Significance
Temperature affects the catalytic rates of all enzymes. However, the impact of temperature on an enzyme's catalytic activity is a complex function of protein sequence, structure, and dynamics. Therefore, the molecular features of enzymes that tune catalytic rates at different temperatures remain poorly understood. Herein we use simulations and mutagenesis experiments to reveal the temperature-tuning mechanism of mesophilic and thermophilic homologs of the C domain of bacterial enzyme l. We find that enzymes can be tuned to their physiological temperatures through a network of temperature-sensitive residue contacts localized in the disordered loops. Furthermore, we find that some exhibit linear and others nonlinear temperature dependence among temperature-sensitive contacts. These clues offer a promising physics-based approach for tuning enzyme activity.
Keywords: enzyme catalysis, thermal adaptation, molecular dynamics, mutagenesis, allostery
Abstract
Homologous enzymes with identical folds often exhibit different thermal and kinetic behaviors. Understanding how an enzyme sequence encodes catalytic activity at functionally optimal temperatures is a fundamental problem in biophysics. Recently it was shown that the residues that tune catalytic activities of thermophilic/mesophilic variants of the C-terminal domain of bacterial enzyme I (EIC) are largely localized within disordered loops, offering a model system with which to investigate this phenomenon. In this work, we use molecular dynamics simulations and mutagenesis experiments to reveal a mechanism of sequence-dependent activity tuning of EIC homologs. We find that a network of contacts in the catalytic loops is particularly sensitive to changes in temperature, with some contacts exhibiting distinct linear or nonlinear temperature-dependent trends. Moreover, these trends define structurally clustered dynamical modes and can distinguish regions that tend toward order or disorder at higher temperatures. Assaying several thermophilic EIC mutants, we show that complementary mesophilic mutations to the most temperature-sensitive positions exhibit the most enhanced activity, while mutations to relatively temperature insensitive positions exhibit the least enhanced activities. These results provide a mechanistic explanation of sequence-dependent temperature tuning and offer a computational method for rational enzyme modification.
Enzymes are sophisticated catalytic machines, designed by billions of years of natural selection for optimal activity at their physiological temperatures (1–3). To fold rapidly and function reliably, enzyme sequences have evolved to minimize strong energetic frustration, a demand met by forming rigid scaffolds (4, 5). However, studies of energy landscapes of proteins have shown that some degree of frustration is necessary for functional dynamics (6). Enzyme active sites in particular have been found to be highly frustrated regardless of oligomeric state, topology, or catalytic mechanism (7, 8). Thus, enzymes are shaped to meet conflicting needs for stable folding and functional dynamics, which manifests in having both rigid scaffolds and disordered regions. The fact that homologous enzymes can share an identical fold but exhibit drastically different rates of conformational exchange (9–11) suggests an important role for disordered regions in tuning temperature-dependent dynamics. Identifying this temperature tuning mechanism is an important step in learning the key design principles of thermostable enzymes.
A homologous mesophilic–thermophilic enzyme pair is an ideal system for investigating this activity tuning mechanism. To this end, we used the well-characterized enzyme I C-terminal domain (EIC) (Fig. 1).
Fig. 1.
EIC hybrid construction from wild type homologs. Center: EIC structure with 18 of the natural substitutions highlighted as red spheres and names of loops shown next to each loop region. Upper Left: eEIC, a mesophilic homolog of EIC. Upper Right: tEIC, a thermophilic homolog of EIC. Bottom Left: etEIC, a hybrid formed with a thermophilic scaffold and mesophilic loops. Bottom Right: teEIC, a hybrid formed with a mesophilic scaffold and thermophilic loops.
Here we used the mesophilic EIC from Escherichia coli (eEIC) with a physiological temperature of 37 °C (for the natural, full-length enzyme), its structurally identical thermophilic counterpart from Thermoanaerobacter tengcongensis (tEIC) with a physiological temperature of 65 °C (full length), and two hybrids composed of each wild types’ scaffold and disordered catalytic loops swapped with one another (Fig. 1). That is, teEIC contains the thermophile’s loops on the mesophile’s scaffold, and etEIC contains the mesophile’s loops on the thermophile’s scaffold (12). There are 21 residue substitutions that distinguish the mesophilic and thermophilic loops; importantly, all of the catalytic residues are conserved and there are no deletions or insertions (SI Appendix, Fig. S2).
The C-terminal dimer catalyzes a phosphoryl transfer reaction from phosphoenolpyruvate (PEP) to water, a reaction that is dependent on the disordered loops assuming a compact conformation (13). The loops can also assume a catalytically incompetent expanded conformation that involves a large magnitude motion of the α3β3 loop away from the active site. The differences in activity between the wild types can largely be explained by the populations of the expanded or compact conformation determined as a function of the distance between K340 (on the α3β3 loop) and PEP (12).
Previous work demonstrated that the catalytic loops of etEIC exhibit the same expanded to compact conformational exchange rate as the wild type mesophile at 37 °C, indicating that this hybrid’s loop dynamics are encoded by the mutations exclusively within the loops (12). This implies that, in the presence of a stable scaffold, catalytically relevant dynamics can be tuned with a local subset of mutations. This is consistent with other studies demonstrating the amenability of thermophilic enzymes to modification (14). In addition to shared dynamics, etEIC and eEIC have similar catalytic rates (12, 15), implying that these dynamics underlie catalysis.
With the loop dynamics isolated, we can easily detect the effects of individual mutations on activity. We hypothesize that the most temperature-sensitive interresidue contacts serve to tune the enzyme’s activity to its physiological temperature. To test our hypothesis we sampled catalytic loop conformational ensembles across a wide range of temperatures for each EIC homolog by using Hamiltonian replica exchange molecular dynamics (HREMD) simulations. We then calculated the contact frequencies of all loop residue pairs at each temperature and applied principal component analysis (PCA) to extract the most temperature-sensitive contacts via their loading scores. Finally, we used these most sensitive contact pairs as a guide to design mutant tEIC enzymes based on the natural substitutions in eEIC. Many of these mutants returned activities corresponding well with their PCA-based temperature sensitivity rankings, particularly those involving the most temperature-sensitive positions. These results strongly support our hypothesis and the utility of our analysis method, which we expect to be a valuable research tool for enzyme design.
Results
Identifying the Temperature-Sensitive Contacts in Enzyme Loops.
In order to identify the contacts in the tEIC catalytic loop conformational ensemble that are most sensitive to temperature changes, we simulated the enzyme across 20 effective temperatures ranging from 310 to 510 K. Sampling is done by HREMD, a sampling scheme also known as replica exchange with solute scaling (16). The objective of HREMD simulations is to enhance conformational sampling by reducing the strength of the nonbonded interactions involving protein atoms. While the entire system is not heated, the effect of Hamiltonian perturbation is similar and has been shown to reproduce melting curves and folding temperatures with high accuracy (17). From the sampled molecular dynamics trajectories we calculated all loop residue contacts, with cutoff distances specific to the chemical groups involved (18). Contact records collected from equilibrium sampling at different temperatures are converted to a contact frequency dataset, which describes the percentage of the simulation in which a given residue pair is in contact. The contact frequency datasets have (NT, NP) shape, where NT (number of rows) corresponds to temperatures sampled and NP (number of columns) corresponds to contacting residue pairs. An example dataset is available in SI Appendix, Fig. S1. To reduce the dimensionality of the dataset and to rank the temperature sensitivity of specific residue interactions, we used PCA.
Classifying Temperature Dependence of Contacts.
Here we used PCA on the contact frequency dataset to identify and rank the residue–residue interactions that are most sensitive to temperature variation. PCA is a linear dimensionality reduction technique that takes in a dataset with N features and returns a set of N orthogonal principal components (PCs) which encode variance of the dataset ranked by the corresponding eigenvalues. Eigenvalues of principal components (PCs) in the present context quantify the degree of temperature-dependent variance of various collective residue contact making and breaking modes (Fig. 2 A and B). The contact pairs’ loading scores (components of eigenvector) describe the contribution of the initial variables (contact frequencies) to a PC’s explained variance (Fig. 2C). In other words, loading scores provide a natural ranking system for a contact’s temperature sensitivity in terms of the dominant trend described by a given PC.
Fig. 2.
(A) tEIC contact frequency explained variance by PC. (B) PC projection versus effective loop temperature. (C) Histograms of PC loading scores with bars indicating the cutoff for the 98th percentile of loading score absolute values. (D) Contact frequency versus temperature for a selection of highly temperature-sensitive contacts from PC1–PC4. (E) Left: All the averaged contacts depicted on one subunit before PCA categorization and ranking. Right: The most temperature-sensitive contacts distilled from the left image.
Our hypothesis predicts that contacts with very high sensitivity to temperature have the most influence on activity. Here we identified a highly temperature-sensitive contact as occurring in the 98th percentile of the normalized loading score distributions. These include the top seven highest ranking contacts on each PC (SI Appendix, Fig. S3), falling entirely within the tail end of the loading score histogram (Fig. 2C). Because our previous work demonstrated that the loop dynamics of tEIC are essentially uninfluenced by scaffold interactions (etEIC kex/kcat), we directed our mutation experiments and focused our simulation analysis on tEIC. While the homologs differ in their individual contact behavior, we noted that they displayed similar PC trends, indicating that tEIC data are representative of the general behavior of the loops regardless of sequence composition (SI Appendix, Fig. S4 and S5).
For tEIC, PC1 describes nearly 85% of the variance and captures a linear change in contact frequencies with temperatures (Fig. 2 A and B). This represents the dominant effect of heating, increasing configurational entropy via progressive contact breaking toward denaturation. The next PCs identify the less obvious effects of heating. Since their eigenvalues decay exponentially, we focused on the first four PCs, which accounted for over 98% of variance, and disregarded the remaining PCs. The first four PC projections are shown in Fig. 2B, and the plots of a selection of highly temperature-sensitive contacts’ frequencies versus temperature from each PC (which reflect the trends shown in Fig. 2B) are shown in Fig. 2D.
PC2 describes less than 10% of the variance in the data; however, it captures an important trend of increasing contact frequencies (Fig. 2 B and D), becoming progressively more stable across a wide range of temperatures. PC3 captures a sharply increasing contact frequency within the physiological temperature range before rapidly decaying at higher temperatures. For tEIC this decay begins around its optimal physiological temperature. PC4’s trend is similar to that of PC3 (Fig. 2B), but its high-ranking contacts include more naturally substituted residues than those of PC3 and was therefore more informative for our experimental purposes (Mutation Experiments section). The remaining PC trends are less obvious and begin to resemble noise after the fourth PC.
By applying PCA and loading score filtering to the contact frequency dataset, we reduced the initially intractable web of contacts to only the contacts with the strongest response to changes in temperature (Fig. 2E).
Mapping Temperature-Sensitive Contact Networks.
A global view of the disordered loop contacts and their PC-ranked temperature sensitivities can be visualized with contact maps (Fig. 3). On PC1 the highly temperature-sensitive contacts form an obvious cluster on the α6β6 loop, which is also apparent when viewed on the structure (Fig. 3). These high-ranked PC1 contacts have a strong tendency to decrease across the full temperature and frequency range.
Fig. 3.
Contact maps showing normalized loading scores (temperature sensitivity) according to the colorbar (Right). Corresponding structures are shown with the top seven most temperature-sensitive contacts for the given PC. Solid lines indicate contacts that tend to increase in frequency in the physiological temperature range. Dashed lines indicate contacts that tend to decrease in frequency in the same range. Grey shade indicates inter-subunit contacts. The tick marks on the axes of the contact maps indicate residues and are colored as follows: yellow, α2β2; green, α3β3, blue, α6β6; magenta, a naturally substituted position.
PC2 is the first PC to capture a number of strongly associating contacts with nonlinear profiles. On PC2, the highest ranking contact involves M351. This natural substitution is in the middle of nine conserved residues on the α3β3 loop, particularly isolated relative to other substitutions, and directly involved in the structurally and functionally vital dimer interface (19). A glutamate in the mesophile, this residue also represents the largest change in hydrophobicity among the loop substitutions. The top sensitive contacts on PC3 and PC4 are entirely devoid of residues in the α6β6 loop and share similar regions of the structure and display similar contact frequency trends. PC4’s contacts, however, are shifted more toward the α2β2 loop, indicating that it better defines this region than PC3.
The loading score values decay differently on different PCs, resulting in some contacts with comparatively low loading scores being considered as highly temperature sensitive (Fig. 4B). For instance, considering the top seven contacts on each PC results in a high loading score cutoff of 0.8 for PC4 but a much lower value of 0.6 for PC3. The loading score contact maps offer additional insight as to which contacts are most important within each PC. Additionally, some contacts can score highly on multiple PCs, as shown in the score plots (SI Appendix, Fig. S6 “F354-N352” of PC3 and PC4, for instance), making some only marginally better defined by one PC than the other. Nevertheless, having identified the temperature-sensitive contacts within the disordered loops of tEIC, we sought experimental evidence to tell us whether or not they have physical significance.
Fig. 4.
(A) Assay results for tEIC mutations colored according to the PC in which they have the highest loading score contact (red, PC1; blue, PC2; green, PC3; purple, PC4). Bars indicate the loading score value cutoff for the 98th percentile for the corresponding PC. (B) Mutant activity versus temperature sensitivity rank on their highest tEIC loading scoring contact PC. Dotted line indicates that the loading score for 468 and 471 comes from the same contact. (C) Contacts involving residues from the mutant assays colored according to the PC on which their highest loading score occurs (lowest activity enhancing mutations on 346 and 347 contacts not shown).
Mutation Experiments.
The EIC homologs provide a known set of function-conserving mutations between the mesophile and the thermophile. If the residues that occur in highly temperature-sensitive contacts are among the natural substitutions, it suggests that these positions have been selected based on their simultaneous tuning of loop dynamics and preservation of catalytic conformational space.
To investigate this, we made point mutations to several of tEIC’s naturally substituted positions with the complementary residues of eEIC. We assayed these mutants for activity by measuring the rate of PEP hydrolysis at 40 °C (a temperature at which tEIC is nearly inactive) and compared their initial rates with etEIC, which provides the hypothetical maximum rate achievable from a subset of complementary mesophilic mutations to tEIC (12). In our model, the hydrolysis rate of PEP indicates how effectively the mutation has enhanced the disordered loop dynamics underlying catalysis. For the natural substitutions that do not appear in the most temperature-sensitive contacts (the top 98th percentile of loading scores on the first four PCs), we expected their complementary point mutation to yield the least enhanced activities.
The assay results ultimately revealed a noteworthy correspondence between several of tEIC’s mutant activities and highest contact temperature sensitivity rankings (Fig. 4B).
Remarkably, the mutations that returned the highest activities are indeed participants in the highest ranked substituted contacts and thus the most temperature-sensitive. The Pearson correlation of the activities and temperature sensitivities of all the assayed mutants is 0.632.
The top PC1 guided mutants (V470I, K471S, E468D) resulted in mixed activity enhancement (Fig. 4A), with the most enhancing mutation from the PC1 rankings being E468D, guided by the top-ranked substituted contact (second overall) involving residue K471.
M351, involved in the highest-ranked temperature-sensitive tEIC contact on PC2, when mutated, resulted in the highest activity enhancement among all of our mutants. Its contact with the conserved K349 exhibits a strong increasing frequency trend, remaining stable well above physiologically relevant temperatures. While having a large impact on activity, very little thermal stability was sacrificed by this mutation or indeed any of our point mutations relative to the destabilization etEIC exhibits from the full complement of mutations (SI Appendix, Fig. S7).
The third highest mutant activity was returned by Y301F, whose contact with the conserved Y344 ranks second and first on PC3 and PC4, respectively.
The F295T mutant returned the fourth highest activity, with its contact to the conserved F299 ranking fourth on PC2 and in the top six of PC4.
The fifth most active mutant, L334M, ranks third on PC4 with its contact to the conserved I336. The only naturally substituted residue outranking it on this PC was Y301. Residues occurring to the left of their respective cutoff line in Fig. 4B were mutated and assayed to compare their rank–activity relationship with the highly temperature-sensitive contact residues. A table of each PC’s top seven temperature-sensitive contacts indicating which residues are naturally substituted is available in SI Appendix, Fig. S8.
Depicting the experimentally mutated residue’s highest ranking contacts such that they are colored according to the PC on which they have the highest loading scores results in a clear structural clustering (Fig. 4C)of the different modes defined by the PCs. In terms of naturally substituted residues, the loops are characterized largely by separate PC modes. Visualizing the contacts according this same color scheme for all of the top contacts (regardless of whether they involve substituted residues) on PC1–PC4 reveals that PC3, with primarily conserved residue contacts, best describes the interaction at the interface of the two subunits’ α3β3 loops (SI Appendix, Fig. S9).
Discussion
Energy landscape theories of proteins have shown that frustration and disorder are evolutionarily conserved features that are necessary for function (7, 8). The nature of interactions that balance the competing needs for having ordered catalytic sites and dynamical disorder, however, is poorly understood. Here we have used molecular dynamics simulations and in vitro assay experiments on EIC to reveal the mechanism underlying activity tuning in mesophilic (eEIC) and thermophilic enzyme homologs (tEIC).
We find that at functionally optimal temperature for a tEIC, critical residue contacts are not accessible in disordered loop motions. As temperature increases, certain contacts break (e.g., PC1), allowing other critical contacts to form (e.g., PC2). Eventually a temperature is reached where the optimal interactions are occurring to cycle the enzyme through catalytically relevant conformations at a rate tuned to the functional needs of the organism. This enhancement can involve a critical contact whose altered dynamics promote relevant conformational sampling. By mutating a specific residue involved in the critical contact, the enzyme can sample the catalytic conformations at a lower temperature.
Furthermore, we present a computational method for ranking temperature-sensitive contacts and identifying residues critical for temperature-sensitive behavior of enzymes. We find highly temperature-sensitive contacts displaying linear and nonlinear temperature-dependent frequency trends. These trends define structurally clustered dynamical modes and can distinguish contacts that tend toward order or disorder at higher temperatures. Assaying several thermophilic EIC mutants, we show that complementary mesophilic mutations to the most temperature-sensitive positions, identified by their high loading scores, exhibit the most enhanced activity, while mutations to relatively temperature insensitive positions exhibit the least enhanced activities.
In contrast to loading scores, we find that a larger eigenvalue is not more predictive of activity enhancing mutations (Fig. 2B), as exemplified by assay results of M351E (PC2) and T301F (PC4) (Fig. 4B). This is because eigenvalues are a measure of collective contact dynamics. Thus PC1 captures the collective melting trend that is the best representation of the entire protein’s response to elevated temperatures, while lower eigenvalue modes describe subtler trends perhaps more specific to catalytic function.
Beyond the activity tuning application outlined here, a number of applications for temperature-sensitive contact analysis are possible. We speculate that regions involving temperature-sensitive contacts might serve as drug targets. Since these residues lie at the center of a dynamical mode and are important for activity, it follows that their activity could be inhibited by disruption of their dynamics with the binding of small molecules. The contact analysis presented here could also be extended to identify pH-sensitive contacts by way of variable protonation state simulation schemes or analysis of multiple independent simulations involving different residue tautomers. Finally, we envision temperature-sensitive contact analysis providing insights into mechanisms of systems such as ion channels, biomolecular condensates, and functionally relevant dynamics of biomolecular assemblies in general.
Materials and Methods
Simulation Protocol.
Crystal structure for tEIC was obtained from Protein Data Bank entry 2BG5 (tEIC). Molecular dynamics simulations were carried out in GROMACS 2018.8 using the leapfrog integration method with 2fs timesteps (20–23). Short-range electrostatic and Lennard-Jones interactions were calculated with a plain coulomb cutoff of 1.2 nm. The particle mesh Ewald electrostatics scheme was used for long-range electrostatics with a grid spacing of 0.16 nm (24). Bonds to hydrogen were constrained via the LINCS algorithm (25). The system was solvated in a dodecahedral simulation box with TIP3P water molecules and neutralized with 100 mM NaCl. The solvent and solute were separately coupled to a modified Berendsen thermostat (Velocity Rescale) with a reference temperature of 310 K. Simulations included PEP to simulate the dynamics relevant to catalysis. The system was described according to the CHARMM 36 force field with the PEP ligand molecule parameters provided by CGenFF (26–28). The system was energy minimized with the steepest descent minimization and equilibrated in the NVT and NPT ensembles for 100 ps.
Hamiltonian Replica Exchange Molecular Dynamics Simulations.
To efficiently sample the temperature-dependent conformational ensembles of enzyme I disordered loops, we used HREMD (29–31), specifically the replica exchange with solute scaling solute tempering scheme. The choice of the Hamiltonian method was motivated by the size of the system, which makes application of temperature replica exchange computationally costly. Residues 291–309, 332–360, and 454–477 within the active site loops of the constructs were selected for Hamiltonian perturbation, which includes 18 of the 21 substituted positions in the hybrid enzyme (the remaining three being on short linkers not enhanced with the Hamiltonian treatment). Residues within these loops were identified as central to catalysis in previous work via nuclear magnetic resonance (NMR) and structure visualization (12). A total of 20 replicas with an effective temperature range of 310–510 K was chosen because it gave an exchange rate around 25%. Hamiltonian replica exchange simulations were performed with GROMACS 2018.8 patched with Plumed 2.5.5 on Xsede’s Comet and Expanse HPC systems (32–34). Exchanges were attempted every 800 timesteps. Trajectory snapshots were extracted every 10 ps. Simulations were run for 200 ns, which generated an effective 400 ns sampling by combining contact data from the two subunits. A wall potential restricting the PEP molecule to within 6.5 Å of cysteine 502, a residue centered beneath the binding site, was used to prevent unbinding of PEP in the high-temperature replicas and ensure enhanced sampling of the relevant motions associated with the bound substrate. A weak 50 kJ/mol dihedral restraint was also applied to the CCOP dihedral angle of PEP to bias the hypothetically catalytically competent PEP conformation.
Contact Analysis.
We calculated the interatomic contacts and contact frequencies of the loop residues with GetContacts package (35). Contacts between directly adjacent residues were discarded as well as contacts whose frequencies did not exceed 5% across the 20 replicas. The frequencies for both subunits were averaged, and contacts not occurring in both subunits were also discarded. This left ∼300 contacts for analysis. All subsequent calculations were performed on the averaged values. The PCA loading scores were normalized according to absolute value/maximum absolute value on the PC. The 98th percentile of these scores was calculated to determine which contacts to consider highly temperature-sensitive. Molecular visualizations were produced with PyMOL.
Mutations.
Point mutations were performed according to the Agilent Quikchange II protocol.
Enzyme Expression.
Plasmids for etEIC and tEIC constructs with His and EIN solubility tags were transformed into BL21 cells and cultured on Luria–Bertani (LB) media overnight. All culture media contained 100 µg/mL ampicillin. Single colonies were grown in 20 mL of LB media overnight at 37 °C and used to inoculate 1 L LB cultures. These were grown to an optical density at 600 nm of 0.6 before cooling to 20 °C and adding 0.238 g of isopropylthio-β-galactoside for overnight expression. Cultures were spun at 4,000 × g for 30 min and resultant pellets frozen at −80 °C.
Enzyme Purification.
Pellets were thawed on ice and cells lysed and homogenized at (1,200 psi) via Avestin EmulsiFlex in 20 mL of buffer containing 50 mM Tris pH 8, 300 mM NaCl, and 5 mM imidazole. Lysate was centrifuged at 37,000 × g for 60 min, followed by filtration through a 10 kDa membrane and loaded on to a Bio-Rad Nuvia Ni-charged column. Protein was eluted with a 500 mM imidazole buffer applied as a gradient. Eluted protein was buffer-exchanged with the original buffer and incubated with TEV protease to remove the solubility tag. Samples were filtered and again passed through the Ni column, where the solubility tag was retained and the eluted enzyme collected. The fractions were buffer exchanged with 20 mM Tris pH 8, 1 mM ethylenediaminetetraacetic acid, and 2 mM dithiothreitol before being applied to a Bio-Rad Enrich Q column and eluted with a 1 M NaCL buffer gradient. The purified product was buffer exchanged with water and stored at −80 °C.
Activity Assays.
(A280/uvVis) values were used with molar extinction coefficients obtained from (Expasy ProtParam) sequence analysis to determine protein concentrations. Enzymes were diluted to a concentration of 50 μM in an NMR buffer containing 3 mM PEP and 1 mM TSP (Trimethylsilylpropanoic acid). Reactions at 40 °C were monitored by the decrease in PEP (vinyl hydrogen?) peak intensity at 5 min intervals on a 700 MHz Bruker NMR over the course of 2 1/2 h. PEP concentration was normalized against TSP peak intensity. Enzyme concentrations from the experimental samples were normalized against the etEIC experimental sample concentration determined by sodium dodecyl sulfate–polyacrylamide gel electrophoresis band intensities in ImageJ (36). The average concentration (band intensities) from the two etEIC replicates was divided by the mutant’s band intensity to produce a normalization coefficient for each corresponding rate.
Supplementary Material
Acknowledgments
This work was supported by funds from the National Institute of General Medical Sciences with grant no. R35GM133488 (to V.V.) and grant no. R35 GM138243 (to D.P.).
Footnotes
The authors declare no competing interest.
This article is a PNAS Direct Submission. D.W. is a guest editor invited by the Editorial Board.
This article contains supporting information online at https://www.pnas.org/lookup/suppl/doi:10.1073/pnas.2210537119/-/DCSupplemental.
Data, Materials, and Software Availability
Scripts used for analyzing molecular dynamics trajectories and for creating all the figures reported in this study have been deposited in GitHub (https://github.com/PotoyanGroup/Temp-sens-contacts). All other study data are included in the article and/or supporting information.
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Associated Data
This section collects any data citations, data availability statements, or supplementary materials included in this article.
Supplementary Materials
Data Availability Statement
Scripts used for analyzing molecular dynamics trajectories and for creating all the figures reported in this study have been deposited in GitHub (https://github.com/PotoyanGroup/Temp-sens-contacts). All other study data are included in the article and/or supporting information.




