. the elderly, see refs. 55,56). It can feed into global climate-mortality assessments and characterize the role of adaptation options in mitigating health risks6,16. In addition, our output data can be used to evaluate the impact of residential air-conditioning usage on power and grid planning and investments in a context of relation to climate mitigation and development policy.",
+            "section_image": []
+        },
+        {
+            "section_name": "Methods",
+            "section_text": "We assemble a globally-relevant household micro data database covering more than 500 sub-national administrative units from 25 countries. Together, these countries represent 62 percent of the world\u2019s population and account for 73% of the global electricity consumption. Supplementary Table\u00a02 lists the countries included in the database, the macro-region of belonging, the year(s) when the interviews were carried out, and the number of households included in the final pooled database for each country. Supplementary Fig.\u00a01 shows the spatial distribution and density of surveyed households across the globe.\n\nFor each survey we gather information on annual electricity expenditure (also on quantity when available), air-conditioning ownership, total household expenditure, electricity prices, and several socio-economic and demographic variables. We limit our sample to non-missing air-conditioning and non-missing electricity data. This means that our data set excludes households that did not have access to electricity during the survey year. As not all the surveys electricity quantity is available, we enrich our data set with information on average electricity prices. Electricity prices are either directly obtained dividing electricity consumption by quantity or collected at country or sub-national level from external sources. Similarly, the variable indicating whether a household lives in urban or in a rural area is not reported for all countries. For this reason, we also collect gridded data on urbanization from Gao et al.57 to construct sub-national shares.\n\nHistorical climate data is drawn from the European Centre for Medium-Range Weather Forecasts\u2019s ERA-5 historical climate reanalysis data product58, covering the period 1970-2019, and having a spatial resolution of 0.25 arc-degrees. We obtain daily average temperature to calculate Cooling and Heating Degree Days (CDDs and HDDs) at each year and pixel, adopting the temperature threshold of 18\u2218 C. Both CDDs and HDDs are constructed at the annual level, and they are defined as the cumulative sum of days with daily average temperature above (CDDs) or below (HDDs) the temperature threshold, T\u2006*, as per Eqs. (1) and (2):\n\nand\n\nwhere \u03b3d is the binary multiplier.\n\nFor all pixels we construct both weather and climate CDDs and HDDs. On the one hand, weather CDDs and HDDs are defined during the survey year. On the other hand, climate CDDs and HDDs are the averages of the annual CDDs and HDDs respectively across the period 1970-survey year. Moreover, we also include climate relative humidity (HURS), which is a further input to the model given its crucial importance for heat perception and impacts59,60. Household data are then merged with this information using the most disaggregated geographical information available (e.g. provinces or districts) in each survey, and the year in which the survey is conducted. Particularly, we collapse across grid cells within each administrative unit using population weights in order to represent temperature exposure for the average person within a unit.\n\nTo project future AC adoption and electricity consumption, we consider Coupled Model Intercomparison Project Phase 6 (CMIP6) climate change projections coming from the NASA Earth Exchange Global Daily Downscaled Projections (NEX-GDDP-CMIP6) dataset61 based on from ScenarioMIP bias-corrected model runs, having a native time resolution of one day and a spatial resolution of 0.25 arc-degrees. We process both historical and future periods Global Climate Models (GCM) output data from each CMIP6 GCMs model (excluding \u2019hot models\u201962) as well as for the GCMs ensemble median to calculate pixel-wise median values for the 1995-2014 historical and 2041-2060 future periods, respectively, along two scenarios. These, consistently with the CMIP6 logic, are based on SSP-RCP combinations63. In particular, we consider the scenarios SSP126, a combination of SSP1 and Representative Concentration Pathway (RCP) 2.6, a scenario of strong reduction of greenhouse gases concentration implying a radiative forcing of 2.6 \\(\\frac{W}{{m}^{2}}\\); SSP245, a combination of SSP264 and RCP 4.5, an intermediate greenhouse gases concentration scenario implying a radiative forcing of 4.5 \\(\\frac{W}{{m}^{2}}\\); SSP370, a combination of SSP3 and RCP 7.0, an high greenhouse gases concentration scenario implying a radiative forcing of 4.5 \\(\\frac{W}{{m}^{2}}\\); and SSP 585, a combination of SSP565 and RCP 8.5, a very high greenhouse gases concentration scenario implying a radiative forcing of 8.5 \\(\\frac{W}{{m}^{2}}\\).\n\nIn addition, to estimate future growth in household expenditure we use yearly per-capita GDP growth rates based on gridded GDP projections compatible with the SSPs66. We extract growth rates at the finest level of geographical disaggregation at which survey data are available for each country (e.g., districts or provinces), and we parse each growth rate to household located in the corresponding area. Similarly, SSP-consistent gridded population growth rates67 are used to project the growth in the number of households for each geographical disaggregation unit in each country. In addition we exploit SSP-consistent gridded urbanization projections57 to assess future change in urban/rural household status. When it comes to country-wide projections data, we draw information on future distribution of households among age, education and gender groups based on the SSP scenarios68. To project future household characteristics and exposure we use both gridded, thus sub-nationally variable data, and national-scale projections. Data on current residential electricity prices (which are assumed to be constant due to the massive uncertainty on their future evolution globally and across countries) is drawn form the Cable.co.uk database https://www.cable.co.uk/energy/worldwide-pricing/and adjusted to the 2011 Purchasing Power Parity (PPP) United States dollars unit to match the model training data. Finally, we adopt the Global Administrative Areas (GADM) database69 as the standard administrative boundaries for each country.\n\nWe train two random forest models on the pooled household sample (trimming the tails of the within-country distributions at the 1st 99th percentiles for all variables). The first model is a classification probability model to assess whether a household owns at least an AC unit. The second model is a regression model to predict household yearly electricity consumption as reported from the survey data. We test a range of modeling techniques and a broad array of hyperparameters to identify the best performing models. In particular, we train:\n\n(Generalized) Linear Models [(G)LM] (parametric, linear modeling)\n\nGeneralized Additive Models [GAM] (semi-parametric, non-linear modeling)\n\nRandom Forests [RF] (tree-based, non-parametric, non-linear modeling)\n\nWe use 10-fold cross validation to optimize the model hyperparameters selection (Supplementary Figs.\u00a06-7). Among the models tested, the random forests (RF) models reveal to be the most effective (see Supplementary Tables\u00a06-7 and Supplementary Fig.\u00a04), as they achieve maximum training set Accuracy and R2 values of 93% and 85% for AC ownership and electricity consumption, respectively (Fig.\u00a04). We also calculate metrics of Cohen\u2019s Kappa and AUC for the AC ownership classification model. The Kappa70 metric is preferred as it is more suitable for evaluating binary classification predictions when the two classes (AC/no AC) are unbalanced, such as for the case of global AC ownership, where the global pool dataset mean stands at about 0.25. The two metrics yield 79% and 88%, respectively, indicating very good agreement71), while the MSE (Mean Squared Error) for the electricity consumption regression model yields 0.2. The two trained RF models are then tested on the complementary stratified random sample which was excluded from the training set. Predictions on the test set yield Accuracy and R2 values of 90% and 75% for AC ownership and electricity consumption, respectively. Cohen\u2019s Kappa and AUC metrics for the test set yield 73% and 86%, respectively (substantial agreement71). The MSE metric yields 0.22 and 0.35 for the training and testing sets, respectively.\n\nAltogether these numbers point at a relatively high accuracy of the models in predicting unseen AC ownership and electricity consumption data, and are thus deemed suitable for producing globally relevant estimates.\n\nTo provide a set of interpretable metrics to assess the contribution of the predictor variables to the two-stage RF models (otherwise challenging to interpret given their non-parametric, \u2019black-box\u2019 nature), we generate a number of additional metrics and plots.\n\nOur first step is to estimate partial dependence values. Consider an outcome, Y, whose values are determined by a set of predictor variables, {X1,\u00a0\u2026,\u00a0XN} through the model relationship, \\(Y=\\Omega \\left[{X}_{1},\\ldots,{X}_{N}\\right]\\). The point partial dependence of the outcome on a focal subset of the inputs, say XF, is the expectation of the outputs of the model evaluated at fixed values, {xF}, in conjunction with a grid (\\({{{\\mathcal{G}}}}[\\cdot ]\\)) of the non-focal variables (Eq. (3)):\n\nIn our analytical setting, \u03c0 represents the conditional expected probabilities for the first stage AC ownership model and conditional expected cooling energy consumption for the second stage electricity demand model. Our focal variables are, in the first stage, cooling degree days and the logarithm of household expenditure, and in the second state, CDDs, log expenditure and the probability of a households owning an AC unit. Figure\u00a01d shows maps of these partial dependence relationships.\n\nThe elasticity of the outcome with respect to the focal variable is defined by Eq. (4):\n\nWe combine (3) and (4) to calculate partial elasticities using the discrete arc-elasticity formula in Eq. (5):\n\nwhere \\({x}_{F}^{0}\\) denotes the anchor value of each focal variable. As a practical matter, we use the minimum value of each focal input variable as its anchor point. The distributions of the partial elasticities of AC ownership and electricity consumption to expenditure and climate variables are shown in Fig.\u00a01e.\n\nTo gain additional insight into the models\u2019 performance, we calculate SHAP (Shapley additive explanations72,73) values that quantify the contribution of each variable to the predicted outcome. SHAP values consider all possible combinations of features and measure their impact on predictions. Supplementary Figs.\u00a08-9 present Shapely values plots, shedding light on the magnitude and direction of features within the RF model and for each specific macro-region considered.\n\nFinally, Supplementary Fig.\u00a010 illustrates a graphical representation of a single decision tree (CART) benchmark model.\n\nTo parse the household surveys to the spatially-explicit datasets described above used to make projections, we refer to the most disaggregated spatial unit available to which each household is assigned in the survey data. This varies by country, but spans from the first level of administrative units (the regions of a country) down to the third level of administrative units (districts). Using these geographical boundaries, we extract raster data and join vector data to calculate the relevant statistics.\n\nWhilst in some instances it is possible to directly parse historical data from the survey variables as their definition and units are consistent (e.g. age, gender), in other instances certain processing steps are required to ensure consistency of the historical data upon which the empirical models are estimated, and the future data used for projections. For instance, as income/expenditure is heterogeneously defined across countries, we first convert it into 2011 PPP United States dollars, and then project the baseline value using the local per-capita GDP growth rates from the downscaled GDP projections66 divided by the downscaled population projections67.\n\nAn additional challenge in making bottom-up model-based projections from disaggregated survey data relates to binary and factor variables, where a set of assumptions need to be made. Finally, for a set of variables (age, gender, education), SSP-consistent projections are only available at a country-level, and thus we assume socio-demographic transformations to be homogeneous within each country.\n\nBesides cross-validation at the household level for model training, hyperparameters tuning, and testing, the models output data are also benchmarked against both national AC rates derived from both the household survey training data, and on recent AC ownership statistics from alternative sources12,14. Note that grid-cell level model outputs for the base year 2010 are compared with survey data and statistics which span between 2011-2019 (depending on the country; see Supplementary Table\u00a02 for reference). Thus, part of the observed bias might be owing do different year of reference in the survey and modeled data.\u2018\n\nSupplementary Fig.\u00a05 illustrates the results of such comparison. The results (yielding R2 values of 97% and 92% for aggregated survey data and national statistics, respectively) show that our estimates are broadly consistent with both aggregated training data and national statistics from external sources (including in countries which are not part of our training data pool). This finding provides important evidence for the reliability of our gridded projections, their representativeness at the country-level, and their external validity.\n\nWe assess the consequences of increased AC energy use in terms of carbon dioxide emissions by combining the gridded AC electricity consumption projections with country or regional-average (depending on data availability) power sector emission factors of different SSP scenarios from the Intergovernmental Panel on Climate Change (IPCC) Sixth Assessment Report (AR6) Database74. Such emission factors are multiplied by the sum of the estimated AC electricity in each country.\n\nTo conclude, we carry out a decomposition analysis of the projections by recursively re-estimating the projections changing the input data to the model one driver per time, and letting the other drivers constant at their base year level. Supplementary Fig.\u00a021 illustrates the results of this supplementary analysis for both AC penetration and electricity consumption.\n\nFurther information on research design is available in the\u00a0Nature Portfolio Reporting Summary linked to this article.",
+            "section_image": []
+        },
+        {
+            "section_name": "Data availability",
+            "section_text": "The input data required to replicate the analysis and the output data generated in this study and the source data to replicate the figures have been deposited in the Zenodo database under accession code 12697821, https://doi.org/10.5281/zenodo.12697821. The output gridded data and the underlying machine learning (ML) model trained on household survey data are made publicly available for future use. In particular, we release global netCDF files with a 0.5 arc-degree spatial resolution (about 55km at the equator) and 10-year time resolution for the period 2010-2050 for the SSP scenarios 1(26), 2(45), 3(70), and 5(85). Dataset for three variables is made available: (i) the AC penetration rate, defined as the fraction of households living at grid cell i in year t owning at least one AC unit; (ii) the population of reference, derived from Gao et al.57 which can be used as a weight to aggregate AC penetration rates at different spatial scales; (iii) the total AC electricity consumption (in gigawatt-hours yr\u22121), defined as the electricity consumed for AC utilization by households at each grid cell i in year t. In addition, source data to replicate figures and tables are provided with this paper.\u00a0Source data are provided with this paper.",
+            "section_image": []
+        },
+        {
+            "section_name": "Code availability",
+            "section_text": "The replication code can be accessed through the following Github repository: https://doi.org/10.5281/zenodo.12671063.",
+            "section_image": []
+        },
+        {
+            "section_name": "Change history",
+            "section_text": "A Correction to this paper has been published: https://doi.org/10.1038/s41467-024-53876-0",
+            "section_image": []
+        },
+        {
+            "section_name": "References",
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+            "section_name": "Acknowledgements",
+            "section_text": "This research was funded by the European Union. Views and opinions expressed are those of the authors only and do not necessarily reflect those of the European Union. Neither the European Union nor the granting authority can be held responsible for them. I.S.W. was supported by the U.S. Department of Energy, Office of Science, Biological and Environmental Research Program, Earth and Environmental Systems Modeling, MultiSector Dynamics under Cooperative Agreements DE-SC0016162 and DE-SC0022141.",
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+            "section_text": "Centro Euro-Mediterraneo sui Cambiamenti Climatici, 30133, Venice, Italy\n\nGiacomo Falchetta,\u00a0Enrica De Cian\u00a0&\u00a0Filippo Pavanello\n\nInternational Institute for Applied Systems Analysis, Schlossplatz, 1, Laxenburg, A-2361, Austria\n\nGiacomo Falchetta\n\nRFF-CMCC European Institute on Economics and the Environment, Venice, Italy\n\nGiacomo Falchetta,\u00a0Enrica De Cian\u00a0&\u00a0Filippo Pavanello\n\nCa\u2019 Foscari University of Venice, Department of Economics, 30121, Venice, Italy\n\nEnrica De Cian\n\nUniversity of Bologna, Department of Economics, Piazza Scaravilli 2, 40125, Bologna, Italy\n\nFilippo Pavanello\n\nBoston University, Dept. of Earth & Environment, Boston, 02215, USA\n\nIan Sue Wing\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nG.F. E.D.C., F.P., and I.S.W. conceptualized the paper; G.F. designed the methodological framework; G.F. and F.P. assembled the global household surveys dataset; G.F. performed the statistical analysis and produced the output data; G.F. and I.S.W. produced the figures. G.F. E.D.C., F.P., and I.S.W. contributed to writing and editing the paper.\n\nCorrespondence to\n                Giacomo Falchetta.",
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+            "section_text": "Falchetta, G., Cian, E.D., Pavanello, F. et al. Inequalities in global residential cooling energy use to 2050.\n                    Nat Commun 15, 7874 (2024). https://doi.org/10.1038/s41467-024-52028-8\n\nDownload citation\n\nReceived: 22 October 2023\n\nAccepted: 22 August 2024\n\nPublished: 16 September 2024\n\nVersion of record: 16 September 2024\n\nDOI: https://doi.org/10.1038/s41467-024-52028-8\n\nAnyone you share the following link with will be able to read this content:\n\nSorry, a shareable link is not currently available for this article.\n\n\n\n\n                            Provided by the Springer Nature SharedIt content-sharing initiative\n                        ",
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+            ]
+        },
+        {
+            "section_name": "This article is cited by",
+            "section_text": "Scientific Data (2025)\n\nHeat and Mass Transfer (2025)\n\nInternational Journal of Biometeorology (2025)\n\nEnvironmental and Resource Economics (2025)",
+            "section_image": []
+        }
+    ]
+}

3ab80f57f86199a145a5b3342311655b26b6e155140b1beaec05562a5b92c1ba/metadata.json

@@ -0,0 +1,137 @@
+{
+    "title": "High-fidelity photonic quantum logic gate based on near-optimal Rydberg single-photon source",
+    "pre_title": "Experimental realization of high-fidelity quantum logic gate between photons",
+    "journal": "Nature Communications",
+    "published": "01 August 2022",
+    "supplementary_0": [
+        {
+            "label": "Supplementary Information",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-022-32083-9/MediaObjects/41467_2022_32083_MOESM1_ESM.pdf"
+        },
+        {
+            "label": "Peer Review File",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-022-32083-9/MediaObjects/41467_2022_32083_MOESM2_ESM.pdf"
+        }
+    ],
+    "supplementary_1": NaN,
+    "supplementary_2": NaN,
+    "source_data": [
+        "https://doi.org/10.5281/zenodo.6552691"
+    ],
+    "code": [],
+    "subject": [
+        "Quantum optics",
+        "Single photons and quantum effects"
+    ],
+    "license": "http://creativecommons.org/licenses/by/4.0/",
+    "preprint_pdf": "https://www.researchsquare.com/article/rs-845893/v1.pdf?c=1659438695000",
+    "research_square_link": "https://www.researchsquare.com//article/rs-845893/v1",
+    "nature_pdf": "https://www.nature.com/articles/s41467-022-32083-9.pdf",
+    "preprint_posted": "08 Sep, 2021",
+    "research_square_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Quantum logic gates with fidelity above fault-tolerant threshold are building blocks for scalable quantum technologies[1,2]. Compared to other types of qubits, photon is one of a kind due to its unparalleled advantages in long-distance quantum information exchange[3-5]. As a result, high-fidelity photonic quantum operations are not only indispensable for photonic quantum computation[6-8] but also critical for quantum network[2,9]. However, two-qubit photonic quantum logic gate with fidelity comparable to that of leading physical systems, i.e. 99.7% for superconducting circuits[10] and 99.9% for trapped ions[11], has not been achieved. A major limitation is the imperfection of single photons[12]. Here, we overcome this limitation by using high-quality single photons generated from Rydberg atoms as qubits for the interference-based gate protocol, and achieve a gate fidelity up to 99.84(3)%. Our work paves the way for scalable photonic quantum applications[13-15] based on near-optimal single-photon qubits and photon-photon gates.Photonics/opticsAtomic and Molecular Physicsquantum logic gateshigh-fidelity photonic quantum operationsRydberg atomsqubits",
+            "section_image": []
+        },
+        {
+            "section_name": "Additional Declarations",
+            "section_text": "There is NO Competing Interest.",
+            "section_image": []
+        },
+        {
+            "section_name": "Supplementary Files",
+            "section_text": "SupplementaryInformation.pdfSupplementary Information",
+            "section_image": []
+        }
+    ],
+    "nature_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Compared to other types of qubits, photon is one of a kind due to its unparalleled advantages in long-distance quantum information exchange. Therefore, photon is a natural candidate for building a large-scale, modular optical quantum computer operating at room temperature. However, low-fidelity two-photon quantum logic gates and their probabilistic nature result in a large resource overhead for fault tolerant quantum computation. While the probabilistic problem can, in principle, be solved by employing multiplexing and error correction, the fidelity of linear-optical quantum logic gate is limited by the imperfections of single photons. Here, we report the demonstration of a linear-optical quantum logic gate with truth table fidelity of 99.84(3)% and entangling gate fidelity of 99.69(4)% post-selected upon the detection of photons. The achieved high gate fidelities are made possible by our near-optimal Rydberg single-photon source. Our work paves the way for scalable photonic quantum applications based on near-optimal single-photon qubits and photon-photon gates.",
+            "section_image": []
+        },
+        {
+            "section_name": "Introduction",
+            "section_text": "Entangling operation is one of the fundamental building blocks for universal quantum computation1,2. A probabilistic, heralded two-photon quantum logic gate is sufficient to achieve scalable linear-optical quantum computing by using the Knill\u2013Laflamme\u2013Milburn (KLM) scheme3, albeit with a substantial resource overhead. The cluster-state model4,5,6, which is based on the local measurement and feeds forward on a large entangled cluster state, can significantly reduce the resource overhead7,8,9. Given that implementing a deterministic two-photon entangling operation is still challenging in linear optics, a large entangled cluster state can be generated by fusing a collection of small clusters7, e.g., three-photon clusters, in a ballistic way8,10,11,12. The resource consumption of the cluster-state computation is then dominated by the preparation of those small clusters13, which depends on the efficiency and quality of single-photon sources, and the ability to generate entanglement with quantum logic gate, i.e., the photon\u2013photon entangling gate fidelity.\n\nAfter the initial proposal of KLM3, a destructive optical controlled-NOT (CNOT) gate (without the entangling gate operation) was experimentally demonstrated in 2002, with a truth table fidelity of 83%14. Qiang et al. employed a different linear-optical scheme15 with four pairs of entangled photons as input and achieved a gate with 98.85% truth table fidelity and 1/64 intrinsic success probability. The first entangling operation using a linear-optical gate was realized in 2003, with an intrinsic success probability of 1/9 and an entangling gate fidelity of 87%16. Optical-related errors, such as photon mode mismatch and polarization imperfection, are reduced over the years, and the entangling gate fidelity has been gradually improved to ~94%17,18,19. Now that many technical sources of error have been addressed, the major obstacle for further suppressing the entangling gate infidelity lies in the quality of single-photon sources20. For example, to achieve a linear-optical quantum logic gate with infidelity below 1%, the minimum requirements on a single-photon source are g(2)(0)\u2009<\u20097\u2009\u00d7\u200910\u22123 and the indistinguishability higher than 99%. To date, these demanding requirements have not been simultaneously achieved by the state-of-the-art single-photon sources.\n\nRecently, significant progress has been made in single-photon sources based on cold Rydberg atoms21,22,23,24. The strong interactions between Rydberg atoms lead to excitation blockade25 and hence the efficient preparation of single atomic excitation, which can be converted into high-quality single photon on demand26 through matter-light quantum state transfer.\n\nHere, we demonstrate a photon\u2013photon quantum logic gate by performing the KLM CNOT gate protocol with single photons generated from Rydberg atoms. Our Rydberg single-photon source features near-optimal purity and indistinguishability and results in a high truth table fidelity of 99.84(3)% and entangling gate fidelity of 99.69(4)%.",
+            "section_image": []
+        },
+        {
+            "section_name": "Results",
+            "section_text": "As illustrated in Fig.\u00a01a, an ensemble of cold 87Rb atoms is prepared in an optical dipole trap and can be coupled from the ground state \\(|{{{{{{{{{\\rm{g}}}}}}}}}} \\rangle\\) to a high-lying Rydberg state \\(|{{{{{{{{{\\rm{r}}}}}}}}}} \\rangle\\) using a two-photon transition with a 780-nm laser field \\({{{\\Omega }}}_{780}^{{{{{{{{{{\\rm{e}}}}}}}}}}}\\) and a 479-nm laser field \\({{{\\Omega }}}_{479}^{{{{{{{{{{\\rm{e}}}}}}}}}}}\\) via an intermediate state \\(|{{{{{{{{{\\rm{e}}}}}}}}}} \\rangle\\). The waists of the Rydberg excitation and the dipole trap beams are chosen such that the entire excitation region is within the Rydberg blockade radius. As a result, multiple Rydberg excitations are suppressed and the entire atomic ensemble involving N atoms can be promoted from the ground state \\(|{{{{{{{{{\\rm{G}}}}}}}}}} \\rangle=\\mathop{\\prod }\\nolimits_{i=1}^{N}|{{{{{{{{{{\\rm{g}}}}}}}}}}}_{i} \\rangle\\) to the single collective excitation state \\(\\vert {{{{{{{{{\\rm{R}}}}}}}}}} \\rangle=\\mathop{\\sum }\\nolimits_{i=1}^{N}|{{{{{{{{{{\\rm{g}}}}}}}}}}}_{1} \\rangle \\ldots|{{{{{{{{{{\\rm{r}}}}}}}}}}}_{i} \\rangle \\ldots|{{{{{{{{{{\\rm{g}}}}}}}}}}}_{N} \\rangle /\\sqrt{N}\\) by a \u03c0 pulse. To generate single photons on demand, a readout field \\({{{\\Omega }}}_{479}^{{{{{{{{{{\\rm{r}}}}}}}}}}}\\) resonant with the \\(|{{{{{{{{{\\rm{e}}}}}}}}}} \\rangle \\leftrightarrow|{{{{{{{{{\\rm{r}}}}}}}}}} \\rangle\\) transition is applied. Assisted by the enhanced atom-light cooperativity, the readout field efficiently converts the Rydberg excitation into a single photon with a well-defined spatial mode.\n\na An ensemble of cold 87Rb atoms with an optical depth of ~5 is confined in a 1012-nm dipole trap. The counter-propagating 780 and 479\u2009nm excitation beams are combined on a dichroic mirror (DM) and tightly focused onto the ensemble, with waists of 6 and 30\u2009\u03bcm, respectively. Atoms are initialized in the ground state \\(|{{{{{{{{{\\rm{g}}}}}}}}}} \\rangle\\) and excited to a high-lying Rydberg state \\(|{{{{{{{{{\\rm{r}}}}}}}}}} \\rangle\\) with a single-photon detuning of \u0394/2\u03c0\u2009=\u2009\u2212200\u2009MHz. After the excitation, a 479-nm readout light resonant with \\(|{{{{{{{{{\\rm{r}}}}}}}}}} \\rangle \\leftrightarrow|{{{{{{{{{\\rm{e}}}}}}}}}} \\rangle\\) transition converts the single collective excitation state \\(|{{{{{{{{{\\rm{R}}}}}}}}}} \\rangle\\) into a single photon that is coupled into a single-mode fiber. The insert shows the atomic levels involved in the excitation and readout processes: ground state \\(\\vert {{{{{{{{{\\rm{g}}}}}}}}}} \\rangle=\\vert 5{{{{{{{{{{\\rm{S}}}}}}}}}}}_{1/2},F=2,{m}_{{{{{{{{{{\\rm{F}}}}}}}}}}}=2 \\rangle\\), intermediate state \\(\\vert {{{{{{{{{\\rm{e}}}}}}}}}} \\rangle=\\vert 5{{{{{{{{{{\\rm{P}}}}}}}}}}}_{3/2},F=3,{m}_{{{{{{{{{{\\rm{F}}}}}}}}}}}=3 \\rangle\\), and Rydberg state \\(|{{{{{{{{{\\rm{r}}}}}}}}}} \\rangle=\\vert 90{{{{{{{{{{\\rm{S}}}}}}}}}}}_{1/2},J=1/2,{m}_{{{{{{{{{{\\rm{J}}}}}}}}}}}=1/2 \\rangle\\). b Two single photons are sequentially generated with an interval of 5\u2009\u03bcs, and their temporal wave packets are well overlapped at the interferometer using a polarization switching electro-optic modulator (EOM) and a 1-km delay fiber. Before the two-photon interference at the first PPBS, two half-wave plates (HWPs) are employed to prepare the input state of the control and target qubits. Two more PPBSs and HWPs are used after the interference to complete the CNOT gate operation. The output state is measured by a polarization-sensitive detection setup consisting of HWPs, polarization beam splitters (PBSs), and SPCMs (c0,1 and t0,1).\n\nTo implement the CNOT gate27,28,29,30, two single photons are consecutively generated from the Rydberg atoms and used as the control and target photonic qubits in a free-space photon\u2013photon interferometer. As shown in Fig.\u00a01b, the non-classical correlations between the control and target qubits can be established via the two-photon quantum interference at a partial polarization beam splitter (PPBS), which has 1/3 reflectivity for horizontally polarized photons and is totally reflective for vertically polarized photons. When the control qubit is in the vertically polarized state, encoded as \\({|0 \\rangle }_{{{{{{{{{{\\rm{C}}}}}}}}}}}\\), two photons do not interfere so the target qubit remains unchanged. In contrast, with the control qubit in the horizontally polarized state, encoded as \\({|1 \\rangle }_{{{{{{{{{{\\rm{C}}}}}}}}}}}\\), the horizontally polarized component of the target qubit acquires a \u03c0-phase shift as a result of the unbalanced two-photon quantum interference, while the vertically polarized component is unaffected. By encoding the diagonally and anti-diagonally polarized states as \\({|0 \\rangle }_{{{{{{{{{{\\rm{T}}}}}}}}}}}\\) and \\({|1 \\rangle }_{{{{{{{{{{\\rm{T}}}}}}}}}}}\\), the target qubit is flipped when the control qubit is in \\({|1 \\rangle }_{{{{{{{{{{\\rm{C}}}}}}}}}}}\\). Therefore, the implemented input-output relation is\n\nwhich defines a CNOT gate operation.\n\nThe fidelity of the photon\u2013photon quantum logic gate critically relies on the purity and indistinguishability of the Rydberg single-photon source. The purity of our Rydberg single-photon source is characterized by a Hanbury Brown\u2013Twiss experiment, in which the photons are coupled into a 50:50 fiber beam splitter followed by two single-photon counting modules (SPCMs). Figure\u00a02a shows the measured second-order intensity correlation function g(2)(\u03c4) as a function of delay \u03c4. As a result of the Rydberg excitation blockade, strong suppression of two-photon events at zero delay is observed. In order to achieve low g(2)(0), efforts are spent on suppressing the background detection events to SPCM dark-count level (see Supplementary Note\u00a01). The measured value for the second-order intensity correlation function at zero delay is g(2)(0)\u2009=\u20097.5(6)\u2009\u00d7\u200910\u22124, which indicates excellent single-photon purity.\n\na Second-order intensity correlation function g(2)(\u03c4) as a function of delay \u03c4. The duration of each experimental cycle is 2.5\u2009\u03bcs. The insert shows g(2)(0) at zero delay. A 200-ns detection window is applied. b The normalized coincidences in HOM experiment as a function of two-photon temporal mismatch \u0394t. The solid curve is a Gaussian fit. The error bars represent the 1\u03c3 standard deviation from photoelectric counting events.\n\nThe scalability of interference-based quantum photonic protocols strongly depends on the indistinguishability of single photons, since distinguishable photons severely deteriorate the operation fidelity. To investigate the indistinguishability, two-photon interference visibility is measured by a Hong\u2013Ou\u2013Mandel (HOM) experiment. Figure\u00a02b displays the measured two-photon coincidence rate as a function of the temporal mismatch \u0394t between two photons. The two photons used in the HOM experiment are sequentially generated from the Rydberg atoms. The first photon is delayed by 5\u2009\u03bcs using an EOM and a 1-km fiber, while the second photon is generated 5\u2009\u03bcs\u2009+\u2009\u0394t after the first one (see Supplementary Note\u00a02). Due to the quantum interference between two single photons, we observe a non-classical suppression of coincidences at zero temporal mismatch with a high visibility of V\u2009=\u200999.43(9)%. Besides photon indistinguishability, V is also affected by background detection events and single-photon impurity characterized by non-zero g(2)(0). By analyzing these contributions, we extract indistinguishability of 99.55(9)%.\n\nWe find that the reduction of indistinguishability from unity is mostly caused by the imperfect interference from photon components in the rising and falling edges of the single-photon temporal profile (see Supplementary Note\u00a02). To further improve the indistinguishability, the single-photon detection window is reduced from 200 to 80\u2009ns, which contains 62% of the photons around the center. The smaller detection window leads to a better indistinguishability of 99.94(8)% and is used for the CNOT gate experiment. The 80-ns detection window also results in a better signal-to-background ratio and a lower g(2)(0) of 4.5(8)\u2009\u00d7\u200910\u22124.\n\nHaving single photons with near-optimal purity and indistinguishability at hand, we proceed to the implementation and characterization of the photonic CNOT gate by inputting different control-target qubits combinations to the gate and measuring the corresponding output states. The truth tables of the CNOT gate are shown in Fig.\u00a03a, b, where the post-selected probabilities for different input-output combinations are displayed on a logarithmic scale. The measured truth table fidelities of the CNOT gate in the computational ZZ basis and the complementary XX basis are \\({F}_{{{{{{{{{{\\rm{CNOT}}}}}}}}}}}^{{{{{{{{{{\\rm{ZZ}}}}}}}}}}}=99.84(3)\\%\\) and \\({F}_{{{{{{{{{{\\rm{CNOT}}}}}}}}}}}^{{{{{{{{{{\\rm{XX}}}}}}}}}}}=99.81(3)\\%\\), which is defined as the probability of detecting the desired output states averaged over input states.\n\na, b Truth tables of the CNOT gate in the computational ZZ basis (a) and the complementary XX basis (b). The ideal input-output relation in the ZZ basis is \\(\\vert 00 \\rangle \\to|00 \\rangle\\), \\(\\vert 01 \\rangle \\to|01 \\rangle\\), \\(\\vert 10 \\rangle \\to|11 \\rangle\\) and \\(\\vert 11 \\rangle \\to|10 \\rangle\\). Similarly, the ideal input-output relation in the XX basis is \\(\\vert {+} {+} \\rangle \\to|{+} {+} \\rangle\\), \\(\\vert+- \\rangle \\to|-- \\rangle\\), \\(\\vert -+\\rangle \\to|-+\\rangle\\) and \\(\\vert -- \\rangle \\to \\vert+- \\rangle\\), with the definitions of \\({\\vert \\pm \\rangle }_{{{{{{{{{{\\rm{C}}}}}}}}}}}=({\\vert 0 \\rangle }_{{{{{{{{{{\\rm{C}}}}}}}}}}}\\pm {\\vert 1 \\rangle }_{{{{{{{{{{\\rm{C}}}}}}}}}}})/\\sqrt{2}\\) for control qubit and \\({|\\pm \\rangle }_{{{{{{{{{{\\rm{T}}}}}}}}}}}=({|0 \\rangle }_{{{{{{{{{{\\rm{T}}}}}}}}}}}\\pm {|1 \\rangle }_{{{{{{{{{{\\rm{T}}}}}}}}}}})/\\sqrt{2}\\) for target qubit. The measured probabilities are shown on a logarithmic scale. c, d Real (c) and imaginary (d) parts of the reconstructed density matrix \u03c1 for the created entangled state.\n\nThe most remarkable feature of a two-photon quantum logic gate is its ability to establish entanglement between two initially uncorrelated photons. With a product state of \\((|0 \\rangle -|1 \\rangle )|1 \\rangle /\\sqrt{2}\\) as input, the CNOT gate ideally generates a maximally entangled Bell state \\(|{{{\\Psi }}}^{-} \\rangle=(|01 \\rangle -|10 \\rangle )/\\sqrt{2}\\). To characterize the entangling gate fidelity, quantum state tomography is performed on the output state and the reconstructed density matrix \u03c1 is shown in Fig.\u00a03c, d. The measured state fidelity, i.e., the entangling gate fidelity, is \\({F}_{{{{\\Psi }}}^{-}}=\\left\\langle {{{\\Psi }}}^{-}\\right|\\rho|{{{\\Psi }}}^{-} \\rangle=99.69(4)\\%\\), which is in good agreement with our analysis (see Supplementary Note\u00a04), and demonstrates the preparation of high-fidelity entangled photon pairs. To the best of our knowledge, the photon\u2013photon quantum logic gate demonstrated here has the highest truth table fidelity and entangling gate fidelity reported until now.\n\nTo further verify the entanglement, we demonstrate the violation of Bell\u2019s inequality with the output state by evaluating the correlation function E(\u03b8c,\u2009\u03b8t) given by\n\nwhere \u03b8c (\u03b8t) is the polarization angle for the measurement of the control (target) output state, and Cij is the coincidence rate between SPCMs ci=0,1 and tj=0,1 in Fig.\u00a01b. Correlation function E(\u03b8c,\u2009\u03b8t) with high fringe visibilities is observed in Fig.\u00a04. The values of E(\u03b8c,\u2009\u03b8t) at polarization angle settings for Bell\u2019s inequality are shown in Table\u00a01, from which the Bell parameter S\u2009=\u2009E(\u03c0/8,\u20090)\u2009+\u2009E(\u03c0/8,\u2009\u03c0/4)\u2009+\u2009E(\u2009\u2212\u2009\u03c0/8,\u20090)\u2009\u2212\u2009E(\u2009\u2212\u2009\u03c0/8,\u2009\u03c0/4) is determined. The measured value S\u2009=\u20092.823(12) approaches the ideal value of \\(|S \\vert=2\\sqrt{2}\\), and violates the Clauser\u2013Horne\u2013Shimony\u2013Holt inequality \u2223S\u2223\u2009\u2264\u20092 by more than 60 standard deviations, thus clearly confirming the entanglement between the output photons and the quantum nature of our gate.\n\nMeasured correlation function E(\u03b8c,\u2009\u03b8t) as a function of \u03b8c with \u03b8t\u2009=\u20090 (diamonds) and \u03b8t\u2009=\u2009\u03c0/4 (circles). Solid curves are sinusoidal fits with 0.99(1) visibility. The error bars represent the 1\u03c3 standard deviation from photoelectric counting events.\n\nTo quantitatively understand the performance of our quantum logic gate, we thoroughly investigate possible sources of error in the experiment, and identify three major contributions to the CNOT gate infidelity. Background detection events, which mainly come from the dark counts of SPCMs, occur randomly and lead to an infidelity of 0.088(4)% for ZZ basis. Moreover, the residual multi-photon components from the single-photon source induce unexpected coincidences in \\(|10 \\rangle\\) and \\(|11 \\rangle\\) bases, and lead to an infidelity of 0.067(19)% for ZZ basis. In addition, the imperfect photon indistinguishability reduces quantum interference visibility and causes errors during the controlled state flip of the target qubit, leading to an infidelity of 0.06(8)% for ZZ basis. The infidelity for XX basis contributed by the above-mentioned mechanisms is comparable. We emphasize that the above-mentioned error mechanisms are not intrinsic to our experiment, and can be mitigated in the future (see Supplementary Note\u00a03).\n\nThe gate performance with 200\u2009ns single-photon detection window is also studied, and the truth table fidelity for XX (ZZ) basis is 99.40(3)% (99.53(3)%). The dominating contribution of infidelity comes from the finite indistinguishability of 99.55(9)%, which is most likely caused by the phase chirps in the rising and falling edges of the single-photon temporal profile. In principle, this effect can be characterized by using a homodyne method to extract the single-photon phase profile and can be compensated by optimally controlling the phase and amplitude of the readout field \\({{{\\Omega }}}_{479}^{{{{{{{{{{\\rm{r}}}}}}}}}}}\\).\n\nThe probabilistic linear-optical gate protocol employed here has an intrinsic efficiency of 1/9, and the probability of having a single photon at the target (control) input is about 7.1% (3.5%) with a 200-ns detection window. Considering the gate protocol efficiency, the single-photon efficiencies, optical losses, and the SPCM detection efficiency, the typical coincidence detection probability is about 7.6\u2009\u00d7\u200910\u22125. The 80-ns detection window further reduces it to 3.3\u2009\u00d7\u200910\u22125. With a repetition rate of 50\u2009kHz, our experiment features a high success rate up to 100\u2009per\u00a0minute even with the 80-ns small detection window. This demonstrates quantum optical operation based on Rydberg single-photon source is competitive in gate success rate to other single-photon sources, while featuring further advantages in single-photon purity, indistinguishability, and quantum logic gate fidelity. The coincidence detection probability and repetition rate can be further improved with future technical efforts (see Supplementary Note\u00a03).\n\nWe emphasize that the achieved high fidelity is not limited to the probabilistic gate scheme used here. For example, deterministic photon\u2013photon gate protocols have been demonstrated using matter-light interactions31,32, and a major source of infidelity in these experiments comes from the detrimental multi-photon components in the photonic qubits, which can be circumvented with our near-optimal single photons.",
+            "section_image": [
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+            ]
+        },
+        {
+            "section_name": "Discussion",
+            "section_text": "In summary, we experimentally demonstrate a photon\u2013photon quantum logic gate with a post-selected truth table fidelity of 99.84(3)% and entangling gate fidelity of 99.69(4)% based on near-optimal single photons generated by Rydberg atoms. When combined with multiplexing techniques and quantum error correction, the demonstration of high-fidelity gate enables the reduction of quantum resource overhead and thus constitutes an important step toward building a large-scale linear-optical quantum computer.\n\nOur results open up new perspectives for highly demanding applications such as photonic quantum information processing and distributed matter-light quantum architectures33 (see Supplementary Note\u00a05 for detailed discussions on potential applications). For example, high-fidelity single photons and two-photon gates enable the preparation of photonic cluster states, which are the key elements of the all-optical quantum repeaters34,35 that circumvent the requirement of long-lived quantum memories. By increasing the size of the cluster states and extending their dimensions to higher than two, fault-tolerant photonic quantum computing can be implemented6. Furthermore, high-quality single photons from Rydberg atoms can be injected into integrated photonic chips36, realizing photonic quantum circuits with excellent multi-photon quantum interference. Last, high-quality single photons and entangled photon pairs enable near-perfect interconnections between distant quantum modules37,38 that employ atomic qubits as local quantum processors, building up large-scale quantum architectures39 with low overall error rates.",
+            "section_image": []
+        },
+        {
+            "section_name": "Methods",
+            "section_text": "To prepare the atomic sample, 87Rb atoms are loaded from the background vapor into a magneto-optical trap (MOT) for 330\u2009ms. Then, the atomic density is increased during the next 50\u2009ms by compressing the MOT with a magnetic field gradient of 50\u2009G\u00a0cm\u22121. Polarization gradient cooling further lowers the atomic temperature to about 10\u2009\u03bcK and the atoms are loaded into a 1012-nm wavelength optical dipole trap. The dipole trap is formed by focusing a linearly polarized laser field, with a transverse waist of 10\u2009\u03bcm and a vertical waist of 50\u2009\u03bcm, respectively. In the next 50\u2009ms the untrapped atoms leave the experimental region through free-fall, and a bias magnetic field of 8\u00a0G is applied to define the quantization axis perpendicular to the propagation direction of 1012\u2009nm dipole trap. To initialize the atoms in the ground state \\(\\vert {{{{{{{{{\\rm{g}}}}}}}}}} \\rangle=\\vert 5{{{{{{{{{{\\rm{S}}}}}}}}}}}_{1/2},F=2,{m}_{{{{{{{{{{\\rm{F}}}}}}}}}}}=2 \\rangle\\), a \u03c3+-polarized optical pumping field is used to drive the \\(|5{{{{{{{{{{\\rm{S}}}}}}}}}}}_{1/2},F=2 \\rangle \\leftrightarrow|5{{{{{{{{{{\\rm{P}}}}}}}}}}}_{1/2},F=2 \\rangle\\) transition, and a repumper light resonant with \\(|5{{{{{{{{{{\\rm{S}}}}}}}}}}}_{1/2},F=1 \\rangle \\leftrightarrow|5{{{{{{{{{{\\rm{P}}}}}}}}}}}_{3/2},F=2 \\rangle\\) depletes the atoms from the hyperfine level \\(|5{{{{{{{{{{\\rm{S}}}}}}}}}}}_{1/2},F=1 \\rangle\\). The atoms are efficiently prepared in the ground state \\(\\vert {{{{{{{{{\\rm{g}}}}}}}}}} \\rangle\\) within 230\u2009\u03bcs and the atomic sample has an optical depth of ~5 for the laser field resonant with \\(\\vert {{{{{{{{{\\rm{g}}}}}}}}}} \\rangle \\leftrightarrow|{{{{{{{{{\\rm{e}}}}}}}}}} \\rangle\\) transition.\n\nTo generate single photons, the 2.5-\u03bcs-long experimental protocol is repeated 50,000 times after every atomic sample preparation. In each experimental cycle, two-photon Rydberg excitation is performed using a \u03c3+-polarized 780-nm laser field and a \u03c3\u2212-polarized 479-nm laser field through the intermediate state \\(\\vert {{{{{{{{{\\rm{e}}}}}}}}}} \\rangle=\\vert 5{{{{{{{{{{\\rm{P}}}}}}}}}}}_{3/2},F=3,{m}_{{{{{{{{{{\\rm{F}}}}}}}}}}}=3 \\rangle\\) with a detuning of \u0394/2\u03c0\u2009=\u2009\u2212200\u2009MHz. The 780 and 479\u2009nm excitation lasers off-resonantly couple \\(\\vert {{{{{{{{{\\rm{g}}}}}}}}}} \\rangle \\leftrightarrow|{{{{{{{{{\\rm{e}}}}}}}}}} \\rangle\\) and \\(\\vert {{{{{{{{{\\rm{e}}}}}}}}}} \\rangle \\leftrightarrow|{{{{{{{{{\\rm{r}}}}}}}}}} \\rangle=\\vert 90{{{{{{{{{{\\rm{S}}}}}}}}}}}_{1/2},J=1/2,{m}_{{{{{{{{{{\\rm{J}}}}}}}}}}}=1/2 \\rangle\\) transitions, respectively. Ideally, Rydberg states with higher principal quantum number n feature stronger interactions and better multi-excitation suppression. However, detrimental effects such as long-lived Rydberg contaminants, ambient electric fields induced level shifts, and density-dependent dephasing also worsen with higher n. To balance the pros and cons, Rydberg state with n\u2009=\u200990 is employed here for the generation of high-quality single photons. The 780-nm laser field is generated from an external cavity diode laser and the 479-nm laser field is produced by a second-harmonic generator that is seeded by power-amplified 959-nm laser light. The 780 and 959\u2009nm lasers are frequency-locked to an ultra-low expansion cavity with a finesse of 20,000 and the linewidths of both lasers are below 10\u2009kHz. The Rabi frequencies of the 780 and 479\u2009nm excitation fields are \\({{{\\Omega }}}_{780}^{{{{{{{{{{\\rm{e}}}}}}}}}}}/2\\pi \\,\\approx\\, 6.4{{{{{{{{{\\rm{MHz}}}}}}}}}}\\) and \\({{{\\Omega }}}_{479}^{{{{{{{{{{\\rm{e}}}}}}}}}}}/2\\pi \\,\\approx\\, 4.2{{{{{{{{{\\rm{MHz}}}}}}}}}}\\), respectively. A 350-ns-long collective \u03c0 pulse with 780 and 479\u2009nm excitation lasers promotes the atoms from the ground state \\(|{{{{{{{{{\\rm{G}}}}}}}}}} \\rangle\\) into the collective single excitation state \\(|{{{{{{{{{\\rm{R}}}}}}}}}} \\rangle\\). After a storage period of 300\u2009ns, a 479-nm readout laser field (\\({{{\\Omega }}}_{479}^{{{{{{{{{{\\rm{r}}}}}}}}}}}\\)) resonant with the \\(|{{{{{{{{{\\rm{r}}}}}}}}}} \\rangle \\leftrightarrow|{{{{{{{{{\\rm{e}}}}}}}}}} \\rangle\\) transition is turned on, and converts the state \\(|{{{{{{{{{\\rm{R}}}}}}}}}} \\rangle\\) into a single-photon field. As a result of collective emission, the generated single photons have the same spatial mode as the 780-nm excitation laser and can be conveniently coupled into a single-mode fiber. A gating acousto-optic modulator is used before the fiber to protect the SPCMs from the strong 780\u2009nm excitation laser pulse.",
+            "section_image": []
+        },
+        {
+            "section_name": "Data availability",
+            "section_text": "Data supporting the plots within this paper are available through Zenodo at https://doi.org/10.5281/zenodo.6552691. Further information is available from the corresponding author upon reasonable request.",
+            "section_image": []
+        },
+        {
+            "section_name": "Code availability",
+            "section_text": "The code used in this study is available from the corresponding authors upon reasonable request.",
+            "section_image": []
+        },
+        {
+            "section_name": "References",
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+        },
+        {
+            "section_name": "Acknowledgements",
+            "section_text": "The authors thank Chao-Yang Lu, Timothy Ralph, Kang Tan, Yiqiu Ma, and Yijia Zhou for valuable discussions. This work was supported by the National Key Research and Development Program of China under Grants No. 2021YFA1402003, the National Natural Science Foundation of China (Grant No. U21A6006, No. 12004127, No. 12005067, and No. 12104173), and the Fundamental Research Funds for the Central Universities, HUST (Grant No. 5003012068).",
+            "section_image": []
+        },
+        {
+            "section_name": "Author information",
+            "section_text": "These authors contributed equally: Shuai Shi, Biao Xu, Kuan Zhang, Gen-Sheng Ye.\n\nMOE Key Laboratory of Fundamental Physical Quantities Measurement, Hubei Key Laboratory of Gravitation and Quantum Physics, PGMF, Institute for Quantum Science and Engineering, School of Physics, Huazhong University of Science and Technology, Wuhan, 430074, China\n\nShuai Shi,\u00a0Biao Xu,\u00a0Kuan Zhang,\u00a0Gen-Sheng Ye,\u00a0De-Sheng Xiang,\u00a0Yubao Liu,\u00a0Jingzhi Wang,\u00a0Daiqin Su\u00a0&\u00a0Lin Li\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nS.S. and L.L. conceived the idea. S.S., B.X., Y.L., and J.W. built the experimental setup. S.S., B.X., G.-S.Y., D.-S.X., and K.Z. performed the experiment and data analysis. K.Z. and D.S. accomplished theoretical calculation and error estimation. L.L. supervised the experiment. The manuscript was written through contributions from all authors.\n\nCorrespondence to\n                Daiqin Su or Lin Li.",
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+            "section_text": "Shi, S., Xu, B., Zhang, K. et al. High-fidelity photonic quantum logic gate based on near-optimal Rydberg single-photon source.\n                    Nat Commun 13, 4454 (2022). https://doi.org/10.1038/s41467-022-32083-9\n\nDownload citation\n\nReceived: 25 March 2022\n\nAccepted: 13 July 2022\n\nPublished: 01 August 2022\n\nVersion of record: 01 August 2022\n\nDOI: https://doi.org/10.1038/s41467-022-32083-9\n\nAnyone you share the following link with will be able to read this content:\n\nSorry, a shareable link is not currently available for this article.\n\n\n\n\n                            Provided by the Springer Nature SharedIt content-sharing initiative\n                        ",
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+            "section_name": "This article is cited by",
+            "section_text": "Communications Materials (2025)\n\nCommunications Physics (2024)\n\nNature Communications (2024)\n\nLight: Science & Applications (2024)\n\nNature Photonics (2023)",
+            "section_image": []
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