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Methods. We present the analysis of a 50 ks exposure taken with the XMM -Newton observatory. It provides medium as well as high-resolution spectroscopy. |
Results. Our high-resolution spectroscopy analysis reveals a very soft spectrum with multiple temperature components (1–6 MK) and an X-ray flux slightly below the ‘canonical’ value ( [MATH] ). The X-ray lines appear surprisingly narrow and unshifted, reminiscent of those of [MATH] Cru and [MATH] Sco. Their relative int... |
Key Words.: X-rays: stars – stars: individual: [MATH] Car– stars: early-type Introduction [MATH] Car (=HD 93030) is a luminous star of type B0.2V belonging to the open cluster IC 2602, situated at 152 pc (Robichon et al., 1999 . The cluster is 30 Myr old, and the massive, hot [MATH] Car therefore appears to be a rare e... |
Because of its peculiar properties, the spectrum of [MATH] Car was investigated several times, notably to search for the presence of a magnetic field (Borra & Landstreet, 1979 ; Hubrig et al., 2008 . The results are rather inconclusive, but an intriguing period of about 9 minutes was detected in the most recent spectro... |
We decided to further study the star in the high-energy domain. As it was detected by Einstein and Rosat, [MATH] Car is known as the brightest X-ray source of IC 2602, but only approximate X-ray properties have up to now been derived. The current generation of X-ray facilities (Chandra, XMM -Newton ) provides a detaile... |
The paper is organized as follows: the data and reduction processes are presented in Sect. 2, the general properties of [MATH] Car in the X-ray domain are examined in Sect. 3.1, the detailed characteristics of the X-ray lines are derived in Sect. 3.2, and we finally conclude in Sect. 4. |
X-ray Observations On 2002 Aug. 13 (Rev. 0490, PI R.Pallavicini), the IC 2602 cluster was observed with XMM -Newton for a total exposure time of 50 ks. We retrieved this dataset from the XMM -Newton public archives, in order to perform a thorough analysis of the high-energy emission of [MATH] Car. We processed these ar... |
For this observation, the three European Photon Imaging Cameras (EPICs) were operated in the standard, full-frame mode and a thick filter was used to reject optical light. After application of the pipeline chains (tasks emproc, epproc ), the EPIC data were filtered as recommended by the SAS team: for the EPIC MOS (Meta... |
In this observation, [MATH] Car appears near the center of the field-of-view (FOV) and some information could therefore be recorded with the Reflection Grating Spectrograph (RGS). However, since [MATH] Car was not exactly at the center of the FOV, the standard processing could not be used: the pipeline chain (task rgsp... |
High-energy properties of [MATH] Car 3.1 General characteristics [MATH] Car appears as the brightest X-ray source in the field of IC 2602. The SAS detection algorithm (task edetect_chain ) indicates that the count rates in the 0.4–10 keV energy band amount to 0.255 [MATH] 0.003 cts s -1 for MOS1 and to 0.258 [MATH] 0.0... |
Two types of spectra are available: the EPIC low-resolution ones and the RGS high-resolution ones (Fig. ). Both datasets show that the majority of the flux is clearly confined to 0.1–2 keV, confirming the softness of the source. |
The thermal nature of the source is further revealed by the presence of lines, without any significant continuum, in the RGS spectra. These lines are triplets from He-like ions (Ne ix , N vi , and O vii ), Lyman lines from H-like ions (Ne , N vii , and O viii ) and features associated with ionized iron. Their emissivit... |
[MATH] 18.97Å and N vii Ly [MATH] [MATH] 24.78Å, [MATH] 700 km s -1 for N vii Ly [MATH] [MATH] 20.91Å, i.e. the observed line width is mainly instrumental and does not reflect the intrinsic line width (see also results of the fits below). |
The EPIC MOS spectra present two broad maxima, at about 0.45 keV and 0.8 keV. While one might then expect the presence of two dominant temperatures, these two peaks actually correspond to the two main groups of lines as revealed by RGS data (strong N lines at long wavelengths for the lower-energy peak and numerous ONeF... |
Unfortunately, the [MATH] model can not reproduce well the exact rest wavelengths of the X-ray lines, as is obvious from a comparison with the high-resolution data, and we must therefore rely on the more recent and more precise [MATH] model. Since no DEM model of the [MATH] -type is available in xspec , we tried to fit... |
Diplas & Savage 1994 ) since the free- [MATH] fits do not suggest any significant additional, circumstellar absorption. For RGS data, both 1T and 2T yield acceptable residuals. In addition to varying the usual [MATH] parameters, two trials were attempted. First, varying the redshift parameter in order to reproduce a gl... |
The parameters of the best-fit models are listed in Table . To interpret these results, some facts must be kept in mind: (1) the RGS data are the most sensitive to abundance variations since the lines are resolved for these spectra whereas the line blends observed in EPIC may yield unrealistic values in some cases (see... |
The unabsorbed flux (i.e. the flux corrected for the interstellar absorption) measured on the RGS+MOS model amounts to 3.8 [MATH] erg cm -2 -1 in the 0.1–10 keV energy band or 1.6 [MATH] erg cm -2 -1 in the 0.5–10 keV energy band, resulting in luminosities of 1.1 [MATH] erg s -1 and 4.4 [MATH] erg s -1 , respectively, ... |
[MATH] Car was observed by both Einstein and ROSAT. It appears in the 2E catalog (Harris et al., 1994 with an IPC count rate of 0.089 [MATH] 0.006 cts s -1 and in the RASS bright source catalog (Voges et al., 1999 with a PSPC count rate of 0.42 [MATH] 0.04 cts s -1 . For ROSAT, Cassinelli et al. ( 1994 further reported... |
3.2 Analysis of the X-ray lines Since there are a few strong, isolated lines recorded on the RGS spectra, we decided to fit these individually using gaussians (including a constant for the pseudo-continuum) within xspec and midas . The results of these fits can be found in Table . First, we focused on single lines of t... |
The relative strengths of the fir lines depend on the plasma temperature, the plasma density, and the stellar radiation field. More precisely, the line is weakened and the line strenghtened when the density or the radiation field are high; for hot stars such as [MATH] Car, the latter has a much stronger impact than the... |
In contrast with the colliding-wind systems where [MATH] (Pollock et al., 2005 , the forbidden lines of [MATH] Car remain undetected in all three triplets (Fig. ). Therefore, only an upper limit can be derived on the f/i ratios: the one-sided 90% confidence interval is 0–0.06 for N vi , 0–0.17 for O vii 0–0.15 for Ne i... |
Turning to the (f+i)/r ratio, the values are 1.19 [MATH] for N vi , 1.34 [MATH] for O vii and 0.66 [MATH] for Ne ix , where indices and exponents give the lower and upper limits of the 90% confidence interval. These values are close to one, suggesting the plasma to be collision-dominated (Porquet et al., 2001 . Compari... |
Another independent temperature estimate relies on the ratio of He-like to H-like line fluxes. The lines fluxes were first dereddenned before estimating this ratio. For nitrogen, it amounts to 1.41 [MATH] 0.14 if one considers the Lyman [MATH] line or 12.6 [MATH] 3.6 for Lyman [MATH] . Interpolating linearly the Spex d... |
Finally, the observed line fluxes in units ph cm -2 -1 were dereddenned and converted to erg cm -2 -1 , in order to derive the emission measures (EM=4 [MATH] ) at a distance of 152pc. The emissivities [MATH] were found in the Spex database, and were summed if several components (like the fir lines) exist. Table present... |
Conclusions XMM -Newton observations revealed the atypical character of [MATH] Car. Overall, its X-ray emission appears very soft as well as rather weak. Almost all the flux is found below 1 keV; indeed, spectral fits indicate a dominant temperature of about 0.2 keV. The total unabsorbed luminosity in the 0.1–10 keV ra... |
The high-resolution spectrum of [MATH] Car, revealed by the RGS, does not show any significant continuum emission but is solely composed of lines of H- and He-like ions of N, O, and Ne as well as some iron lines. To the resolution limits of the RGS, these lines appear narrow and unshifted: the observed width of these l... |
With its soft X-ray spectrum and its narrow X-ray lines, [MATH] Car clearly appears different from O-type stars. Comparing [MATH] Car to other B-type objects with high-resolution spectra, we find that the temperature distribution is quite typical of ‘normal’ B stars: the DEM is similar to that of [MATH] Ori and only sl... |
Acknowledgements. We acknowledge support from the Fonds National de la Recherche Scientifique (Belgium) and the PRODEX XMM and Integral contracts. We thank S. Hubrig for giving us the opportunity to read her paper before acceptance, and T. Morel for useful discussions. |
# Source: arxiv 0809.0527 # Title: A quantitative comparison of sRNA-based and protein-based gene regulation # Sections: all # Downloaded: 2026-03-03T05:14:12.963683+00:00 |
A quantitative comparison of sRNA-based and protein-based gene regulation Subject categories: Metabolic and regulatory networks; Signal Transduction; RNA |
Keywords: genetic networks / small RNA / signal processing / biophysics Character count: 47450 Abstract Small, non-coding RNAs (sRNAs) play important roles as genetic regulators in prokaryotes. sRNAs act post-transcriptionally via complementary pairing with target mRNAs to regulate protein expression. We use a quantita... |
Introduction It is now clear that small non-coding RNAs (sRNAs) play a crucial role in prokaryotic gene regulation as both positive and negative regulators. sRNAs are involved in many biological functions including quorum sensing (Lenz et al , 2004; Fuqua et al , 2001), stress response and virulence factor regulation (... |
Whereas transcription factor (TF)-based regulation is ubiquitous in prokaryotic gene circuits (Ptashne and Gann, 2001), thus far sRNAs have largely been found in circuits responding to strong environmental cues (e.g. extreme nutrient limitation). This leads to a natural question: are transcriptional regulation by TFs a... |
To address this question, we report a quantitative comparison of the signaling properties of TF-based and sRNA-based gene regulation. In general, a signaling system can be characterized by how it processes different types of inputs. We therefore treat TF-based and sRNA-based regulation as signal-processing systems with... |
Results In the main text, we focus on the case where sRNAs negatively regulate a target mRNA. Positive regulation by sRNAs is discussed in the Supplementary Information (SI). Post-transcriptional regulation via sRNAs is modeled using mass-action equations with three molecular species: the number of sRNA molecules [MATH... |
[EQUATION] The terms can be interpreted as follows. sRNAs (mRNAs) are transcribed at a rate [MATH] [MATH] ), and are degraded at a rate [MATH] [MATH] ). Additionally, sRNAs and mRNAs are both stoichiometrically degraded by pairing via Hfq at a rate that depends on the sRNA-mRNA interaction strength [MATH] . Proteins ar... |
[MATH] and are degraded at a rate [MATH] The Langevin terms, [MATH] , model intrinsic noise by treating the birth and death processes of the various species in Eq. ( ) as independent Poisson processes (van Kampen, 1981). |
[MATH] [MATH] , and [MATH] model the noise in the creation and degradation of individual sRNAs, mRNAs, and the regulated protein, respectively. [MATH] models sRNA-mRNA mutual-degradation noise. The Langevin terms are characterized within the linear-noise approximation by two-point time-correlation functions ( [MATH] ) ... |
[EQUATION] with [MATH] [MATH] [MATH] , and [MATH] where [MATH] [MATH] and [MATH] denote the mean number of sRNA, mRNA, and protein molecules, respectively. Notice we have separated the noise due to RNA production and degradation, [MATH] and [MATH] , from the noise due to the binary reaction between mRNAs and sRNAs, [MA... |
Recent evidence suggests that prokaryotic transcription may occur with RNA molecules being made in short intense bursts (Golding et al , 2005). The effects of transcriptional bursting can be incorporated into our model by allowing two states of gene activation, as reviewed below (for a detailed discussion see Paulsson,... |
[EQUATION] with [MATH] being the mean transcription rate of the relevant RNA when the gene is always on. We model the dynamics of a repressor-controlled gene using the equation |
[EQUATION] where [MATH] and [MATH] are the unbinding and binding rates of the repressor and [MATH] is a Langevin noise term. At steady state, it follows from the fluctuation-dissipation theorem that [MATH] with |
[MATH] (Bialek and Setayeshgar, 2005). Thus, a full model that includes transcriptional bursting is described by Eq. in conjunction with Eqs. ( ) and ( ). |
For completeness, we also briefly review the equations describing transcriptional regulation (Elowitz et al , 2002; Thattai and van Oudenaarden, 2001; Paulsson, 2004; Swain et al , 2002). The kinetics of transcription regulation is modeled using the Langevin equations |
[EQUATION] with [MATH] the number of mRNA molecules, [MATH] the number of proteins, [MATH] the average rate of transcription, [MATH] the average rate of translation, and [MATH] and |
[MATH] the first-order degradation rates of mRNA molecules and proteins, respectively. The two Langevin terms, [MATH] and [MATH] , model noise in the synthesis and degradation of the mRNA and protein, respectively, (see SI) and obey the equations ( [MATH] |
[EQUATION] The effects of transcriptional bursting can also be included in this model using Eqs. ( ) and ( ). Mean steady-state protein number |
The mean steady-state protein number for regulation via sRNAs can be approximated by ignoring the Langevin terms and setting the time-derivatives to zero in Eq. |
(see Supporting information (SI) and Paulsson, 2004, Levine et al , 2007) The mean as calculated within this mean-field approximation may differ from the actual mean especially where noise is large. Nonetheless, the qualitative steady-state behavior of the mean can be understood within this approximation. |
As shown in (Levine et al , 2007) and (Elf et al , 2005), the mean protein number exhibits a threshold-linear behavior as a function of the mRNA transcription rate [MATH] , with the threshold at [MATH] |
(see Fig. ). This behavior should be contrasted with transcriptional regulation via TFs for which the mean protein number is a linear function of [MATH] (Elowitz et al , 2002; Thattai and van Oudenaarden, 2001; Paulsson, 2004; Swain et al , 2002). For sRNA-based regulation, the mean steady-state protein number depends ... |
[MATH] , and a crossover regime [MATH] . Increasing the sRNA-mRNA interaction strength [MATH] results in a sharper crossover between the repressed and expressing regimes. The dashed line in Fig. depicts the [MATH] |
threshold-linear behavior. In the repressed regime, on average, there are many more sRNAs transcribed than mRNAs. Consequently, almost all free mRNAs are quickly bound by sRNAs and degraded. This results in low levels of expression of the regulated protein. By contrast, in the expressing regime the average number of mR... |
Signal transduction To compare the signal-transduction properties of sRNA-based regulation with TF-based regulation, we consider the two regulation schemes as signal-processing systems. Figure depicts how sRNA-based regulation, e.g. in quorum sensing, can be viewed as a signal-processing system (see also SI and Fig. ).... |
The fidelity of a signaling system is ultimately limited by the output noise of the system. The output noise, defined as the ratio of the variance in the output-protein number to the square of the mean output-protein number, can be thought of as the square of the “percentage error” in the output. The higher the output ... |
Gene regulation takes place as part of a larger genetic and biomolecular network whose purpose is to convert a measured signal into a concentration of the regulated protein. A simple but important observation is that sRNA-based regulation also requires protein regulators in order to couple to external signals. In parti... |
Intrinsic noise Gene regulation is intrinsically noisy. In this paper, we define intrinsic noise as the fluctuations in the output-protein number, given a fixed steady-state input, due to the stochastic nature of the underlying biochemical reactions. When calculating intinsic noise we neglect the contributions to outpu... |
We start by summarizing the noise properties of transcriptional regulation. For ordinary transcriptional regulation by a repressor, the intrinsic noise – defined as the variance in protein number divided by the mean protein number squared, [MATH] , is given by (Elowitz et al , 2002; Thattai and van Oudenaarden, 2001; P... |
[EQUATION] where [MATH] is the protein burst size (the average number of proteins made from an mRNA molecule) and [MATH] is the mean protein level in the absence of repressor. The first term in Eq. ( ) captures the noise due to translational bursting (the protein burst from each mRNA due to the translation of multiple ... |
The intrinsic noise of an sRNA-regulated protein differs significantly from that of a transcriptionally regulated protein. Noise in stoichiometrically coupled systems such as sRNA-based gene regulation has been studied previously (Elf and Ehrenberg, 2003; Elf et al , 2003; Paulsson and Ehrenberg, 2001). It was found by... |
The full expressions for the intrinsic noise are lengthy and in the main text we present only our major findings. Figs. and show typical intrinsic noise profiles as functions of the transcription-rate ratio, [MATH] , and of the average protein level of the regulated protein, for various magnitudes of transcriptional bu... |
(see Fig. ) as expected for a stoichiometric system. We have also obtained simplified, asymptotic expressions for the noise in the repressing and expressing regimes when [MATH] , and there is no transcriptional bursting (see SI). The expressions for the intrinsic noise in the repressing and expressing regimes are given... |
[EQUATION] (where [MATH] and [MATH] is the new “effective” protein burst size (see SI and (Levine et al , 2007)), and [EQUATION] |
We have written these expressions so that the contribution of sRNA-mRNA mutual-degradation noise is contained entirely in the second term of Eqs.( ) and( ). |
Comparing the intrinsic noise of protein- and sRNA- based regulators in Fig. , we observe that sRNA regulators are significantly less noisy than TFs in the repressed regime. The dominant source of intrinsic noise for a TF-regulated protein, in the limit [MATH] , is that proteins are made in bursts of average size [MATH... |
The fidelity of a signaling system can be characterized by the output noise [MATH] . In general, high-fidelity signaling requires [MATH] . Thus, from Fig. it is clear that over a large range of output protein levels the large intrinsic noise due to transcriptional bursting makes it difficult for sRNAs to perform high-f... |
One of the most striking features of Fig. is that sRNA-based regulation is much more sensitive to transcriptional bursting than is protein-based regulation. For sRNAs, transcriptional bursting greatly enhances the near-critical fluctuations because the production of RNAs in bursts increases the anti-correlated sRNA-mRN... |
The large intrinsic noise in the crossover regime, [MATH] can be understood by considering the special case [MATH] for very strong sRNA-mRNA binding, |
[MATH] . In this limit, sRNAs and mRNAs, transcribed at the same average rate, quickly bind to each other and degrade and almost no protein is made. However, once in a while there is a fluctuation that produces more mRNAs than average. In this case, unless there is a corresponding fluctuation in sRNAs, the mRNAs cannot... |
Gain and Filtering We now consider, in the absence of noise, the change in output-protein number about some steady state or “operating point” in response to a small, time-varying input signal. A small time-varying change from the steady-state value of the number of proteins controlling the sRNA transcription rate, |
[MATH] , results in a corresponding time-varying change of the output-protein number from its steady-state value, [MATH] . For small enough signals, the dynamics are captured by linearized versions of the mass-action equations (Eq. (see SI). In the frequency-domain, the relationship between the output protein response ... |
[EQUATION] where the frequency-dependent gain is given by [EQUATION] with [MATH] the characteristic time the sRNA gene is ”on” and [MATH] two times related to – and of the same order of magnitude as– the mRNA and sRNA lifetimes (see SI for exact definition of [MATH] ). Each term of the form [MATH] can be interpreted as... |
The underlying reason for the enhanced noise filtering properties of sRNAs is that sRNA-based regulation involves an additional step when compared to transcriptional regulation. Namely, the input signal from upstream components in the genetic network is transmitted to the mRNAs encoding the output protein via sRNAs, wh... |
The above results hold only when the input signal is coupled to the sRNAs. Small input signals can also modulate the transcription of the protein-coding mRNAs instead of the sRNAs. In this case, at high frequencies, the gain falls off as [MATH] as in TF-based regulation since the input signal does not pass through the ... |
Fidelity of small-signal response Intrinsic noise limits the ability of a signaling system to faithfully respond to small signals. Typically, the ability of a system to transduce small signals is quantified by its gain (amplification factor) (Detwiler et al , 2000; Elf et al , 2003; Elf and Ehrenberg, 2003). A large ga... |
As discussed above, the noise in the output protein limits the detection of small input signals. In order for an input signal to be detectable, the corresponding output signal must be greater than the output noise (Detwiler et al , 2000). In particular, the power of the output signal must be greater than the power of t... |
[EQUATION] On the other hand, the power of the output noise is calculated by integrating fluctuations over all frequencies, and is given within the linear-noise approximation by the expression |
[EQUATION] where [MATH] is just the fluctuation in the output-protein level at a frequency [MATH] due to intrinsic noise as calculated in the SI. For a signal to be detectable, we must have |
[EQUATION] For a step-input signal with amplitude [MATH] [MATH] in the above expressions), the requirement that the output signal is larger than the noise sets a lower-bound on the detectable input signal |
[MATH] (Detwiler et al , 2000). Of course, by time-averaging the output, one can reduce the output noise and hence detect smaller signals, but this does not affect our comparison. Therefore, we computed the minimum input signal without time-averaging for both sRNA-based and TF-based regulation and found that, for even ... |
Consequently, contrary to previous speculations (Levine et al , 2007), results indicate that sRNA-based regulation is unlikely to be useful for amplifying small signals despite the large gain of sRNA-based regulation in the crossover region. Our results also imply that it is more advantageous to use transcription facto... |
Large-signal response In nature, an organism may benefit from switching quickly between two different gene-expression states in response to a large persistent input signal. We have compared here the rates at which a regulated protein can switch between an “off” and “on” state in response to an input signal when its mRN... |
Fig. shows the time evolution of the average mRNA level for both sRNA-based and TF-based regulation in response to a step change in the input. The response for sRNA-based regulation depends on the initial conditions, and can be tuned by changing where in the repressed regime the system is initially. In particular, the ... |
We find that using sRNAs to switch protein expression on, i.e., going from low output-protein number to high output-protein number, is slower than direct TF regulation. This slower response is due to the sRNA pool that needs to be depleted before target mRNAs can accumulate. On the other hand, sRNA-based regulation can... |
Thus far we have considered the case where a protein is negatively regulated by sRNAs. However, a protein can also be positively regulated by sRNAs (see (Storz et al , 2004; Hammer and Bassler, 2007 and SI), and in this case switching protein expression on using sRNAs can be faster than TF-based regulation. Typically, ... |
Discussion Small non-coding RNAs (sRNAs) play an important regulatory role in prokaryotic gene circuits. sRNAs are involved in a variety of critical physiological tasks such as quorum sensing, stress response, and the regulation of outer-membrane proteins. Yet, sRNAs are not currently thought to be as common as transcr... |
Our analysis shows that for a large (intermediate to high) range of output-protein levels, the intrinsic noise for sRNA-based regulation is much larger than for TF-based regulation. However, even at a high level of transcriptional bursting, sRNA-based regulation is less noisy than TF-based regulation at low protein lev... |
Indeed, sRNAs are often found in genetic circuits that switch gene-expression states in response to strong environmental cues. For example under iron limitation, the sRNA RyhB rapidly shuts off synthesis of several iron-binding proteins, making iron available for essential proteins (Masse and Gottesman, 2002). In the q... |
We have considered the case where a single sRNA species regulates a single mRNA species. However, as in the Vibrio quorum-sensing circuit, multiple sRNAs may regulate multiple mRNAs (Lenz et al , 2004; Mitarai et al , 2007; Repoila et al , 2003). Even in such a case, mean steady-state protein numbers are expected to ex... |
There are additional considerations that may favor sRNA-based or TF-based regulation. For example, TFs are likely to be better global regulators than sRNAs – since sRNAs degrade mRNAs stochiometrically, only a limited number of genes can be regulated by a given sRNA. Also, the cost in space on the genome is generally l... |
In this paper, we have considered gene regulation by non-coding RNAs in prokaryotes. Regulatory RNAs are also found in eukaryotes. In eukaryotes, these regulatory RNAs are believed to act catalytically, not stoichiometrically. Nonetheless, our analysis suggests that, even in eukaryotes, regulatory RNAs are better at ke... |
Recently, it has been shown that noise in protein expression may exhibit a universal behavior (Bar-Even et al , 2006). However, our analysis for the intrinsic noise of an sRNA-regulated protein differs significantly from the proposed universal behavior in the presence of transcriptional bursting (see also (Tkacik et al... |
The analogy between biochemical circuits and signal-processing systems in engineering provides a general framework for characterizing the signal-transduction pathways found in biology (Detwiler et al , 2000). Different biological tasks place different requirements on signal-transduction circuits. For example, in chemot... |
Materials and Methods The analyses were carried out using rate-equation models extended to include stochastic fluctuations and our results were tested using Monte-Carlo (Gillespie) simulations. The equations account for the concentration of each component in the circuit, and for noise around the means of these componen... |
Acknowledgments We would like to thank Bonnie Bassler, Matthias Kaschube Anirvan Sengupta, Gasper Tkacik, Chris Waters and Kerwyn C. Huang for helpful discussions and suggestions on the manuscript. This work was partially supported by US National Institutes of Health (NIH) Grant PSO GM071508, the Defense Advanced Resea... |
# Source: arxiv 0809.2871 # Title: Dynamics of protein-protein encounter: a Langevin equation approach with reaction patches # Sections: all # Downloaded: 2026-03-03T05:14:03.598977+00:00 |
Dynamics of protein-protein encounter: a Langevin equation approach with reaction patches Abstract We study the formation of protein-protein encounter complexes with a Langevin equation approach that considers direct, steric and thermal forces. As three model systems with distinctly different properties we consider the... |
Introduction Protein-protein interactions play key roles in many cellular processes such as signal transduction, bioenergetics, and the immune response |
Helms ( 2008 . Moreover, many proteins function in the context of protein complexes of variable sizes and lifetimes. Examples of such complexes are ribosomes, polymerases, spliceosomes, nuclear pore complexes, cytoskeletal structures like the mitotic spindle or actin stress fibers, adhesion contacts, the anaphase-promo... |
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