A Gaussian-chain model for treating residual charge-charge interactions in the unfolded state of proteins

JAK3 Y841 Autophosphorylation Is Critical for STAT5B Activation, Kinase Domain Stability and Dimer Formation

Janus tyrosine kinase 3 (JAK3) is primarily expressed in immune cells and is needed for signaling by the common gamma chain (γc) family of cytokines. Abnormal JAK3 signal transduction can manifest as hematological disorders, e.g., leukemia, severe combined immunodeficiency (SCID) and autoimmune disease states. While regulatory JAK3 phosphosites have been well studied, here a functional proteomics approach coupling a JAK3 autokinase assay to mass spectrometry revealed ten previously unreported autophosphorylation sites (Y105, Y190, Y238, Y399, Y633, Y637, Y738, Y762, Y824, and Y841). Of interest, Y841 was determined to be evolutionarily conserved across multiple species and JAK family members, suggesting a broader role for this residue. Phospho-substitution mutants confirmed that Y841 is also required for STAT5 tyrosine phosphorylation. The homologous JAK1 residue Y894 elicited a similar response to mutagenesis, indicating the shared importance for this site in JAK family members. Phospho-specific Y841-JAK3 antibodies recognized activated kinase from various T-cell lines and transforming JAK3 mutants. Computational biophysics analysis linked Y841 phosphorylation to enhanced JAK3 JH1 domain stability across pH environments, as well as to facilitated complementary electrostatic JH1 dimer formation. Interestingly, Y841 is not limited to tyrosine kinases, suggesting it represents a conserved ubiquitous enzymatic function that may hold therapeutic potential across multiple kinase families.

Characterization and exploration of an artifact in the reducing capillary electrophoresis-sodium dodecyl sulfate analysis of the 'me-too' drug zuberitamab related to rituximab

For monoclonal antibody (mAb) drugs, the 'me-too' drug is a pharmacologically active compound that is structurally similar to the first-in-class drugs, acting on the same target and is used for the same therapeutic purposes, but it may differ in drug-drug interactions and adverse drug reactions. Capillary electrophoresis-sodium dodecyl sulfate (CE-SDS) has been widely used for quality evaluation of mAb drugs. The properties of the detected substances can interfere with the credibility and accuracy of the method. In the routine comparison analysis for both innovator rituximab and 'me-too' drug zuberitamab samples, an uncommon artifact related to the heavy chain (HC) of zuberitamab was observed in reducing CE-SDS and interfered with our identification of the purity of samples. In this work, the overall hydrophobicity of the HCs of rituximab, zuberitamab, and several other common mAbs was characterized and determined by reversed-phase high-performance liquid chromatography. Additionally, the local hydrophobicity and surface charge were compared using Expasy ProtScale and PyMOL software simulations. We concluded that noncovalent protein aggregation can be related to strong hydrophobicity and low electrostatic repulsion of local amino acid regions, which complicates drug quality control. These findings shed light on the relationship between protein aggregation and the local hydrophobicity region, and broaden the way to analyze the detection 'artifacts' in reducing CE-SDS studies of therapeutic proteins.

An efficient method to predict protein thermostability in alanine mutation

The relationship between protein sequence and its thermodynamic stability is a critical aspect of computational protein design. In this work, we present a new theoretical method to calculate the free energy change (ΔΔG) resulting from a single-point amino acid mutation to alanine in a protein sequence. The method is derived based on physical interactions and is very efficient in estimating the free energy changes caused by a series of alanine mutations from just a single molecular dynamics (MD) trajectory. Numerical calculations are carried out on a total of 547 alanine mutations in 19 diverse proteins whose experimental results are available. The comparison between the experimental ΔΔG_exp and the calculated values shows a generally good correlation with a correlation coefficient of 0.67. Both the advantages and limitations of this method are discussed. This method provides an efficient and valuable tool for protein design and engineering.

The pH Effects on SARS-CoV and SARS-CoV-2 Spike Proteins in the Process of Binding to hACE2

COVID-19 has been threatening human health since the late 2019, and has a significant impact on human health and economy. Understanding SARS-CoV-2 and other coronaviruses is important to develop effective treatments for COVID-19 and other coronavirus-caused diseases. In this work, we applied multi-scale computational approaches to study the electrostatic features of spike (S) proteins for SARS-CoV and SARS-CoV-2. From our results, we found that SARS-CoV and SARS-CoV-2 have similar charge distributions and electrostatic features when binding with the human angiotensin-converting enzyme 2 (hACE2). Energy pH-dependence calculations revealed that the complex structures of hACE2 and the S proteins of SARS-CoV/SARS-CoV-2 are stable at pH values ranging from 7.5 to 9. Three independent 100 ns molecular dynamics (MD) simulations were performed using NAMD to investigate the hydrogen bonds between S proteins RBD and hACE2 RBD. From MD simulations, we found that SARS-CoV-2 forms 19 pairs (average of three simulations) of hydrogen bonds with high occupancy (>50%) to hACE2, compared to 16 pairs between SARS-CoV and hACE2. Additionally, SARS-CoV viruses prefer sticking to the same hydrogen bond pairs, while SARS-CoV-2 tends to have a larger range of selections on hydrogen bonds acceptors. We also labelled key residues involved in forming the top five hydrogen bonds that were found in all three independent 100 ns simulations. This identification is important to potential drug designs for COVID-19 treatments. Our work will shed the light on current and future coronavirus-caused diseases.

Knowledge-Based Unfolded State Model for Protein Design

The design of proteins and miniproteins is an important challenge. Designed variants should be stable, meaning the folded/unfolded free energy difference should be large enough. Thus, the unfolded state plays a central role. An extended peptide model is often used, where side chains interact with solvent and nearby backbone, but not each other. The unfolded energy is then a function of sequence composition only and can be empirically parametrized. If the space of sequences is explored with a Monte Carlo procedure, protein variants will be sampled according to a well-defined Boltzmann probability distribution. We can then choose unfolded model parameters to maximize the probability of sampling native-like sequences. This leads to a well-defined maximum likelihood framework. We present an iterative algorithm that follows the likelihood gradient. The method is presented in the context of our Proteus software, as a detailed downloadable tutorial. The unfolded model is combined with a folded model that uses molecular mechanics and a Generalized Born solvent. It was optimized for three PDZ domains and then used to redesign them. The sequences sampled are native-like and similar to a recent PDZ design study that was experimentally validated.

The contribution of electrostatics to hydrogen exchange in the unfolded protein state

Although electrostatics have long been recognized to play an important role in hydrogen exchange (HX) with solvent, the quantitative assessment of its magnitude in the unfolded state has hitherto been lacking. This limits the utility of HX as a quantitative method to study protein stability, folding, and dynamics. Using the intrinsically disordered human protein α-synuclein as a proxy for the unfolded state, we show that a hybrid mean-field approach can effectively compute the electrostatic potential at all backbone amide positions along the chain. From the electrochemical potential, a fourfold reduction in hydroxide concentration near the protein backbone is predicted for the C-terminal domain, a prognosis that is in direct agreement with experimentally derived protection factors from NMR spectroscopy. Thus, impeded HX for the C-terminal region of α-synuclein is not the result of intramolecular hydrogen bonding and/or structure formation.

Modeling pKas of unfolded proteins to probe structural models of unfolded state

Modeling unfolded states of proteins has implications for protein folding and stability. Since in unfolded state proteins adopt multiple conformations, any experimentally measured quantity is ensemble averaged, therefore the computed quantity should be ensemble averaged as well. Here, we investigate the possibility that one can model an unfolded state ensemble with the coil model approach, algorithm such as “flexible-meccano” [Ozenne V et al., Flexible-meccano: A tool for the generation of explicit ensemle descriptions of intrinsically disordered proteins and their associated experimental observables, Bioinformatics 28:1463–1470, 2012], developed to generate structures for intrinsically disordered proteins. We probe such a possibility by using generated structures to calculate pKas of titratable groups and compare with experimental data. It is demonstrated that even with a small number of representative structures of unfolded state, the average calculated pKas are in very good agreement with experimentally measured pKas. Also, predictions are made for titratable groups for which there is no experimental data available. This suggests that the coil model approach is suitable for generating 3D structures of unfolded state of proteins. To make the approach suitable for large-scale modeling, which requires limited number of structures, we ranked the structures according to their solvent accessible surface area (SASA). It is shown that in the majority of cases, the top structures with smallest SASA are enough to represent unfolded state.

Side chain electrostatic interactions and pH-dependent expansion of the intrinsically disordered, highly acidic carboxyl-terminus of γ-tubulin

Intramolecular electrostatic attraction and repulsion strongly influence the conformational sampling of intrinsically disordered proteins and domains (IDPs). In order to better understand this complex relationship, we have used nuclear magnetic resonance to measure side chain pK_a values and pH-dependent translational diffusion coefficients for the unstructured and highly acidic carboxyl-terminus of γ-tubulin (γ-CT), providing insight into how the net charge of an IDP relates to overall expansion or collapse of the conformational ensemble. Many of the pK_a values in the γ-CT are shifted upward by 0.3-0.4 units and exhibit negatively cooperative ionization pH profiles, likely due to the large net negative charge that accumulates on the molecule as the pH is raised. pK_a shifts of this magnitude correspond to electrostatic interaction energies between the affected residues and the rest of the charged molecule that are each on the order of 1 kcal mol^-1 . Diffusion of the γ-CT slowed with increasing net charge, indicative of an expanding hydrodynamic radius (r_H ). The degree of expansion agreed quantitatively with what has been seen from comparisons of IDPs with different charge content, yielding the general trend that every 0.1 increase in relative charge (|Q|/res) produces a roughly 5% increase in r_H . While γ-CT pH titration data followed this trend nearly perfectly, there were substantially larger deviations for the database of different IDP sequences. This suggests that other aspects of an IDP's primary amino acid sequence beyond net charge influence the sensitivity of r_H to electrostatic interactions.

Sequence charge decoration dictates coil-globule transition in intrinsically disordered proteins

We present an analytical theory to compute conformations of heteropolymers-applicable to describe disordered proteins-as a function of temperature and charge sequence. The theory describes coil-globule transition for a given protein sequence when temperature is varied and has been benchmarked against the all-atom Monte Carlo simulation (using CAMPARI) of intrinsically disordered proteins (IDPs). In addition, the model quantitatively shows how subtle alterations of charge placement in the primary sequence-while maintaining the same charge composition-can lead to significant changes in conformation, even as drastic as a coil (swelled above a purely random coil) to globule (collapsed below a random coil) and vice versa. The theory provides insights on how to control (enhance or suppress) these changes by tuning the temperature (or solution condition) and charge decoration. As an application, we predict the distribution of conformations (at room temperature) of all naturally occurring IDPs in the DisProt database and notice significant size variation even among IDPs with a similar composition of positive and negative charges. Based on this, we provide a new diagram-of-states delineating the sequence-conformation relation for proteins in the DisProt database. Next, we study the effect of post-translational modification, e.g., phosphorylation, on IDP conformations. Modifications as little as two-site phosphorylation can significantly alter the size of an IDP with everything else being constant (temperature, salt concentration, etc.). However, not all possible modification sites have the same effect on protein conformations; there are certain "hot spots" that can cause maximal change in conformation. The location of these "hot spots" in the parent sequence can readily be identified by using a sequence charge decoration metric originally introduced by Sawle and Ghosh. The ability of our model to predict conformations (both expanded and collapsed states) of IDPs at a high-throughput level can provide valuable insights into the different mechanisms by which phosphorylation/charge mutation controls IDP function.

Modulating charge patterning and ionic strength as a strategy to induce conformational changes in intrinsically disordered proteins

We present an analytical theory to describe conformational changes as a function of salt for polymers with a given sequence of charges. We apply this model to describe Intrinsically Disordered Proteins (IDPs) by explicitly accounting for charged residues and their exact placement in the primary sequence while approximating the effect of non-electrostatic interactions at a mean-field level by effective short-range (two body and three-body) interaction parameters. The effect of ions is introduced by treating electrostatic interactions within Debye-Huckle approximation. Using typical values of the short-range mean-field parameters derived from all-atom Monte Carlo simulations (at zero salt), we predict the conformational changes as a function of salt concentration. We notice that conformational transitions in response to changes in ionic strength strongly depend on sequence specific charge patterning. For example, globule to coil transition can be observed upon increasing salt concentration, in stark contrast to uniformly charged polyelectrolyte theories based on net charge only. In addition, it is possible to observe non-monotonic behavior with salt as well. Drastic differences in salt-induced conformational transitions is also evident between two doubly phosphorylated sequences-derived from the same wild type sequence-that only differ in the site of phosphorylation. Similar effects are also predicted between two sequences derived from the same parent sequence differing by a single site mutation where a negative charge is replaced by a positive charge. These effects are purely a result of charge decoration and can only be understood in terms of metrics based on specific placement of charges, and cannot be explained by models based on charge composition alone. Identifying sequences and hot spots within sequences-for post translational modification or charge mutation-using our high-throughput theory will yield fundamental insights into design and biological regulation mediated by phosphorylation and/or local changes in salt concentration.

Conformational response to charge clustering in synthetic intrinsically disordered proteins

BACKGROUND

Recent theoretical and computational studies have shown that the charge content and, most importantly, the linear distribution of opposite charges are major determinants of conformational properties of intrinsically disordered proteins (IDPs). Charge segregation in a sequence can be measured through κ, which represents a normalized measure of charge asymmetry. A strong inverse correlation between κ and radius of gyration has been previously demonstrated for two independent sets of permutated IDP sequences.

METHODS

We used two well-characterized IDPs, namely measles virus N_TAIL and Hendra virus PNT4, sharing a very similar fraction of charged residues and net charge per residue, but differing in proline (Pro) content. For each protein, we have rationally designed a low- and a high-κ variant endowed with the highest and the lowest κ values compatible with their natural amino acid composition. Then, the conformational properties of wild-type and κ-variants have been assessed by biochemical and biophysical techniques.

RESULTS

We confirmed a direct correlation between κ and protein compaction. The analysis of our original data along with those available from the literature suggests that Pro content may affects the responsiveness to charge clustering.

CONCLUSIONS

Charge clustering promotes IDP compaction, but the extent of its effects depends on the sequence context. Proline residues seem to play a role contrasting compaction.

GENERAL SIGNIFICANCE

These results contribute to the identification of sequence determinants of IDP conformational properties. They may also serve as an asset for rational design of non-natural IDPs with tunable degree of compactness.

Electrostatic Interactions in Protein Structure, Folding, Binding, and Condensation

Charged and polar groups, through forming ion pairs, hydrogen bonds, and other less specific electrostatic interactions, impart important properties to proteins. Modulation of the charges on the amino acids, e.g., by pH and by phosphorylation and dephosphorylation, have significant effects such as protein denaturation and switch-like response of signal transduction networks. This review aims to present a unifying theme among the various effects of protein charges and polar groups. Simple models will be used to illustrate basic ideas about electrostatic interactions in proteins, and these ideas in turn will be used to elucidate the roles of electrostatic interactions in protein structure, folding, binding, condensation, and related biological functions. In particular, we will examine how charged side chains are spatially distributed in various types of proteins and how electrostatic interactions affect thermodynamic and kinetic properties of proteins. Our hope is to capture both important historical developments and recent experimental and theoretical advances in quantifying electrostatic contributions of proteins.

A pH-dependent computational approach to the effect of mutations on protein stability

This article describes a novel software implementation for high-throughput scanning mutagenesis with a focus on protein stability. The approach combines molecular mechanics calculations with calculations of protein ionization and a Gaussian-chain model of electrostatic interactions in unfolded state. Comprehensive testing demonstrates a state-of-the-art accuracy for predicted free energy differences on single, double, and triple mutations with a correlation coefficient R above 0.7, which takes about 1.5 min per mutation on a single CPU. Unlike most of existing in silico methods for fast mutagenesis, the stability changes are reported as a continuous function of solution pH for wide pH intervals. We also propose a novel in silico strategy for searching stabilized protein variants that is based on combinatorial scanning mutagenesis using representative amino acid types. Our in silico predictions are in excellent agreement with the hyper-stabilized variants of mesophilic cold shock protein found using the Proside method of direct evolution. © 2016 Wiley Periodicals, Inc.

Studying the role of cooperative hydration in stabilizing folded protein states

Understanding and modelling protein folding remains a key scientific and engineering challenge. Two key questions in protein folding are (1) why many proteins adopt a folded state and (2) how these proteins transition from the random coil ensemble to a folded state. In this paper we employ molecular dynamics simulations to address the first of these questions. Computational methods are well-placed to address this issue due to their ability to analyze systems at atomic-level resolution. Traditionally, the stability of folded proteins has been ascribed to the balance of two types of intermolecular interactions: hydrogen-bonding interactions and hydrophobic contacts. In this study, we explore a third type of intermolecular interaction: cooperative hydration of protein surface residues. To achieve this, we consider multiple independent simulations of the villin headpiece domain to quantify the contributions of different interactions to the energy of the native and fully extended states. In addition, we consider whether these findings are robust with respect to the protein forcefield, the water model, and the presence of salt. In all cases, we identify many cooperatively hydrated interactions that are transient but energetically favor the native state. Whilst further work on additional protein structures, forcefields, and water models is necessary, these results suggest a role for cooperative hydration in protein folding that should be explored further. Rational design of cooperative hydration on the protein surface could be a viable strategy for increasing protein stability.

Electrostatic effects on the folding stability of FKBP12

The roles of electrostatic interactions in protein folding stability have been a matter of debate, largely due to the complexity in the theoretical treatment of these interactions. We have developed computational methods for calculating electrostatic effects on protein folding stability. To rigorously test and further refine these methods, here we carried out experimental studies into electrostatic effects on the folding stability of the human 12-kD FK506 binding protein (FKBP12). This protein has a close homologue, FKBP12.6, with amino acid substitutions in only 18 of their 107 residues. Of the 18 substitutions, 8 involve charged residues. Upon mutating FKBP12 residues at these 8 positions individually into the counterparts in FKBP12.6, the unfolding free energy (ΔGu) of FKBP12 changed by -0.3 to 0.7 kcal/mol. Accumulating stabilizing substitutions resulted in a mutant with a 0.9 kcal/mol increase in stability. Additional charge mutations were grafted from a thermophilic homologue, MtFKBP17, which aligns to FKBP12 with 31% sequence identity over 89 positions. Eleven such charge mutations were studied, with ΔΔGu varying from -2.9 to 0.1 kcal/mol. The predicted electrostatic effects by our computational methods with refinements herein had a root-mean-square deviation of 0.9 kcal/mol from the experimental ΔΔGu values on 16 single mutations of FKBP12. The difference in ΔΔGu between mutations grafted from FKBP12.6 and those from MtFKBP17 suggests that more distant homologues are less able to provide guidance for enhancing folding stability.

Evaluation of Genetically Encoded Chemical Tags as Orthogonal Fluorophore Labeling Tools for Single-Molecule FRET Applications

Fluorescence resonance energy transfer (FRET) is a superb technique for measuring conformational changes of proteins on the single molecule level (smFRET) in real time. It requires introducing a donor and acceptor fluorophore pair at specific locations on the protein molecule of interest, which has often been a challenging task. By using two different self-labeling chemical tags, such as Halo-, TMP-, SNAP- and CLIP-tags, orthogonal labeling may be achieved rapidly and reliably. However, these comparatively large tags add extra distance and flexibility between the desired labeling location on the protein and the fluorophore position, which may affect the results. To systematically characterize chemical tags for smFRET measurement applications, we took the SNAP-tag/CLIP-tag combination as a model system and fused a flexible unstructured peptide, rigid polyproline peptides of various lengths, and the calcium sensor protein calmodulin between the tags. We could reliably identify length variations as small as four residues in the polyproline peptide. In the calmodulin system, the added length introduced by these tags was even beneficial for revealing subtle conformational changes upon variation of the buffer conditions. This approach opens up new possibilities for studying conformational dynamics, especially in large protein systems that are difficult to specifically conjugate with fluorophores.

Rational modification of protein stability by targeting surface sites leads to complicated results

The rational modification of protein stability is an important goal of protein design. Protein surface electrostatic interactions are not evolutionarily optimized for stability and are an attractive target for the rational redesign of proteins. We show that surface charge mutants can exert stabilizing effects in distinct and unanticipated ways, including ones that are not predicted by existing methods, even when only solvent-exposed sites are targeted. Individual mutation of three solvent-exposed lysines in the villin headpiece subdomain significantly stabilizes the protein, but the mechanism of stabilization is very different in each case. One mutation destabilizes native-state electrostatic interactions but has a larger destabilizing effect on the denatured state, a second removes the desolvation penalty paid by the charged residue, whereas the third introduces unanticipated native-state interactions but does not alter electrostatics. Our results show that even seemingly intuitive mutations can exert their effects through unforeseen and complex interactions.

Backtracking due to residual structure in the unfolded state changes the folding of the third fibronectin type III domain from tenascin-C

Residual structure in the unfolded state of a protein may play a crucial role in folding and stability. In the present study, using an all (heavy)-atom structure based model and replica exchange molecular dynamics simulations, we explored the folding landscape of the third fibronectin type III domain from tenascin-C (TNfn3). Specifically, both the wild type (WT) and a variant with two additional amino acids, Gly-Leu (GL), at the C-terminus (WT(+GL)) were studied. We found that, although both domains of TNfn3 are topologically frustrated, the early formation of the native contacts from the C-terminal end of WT(+GL) causes more "backtracking" than in the WT. As a result, the WT exhibits a two-state folding behavior with a broad transition-state ensemble, whereas the WT(+GL) folds through a metastable intermediate state. Furthermore, our study confirmed that the core of both proteins is conformationally heterogeneous and noncompact, and folds late mainly due to backtracking of the part of the core. Finally, in agreement with the previous experimental studies, our results clearly demonstrated distinct thermodynamic behavior of the two proteins with WT(+GL) being more stable.

Predicting folding free energy changes upon single point mutations

MOTIVATION

The folding free energy is an important characteristic of proteins stability and is directly related to protein's wild-type function. The changes of protein's stability due to naturally occurring mutations, missense mutations, are typically causing diseases. Single point mutations made in vitro are frequently used to assess the contribution of given amino acid to the stability of the protein. In both cases, it is desirable to predict the change of the folding free energy upon single point mutations in order to either provide insights of the molecular mechanism of the change or to design new experimental studies.

RESULTS

We report an approach that predicts the free energy change upon single point mutation by utilizing the 3D structure of the wild-type protein. It is based on variation of the molecular mechanics Generalized Born (MMGB) method, scaled with optimized parameters (sMMGB) and utilizing specific model of unfolded state. The corresponding mutations are built in silico and the predictions are tested against large dataset of 1109 mutations with experimentally measured changes of the folding free energy. Benchmarking resulted in root mean square deviation = 1.78 kcal/mol and slope of the linear regression fit between the experimental data and the calculations was 1.04. The sMMGB is compared with other leading methods of predicting folding free energy changes upon single mutations and results discussed with respect to various parameters.

AVAILABILITY

All the pdb files we used in this article can be downloaded from http://compbio.clemson.edu/downloadDir/mentaldisorders/sMMGB_pdb.rar.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Kinetic consequences of native state optimization of surface-exposed electrostatic interactions in the Fyn SH3 domain

Optimization of surface exposed charge-charge interactions in the native state has emerged as an effective means to enhance protein stability; but the effect of electrostatic interactions on the kinetics of protein folding is not well understood. To investigate the kinetic consequences of surface charge optimization, we characterized the folding kinetics of a Fyn SH3 domain variant containing five amino acid substitutions that was computationally designed to optimize surface charge-charge interactions. Our results demonstrate that this optimized Fyn SH3 domain is stabilized primarily through an eight-fold acceleration in the folding rate. Analyses of the constituent single amino acid substitutions indicate that the effects of optimization of charge-charge interactions on folding rate are additive. This is in contrast to the trend seen in folded state stability, and suggests that electrostatic interactions are less specific in the transition state compared to the folded state. Simulations of the transition state using a coarse-grained chain model show that native electrostatic contacts are weakly formed, thereby making the transition state conducive to nonspecific, or even nonnative, electrostatic interactions. Because folding from the unfolded state to the folding transition state for small proteins is accompanied by an increase in charge density, nonspecific electrostatic interactions, that is, generic charge density effects can have a significant contribution to the kinetics of protein folding. Thus, the interpretation of the effects of amino acid substitutions at surface charged positions may be complicated and consideration of only native-state interactions may fail to provide an adequate picture.

A semi-analytical description of protein folding that incorporates detailed geometrical information

Much has been done to study the interplay between geometric and energetic effects on the protein folding energy landscape. Numerical techniques such as molecular dynamics simulations are able to maintain a precise geometrical representation of the protein. Analytical approaches, however, often focus on the energetic aspects of folding, including geometrical information only in an average way. Here, we investigate a semi-analytical expression of folding that explicitly includes geometrical effects. We consider a Hamiltonian corresponding to a Gaussian filament with structure-based interactions. The model captures local features of protein folding often averaged over by mean-field theories, for example, loop contact formation and excluded volume. We explore the thermodynamics and folding mechanisms of beta-hairpin and alpha-helical structures as functions of temperature and Q, the fraction of native contacts formed. Excluded volume is shown to be an important component of a protein Hamiltonian, since it both dominates the cooperativity of the folding transition and alters folding mechanisms. Understanding geometrical effects in analytical formulae will help illuminate the consequences of the approximations required for the study of larger proteins.

Gaussian fluctuations in tethered DNA chains

In a recent work [Gao et al., Appl. Phys. Lett. 134, 113902 (2007)], we reported a novel DNA separation method by tethering DNA chains to a solid surface and then stretching the DNA chains with an electric field. The anchor is such designed that the critical force to detach a DNA chain is independent of its length. Because the stretching force is proportional to the DNA net charge, a gradual increase of the electric field leads to size-based removal of the DNA strands from the surface and thus DNA separation. Originally proposed for separation of long double-stranded DNA chains (>10 000 bps), this method has been proven useful also for short single-stranded DNA fragments (<100 bases) for which the fluctuation force induced by the solvent becomes significant. Here we show that the fluctuation force can be approximately represented by a gaussian model for tethered DNA chains. Analytical expressions have been derived to account for the dependence of the fluctuation force on the surface confinement, the polymer chain length, and the DNA tethering potential. The theoretical predictions are found to coincide with experiment.

pK(a) values for the unfolded state under native conditions explain the pH-dependent stability of PGB1

Understanding the role of electrostatics in protein stability requires knowledge of these interactions in both the folded and unfolded states. Electrostatic interactions can be probed experimentally by characterizing ionization equilibria of titrating groups, parameterized as pK(a) values. However, pK(a) values of the unfolded state are rarely accessible under native conditions, where the unfolded state has a very low population. Here, we report pK(a) values under nondenaturing conditions for two unfolded fragments of the protein G B1 domain that mimic the unfolded state of the intact protein. pK(a) values were determined for carboxyl groups by monitoring their pH-dependent (13)C chemical shifts. Monte Carlo simulations using a Gaussian chain model provide corrections for changes in electrostatic interactions that arise from fragmentation of the protein. Most pK(a) values for the unfolded state agree well with model values, but some residues show significant perturbations that can be rationalized by local electrostatic interactions. The pH-dependent stability was calculated from the experimental pK(a) values of the folded and unfolded states and compared to experimental stability data. The use of experimental pK(a) values for the unfolded state results in significantly improved agreement with experimental data, as compared to calculations based on model data alone.

In silico modeling of pH-optimum of protein-protein binding

Protein-protein association is a pH-dependent process and thus the binding affinity depends on the local pH. In vivo the association occurs in a particular cellular compartment, where the individual monomers are supposed to meet and form a complex. Since the monomers and the complex exist in the same micro environment, it is plausible that they coevolved toward its properties, in particular, toward the characteristic subcellular pH. Here we show that the pH at which the monomers are most stable (pH-optimum) or the pH at which stability is almost pH-independent (pH-flat) of monomers are correlated with the pH-optimum of maximal affinity (pH-optimum of binding) or pH interval at which affinity is almost pH-independent (pH-flat of binding) of the complexes made of the corresponding monomers. The analysis of interfacial properties of protein complexes demonstrates that pH-dependent properties can be roughly estimated using the interface charge alone. In addition, we introduce a parameter beta, proportional to the square root of the absolute product of the net charges of monomers, and show that protein complexes characterized with small or very large beta tend to have neutral pH-optimum. Further more, protein complexes made of monomers carrying the same polarity net charge at neutral pH have either very low or very high pH-optimum of binding. These findings are used to propose empirical rule for predicting pH-optimum of binding provided that the amino acid compositions of the corresponding monomers are available.

Uncovering specific electrostatic interactions in the denatured states of proteins

The stability and folding of proteins are modulated by energetically significant interactions in the denatured state that is in equilibrium with the native state. These interactions remain largely invisible to current experimental techniques, however, due to the sparse population and conformational heterogeneity of the denatured-state ensemble under folding conditions. Molecular dynamics simulations using physics-based force fields can in principle offer atomistic details of the denatured state. However, practical applications are plagued with the lack of rigorous means to validate microscopic information and deficiencies in force fields and solvent models. This study presents a method based on coupled titration and molecular dynamics sampling of the denatured state starting from the extended sequence under native conditions. The resulting denatured-state pK(a)s allow for the prediction of experimental observables such as pH- and mutation-induced stability changes. I show the capability and use of the method by investigating the electrostatic interactions in the denatured states of wild-type and K12M mutant of NTL9 protein. This study shows that the major errors in electrostatics can be identified by validating the titration properties of the fragment peptides derived from the sequence of the intact protein. Consistent with experimental evidence, our simulations show a significantly depressed pK(a) for Asp(8) in the denatured state of wild-type, which is due to a nonnative interaction between Asp(8) and Lys(12). Interestingly, the simulation also shows a nonnative interaction between Asp(8) and Glu(48) in the denatured state of the mutant. I believe the presented method is general and can be applied to extract and validate microscopic electrostatics of the entire folding energy landscape.

From the Cover: Charge interactions can dominate the dimensions of intrinsically disordered proteins

Many eukaryotic proteins are disordered under physiological conditions, and fold into ordered structures only on binding to their cellular targets. Such intrinsically disordered proteins (IDPs) often contain a large fraction of charged amino acids. Here, we use single-molecule Förster resonance energy transfer to investigate the influence of charged residues on the dimensions of unfolded and intrinsically disordered proteins. We find that, in contrast to the compact unfolded conformations that have been observed for many proteins at low denaturant concentration, IDPs can exhibit a prominent expansion at low ionic strength that correlates with their net charge. Charge-balanced polypeptides, however, can exhibit an additional collapse at low ionic strength, as predicted by polyampholyte theory from the attraction between opposite charges in the chain. The pronounced effect of charges on the dimensions of unfolded proteins has important implications for the cellular functions of IDPs.

Computing protein stabilities from their chain lengths

New amino acid sequences of proteins are being learned at a rapid rate, thanks to modern genomics. The native structures and functions of those proteins can often be inferred using bioinformatics methods. We show here that it is also possible to infer the stabilities and thermal folding properties of proteins, given only simple genomics information: the chain length and the numbers of charged side chains. In particular, our model predicts DeltaH(T), DeltaS(T), DeltaC(p), and DeltaF(T)--the folding enthalpy, entropy, heat capacity, and free energy--as functions of temperature T; the denaturant m values in guanidine and urea; the pH-temperature-salt phase diagrams, and the energy of confinement F(s) of the protein inside a cavity of radius s. All combinations of these phase equilibria can also then be computed from that information. As one illustration, we compute the pH and salt conditions that would denature a protein inside a small confined cavity. Because the model is analytical, it is computationally efficient enough that it could be used to automatically annotate whole proteomes with protein stability information.

Protein stabilization by the rational design of surface charge-charge interactions

The design of proteins with increased stability has many important applications in biotechnology. In recent years, strategies involving directed evolution, sequence-based design, or computational design have proven successful for generating stabilized proteins. A brief overview of the various methods that have been used to increase protein stability is presented, followed by a detailed example of how the rational design of surface charge-charge interactions has provided a robust method for protein stabilization.

A computational approach for the rational design of stable proteins and enzymes: optimization of surface charge-charge interactions

The design of stable proteins and enzymes is not only of particular biotechnological importance, but also addresses some important fundamental questions. While there are a number of different options available for designing or engineering stable proteins, the field of computational design provides fast and universal methods for stabilizing proteins of interest. One of the successful computational design strategies focuses on stabilizing proteins through the optimization of charge-charge interactions on the protein surface. By optimizing surface interactions, it is possible to alleviate some of the challenges that accompany efforts to redesign the protein core. The rational design of surface charge-charge interactions also allows one to optimize only the interactions that are distant from binding sites or active sites, making it possible to increase stability without adversely affecting activity. The optimization of surface charge-charge interactions is discussed in detail along with the experimental evidence to demonstrate that this is a robust and universal approach to designing proteins with enhanced stability.

Defining the role of salt bridges in protein stability

Although the energetic balance of forces stabilizing proteins has been established qualitatively over the last decades, quantification of the energetic contribution of particular interactions still poses serious problems. The reasons are the strong cooperativity and the interdependence ofnoncovalent interactions. Salt bridges are a typical example. One expects that ionizable side chains frequently form ion pairs in innumerable crystal structures. Since electrostatic attraction between opposite charges is strong per se, salt bridges can intuitively be regarded as an important factor stabilizing the native structure. Is that really so? In this chapter we critically reassess the available methods to delineate the role ofelectrostatic interactions and salt bridges to protein stability, and discuss the progress and the obstacles in this endeavor. The basic problem is that formation of salt bridges depends on the ionization properties of the participating groups, which is significantly influenced by the protein environment. Furthermore, salt bridges experience thermal fluctuations, continuously break and re-form, and their lifespan in solution is governed by the flexibility of the protein. Finally, electrostatic interactions are long-range and might be significant in the unfolded state, thus seriously influencing the energetic profile. Elimination of salt bridges by protonation/deprotonation at extreme pH or by mutation provides only rough energetic estimates, since there is no way to account for the nonadditive response of the protein moiety. From what we know so far, the strength of electrostatic interactions is strongly context-dependent, yet it is unlikely that salt bridges are dominant factors governing protein stability. Nevertheless, proteins from thermophiles and hyperthermophiles exhibit more, and frequently networked, salt bridges than proteins from the mesophilic counterparts. Increasing the thermal (not the thermodynamic) stability of proteins by optimization of charge-charge interactions is a good example for an evolutionary solution utilizing physical factors.

Accurate Calculations of Binding, Folding, and Transfer Free Energies by a Scaled Generalized Born Method

The Poisson-Boltzmann (PB) equation is widely used for modeling solvation effects. The computational cost of PB has restricted its applications largely to single-conformation calculations. The generalized Born (GB) model provides an approximation at substantially reduced cost. Currently the best GB methods reproduce PB results for electrostatic solvation energies with errors at ~5 kcal/mol. When two proteins form a complex, the net electrostatic contributions to the binding free energy are typically of the order of 5 to 10 kcal/mol. Similarly, the net contributions of individual residues to protein folding free energy are < 5 kcal/mol. Clearly in these applications the accuracy of current GB methods is insufficient. Here we present a simple scaling scheme that allows our GB method, GBr⁶, to reproduce PB results for binding, folding, and transfer free energies with high accuracy. From an ensemble of conformations sampled from molecular dynamics simulations, five were judiciously selected for PB calculations. These PB results were used for scaling GBr⁶. Tests on the binding free energies of the barnase-barstar, GTPase-WASp, and U1A-U1hpII complexes and on the folding free energy of FKBP show that the effects of point mutations calculated by scaled GBr⁶ are accurate to within 0.3 kcal/mol of PB results. Similar accuracy was also achieved for the free energies of transfer for ribonuclease Sa and insulin from the crystalline phase to the solution phase at various pH's. This method makes it possible to thoroughly sample the transient-complex ensemble in predicting protein binding rate constants and to incorporate conformational sampling in electrostatic modeling (such as done in the MM-GBSA approach) without loss of accuracy.

Structure-based pKa calculations using continuum electrostatics methods

Electrostatic free energy is useful for correlating structure with function in proteins in which ionizable groups play essential functional roles. To this end, the pK(a) values of ionizable groups must be known and their molecular determinants must be understood. Structure-based calculations of electrostatic energies and pK(a) values are necessary for this purpose. This unit describes protocols for pK(a) calculations with continuum electrostatics methods based on the numerical solution of the linearized Poisson-Boltzmann equation by the method of finite differences. Critical discussion of key parameters, approximations, and shortcomings of these methods is included. Two protocols are described for calculations with methods modified empirically to maximize agreement between measured and calculated pK(a) values. Applied judiciously, these methods can contribute useful and novel insight into properties of surface ionizable groups in proteins.

Electrostatic contribution to the thermodynamic and kinetic stability of the homotrimeric coiled coil Lpp-56: A computational study

The protein moiety of the Braun's E. coli outer membrane lipoprotein (Lpp-56) is an attractive object of biophysical investigation in several aspects. It is a homotrimeric, parallel coiled coil, a class of coiled coils whose stability and folding have been studied only occasionally. Lpp-56 possesses unique structural properties and exhibits extremely low rates of folding and unfolding. It is natural to ask how the specificity of the structure determines the extraordinary physical chemical properties of this protein. Recently, a seemingly controversial data on the stability and unfolding rate of Lpp-56 have been published (Dragan et al., Biochemistry 2004;43: 14891-14900; Bjelic et al., Biochemistry 2006;45:8931-8939). The unfolding rate constant measured using GdmCl as the denaturing agent, though extremely low, was substantially higher than that obtained on the basis of thermal unfolding. If this large difference arises from the effect of screening of electrostatic interactions induced by GdmCl, electrostatic interactions would appear to be an important factor determining the unusual properties of Lpp-56. We present here a computational analysis of the electrostatic properties of Lpp-56 combining molecular dynamics simulations and continuum pK calculations. The pH-dependence of the unfolding free energy is predicted in good agreement with the experimental data: the change in DeltaG between pH 3 and pH 7 is approximately 60 kJ mol(-1). The results suggest that the difference in the stability of the protein observed using different experimental methods is mainly because of the effect of the reduction of electrostatic interactions when the salt (GdmCl) concentration increases. We also find that the occupancy of the interhelical salt bridges is unusually high. We hypothesize that electrostatic interactions, and the interhelical salt bridges in particular, are an important factor determining the low unfolding rate of Lpp-56.

Electrostatic effects in unfolded staphylococcal nuclease

Structure-based calculations of pKa values and electrostatic free energies of proteins assume that electrostatic effects in the unfolded state are negligible. In light of experimental evidence showing that this assumption is invalid for many proteins, and with increasing awareness that the unfolded state is more structured and compact than previously thought, a detailed examination of electrostatic effects in unfolded proteins is warranted. Here we address this issue with structure-based calculations of electrostatic interactions in unfolded staphylococcal nuclease. The approach involves the generation of ensembles of structures representing the unfolded state, and calculation of Coulomb energies to Boltzmann weight the unfolded state ensembles. Four different structural models of the unfolded state were tested. Experimental proton binding data measured with a variant of nuclease that is unfolded under native conditions were used to establish the validity of the calculations. These calculations suggest that weak Coulomb interactions are an unavoidable property of unfolded proteins. At neutral pH, the interactions are too weak to organize the unfolded state; however, at extreme pH values, where the protein has a significant net charge, the combined action of a large number of weak repulsive interactions can lead to the expansion of the unfolded state. The calculated pKa values of ionizable groups in the unfolded state are similar but not identical to the values in small peptides in water. These studies suggest that the accuracy of structure-based calculations of electrostatic contributions to stability cannot be improved unless electrostatic effects in the unfolded state are calculated explicitly.

Denaturant-induced expansion and compaction of a multi-domain protein: IgG

It is generally believed that unfolded or denatured proteins show random-coil statistics and hence their radius of gyration simply scales with solvent quality (or concentration of denaturant). Indeed, nearly all proteins studied thus far have been shown to undergo a gradual and continuous expansion with increasing concentration of denaturant. Here, we use fluorescence correlation spectroscopy (FCS) to show that while protein A, a multi-domain and predominantly helical protein, expands gradually and continuously with increasing concentration of guanidine hydrochloride (GdnHCl), the F(ab')2 fragment of goat anti-rabbit antibody IgG, a multi-subunit all beta-sheet protein does not show such continuous expansion behavior. Instead, it first expands and then contracts with increasing concentration of GdnHCl. Even more striking is the fact that the hydrodynamic radius of the most expanded F(ab')2 ensemble, observed at 3-4 M GdnHCl, is approximately 3.6 times that of the native protein. Further FCS measurements involving urea and NaCl show that the unusually expanded F(ab')2 conformations might be due to electrostatic repulsions. Taken together, these results suggest that specific interactions need to be considered while assessing the conformational and statistical properties of unfolded proteins, particularly under conditions of low solvent quality.

Electrostatic contributions to the stability of the GCN4 leucine zipper structure

Ion pairs are ubiquitous in X-ray structures of coiled coils, and mutagenesis of charged residues can result in large stability losses. By contrast, pK(a) values determined by NMR in solution often predict only small contributions to stability from charge interactions. To help reconcile these results we used triple-resonance NMR to determine pK(a) values for all groups that ionize between pH 1 and 13 in the 33 residue leucine zipper fragment, GCN4p. In addition to the native state we also determined comprehensive pK(a) values for two models of the GCN4p denatured state: the protein in 6 M urea, and unfolded peptide fragments of the protein in water. Only residues that form ion pairs in multiple X-ray structures of GCN4p gave large pK(a) differences between the native and denatured states. Moreover, electrostatic contributions to stability were not equivalent for oppositely charged partners in ion pairs, suggesting that the interactions between a charge and its environment are as important as those within the ion pair. The pH dependence of protein stability calculated from NMR-derived pK(a) values agreed with the stability profile measured from equilibrium urea-unfolding experiments as a function of pH. The stability profile was also reproduced with structure-based continuum electrostatic calculations, although contributions to stability were overestimated at the extremes of pH. We consider potential sources of errors in the calculations, and how pK(a) predictions could be improved. Our results show that although hydrophobic packing and hydrogen bonding have dominant roles, electrostatic interactions also make significant contributions to the stability of the coiled coil.

Role of the Charge–Charge Interactions in Defining Stability and Halophilicity of the CspB Proteins

Charge-charge interactions on the surface of native proteins are important for protein stability and can be computationally redesigned in a rational way to modulate protein stability. Such computational effort led to an engineered protein, CspB-TB that has the same core as the mesophilic cold shock protein CspB-Bs from Bacillus subtilis, but optimized distribution of charge-charge interactions on the surface. The CspB-TB protein shows an increase in the transition temperature by 20 degrees C relative to the unfolding temperature of CspB-Bs. The CspB-TB and CspB-Bs protein pair offers a unique opportunity to further explore the energetics of charge-charge interactions as the substitutions at the same sequence positions are done in largely similar structural but different electrostatic environments. In particular we addressed two questions. What is the contribution of charge-charge interactions in the unfolded state to the protein stability and how amino acid substitutions modulate the effect of increase in ionic strength on protein stability (i.e. protein halophilicity). To this end, we experimentally measured the stabilities of over 100 variants of CspB-TB and CspB-Bs proteins with substitutions at charged residues. We also performed computational modeling of these protein variants. Analysis of the experimental and computational data allowed us to conclude that the charge-charge interactions in the unfolded state of two model proteins CspB-Bs and CspB-TB are not very significant and computational models that are based only on the native state structure can adequately, i.e. qualitatively (stabilizing versus destabilizing) and semi-quantitatively (relative rank order), predict the effects of surface charge neutralization or reversal on protein stability. We also show that the effect of ionic strength on protein stability (protein halophilicity) appears to be mainly due to the screening of the long-range charge-charge interactions.

pK(a) values for side-chain carboxyl groups of a PGB1 variant explain salt and pH-dependent stability

Determination of pK(a) values of titrating residues in proteins provides a direct means of studying electrostatic coupling as well as pH-dependent stability. The B1 domain of protein G provides an excellent model system for such investigations. In this work, we analyze the observed pK(a) values of all carboxyl groups in a variant of PGB1 (T2Q, N8D, N37D) at low and high ionic strength as determined using (1)H-(13)C heteronuclear NMR in a structural context. The pK(a) values are used to calculate the pH-dependent stability in low and high salt and to investigate electrostatic coupling in the system. The observed pK(a) values can explain the pH dependence of protein stability but require pK(a) shifts relative to model values in the unfolded state, consistent with persistent residual structure in the denatured state. In particular, we find that most of the deviations from the expected random coil values can be explained by a significantly upshifted pK(a) value. We show also that (13)C backbone carbonyl data can be used to study electrostatic coupling in proteins and provide specific information on hydrogen bonding and electrostatic potential at nontitrating sites.

Interplay of secondary structures and side-chain contacts in the denatured state of BBA1

The denatured state of a miniprotein BBA1 is studied under the native condition with the AMBER/Poisson-Boltzmann energy model and with the self-guided enhanced sampling technique. Forty independent trajectories are collected to sample the highly diversified denatured structures. Our simulation data show that the denatured BBA1 contains high percentage of native helix and native turn, but low percentage of native hairpin. Conditional population analysis indicates that the native helix formation and the native hairpin formation are not cooperative in the denatured state. Side-chain analysis shows that the native hydrophobic contacts are more preferred than the non-native hydrophobic contacts in the denatured BBA1. In contrast, the salt-bridge contacts are more or less nonspecific even if their populations are higher than those of hydrophobic contacts. Analysis of the trajectories shows that the native helix mostly initiates near the N terminus and propagates to the C terminus, and mostly forms from 3(10)-helix/turn to alpha helix. The same analysis shows that the native turn is important but not necessary in its formation in the denatured BBA1. In addition, the formations of the two strands in the native hairpin are rather asymmetric, demonstrating the likely influence of the protein environment. Energetic analysis shows that the native helix formation is largely driven by electrostatic interactions in denatured BBA1. Further, the native helix formation is associated with the breakup of non-native salt-bridge contacts and the accumulation of native salt-bridge contacts. However, the native hydrophobic contacts only show a small increase upon the native helix formation while the non-native hydrophobic contacts stay essentially the same, different from the evolution of hydrophobic contacts observed in an isolated helix folding.

Toward an accurate theoretical framework for describing ensembles for proteins under strongly denaturing conditions

Our focus is on an appropriate theoretical framework for describing highly denatured proteins. In high concentrations of denaturants, proteins behave like polymers in a good solvent and ensembles for denatured proteins can be modeled by ignoring all interactions except excluded volume (EV) effects. To assay conformational preferences of highly denatured proteins, we quantify a variety of properties for EV-limit ensembles of 23 two-state proteins. We find that modeled denatured proteins can be best described as follows. Average shapes are consistent with prolate ellipsoids. Ensembles are characterized by large correlated fluctuations. Sequence-specific conformational preferences are restricted to local length scales that span five to nine residues. Beyond local length scales, chain properties follow well-defined power laws that are expected for generic polymers in the EV limit. The average available volume is filled inefficiently, and cavities of all sizes are found within the interiors of denatured proteins. All properties characterized from simulated ensembles match predictions from rigorous field theories. We use our results to resolve between conflicting proposals for structure in ensembles for highly denatured states.

Similarity and difference in the unfolding of thermophilic and mesophilic cold shock proteins studied by molecular dynamics simulations

Molecular dynamics simulations were performed to unfold a homologous pair of thermophilic and mesophilic cold shock proteins at high temperatures. The two proteins differ in just 11 of 66 residues and have very similar structures with a closed five-stranded antiparallel beta-barrel. A long flexible loop connects the N-terminal side of the barrel, formed by three strands (beta1-beta3), with the C-terminal side, formed by two strands (beta4-beta5). The two proteins were found to follow the same unfolding pathway, but with the thermophilic protein showing much slower unfolding. Unfolding started with the melting of C-terminal strands, leading to exposure of the hydrophobic core. Subsequent melting of beta3 and the beta-hairpin formed by the first two strands then resulted in unfolding of the whole protein. The slower unfolding of the thermophilic protein could be attributed to ion pair formation of Arg-3 with Glu-46, Glu-21, and the C-terminal. These ion pairs were also found to be important for the difference in folding stability between the pair of proteins. Thus electrostatic interactions appear to play similar roles in the difference in folding stability and kinetics between the pair of proteins.

Electrostatic Interactions in the Denatured State and in the Transition State for Protein Folding: Effects of Denatured State Interactions on the Analysis of Transition State Structure

The development of electrostatic interactions during the folding of the N-terminal domain of the ribosomal protein L9 (NTL9) is investigated by pH-dependent rate equilibrium free energy relationships. We show that Asp8, among six acidic residues, is involved in non-native, electrostatic interactions with K12 in the transition state for folding as well as in the denatured state. The perturbed native state pK(a) of D8 (pK(a) = 3.0) appears to be maintained through non-native interactions in both the transition state and the denatured state. Mutational effects on the stability of the transition state for protein (un)folding are often analyzed in respect to change in ground states. Thus, the interpretation of transition state analysis critically depends on an understanding of mutational effects on both the native and denatured state. Increasing evidence for structurally biased denatured states under physiological conditions raises concerns about possible denatured state effects on folding studies. We show that the structural interpretation of transition state analysis can be altered dramatically by denatured state effects.

Conserved quantitative stability/flexibility relationships (QSFR) in an orthologous RNase H pair

Many reports qualitatively describe conserved stability and flexibility profiles across protein families, but biophysical modeling schemes have not been available to robustly quantify both. Here we investigate an orthologous RNase H pair by using a minimal distance constraint model (DCM). The DCM is an all atom microscopic model [Jacobs and Dallakyan, Biophys J 2005;88(2):903-915] that accurately reproduces heat capacity measurements [Livesay et al., FEBS Lett 2004;576(3):468-476], and is unique in its ability to harmoniously calculate thermodynamic stability and flexibility in practical computing times. Consequently, quantified stability/flexibility relationships (QSFR) can be determined using the DCM. For the first time, a comparative QSFR analysis is performed, serving as a paradigm study to illustrate the utility of a QSFR analysis for elucidating evolutionarily conserved stability and flexibility profiles. Despite global conservation of QSFR profiles, distinct enthalpy-entropy compensation mechanisms are identified between the RNase H pair. In both cases, local flexibility metrics parallel H/D exchange experiments by correctly identifying the folding core and several flexible regions. Remarkably, at appropriately shifted temperatures (e.g., melting temperature), these differences lead to a global conservation in Landau free energy landscapes, which directly relate thermodynamic stability to global flexibility. Using ensemble-based sampling within free energy basins, rigidly, and flexibly correlated regions are quantified through cooperativity correlation plots. Five conserved flexible regions are identified within the structures of the orthologous pair. Evolutionary conservation of these flexibly correlated regions is strongly suggestive of their catalytic importance. Conclusions made herein are demonstrated to be robust with respect to the DCM parameterization.

Statistical Studies of Flexible Nonhomogeneous Polypeptide Chains

Unfolded proteins attract increasing attention nowadays because of the accumulation of experimental evidence that they play an important role in different biological processes. Therefore, studies of various statistical properties of flexible protein-like polypeptide chains are becoming increasingly important as well. This paper presents distributions (histograms) of distances between atoms of titratable residues for flexible polypeptide chains with various residue compositions and with the hard-spheres potential taken into consideration. The factors influencing the parameters of the obtained histograms have been identified and analyzed. It was found that the sensitivity of the distributions with respect to the internal structure of intermediate residues increases with the number of residues between the considered charged residues. It was shown that branching at C(beta) atoms of the side chains of the intermediate residues is among the most considerable factors influencing the shape of the distance distribution and the average distance between atoms in flexible chains. Despite the model simplicity, the results of the calculations can be applied for systems with other types of interactions presented, and this was demonstrated for the charge-charge interactions. In particular, it was shown that those interactions have a significant effect on distances between the unlike charges, while such an effect for the like charges is much less pronounced. The comparison of predictions made on the basis of the presented calculations to some experimental data is also given, and possible applications of the theoretical concept described in the paper are discussed.

Effects of pH, salt, and macromolecular crowding on the stability of FK506-binding protein: an integrated experimental and theoretical study

Environmental variables can exert significant influences on the folding stability of a protein, and elucidating these influences provides insight on the determinants of protein stability. Here, experimental data on the stability of FKBP12 are reported for the effects of three environmental variables: pH, salt, and macromolecular crowding. In the pH range of 5-9, contribution to the pH dependence of the unfolding free energy from residual charge-charge interactions in the unfolded state was found to be negligible. The negligible contribution was attributed to the lack of sequentially nearest neighboring charged residues around groups that titrate in the pH range. KCl lowered the stability of FKBP12 and the E31Q/D32N double mutant at small salt concentrations but raised stability after approximately 0.5 M salt. Such a turnover behavior was accounted for by the balance of two opposing types of protein-salt interactions: the Debye-Hückel type, modeling the response of the ions to protein charges, favors the unfolded state while the Kirkwood type, accounting for the disadvantage of the ions moving toward the low-dielectric protein cavity from the bulk solvent, disfavors the unfolded state. Ficoll 70 as a crowding agent was found to have a modest effect on protein stability, in qualitative agreement with a simple model suggesting that the folded and unfolded states are nearly equally adversely affected by macromolecular crowding. For any environmental variable, it is the balance of its effects on the folded and unfolded states that determines the outcome on the folding stability.