Normal-modes-based prediction of protein conformational changes guided by distance constraints

Exploring Conformational Landscapes Along Anharmonic Low-Frequency Vibrations

We aim to automatize the identification of collective variables to simplify and speed up enhanced sampling simulations of conformational dynamics in biomolecules. We focus on anharmonic low-frequency vibrations that exhibit fluctuations on time scales faster than conformational transitions but describe a path of least resistance toward structural change. A key challenge is that harmonic approximations are ill-suited to characterize these vibrations, which are observed at far-infrared frequencies and are easily excited by thermal collisions at room temperature. Here, we approached this problem with a frequency-selective anharmonic (FRESEAN) mode analysis that does not rely on harmonic approximations and successfully isolates anharmonic low-frequency vibrations from short molecular dynamics simulation trajectories. We applied FRESEAN mode analysis to simulations of alanine dipeptide, a common test system for enhanced sampling simulation protocols, and compared the performance of isolated low-frequency vibrations to conventional user-defined collective variables (here backbone dihedral angles) in enhanced sampling simulations. The comparison shows that enhanced sampling along anharmonic low-frequency vibrations not only reproduces known conformational dynamics but can even further improve the sampling of slow transitions compared to user-defined collective variables. Notably, free energy surfaces spanned by low-frequency anharmonic vibrational modes exhibit lower barriers associated with conformational transitions relative to representations in backbone dihedral space. We thus conclude that anharmonic low-frequency vibrations provide a promising path for highly effective and fully automated enhanced sampling simulations of conformational dynamics in biomolecules.

Surveying the energy landscape of coarse-grained mappings

Simulations of soft materials often adopt low-resolution coarse-grained (CG) models. However, the CG representation is not unique and its impact upon simulated properties is poorly understood. In this work, we investigate the space of CG representations for ubiquitin, which is a typical globular protein with 72 amino acids. We employ Monte Carlo methods to ergodically sample this space and to characterize its landscape. By adopting the Gaussian network model as an analytically tractable atomistic model for equilibrium fluctuations, we exactly assess the intrinsic quality of each CG representation without introducing any approximations in sampling configurations or in modeling interactions. We focus on two metrics, the spectral quality and the information content, that quantify the extent to which the CG representation preserves low-frequency, large-amplitude motions and configurational information, respectively. The spectral quality and information content are weakly correlated among high-resolution representations but become strongly anticorrelated among low-resolution representations. Representations with maximal spectral quality appear consistent with physical intuition, while low-resolution representations with maximal information content do not. Interestingly, quenching studies indicate that the energy landscape of mapping space is very smooth and highly connected. Moreover, our study suggests a critical resolution below which a "phase transition" qualitatively distinguishes good and bad representations.

Modeling of protein conformational changes with Rosetta guided by limited experimental data

Conformational changes are an essential component of functional cycles of many proteins, but their characterization often requires an integrative structural biology approach. Here, we introduce and benchmark ConfChangeMover (CCM), a new method built into the widely used macromolecular modeling suite Rosetta that is tailored to model conformational changes in proteins using sparse experimental data. CCM can rotate and translate secondary structural elements and modify their backbone dihedral angles in regions of interest. We benchmarked CCM on soluble and membrane proteins with simulated Cα-Cα distance restraints and sparse experimental double electron-electron resonance (DEER) restraints, respectively. In both benchmarks, CCM outperformed state-of-the-art Rosetta methods, showing that it can model a diverse array of conformational changes. In addition, the Rosetta framework allows a wide variety of experimental data to be integrated with CCM, thus extending its capability beyond DEER restraints. This method will contribute to the biophysical characterization of protein dynamics.

Computation of the Protein Conformational Transition Pathway on Ligand Binding by Linear Response-Driven Molecular Dynamics

While extremely important for relating the protein structure to its biological function, determination of the protein conformational transition pathway upon ligand binding is made difficult due to the transient nature of intermediates, a large and rugged conformational space, and coupling between protein dynamics and ligand-protein interactions. Existing methods that rely on prior knowledge of the bound (holo) state structure are restrictive. A second concern relates to the correspondence of intermediates obtained to the metastable states on the apo → holo transition pathway. Here, we have taken the protein apo structure and ligand-binding site as only inputs and combined an elastic network model (ENM) representation of the protein Hamiltonian with linear response theory (LRT) for protein-ligand interactions to identify the set of slow normal modes of protein vibrations that have a high overlap with the direction of the protein conformational change. The structural displacement along the chosen direction was performed using excited normal modes molecular dynamics (MDeNM) simulations rather than by the direct use of LRT. Herein, the MDeNM excitation velocity was optimized on-the-fly on the basis of its coupling to protein dynamics and ligand-protein interactions. Thus, a determined set of structures was validated against crystallographic and simulation data on four protein-ligand systems, namely, adenylate kinase-di(adenosine-5')pentaphosphate, ribose binding protein-β-d-ribopyranose, DNA β-glucosyltransferase-uridine-5'-diphosphate, and G-protein α subunit-guanosine-5'-triphosphate, which present important differences in protein conformational heterogeneity, ligand binding mechanism, viz. induced-fit or conformational selection, extent, and nonlinearity in protein conformational changes upon ligand binding, and presence of allosteric effects. The obtained set of intermediates was used as an input to path metadynamics simulations to obtain the free energy profile for the apo → holo transition.

Protein Fluctuations in Response to Random External Forces

Elastic network models (ENMs) have been widely used in the last decades to investigate protein motions and dynamics. There the intrinsic fluctuations based on the isolated structures are obtained from the normal modes of these elastic networks, and they generally show good agreement with the B-factors extracted from X-ray crystallographic experiments, which are commonly considered to be indicators of protein flexibility. In this paper, we propose a new approach to analyze protein fluctuations and flexibility, which has a more appropriate physical basis. It is based on the application of random forces to the protein ENM to simulate the effects of collisions of solvent on a protein structure. For this purpose, we consider both the Cα-atom coarse-grained anisotropic network model (ANM) and an elastic network augmented with points included for the crystallized waters. We apply random forces to these protein networks everywhere, as well as only on the protein surface alone. Despite the randomness of the directions of the applied perturbations, the computed average displacements of the protein network show a remarkably good agreement with the experimental B-factors. In particular, for our set of 919 protein structures, we find that the highest correlation with the B-factors is obtained when applying forces to the external surface of the water-augmented ANM (an overall gain of 3% in the Pearson’s coefficient for the entire dataset, with improvements up to 30% for individual proteins), rather than when evaluating the fluctuations obtained from the normal modes of a standard Cα-atom coarse-grained ANM. It follows that protein fluctuations should be considered not just as the intrinsic fluctuations of the internal dynamics, but also equally well as responses to external solvent forces, or as a combination of both.

Normal-mode driven exploration of protein domain motions

Domain motions involved in the function of proteins can often be well described as a combination of motions along a handfull of low-frequency modes, that is, with the values of a few normal coordinates. This means that, when the functional motion of a protein is unknown, it should prove possible to predict it, since it amounts to guess a few values. However, without the help of additional experimental data, using normal coordinates for generating accurate conformers far away from the initial one is not so straightforward. To do so, a new approach is proposed: instead of building conformers directly with the values of a subset of normal coordinates, they are built in two steps, the conformer built with normal coordinates being just used for defining a set of distance constraints, the final conformer being built so as to match them. Note that this approach amounts to transform the problem of generating accurate protein conformers using normal coordinates into a better known one: the distance-geometry problem, which is herein solved with the help of the ROSETTA software. In the present study, this approach allowed to rebuild accurately six large amplitude conformational changes, using at most six low-frequency normal coordinates. As a consequence of the low-dimensionality of the corresponding subspace, random exploration also proved enough for generating low-energy conformers close to the known end-point of the conformational change of the LAO binding protein, lysozyme T4 and adenylate kinase.

Fast computational mutation-response scanning of proteins

Studying the effect of perturbations on protein structure is a basic approach in protein research. Important problems, such as predicting pathological mutations and understanding patterns of structural evolution, have been addressed by computational simulations that model mutations using forces and predict the resulting deformations. In single mutation-response scanning simulations, a sensitivity matrix is obtained by averaging deformations over point mutations. In double mutation-response scanning simulations, a compensation matrix is obtained by minimizing deformations over pairs of mutations. These very useful simulation-based methods may be too slow to deal with large proteins, protein complexes, or large protein databases. To address this issue, I derived analytical closed formulas to calculate the sensitivity and compensation matrices directly, without simulations. Here, I present these derivations and show that the resulting analytical methods are much faster than their simulation counterparts.

HOPMA: Boosting Protein Functional Dynamics with Colored Contact Maps

In light of the recent very rapid progress in protein structure prediction, accessing the multitude of functional protein states is becoming more central than ever before. Indeed, proteins are flexible macromolecules, and they often perform their function by switching between different conformations. However, high-resolution experimental techniques such as X-ray crystallography and cryogenic electron microscopy can catch relatively few protein functional states. Many others are only accessible under physiological conditions in solution. Therefore, there is a pressing need to fill this gap with computational approaches. We present HOPMA, a novel method to predict protein functional states and transitions by using a modified elastic network model. The method exploits patterns in a protein contact map, taking its 3D structure as input, and excludes some disconnected patches from the elastic network. Combined with nonlinear normal mode analysis, this strategy boosts the protein conformational space exploration, especially when the input structure is highly constrained, as we demonstrate on a set of more than 400 transitions. Our results let us envision the discovery of new functional conformations, which were unreachable previously, starting from the experimentally known protein structures. The method is computationally efficient and available at https://github.com/elolaine/HOPMA and https://team.inria.fr/nano-d/software/nolb-normal-modes.

Increasing the Sampling Efficiency of Protein Conformational Change by Combining a Modified Replica Exchange Molecular Dynamics and Normal Mode Analysis

Understanding conformational change at an atomic level is significant when determining a protein functional mechanism. Replica exchange molecular dynamics (REMD) is a widely used enhanced sampling method to explore protein conformational space. However, REMD with an explicit solvent model requires huge computational resources, immensely limiting its application. In this study, a variation of parallel tempering metadynamics (PTMetaD) with the omission of solvent-solvent interactions in exchange attempts and the use of low-frequency modes calculated by normal-mode analysis (NMA) as collective variables (CVs), namely ossPTMetaD, is proposed with the aim to accelerate MD simulations simultaneously in temperature and geometrical spaces. For testing the performance of ossPTMetaD, five protein systems with diverse biological functions and motion patterns were selected, including large-scale domain motion (AdK), flap movement (HIV-1 protease and BACE1), and DFG-motif flip in kinases (p38α and c-Abl). The simulation results showed that ossPTMetaD requires much fewer numbers of replicas than temperature REMD (T-REMD) with a reduction of ∼70% to achieve a similar exchange ratio. Although it does not obey the detailed balance condition, ossPTMetaD provides consistent results with T-REMD and experimental data. The high accessibility of the large conformational change of protein systems by ossPTMetaD, especially in simulating the very challenging DFG-motif flip of protein kinases, demonstrated its high efficiency and robustness in the characterization of the large-scale protein conformational change pathway and associated free energy profile.

Exploring Conformational Space with Thermal Fluctuations Obtained by Normal-Mode Analysis

Proteins in their native states can be represented as ensembles of conformers in dynamical equilibrium. Thermal fluctuations are responsible for transitions between these conformers. Normal-modes analysis (NMA) using elastic network models (ENMs) provides an efficient procedure to explore global dynamics of proteins commonly associated with conformational transitions. In the present work, we present an iterative approach to explore protein conformational spaces by introducing structural distortions according to their equilibrium dynamics at room temperature. The approach can be used either to perform unbiased explorations of conformational space or to explore guided pathways connecting two different conformations, e.g., apo and holo forms. In order to test its performance, four proteins with different magnitudes of structural distortions upon ligand binding have been tested. In all cases, the conformational selection model has been confirmed and the conformational space between apo and holo forms has been encompassed. Different strategies have been tested that impact on the efficiency either to achieve a desired conformational change or to achieve a balanced exploration of the protein conformational multiplicity.

Normal Mode Analysis as a Routine Part of a Structural Investigation

Normal mode analysis (NMA) is a technique that can be used to describe the flexible states accessible to a protein about an equilibrium position. These states have been shown repeatedly to have functional significance. NMA is probably the least computationally expensive method for studying the dynamics of macromolecules, and advances in computer technology and algorithms for calculating normal modes over the last 20 years have made it nearly trivial for all but the largest systems. Despite this, it is still uncommon for NMA to be used as a component of the analysis of a structural study. In this review, we will describe NMA, outline its advantages and limitations, explain what can and cannot be learned from it, and address some criticisms and concerns that have been voiced about it. We will then review the most commonly used techniques for reducing the computational cost of this method and identify the web services making use of these methods. We will illustrate several of their possible uses with recent examples from the literature. We conclude by recommending that NMA become one of the standard tools employed in any structural study.

Refinement of Highly Flexible Protein Structures using Simulation-Guided Spectroscopy

Highly flexible proteins present a special challenge for structure determination because they are multi-structured yet not disordered, so their conformational ensembles are essential for understanding function. Because spectroscopic measurements of multiple conformational populations often provide sparse data, experiment selection is a limiting factor in conformational refinement. A molecular simulations- and information-theory based approach to select which experiments best refine conformational ensembles has been developed. This approach was tested on three flexible proteins. For proteins where a clear mechanistic hypothesis exists, experiments that test this hypothesis were systematically identified. When available data did not yield such mechanistic hypotheses, experiments that significantly outperform structure-guided approaches in conformational refinement were identified. This approach offers a particular advantage when refining challenging, underdetermined protein conformational ensembles.

Flexible Fitting of Atomic Models into Cryo-EM Density Maps Guided by Helix Correspondences

Although electron cryo-microscopy (cryo-EM) has recently achieved resolutions of better than 3 Å, at which point molecular modeling can be done directly from the density map, analysis and annotation of a cryo-EM density map still primarily rely on fitting atomic or homology models to the density map. In this article, we present, to our knowledge, a new method for flexible fitting of known or modeled protein structures into cryo-EM density maps. Unlike existing methods that are guided by local density gradients, our method is guided by correspondences between the α-helices in the density map and model, and does not require an initial rigid-body fitting step. Compared with current methods on both simulated and experimental density maps, our method not only achieves greater accuracy for proteins with large deformations but also runs as fast or faster than many of the other flexible fitting routines.

Gaussian network model can be enhanced by combining solvent accessibility in proteins

Gaussian network model (GNM), regarded as the simplest and most representative coarse-grained model, has been widely adopted to analyze and reveal protein dynamics and functions. Designing a variation of the classical GNM, by defining a new Kirchhoff matrix, is the way to improve the residue flexibility modeling. We combined information arising from local relative solvent accessibility (RSA) between two residues into the Kirchhoff matrix of the parameter-free GNM. The undetermined parameters in the new Kirchhoff matrix were estimated by using particle swarm optimization. The usage of RSA was motivated by the fact that our previous work using RSA based linear regression model resulted out higher prediction quality of the residue flexibility when compared with the classical GNM and the parameter free GNM. Computational experiments, conducted based on one training dataset, two independent datasets and one additional small set derived by molecular dynamics simulations, demonstrated that the average correlation coefficients of the proposed RSA based parameter-free GNM, called RpfGNM, were significantly increased when compared with the parameter-free GNM. Our empirical results indicated that a variation of the classical GNMs by combining other protein structural properties is an attractive way to improve the quality of flexibility modeling.

Jumping between protein conformers using normal modes

The relationship between the normal modes of a protein and its functional conformational change has been studied for decades. However, using this relationship in a predictive context remains a challenge. In this work, we demonstrate that, starting from a given protein conformer, it is possible to generate in a single step model conformers that are less than 1 Å (C_α -RMSD) from the conformer which is the known endpoint of the conformational change, particularly when the conformational change is collective in nature. Such accurate model conformers can be generated by following either the so-called robust or the 50 lowest-frequency modes obtained with various Elastic Network Models (ENMs). Interestingly, the quality of many of these models compares well with actual crystal structures, as assessed by the ROSETTA scoring function and PROCHECK. The most accurate and best quality conformers obtained in the present study were generated by using the 50 lowest-frequency modes of an all-atom ENM. However, with less than ten robust modes, which are identified without any prior knowledge of the nature of the conformational change, nearly 90% of the motion described by the 50 lowest-frequency modes of a protein can be captured. Such results strongly suggest that exploring the robust modes of ENMs may prove efficient for sampling the functionally relevant conformational repertoire of many proteins. © 2017 Wiley Periodicals, Inc.

Identification of Hot Spots in Protein Structures Using Gaussian Network Model and Gaussian Naive Bayes

Residue fluctuations in protein structures have been shown to be highly associated with various protein functions. Gaussian network model (GNM), a simple representative coarse-grained model, was widely adopted to reveal function-related protein dynamics. We directly utilized the high frequency modes generated by GNM and further performed Gaussian Naive Bayes (GNB) to identify hot spot residues. Two coding schemes about the feature vectors were implemented with varying distance cutoffs for GNM and sliding window sizes for GNB based on tenfold cross validations: one by using only a single high mode and the other by combining multiple modes with the highest frequency. Our proposed methods outperformed the previous work that did not directly utilize the high frequency modes generated by GNM, with regard to overall performance evaluated using F1 measure. Moreover, we found that inclusion of more high frequency modes for a GNB classifier can significantly improve the sensitivity. The present study provided additional valuable insights into the relation between the hot spots and the residue fluctuations.

ClustENM: ENM-Based Sampling of Essential Conformational Space at Full Atomic Resolution

Accurate sampling of conformational space and, in particular, the transitions between functional substates has been a challenge in molecular dynamic (MD) simulations of large biomolecular systems. We developed an Elastic Network Model (ENM)-based computational method, ClustENM, for sampling large conformational changes of biomolecules with various sizes and oligomerization states. ClustENM is an iterative method that combines ENM with energy minimization and clustering steps. It is an unbiased technique, which requires only an initial structure as input, and no information about the target conformation. To test the performance of ClustENM, we applied it to six biomolecular systems: adenylate kinase (AK), calmodulin, p38 MAP kinase, HIV-1 reverse transcriptase (RT), triosephosphate isomerase (TIM), and the 70S ribosomal complex. The generated ensembles of conformers determined at atomic resolution show good agreement with experimental data (979 structures resolved by X-ray and/or NMR) and encompass the subspaces covered in independent MD simulations for TIM, p38, and RT. ClustENM emerges as a computationally efficient tool for characterizing the conformational space of large systems at atomic detail, in addition to generating a representative ensemble of conformers that can be advantageously used in simulating substrate/ligand-binding events.

Model of the Ankyrin and SOCS Box Protein, ASB9, E3 Ligase Reveals a Mechanism for Dynamic Ubiquitin Transfer

Cullin-RING E3 ligases (CRLs) are elongated and bowed protein complexes that transfer ubiquitin over 60 Å to proteins targeted for proteasome degradation. One such CRL contains the ankyrin repeat and SOCS box protein 9 (ASB9), which binds to and partially inhibits creatine kinase (CK). While current models for the ASB9-CK complex contain some known interface residues, the overall structure and precise interface of the ASB9-CK complex remains unknown. Through an integrative modeling approach, we report a third-generation model that reveals precisely the interface interactions and also fits the shape of the ASB9-CK complex as determined by small-angle X-ray scattering. We constructed an atomic model for the entire CK-targeting CRL to uncover dominant modes of motion that could permit ubiquitin transfer. Remarkably, only the correctly docked CK-containing E3 ligase and not incorrectly docked structures permitted close approach of ubiquitin to the CK substrate.

Ligand Docking to Intermediate and Close-To-Bound Conformers Generated by an Elastic Network Model Based Algorithm for Highly Flexible Proteins

Incorporating receptor flexibility in small ligand-protein docking still poses a challenge for proteins undergoing large conformational changes. In the absence of bound structures, sampling conformers that are accessible by apo state may facilitate docking and drug design studies. For this aim, we developed an unbiased conformational search algorithm, by integrating global modes from elastic network model, clustering and energy minimization with implicit solvation. Our dataset consists of five diverse proteins with apo to complex RMSDs 4.7-15 Å. Applying this iterative algorithm on apo structures, conformers close to the bound-state (RMSD 1.4-3.8 Å), as well as the intermediate states were generated. Dockings to a sequence of conformers consisting of a closed structure and its "parents" up to the apo were performed to compare binding poses on different states of the receptor. For two periplasmic binding proteins and biotin carboxylase that exhibit hinge-type closure of two dynamics domains, the best pose was obtained for the conformer closest to the bound structure (ligand RMSDs 1.5-2 Å). In contrast, the best pose for adenylate kinase corresponded to an intermediate state with partially closed LID domain and open NMP domain, in line with recent studies (ligand RMSD 2.9 Å). The docking of a helical peptide to calmodulin was the most challenging case due to the complexity of its 15 Å transition, for which a two-stage procedure was necessary. The technique was first applied on the extended calmodulin to generate intermediate conformers; then peptide docking and a second generation stage on the complex were performed, which in turn yielded a final peptide RMSD of 2.9 Å. Our algorithm is effective in producing conformational states based on the apo state. This study underlines the importance of such intermediate states for ligand docking to proteins undergoing large transitions.

GroEL2 of Mycobacterium tuberculosis Reveals the Importance of Structural Pliability in Chaperonin Function

Intracellular protein folding is mediated by molecular chaperones, the best studied among which are the chaperonins GroEL and GroES. Conformational changes and allosteric transitions between different metastable states are hallmarks of the chaperonin mechanism. These conformational transitions between three structural domains of GroEL are anchored at two hinges. Although hinges are known to be critical for mediating the communication between different domains of GroEL, the relative importance of hinges on GroEL oligomeric assembly, ATPase activity, conformational changes, and functional activity is not fully characterized. We have exploited the inability of Mycobacterium tuberculosis GroEL2 to functionally complement an Escherichia coli groEL mutant to address the importance of hinge residues in the GroEL mechanism. Various chimeras of M. tuberculosis GroEL2 and E. coli GroEL allowed us to understand the role of hinges and dissect the consequences of oligomerization and substrate binding capability on conformational transitions. The present study explains the concomitant conformational changes observed with GroEL hinge variants and is best supported by the normal mode analysis.

IMPORTANCE

Conformational changes and allosteric transitions are hallmarks of the chaperonin mechanism. We have exploited the inability of M. tuberculosis GroEL2 to functionally complement a strain of E. coli in which groEL expression is repressed to address the importance of hinges. The significance of conservation at the hinge regions stands out as a prominent feature of the GroEL mechanism in binding to GroES and substrate polypeptides. The hinge residues play a significant role in the chaperonin activity in vivo and in vitro.

Decrypting the structural, dynamic, and energetic basis of a monomeric kinesin interacting with a tubulin dimer in three ATPase states by all-atom molecular dynamics simulation

We have employed molecular dynamics (MD) simulation to investigate, with atomic details, the structural dynamics and energetics of three major ATPase states (ADP, APO, and ATP state) of a human kinesin-1 monomer in complex with a tubulin dimer. Starting from a recently solved crystal structure of ATP-like kinesin-tubulin complex by the Knossow lab, we have used flexible fitting of cryo-electron-microscopy maps to construct new structural models of the kinesin-tubulin complex in APO and ATP state, and then conducted extensive MD simulations (total 400 ns for each state), followed by flexibility analysis, principal component analysis, hydrogen bond analysis, and binding free energy analysis. Our modeling and simulation have revealed key nucleotide-dependent changes in the structure and flexibility of the nucleotide-binding pocket (featuring a highly flexible and open switch I in APO state) and the tubulin-binding site, and allosterically coupled motions driving the APO to ATP transition. In addition, our binding free energy analysis has identified a set of key residues involved in kinesin-tubulin binding. On the basis of our simulation, we have attempted to address several outstanding issues in kinesin study, including the possible roles of β-sheet twist and neck linker docking in regulating nucleotide release and binding, the structural mechanism of ADP release, and possible extension and shortening of α4 helix during the ATPase cycle. This study has provided a comprehensive structural and dynamic picture of kinesin's major ATPase states, and offered promising targets for future mutational and functional studies to investigate the molecular mechanism of kinesin motors.

On the relationship between low-frequency normal modes and the large-scale conformational changes of proteins

Normal mode analysis is a computational technique that allows to study the dynamics of biological macromolecules. It was first applied to small protein cases, more than thirty years ago. The interest in this technique then raised when it was realized that it can provide insights about the large-scale conformational changes a protein can experience, for instance upon ligand binding. As it was also realized that studying highly simplified protein models can provide similar insights, meaning that this kind of analysis can be both quick and simple to handle, several applications were proposed, in the context of various structural biology techniques. This review focuses on these applications, as well as on how the functional relevance of the lowest-frequency modes of proteins was established.

Computing ensembles of transitions with molecular dynamics simulations

A molecular understanding of conformational change is important for connecting structure and function. Without the ability to sample on the meaningful large-scale conformational changes, the ability to infer biological function and to understand the effect of mutations and changes in environment is not possible. Our Dynamic Importance Sampling method (DIMS), part of the CHARMM simulation package, is a method that enables sampling over ensembles of transition intermediates. This chapter outlines the context for the method and the usage within the program.

High-resolution modeling of protein structures based on flexible fitting of low-resolution structural data

To circumvent the difficulty of directly solving high-resolution biomolecular structures, low-resolution structural data from Cryo-electron microscopy (EM) and small angle solution X-ray scattering (SAXS) are increasingly used to explore multiple conformational states of biomolecular assemblies. One promising venue to obtain high-resolution structural models from low-resolution data is via data-constrained flexible fitting. To this end, we have developed a new method based on a coarse-grained Cα-only protein representation, and a modified form of the elastic network model (ENM) that allows large-scale conformational changes while maintaining the integrity of local structures including pseudo-bonds and secondary structures. Our method minimizes a pseudo-energy which linearly combines various terms of the modified ENM energy with an EM/SAXS-fitting score and a collision energy that penalizes steric collisions. Unlike some previous flexible fitting efforts using the lowest few normal modes, our method effectively utilizes all normal modes so that both global and local structural changes can be fully modeled with accuracy. This method is also highly efficient in computing time. We have demonstrated our method using adenylate kinase as a test case which undergoes a large open-to-close conformational change. The EM-fitting method is available at a web server (http://enm.lobos.nih.gov), and the SAXS-fitting method is available as a pre-compiled executable upon request.

Nonlinear excitations match correlated motions unveiled by NMR in proteins: a new perspective on allosteric cross-talk

In this paper we propose a novel theoretical framework for interpreting long-range dynamical correlations unveiled in proteins through NMR measurements. The theoretical rationale relies on the hypothesis that correlated motions in proteins may be reconstructed as large-scale, collective modes sustained by long-lived nonlinear vibrations known as discrete breathers (DB) localized at key, hot-spot sites. DBs are spatially localized modes, whose nonlinear nature hinders resonant coupling with the normal modes, thus conferring them long lifetimes as compared to normal modes. DBs have been predicted to exist in proteins, localized at few hot-spot residues typically within the stiffest portions of the structure. We compute DB modes analytically in the framework of the nonlinear network model, showing that the displacement patterns of many DBs localized at key sites match to a remarkable extent the experimentally uncovered correlation blueprint. The computed dispersion relations prove that it is physically possible for some of these DBs to be excited out of thermal fluctuations at room temperature. Based on our calculations, we speculate that transient energy redistribution among the vibrational modes in a protein might favor the emergence of DB-like bursts of long-lived energy at hot-spot sites with lifetimes in the ns range, able to sustain critical, function-encoding correlated motions. More generally, our calculations provide a novel quantitative tool to predict fold-spanning dynamical pathways of correlated residues that may be central to allosteric cross-talk in proteins.

Sequence-based Gaussian network model for protein dynamics

Motivation: Gaussian network model (GNM) is widely adopted to analyze and understand protein dynamics, function and conformational changes. The existing GNM-based approaches require atomic coordinates of the corresponding protein and cannot be used when only the sequence is known.

Results: We report, first of its kind, GNM model that allows modeling using the sequence. Our linear regression-based, parameter-free, sequence-derived GNM (L-pfSeqGNM) uses contact maps predicted from the sequence and models local, in the sequence, contact neighborhoods with the linear regression. Empirical benchmarking shows relatively high correlations between the native and the predicted with L-pfSeqGNM B-factors and between the cross-correlations of residue fluctuations derived from the structure- and the sequence-based GNM models. Our results demonstrate that L-pfSeqGNM is an attractive platform to explore protein dynamics. In contrast to the highly used GNMs that require protein structures that number in thousands, our model can be used to study motions for the millions of the readily available sequences, which finds applications in modeling conformational changes, protein–protein interactions and protein functions.

Contact:zerozhua@126.com

Supplementary information:Supplementary data are available at Bioinformatics online.

Conformational changes in DNA-binding proteins: relationships with precomplex features and contributions to specificity and stability

Both Proteins and DNA undergo conformational changes in order to form functional complexes and also to facilitate interactions with other molecules. These changes have direct implications for the stability and specificity of the complex, as well as the cooperativity of interactions between multiple entities. In this work, we have extensively analyzed conformational changes in DNA-binding proteins by superimposing DNA-bound and unbound pairs of protein structures in a curated database of 90 proteins. We manually examined each of these pairs, unified the authors' annotations, and summarized our observations by classifying conformational changes into six structural categories. We explored a relationship between conformational changes and functional classes, binding motifs, target specificity, biophysical features of unbound proteins, and stability of the complex. In addition, we have also investigated the degree to which the intrinsic flexibility can explain conformational changes in a subset of 52 proteins with high quality coordinate data. Our results indicate that conformational changes in DNA-binding proteins contribute significantly to both the stability of the complex and the specificity of targets recognized by them. We also conclude that most conformational changes occur in proteins interacting with specific DNA targets, even though unbound protein structures may have sufficient information to interact with DNA in a nonspecific manner.

Coarse-grained and all-atom modeling of structural states and transitions in hemoglobin

Hemoglobin (Hb), an oxygen-binding protein composed of four subunits (α1, α2, β1, and β2), is a well-known example of allosteric proteins that are capable of cooperative ligand binding. Despite decades of studies, the structural basis of its cooperativity remains controversial. In this study, we have integrated coarse-grained (CG) modeling, all-atom simulation, and structural data from X-ray crystallography and wide-angle X-ray scattering (WAXS), aiming to probe dynamic properties of the two structural states of Hb (T and R state) and the transitions between them. First, by analyzing the WAXS data of unliganded and liganded Hb, we have found that the structural ensemble of T or R state is dominated by one crystal structure of Hb with small contributions from other crystal structures of Hb. Second, we have used normal mode analysis to identify two distinct quaternary rotations between the α1β1 and α2β2 dimer, which drive the transitions between T and R state. We have also identified the hot-spot residues whose mutations are predicted to greatly change these quaternary motions. Third, we have generated a CG transition pathway between T and R state, which predicts a clear order of quaternary and tertiary changes involving α and β subunits in Hb. Fourth, we have used the accelerated molecular dynamics to perform an all-atom simulation starting from the T state of Hb, and we have observed a transition toward the R state of Hb. Further analysis of crystal structural data and the all-atom simulation trajectory has corroborated the order of quaternary and tertiary changes predicted by CG modeling.

All-atom structural investigation of kinesin-microtubule complex constrained by high-quality cryo-electron-microscopy maps

In this study, we have performed a comprehensive structural investigation of three major biochemical states of a kinesin complexed with microtubule under the constraint of high-quality cryo-electron-microscopy (EM) maps. In addition to the ADP and ATP state which were captured by X-ray crystallography, we have also modeled the nucleotide-free or APO state for which no crystal structure is available. We have combined flexible fitting of EM maps with regular molecular dynamics simulations, hydrogen-bond analysis, and free energy calculation. Our APO-state models feature a subdomain rotation involving loop L2 and α6 helix of kinesin, and local structural changes in active site similar to a related motor protein, myosin. We have identified a list of hydrogen bonds involving key residues in the active site and the binding interface between kinesin and microtubule. Some of these hydrogen bonds may play an important role in coupling microtubule binding to ATPase activities in kinesin. We have validated our models by calculating the binding free energy between kinesin and microtubule, which quantitatively accounts for the observation of strong binding in the APO and ATP state and weak binding in the ADP state. This study will offer promising targets for future mutational and functional studies to investigate the mechanism of kinesin motors.

Towards the prediction of order parameters from molecular dynamics simulations in proteins

A molecular understanding of how protein function is related to protein structure requires an ability to understand large conformational changes between multiple states. Unfortunately these states are often separated by high free energy barriers and within a complex energy landscape. This makes it very difficult to reliably connect, for example by all-atom molecular dynamics calculations, the states, their energies, and the pathways between them. A major issue needed to improve sampling on the intermediate states is an order parameter--a reduced descriptor for the major subset of degrees of freedom--that can be used to aid sampling for the large conformational change. We present a method to combine information from molecular dynamics using non-linear time series and dimensionality reduction, in order to quantitatively determine an order parameter connecting two large-scale conformationally distinct protein states. This new method suggests an implementation for molecular dynamics calculations that may be used to enhance sampling of intermediate states.

Accurate flexible fitting of high-resolution protein structures to small-angle x-ray scattering data using a coarse-grained model with implicit hydration shell

Small-angle x-ray scattering (SAXS) is a powerful technique widely used to explore conformational states and transitions of biomolecular assemblies in solution. For accurate model reconstruction from SAXS data, one promising approach is to flexibly fit a known high-resolution protein structure to low-resolution SAXS data by computer simulations. This is a highly challenging task due to low information content in SAXS data. To meet this challenge, we have developed what we believe to be a novel method based on a coarse-grained (one-bead-per-residue) protein representation and a modified form of the elastic network model that allows large-scale conformational changes while maintaining pseudobonds and secondary structures. Our method optimizes a pseudoenergy that combines the modified elastic-network model energy with a SAXS-fitting score and a collision energy that penalizes steric collisions. Our method uses what we consider a new implicit hydration shell model that accounts for the contribution of hydration shell to SAXS data accurately without explicitly adding waters to the system. We have rigorously validated our method using five test cases with simulated SAXS data and three test cases with experimental SAXS data. Our method has successfully generated high-quality structural models with root mean-squared deviation of 1 ∼ 3 Å from the target structures.

Predicting protein ligand binding motions with the conformation explorer

BACKGROUND

Knowledge of the structure of proteins bound to known or potential ligands is crucial for biological understanding and drug design. Often the 3D structure of the protein is available in some conformation, but binding the ligand of interest may involve a large scale conformational change which is difficult to predict with existing methods.

RESULTS

We describe how to generate ligand binding conformations of proteins that move by hinge bending, the largest class of motions. First, we predict the location of the hinge between domains. Second, we apply an Euler rotation to one of the domains about the hinge point. Third, we compute a short-time dynamical trajectory using Molecular Dynamics to equilibrate the protein and ligand and correct unnatural atomic positions. Fourth, we score the generated structures using a novel fitness function which favors closed or holo structures. By iterating the second through fourth steps we systematically minimize the fitness function, thus predicting the conformational change required for small ligand binding for five well studied proteins.

CONCLUSIONS

We demonstrate that the method in most cases successfully predicts the holo conformation given only an apo structure.

pH replica-exchange method based on discrete protonation states

We propose a new algorithm for obtaining proton titration curves of ionizable residues. The algorithm is a pH replica-exchange method (PHREM), which is based on the constant pH algorithm of Mongan et al. (J Comput Chem 2004;25:2038-2048). In the original replica-exchange method, simulations of different replicas are performed at different temperatures, and the temperatures are exchanged between the replicas. In our PHREM, simulations of different replicas are performed at different pH values, and the pHs are exchanged between the replicas. The PHREM was applied to a blocked amino acid and to two protein systems (snake cardiotoxin and turkey ovomucoid third domain), in conjunction with a generalized Born implicit solvent. The performance and accuracy of this algorithm and the original constant pH method (PHMD) were compared. For a single set of simulations at different pHs, the use of PHREM yields more accurate Hill coefficients of titratable residues. By performing multiple sets of constant pH simulations started with different initial states, the accuracy of predicted pK(a) values and Hill coefficients obtained with PHREM and PHMD methods becomes comparable. However, the PHREM algorithm exhibits better samplings of the protonation states of titratable residues and less scatter of the titration points and thus better precision of measured pK(a) values and Hill coefficients. In addition, PHREM exhibits faster convergence of individual simulations than the original constant pH algorithm.

Separating the role of protein restraints and local metal-site interaction chemistry in the thermodynamics of a zinc finger protein

We express the effective Hamiltonian of an ion-binding site in a protein as a combination of the Hamiltonian of the ion-bound site in vacuum and the restraints of the protein on the site. The protein restraints are described by the quadratic elastic network model. The Hamiltonian of the ion-bound site in vacuum is approximated as a generalized Hessian around the minimum energy configuration. The resultant of the two quadratic Hamiltonians is cast into a pure quadratic form. In the canonical ensemble, the quadratic nature of the resultant Hamiltonian allows us to express analytically the excess free energy, enthalpy, and entropy of ion binding to the protein. The analytical expressions allow us to separate the roles of the dynamic restraints imposed by the protein on the binding site and the temperature-independent chemical effects in metal-ligand coordination. For the consensus zinc-finger peptide, relative to the aqueous phase, the calculated free energy of exchanging Zn(2+) with Fe(2+), Co(2+), Ni(2+), and Cd(2+) are in agreement with experiments. The predicted excess enthalpy of ion exchange between Zn(2+) and Co(2+) also agrees with the available experimental estimate. The free energy of applying the protein restraints reveals that relative to Zn(2+), the Co(2+), and Cd(2+)-site clusters are more destabilized by the protein restraints. This leads to an experimentally testable hypothesis that a tetrahedral metal binding site with minimal protein restraints will be less selective for Zn(2+) over Co(2+) and Cd(2+) compared to a zinc finger peptide. No appreciable change is expected for Fe(2+) and Ni(2+). The framework presented here may prove useful in protein engineering to tune metal selectivity.

Probing the structural and energetic basis of kinesin-microtubule binding using computational alanine-scanning mutagenesis

Kinesin-microtubule (MT) binding plays a critical role in facilitating and regulating the motor function of kinesins. To obtain a detailed structural and energetic picture of kinesin-MT binding, we performed large-scale computational alanine-scanning mutagenesis based on long-time molecular dynamics (MD) simulations of the kinesin-MT complex in both ADP and ATP states. First, we built three all-atom kinesin-MT models: human conventional kinesin bound to ADP and mouse KIF1A bound to ADP and ATP. Then, we performed 30 ns MD simulations followed by kinesin-MT binding free energy calculations for both the wild type and mutants obtained after substitution of each charged residue of kinesin with alanine. We found that the kinesin-MT binding free energy is dominated by van der Waals interactions and further enhanced by electrostatic interactions. The calculated mutational changes in kinesin-MT binding free energy are in excellent agreement with results of an experimental alanine-scanning study with a root-mean-square error of ~0.32 kcal/mol [Woehlke, G., et al. (1997) Cell 90, 207-216]. We identified a set of important charged residues involved in the tuning of kinesin-MT binding, which are clustered on several secondary structural elements of kinesin (including well-studied loops L7, L8, L11, and L12, helices α4, α5, and α6, and less-explored loop L2). In particular, we found several key residues that make different contributions to kinesin-MT binding in ADP and ATP states. The mutations of these residues are predicted to fine-tune the motility of kinesin by modulating the conformational transition between the ADP state and the ATP state of kinesin.

Discrete breathers in a realistic coarse-grained model of proteins

We report the results of molecular dynamics simulations of an off-lattice protein model featuring a physical force-field and amino-acid sequence. We show that localized modes of nonlinear origin, discrete breathers (DBs), emerge naturally as continuations of a subset of high-frequency normal modes residing at specific sites dictated by the native fold. DBs are time-periodic, space-localized vibrational modes that exist generically in nonlinear discrete systems and are known for their resilience and ability to concentrate energy for long times. In the case of the small β-barrel structure that we consider, DB-mediated localization occurs on the turns connecting the strands. At high energies, DBs stabilize the structure by concentrating energy on a few sites, while their collapse marks the onset of large-amplitude fluctuations of the protein. Furthermore, we show how breathers develop as energy-accumulating centres following perturbations even at distant locations, thus mediating efficient and irreversible energy transfers. Remarkably, due to the presence of angular potentials, the breather induces a local static distortion of the native fold. Altogether, the combination of these two nonlinear effects may provide a ready means for remotely controlling local conformational changes in proteins.

Accurate flexible fitting of high-resolution protein structures into cryo-electron microscopy maps using coarse-grained pseudo-energy minimization

Cryo-electron microscopy (cryo-EM) has been widely used to explore conformational states of large biomolecular assemblies. The detailed interpretation of cryo-EM data requires the flexible fitting of a known high-resolution protein structure into a low-resolution cryo-EM map. To this end, we have developed what we believe is a new method based on a two-bead-per-residue protein representation, and a modified form of the elastic network model that allows large-scale conformational changes while maintaining pseudobonds and secondary structures. Our method minimizes a pseudo-energy which linearly combines various terms of the modified elastic network model energy with a cryo-EM-fitting score and a collision energy that penalizes steric collisions. Unlike previous flexible fitting efforts using the lowest few normal modes, our method effectively utilizes all normal modes so that both global and local structural changes can be fully modeled. We have validated our method for a diverse set of 10 pairs of protein structures using simulated cryo-EM maps with a range of resolutions and in the absence/presence of random noise. We have shown that our method is both accurate and efficient compared with alternative techniques, and its performance is robust to the addition of random noise. Our method is also shown to be useful for the flexible fitting of three experimental cryo-EM maps.

MSCALE: A General Utility for Multiscale Modeling

The combination of theoretical models of macromolecules that exist at different spatial and temporal scales has become increasingly important for addressing complex biochemical problems. This work describes the extension of concurrent multiscale approaches, introduces a general framework for carrying out calculations, and describes its implementation into the CHARMM macromolecular modeling package. This functionality, termed MSCALE, generalizes both the additive and subtractive multiscale scheme (e.g. QM/MM ONIOM-type), and extends its support to classical force fields, coarse grained modeling (e.g. ENM, GNM, etc.), and a mixture of them all. The MSCALE scheme is completely parallelized with each subsystem running as an independent, but connected calculation. One of the most attractive features of MSCALE is the relative ease of implementation using the standard MPI communication protocol. This allows external access to the framework and facilitates the combination of functionality previously isolated in separate programs. This new facility is fully integrated with free energy perturbation methods, Hessian based methods, and the use of periodicity and symmetry, which allows the calculation of accurate pressures. We demonstrate the utility of this new technique with four examples; (1) subtractive QM/MM and QM/QM calculations; (2) multi-force field alchemical free energy perturbation; (3) integration with the SANDER module of AMBER and the TINKER package to gain access to potentials not available in CHARMM; and (4) mixed resolution (i.e. coarse grain / all-atom) normal mode analysis. The potential of this new tool is clearly established and in conclusion an interesting mathematical problem is highlighted and future improvements are proposed.

Computing ensembles of transitions from stable states: Dynamic importance sampling

There is an increasing dataset of solved biomolecular structures in more than one conformation and increasing evidence that large-scale conformational change is critical for biomolecular function. In this article, we present our implementation of a dynamic importance sampling (DIMS) algorithm that is directed toward improving our understanding of important intermediate states between experimentally defined starting and ending points. This complements traditional molecular dynamics methods where most of the sampling time is spent in the stable free energy wells defined by these initial and final points. As such, the algorithm creates a candidate set of transitions that provide insights for the much slower and probably most important, functionally relevant degrees of freedom. The method is implemented in the program CHARMM and is tested on six systems of growing size and complexity. These systems, the folding of Protein A and of Protein G, the conformational changes in the calcium sensor S100A6, the glucose-galactose-binding protein, maltodextrin, and lactoferrin, are also compared against other approaches that have been suggested in the literature. The results suggest good sampling on a diverse set of intermediates for all six systems with an ability to control the bias and thus to sample distributions of trajectories for the analysis of intermediate states.

Structure modeling from small angle X-ray scattering data with elastic network normal mode analysis

Computational algorithms to construct structural models from SAXS experimental data are reviewed. SAXS data provides a wealth of information to study the structure and dynamics of biological molecules, however it does not provide atomic details of structures. Thus combining the low-resolution data with already known X-ray structure is a common approach to study conformational transitions of biological molecules. This review provides a survey of SAXS modeling approaches. In addition, we will discuss theoretical backgrounds and performance of our approach, in which elastic network normal mode analysis is used to predict reasonable conformational transitions from known X-ray structures, and find alternative conformations that are consistent with SAXS data.

Vibrational entropy and the structural organization of proteins

In this paper we analyze the vibrational spectra of a large ensemble of non-homologous protein structures by means of a novel tool, that we coin Hierarchical Network Model (HNM). Our coarse-grained scheme accounts for the intrinsic heterogeneity of force constants displayed by protein arrangements and also incorporates side chain degrees of freedom. Our analysis shows that vibrational entropy per unit residue correlates with the content of secondary structure. Furthermore, we assess the individual contribution to vibrational entropy of the novel features of our scheme as compared with the predictions of state-of-the-art network models. This analysis highlights the importance of properly accounting for the intrinsic hierarchy in force strengths typical of the different atomic bonds that build up and stabilize protein scaffolds. Finally, we discuss possible implications of our findings in the context of protein aggregation phenomena.

A flexible docking scheme to explore the binding selectivity of PDZ domains

Modeling of protein binding site flexibility in molecular docking is still a challenging problem due to the large conformational space that needs sampling. Here, we propose a flexible receptor docking scheme: A dihedral restrained replica exchange molecular dynamics (REMD), where we incorporate the normal modes obtained by the Elastic Network Model (ENM) as dihedral restraints to speed up the search towards correct binding site conformations. To our knowledge, this is the first approach that uses ENM modes to bias REMD simulations towards binding induced fluctuations in docking studies. In our docking scheme, we first obtain the deformed structures of the unbound protein as initial conformations by moving along the binding fluctuation mode, and perform REMD using the ENM modes as dihedral restraints. Then, we generate an ensemble of multiple receptor conformations (MRCs) by clustering the lowest replica trajectory. Using ROSETTALIGAND, we dock ligands to the clustered conformations to predict the binding pose and affinity. We apply this method to postsynaptic density-95/Dlg/ZO-1 (PDZ) domains; whose dynamics govern their binding specificity. Our approach produces the lowest energy bound complexes with an average ligand root mean square deviation of 0.36 A. We further test our method on (i) homologs and (ii) mutant structures of PDZ where mutations alter the binding selectivity. In both cases, our approach succeeds to predict the correct pose and the affinity of binding peptides. Overall, with this approach, we generate an ensemble of MRCs that leads to predict the binding poses and specificities of a protein complex accurately.

Normal modes and phase transition of the protein chain based on the Hamiltonian formalism

We use the torsional angles of the protein chain as generalized coordinates in the canonical formalism, derive canonical equations of motion, and investigate the coordinate dependence of the kinetic energy expressed in terms of the canonical momenta. We use the formalism to compute the normal-frequency distributions of the α helix and the β sheet, under the assumption that they are stabilized purely through hydrogen bonding. In addition, we obtain the free-energy relations of the α helix, the β sheet, and the random coil of a 15-residue polyalanine. Interestingly, our results predict a phase transition from an α helix to a β sheet at a critical temperature.

A perturbative view of protein structural variation

It was recently found that the lowest-energy collective normal modes dominate the evolutionary divergence of protein structures. This was attributed to a presumed functional importance of such motions, i.e., to natural selection. In contrast to this selectionist explanation, we proposed that the observed behavior could be just the expected physical response of proteins to random mutations. This proposal was based on the success of a linearly forced elastic network model (LFENM) of mutational effects on structure to account for the observed pattern of structural divergence. Here, to further test the mutational explanation and the LFENM, we analyze the structural differences observed not only in homologous (globin-like) proteins but also in unselected experimentally engineered myoglobin mutants and in wild-type variants subject to other perturbations such as ligand-binding and pH changes. We show that the lowest normal modes dominate structural change in all the cases considered and that the LFENM reproduces this behavior quantitatively. The collective nature of the lowest normal modes results in global conformational changes that depend little on the exact nature or location of the perturbation. Significantly, the evolutionarily conserved structural core matches the regions observed to be more robust with respect to mutations, so that the core would be more conserved even under unselected random mutations. In a word, the observed patterns of structural variation can be seen as the natural response of proteins to perturbations and can be adequately modeled using the LFENM, which serves as a common framework to relate a priori different phenomena.

Identification of specificity and promiscuity of PDZ domain interactions through their dynamic behavior

PDZ domains (PDZs), the most common interaction domain proteins, play critical roles in many cellular processes. PDZs perform their job by binding specific protein partners. However, they are very promiscuous, binding to more than one protein, yet selective at the same time. We examined the binding related dynamics of various PDZs to have insight about their specificity and promiscuity. We used full atomic normal mode analysis and a modified coarse-grained elastic network model to compute the binding related dynamics. In the latter model, we introduced specificity for each single parameter constant and included the solvation effect implicitly. The modified model, referred to as specific-Gaussian Network Model (s-GNM), highlights some interesting differences in the conformational changes of PDZs upon binding to Class I or Class II type peptides. By clustering the residue fluctuation profiles of PDZs, we have shown: (i) binding selectivities can be discriminated from their dynamics, and (ii) the dynamics of different structural regions play critical roles for Class I and Class II specificity. s-GNM is further tested on a dual-specific PDZ which showed only Class I specificity when a point mutation exists on the betaA-betaB loop. We observe that the binding dynamics change consistently in the mutated and wild type structures. In addition, we found that the binding induced fluctuation profiles can be used to discriminate the binding selectivity of homolog structures. These results indicate that s-GNM can be a powerful method to study the changes in binding selectivities for mutant or homolog PDZs.