Protein flexibility and dynamics using constraint theory

Rigidity through a Projective Lens

In this paper, we offer an overview of a number of results on the static rigidity and infinitesimal rigidity of discrete structures which are embedded in projective geometric reasoning, representations, and transformations. Part I considers the fundamental case of a bar–joint framework in projective d-space and places particular emphasis on the projective invariance of infinitesimal rigidity, coning between dimensions, transfer to the spherical metric, slide joints and pure conditions for singular configurations. Part II extends the results, tools and concepts from Part I to additional types of rigid structures including body-bar, body–hinge and rod-bar frameworks, all drawing on projective representations, transformations and insights. Part III widens the lens to include the closely related cofactor matroids arising from multivariate splines, which also exhibit the projective invariance. These are another fundamental example of abstract rigidity matroids with deep analogies to rigidity. We conclude in Part IV with commentary on some nearby areas.

Flexibility and mobility of SARS-CoV-2-related protein structures

The worldwide CoVid-19 pandemic has led to an unprecedented push across the whole of the scientific community to develop a potent antiviral drug and vaccine as soon as possible. Existing academic, governmental and industrial institutions and companies have engaged in large-scale screening of existing drugs, in vitro, in vivo and in silico. Here, we are using in silico modelling of possible SARS-CoV-2 drug targets, as deposited on the Protein Databank (PDB), and ascertain their dynamics, flexibility and rigidity. For example, for the SARS-CoV-2 spike protein—using its complete homo-trimer configuration with 2905 residues—our method identifies a large-scale opening and closing of the S1 subunit through movement of the S\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${}^\text{B}$$\end{document}B domain. We compute the full structural information of this process, allowing for docking studies with possible drug structures. In a dedicated database, we present similarly detailed results for the further, nearly 300, thus far resolved SARS-CoV-2-related protein structures in the PDB.

Analysis of Protein Disorder Predictions in the Light of a Protein Structural Alphabet

Intrinsically-disordered protein (IDP) characterization was an amazing change of paradigm in our classical sequence-structure-function theory. Moreover, IDPs are over-represented in major disease pathways and are now often targeted using small molecules for therapeutic purposes. This has had created a complex continuum from order-that encompasses rigid and flexible regions-to disorder regions; the latter being not accessible through classical crystallographic methodologies. In X-ray structures, the notion of order is dictated by access to resolved atom positions, providing rigidity and flexibility information with low and high experimental B-factors, while disorder is associated with the missing (non-resolved) residues. Nonetheless, some rigid regions can be found in disorder regions. Using ensembles of IDPs, their local conformations were analyzed in the light of a structural alphabet. An entropy index derived from this structural alphabet allowed us to propose a continuum of states from rigidity to flexibility and finally disorder. In this study, the analysis was extended to comparing these results to disorder predictions, underlying a limited correlation, and so opening new ideas to characterize and predict disorder.

Macrophages show higher levels of engulfment after disruption of cis interactions between CD47 and the checkpoint receptor SIRPα

The macrophage checkpoint receptor SIRPα signals against phagocytosis by binding CD47 expressed on all cells - including macrophages. Here, we found that inhibiting cis interactions between SIRPα and CD47 on the same macrophage increased engulfment ('eating') by approximately the same level as inhibiting trans interactions. Antibody blockade of CD47, as pursued in clinical trials against cancer, was applied separately to human-derived macrophages and to red blood cell (RBC) targets for phagocytosis, and both scenarios produced surprisingly similar increases in RBC engulfment. Blockade of both macrophages and targets resulted in hyper-phagocytosis, and knockdown of macrophage-CD47 likewise increased engulfment of 'foreign' cells and particles, decreased the baseline inhibitory signaling of SIRPα, and linearly increased binding of soluble CD47 in trans, consistent with cis-trans competition. Many cell types express both SIRPα and CD47, including mouse melanoma B16 cells, and CRISPR-mediated deletions modulate B16 phagocytosis, consistent with cis-trans competition. Additionally, soluble SIRPα binding to human CD47 displayed on Chinese hamster ovary (CHO) cells was suppressed by SIRPα co-display, and atomistic computations confirm SIRPα bends and binds CD47 in cis Safety and efficacy profiles for CD47-SIRPα blockade might therefore reflect a disruption of both cis and trans interactions.

Kinematic Flexibility Analysis: Hydrogen Bonding Patterns Impart a Spatial Hierarchy of Protein Motion

Elastic network models (ENMs) and constraint-based, topological rigidity analysis are two distinct, coarse-grained approaches to study conformational flexibility of macromolecules. In the two decades since their introduction, both have contributed significantly to insights into protein molecular mechanisms and function. However, despite a shared purpose of these approaches, the topological nature of rigidity analysis, and thereby the absence of motion modes, has impeded a direct comparison. Here, we present an alternative, kinematic approach to rigidity analysis, which circumvents these drawbacks. We introduce a novel protein hydrogen bond network spectral decomposition, which provides an orthonormal basis for collective motions modulated by noncovalent interactions, analogous to the eigenspectrum of normal modes. The zero modes decompose proteins into rigid clusters identical to those from topological rigidity, while nonzero modes rank protein motions by their hydrogen bond collective energy penalty. Our kinematic flexibility analysis bridges topological rigidity theory and ENM, enabling a detailed analysis of motion modes obtained from both approaches. Analysis of a large, structurally diverse data set revealed that collectivity of protein motions, reported by the Shannon entropy, is significantly reduced for rigidity theory compared to normal mode approaches. Strikingly, kinematic flexibility analysis suggests that the hydrogen bonding network encodes a protein-fold specific, spatial hierarchy of motions, which goes nearly undetected in ENM. This hierarchy reveals distinct motion regimes that rationalize experimental and simulated protein stiffness variations. Kinematic motion modes highly correlate with reported crystallographic B factors and molecular dynamics simulations of adenylate kinase. A formal expression for changes in free energy derived from the spectral decomposition indicates that motions across nearly 40% of modes obey enthalpy-entropy compensation. Taken together, our results suggest that hydrogen bond networks have evolved to modulate protein structure and dynamics, which can be efficiently probed by kinematic flexibility analysis.

Green function of correlated genes in a minimal mechanical model of protein evolution

The function of proteins arises from cooperative interactions and rearrangements of their amino acids, which exhibit large-scale dynamical modes. Long-range correlations have also been revealed in protein sequences, and this has motivated the search for physical links between the observed genetic and dynamic cooperativity. We outline here a simplified theory of protein, which relates sequence correlations to physical interactions and to the emergence of mechanical function. Our protein is modeled as a strongly coupled amino acid network with interactions and motions that are captured by the mechanical propagator, the Green function. The propagator describes how the gene determines the connectivity of the amino acids and thereby, the transmission of forces. Mutations introduce localized perturbations to the propagator that scatter the force field. The emergence of function is manifested by a topological transition when a band of such perturbations divides the protein into subdomains. We find that epistasis-the interaction among mutations in the gene-is related to the nonlinearity of the Green function, which can be interpreted as a sum over multiple scattering paths. We apply this mechanical framework to simulations of protein evolution and observe long-range epistasis, which facilitates collective functional modes.

Ensemble- and Rigidity Theory-Based Perturbation Approach To Analyze Dynamic Allostery

Allostery describes the functional coupling between sites in biomolecules. Recently, the role of changes in protein dynamics for allosteric communication has been highlighted. A quantitative and predictive description of allostery is fundamental for understanding biological processes. Here, we integrate an ensemble-based perturbation approach with the analysis of biomolecular rigidity and flexibility to construct a model of dynamic allostery. Our model, by definition, excludes the possibility of conformational changes, evaluates static, not dynamic, properties of molecular systems, and describes allosteric effects due to ligand binding in terms of a novel free-energy measure. We validated our model on three distinct biomolecular systems: eglin c, protein tyrosine phosphatase 1B, and the lymphocyte function-associated antigen 1 domain. In all cases, it successfully identified key residues for signal transmission in very good agreement with the experiment. It correctly and quantitatively discriminated between positively or negatively cooperative effects for one of the systems. Our model should be a promising tool for the rational discovery of novel allosteric drugs.

On the potential alternate binding change mechanism in a dimeric structure of Pyruvate Phosphate Dikinase

The pyruvate phosphate dikinase (PPDK) reaction mechanism is characterized by a distinct spatial separation of reaction centers and large conformational changes involving an opening-closing motion of the nucleotide-binding domain (NBD) and a swiveling motion of the central domain (CD). However, why PPDK is active only in a dimeric form and to what extent an alternate binding change mechanism could underlie this fact has remained elusive. We performed unbiased molecular dynamics simulations, configurational free energy computations, and rigidity analysis to address this question. Our results support the hypothesis that PPDK dimerization influences the opening-closing motion of the NBDs, and that this influence is mediated via the CDs of both chains. Such an influence would be a prerequisite for an alternate binding change mechanism to occur. To the best of our knowledge, this is the first time that a possible explanation has been suggested as to why only dimeric PPDK is active.

Structure-based prediction of transcription factor binding specificity using an integrative energy function

Transcription factors (TFs) regulate gene expression through binding to specific target DNA sites. Accurate annotation of transcription factor binding sites (TFBSs) at genome scale represents an essential step toward our understanding of gene regulation networks. In this article, we present a structure-based method for computational prediction of TFBSs using a novel, integrative energy (IE) function. The new energy function combines a multibody (MB) knowledge-based potential and two atomic energy terms (hydrogen bond and π interaction) that might not be accurately captured by the knowledge-based potential owing to the mean force nature and low count problem. We applied the new energy function to the TFBS prediction using a non-redundant dataset that consists of TFs from 12 different families. Our results show that the new IE function improves the prediction accuracy over the knowledge-based, statistical potentials, especially for homeodomain TFs, the second largest TF family in mammals.

CONTACT

jguo4@uncc.edu

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

An efficient algorithm for improving structure-based prediction of transcription factor binding sites

Background

Gene expression is regulated by transcription factors binding to specific target DNA sites. Understanding how and where transcription factors bind at genome scale represents an essential step toward our understanding of gene regulation networks. Previously we developed a structure-based method for prediction of transcription factor binding sites using an integrative energy function that combines a knowledge-based multibody potential and two atomic energy terms. While the method performs well, it is not computationally efficient due to the exponential increase in the number of binding sequences to be evaluated for longer binding sites. In this paper, we present an efficient pentamer algorithm by splitting DNA binding sequences into overlapping fragments along with a simplified integrative energy function for transcription factor binding site prediction.

Results

A DNA binding sequence is split into overlapping pentamers (5 base pairs) for calculating transcription factor-pentamer interaction energy. To combine the results from overlapping pentamer scores, we developed two methods, Kmer-Sum and PWM (Position Weight Matrix) stacking, for full-length binding motif prediction. Our results show that both Kmer-Sum and PWM stacking in the new pentamer approach along with a simplified integrative energy function improved transcription factor binding site prediction accuracy and dramatically reduced computation time, especially for longer binding sites.

Conclusion

Our new fragment-based pentamer algorithm and simplified energy function improve both efficiency and accuracy. To our knowledge, this is the first fragment-based method for structure-based transcription factor binding sites prediction.

Electronic supplementary material

The online version of this article (doi:10.1186/s12859-017-1755-0) contains supplementary material, which is available to authorized users.

Designing allostery-inspired response in mechanical networks

Recent advances in designing metamaterials have demonstrated that global mechanical properties of disordered spring networks can be tuned by selectively modifying only a small subset of bonds. Here, using a computationally efficient approach, we extend this idea to tune more general properties of networks. With nearly complete success, we are able to produce a strain between any two target nodes in a network in response to an applied source strain on any other pair of nodes by removing only ∼1% of the bonds. We are also able to control multiple pairs of target nodes, each with a different individual response, from a single source, and to tune multiple independent source/target responses simultaneously into a network. We have fabricated physical networks in macroscopic 2D and 3D systems that exhibit these responses. This work is inspired by the long-range coupled conformational changes that constitute allosteric function in proteins. The fact that allostery is a common means for regulation in biological molecules suggests that it is a relatively easy property to develop through evolution. In analogy, our results show that long-range coupled mechanical responses are similarly easy to achieve in disordered networks.

The flexibility and dynamics of protein disulfide isomerase

We have studied the mobility of the multidomain folding catalyst, protein disulfide isomerase (PDI), by a coarse‐graining approach based on flexibility. We analyze our simulations of yeast PDI (yPDI) using measures of backbone movement, relative positions and orientations of domains, and distances between functional sites. We find that there is interdomain flexibility at every interdomain junction but these show very different characteristics. The extent of interdomain flexibility is such that yPDI's two active sites can approach much more closely than is found in crystal structures—and indeed hinge motion to bring these sites into proximity is the lowest energy normal mode of motion of the protein. The flexibility predicted for yPDI (based on one structure) includes the other known conformation of yPDI and is consistent with (i) the mobility observed experimentally for mammalian PDI and (ii) molecular dynamics. We also observe intradomain flexibility and clear differences between the domains in their propensity for internal motion. Our results suggest that PDI flexibility enables it to interact with many different partner molecules of widely different sizes and shapes, and highlights considerable similarities of yPDI and mammalian PDI. Proteins 2016; 84:1776–1785. © 2016 Wiley Periodicals, Inc.

Flexibility of Bricard's linkages and other structures via resultants and computer algebra

Flexibility of structures is extremely important for chemistry and robotics. Following our earlier work, we study flexibility using polynomial equations, resultants, and a symbolic algorithm of our creation that analyzes the resultant. We show that the software solves a classic arrangement of quadrilaterals in the plane due to Bricard. We fill in several gaps in Bricard's work and discover new flexible arrangements that he was apparently unaware of. This provides strong evidence for the maturity of the software, and is a wonderful example of mathematical discovery via computer assisted experiment.

Molecular dynamics simulation study on the interaction of collagen-like peptides with gelatinase-A (MMP-2)

Although several models have been proposed for the interaction of collagen with gelatinase-A (matrix metalloproteinases-2 (MMP-2)), the extensive role of each domain of gelatinase A in hydrolyzing the collagens with and without interruptions is still elusive. Molecular docking, molecular dynamics (MD) simulation, normal mode analysis (NMA) and framework rigidity optimized dynamics algorithm (FRODAN) based analysis were carried out to understand the function of various domains of MMP-2 upon interaction with collagen like peptides. The results reveal that the collagen binding domain (CBD) binds to the C-terminal of collagen like peptide with interruption. CBD helps in unwinding the loosely packed interrupted region of triple helical structure to a greater extent. It can be possible to speculate that the role of hemopexin (HPX) domain is to prevent further unwinding of collagen like peptide by binding to the other end of the collagen like peptide. The catalytic (CAT) domain then reorients itself to interact with the part of the unwound region of collagen like peptide for further hydrolysis. In conclusion the CBD of MMP-2 recognizes the collagen and aids in unwinding the collagen like peptide with interruptions, and the HPX domain of MMP-2 binds to the other end of the collagen allowing CAT domain to access the cleavage site. This study provides a comprehensive understanding of the structural basis of collagenolysis by MMP-2.

Innovative computer-aided methods for the discovery of new kinase ligands

Recent evidence points to significant roles played by protein kinases in cell signaling and cellular proliferation. Faulty protein kinases are involved in cancer, diabetes and chronic inflammation. Efforts are continuously carried out to discover new inhibitors for selected protein kinases. In this review, we discuss two new computer-aided methodologies we developed to mine virtual databases for new bioactive compounds. One method is ligand-based exploration of the pharmacophoric space of inhibitors of any particular biotarget followed by quantitative structure–activity relationship-based selection of the best pharmacophore(s). The second approach is structure-based assuming that potent ligands come into contact with binding site spots distinct from those contacted by weakly potent ligands. Both approaches yield pharmacophores useful as 3D search queries for the discovery of new bioactive (kinase) inhibitors.

Tuning protein mechanics through an ionic cluster graft from an extremophilic protein

Proteins from extremophilic organisms provide excellent model systems to determine the role of non-covalent interactions in defining protein stability and dynamics as well as being attractive targets for the development of robust biomaterials. Hyperthermophilic proteins have a prevalence of salt bridges, relative to their mesophilic homologues, which are thought to be important for enhanced thermal stability. However, the impact of salt bridges on the mechanical properties of proteins is far from understood. Here, a combination of protein engineering, biophysical characterisation, single molecule force spectroscopy (SMFS) and molecular dynamics (MD) simulations directly investigates the role of salt bridges in the mechanical stability of two cold shock proteins; BsCSP from the mesophilic organism Bacillus subtilis and TmCSP from the hyperthermophilic organism Thermotoga maritima. Single molecule force spectroscopy shows that at ambient temperatures TmCSP is mechanically stronger yet, counter-intuitively, its native state can withstand greater deformation before unfolding (i.e. it is mechanically soft) compared with BsCSP. MD simulations were used to identify the location and quantify the population of salt bridges, and reveal that TmCSP contains a larger number of highly occupied salt bridges than BsCSP. To test the hypothesis that salt-bridges endow these mechanical properties on the hyperthermophilic CSP, a charged triple mutant (CTM) variant of BsCSP was generated by grafting an ionic cluster from TmCSP into the BsCSP scaffold. As expected CTM is thermodynamically more stable and mechanically softer than BsCSP. We show that a grafted ionic cluster can increase the mechanical softness of a protein and speculate that it could provide a mechanical recovery mechanism and that it may be a design feature applicable to other proteins.

The Hydrophobic Effect Contributes to the Closed State of a Simplified Ion Channel through a Conserved Hydrophobic Patch at the Pore-Helix Crossing

Ion selectivity-filter structures are strikingly similar throughout the large family of K⁺⁺ channels and other p-loop-like receptors (i.e., glutamate receptors). At the same time, the triggers for opening these channels, or gating, are diverse. Two questions that remain unanswered regarding these channels are: (1) what force(s) stabilize the closed non-conducting channel-pore conformation? And (2) what is the free energy associated with transitioning from a closed (non-conducting) to an open (conducting) channel-pore conformation? The effects of charge and hydrophobicity on the conformational states of a model tetrameric biological ion channel are shown utilizing the amino acid sequence from the K⁺ channel KcsA as the model “channel”. Its widely conserved hydrophobic bundle crossing located adjacent to the lipid head-groups at the intracellular side of the membrane was calculated to have a 5 kcal/mol free energy difference between modeled open and closed conformations. Simulated mutants of amino acids within the hydrophobic region significantly contribute to the size of this difference. Specifically for KcsA, these residues are part of the pH sensor important for channel gating and our results are in agreement with published electrophysiology data. Our simulations support the idea that the hydrophobic effect contributes significantly to the stability of the closed conformation in tetrameric ion channels with a hydrophobic bundle crossing positioned in proximity to the lipid head groups of the biological membrane.

Partial unfolding and refolding for structure refinement: A unified approach of geometric simulations and molecular dynamics

The most successful protein structure prediction methods to date have been template-based modeling (TBM) or homology modeling, which predicts protein structure based on experimental structures. These high accuracy predictions sometimes retain structural errors due to incorrect templates or a lack of accurate templates in the case of low sequence similarity, making these structures inadequate in drug-design studies or molecular dynamics simulations. We have developed a new physics based approach to the protein refinement problem by mimicking the mechanism of chaperons that rehabilitate misfolded proteins. The template structure is unfolded by selectively (targeted) pulling on different portions of the protein using the geometric based technique FRODA, and then refolded using hierarchically restrained replica exchange molecular dynamics simulations (hr-REMD). FRODA unfolding is used to create a diverse set of topologies for surveying near native-like structures from a template and to provide a set of persistent contacts to be employed during re-folding. We have tested our approach on 13 previous CASP targets and observed that this method of folding an ensemble of partially unfolded structures, through the hierarchical addition of contact restraints (that is, first local and then nonlocal interactions), leads to a refolding of the structure along with refinement in most cases (12/13). Although this approach yields refined models through advancement in sampling, the task of blind selection of the best refined models still needs to be solved. Overall, the method can be useful for improved sampling for low resolution models where certain of the portions of the structure are incorrectly modeled.

The Unfolding MD Simulations of Cyclophilin: Analyzed by Surface Contact Networks and Their Associated Metrics

Currently, considerable interest exists with regard to the dissociation of close packed aminoacids within proteins, in the course of unfolding, which could result in either wet or dry moltenglobules. The progressive disjuncture of residues constituting the hydrophobic core ofcyclophilin from L. donovani (LdCyp) has been studied during the thermal unfolding of the molecule, by molecular dynamics simulations. LdCyp has been represented as a surface contactnetwork (SCN) based on the surface complementarity (Sm) of interacting residues within themolecular interior. The application of Sm to side chain packing within proteins make it a very sensitive indicator of subtle perturbations in packing, in the thermal unfolding of the protein. Network based metrics have been defined to track the sequential changes in the disintegration ofthe SCN spanning the hydrophobic core of LdCyp and these metrics prove to be highly sensitive compared to traditional metrics in indicating the increased conformational (and dynamical) flexibility in the network. These metrics have been applied to suggest criteria distinguishing DMG, WMG and transition state ensembles and to identify key residues involved in crucial conformational/topological events during the unfolding process.

CAB-Align: A Flexible Protein Structure Alignment Method Based on the Residue-Residue Contact Area

Proteins are flexible, and this flexibility has an essential functional role. Flexibility can be observed in loop regions, rearrangements between secondary structure elements, and conformational changes between entire domains. However, most protein structure alignment methods treat protein structures as rigid bodies. Thus, these methods fail to identify the equivalences of residue pairs in regions with flexibility. In this study, we considered that the evolutionary relationship between proteins corresponds directly to the residue–residue physical contacts rather than the three-dimensional (3D) coordinates of proteins. Thus, we developed a new protein structure alignment method, contact area-based alignment (CAB-align), which uses the residue–residue contact area to identify regions of similarity. The main purpose of CAB-align is to identify homologous relationships at the residue level between related protein structures. The CAB-align procedure comprises two main steps: First, a rigid-body alignment method based on local and global 3D structure superposition is employed to generate a sufficient number of initial alignments. Then, iterative dynamic programming is executed to find the optimal alignment. We evaluated the performance and advantages of CAB-align based on four main points: (1) agreement with the gold standard alignment, (2) alignment quality based on an evolutionary relationship without 3D coordinate superposition, (3) consistency of the multiple alignments, and (4) classification agreement with the gold standard classification. Comparisons of CAB-align with other state-of-the-art protein structure alignment methods (TM-align, FATCAT, and DaliLite) using our benchmark dataset showed that CAB-align performed robustly in obtaining high-quality alignments and generating consistent multiple alignments with high coverage and accuracy rates, and it performed extremely well when discriminating between homologous and nonhomologous pairs of proteins in both single and multi-domain comparisons. The CAB-align software is freely available to academic users as stand-alone software at http://www.pharm.kitasato-u.ac.jp/bmd/bmd/Publications.html.

Geometric analysis characterizes molecular rigidity in generic and non-generic protein configurations

Proteins operate and interact with partners by dynamically exchanging between functional substates of a conformational ensemble on a rugged free energy landscape. Understanding how these substates are linked by coordinated, collective motions requires exploring a high-dimensional space, which remains a tremendous challenge. While molecular dynamics simulations can provide atomically detailed insight into the dynamics, computational demands to adequately sample conformational ensembles of large biomolecules and their complexes often require tremendous resources. Kinematic models can provide high-level insights into conformational ensembles and molecular rigidity beyond the reach of molecular dynamics by reducing the dimensionality of the search space. Here, we model a protein as a kinematic linkage and present a new geometric method to characterize molecular rigidity from the constraint manifold Q and its tangent space Q at the current configuration q. In contrast to methods based on combinatorial constraint counting, our method is valid for both generic and non-generic, e.g., singular configurations. Importantly, our geometric approach provides an explicit basis for collective motions along floppy modes, resulting in an efficient procedure to probe conformational space. An atomically detailed structural characterization of coordinated, collective motions would allow us to engineer or allosterically modulate biomolecules by selectively stabilizing conformations that enhance or inhibit function with broad implications for human health.

Activity enhancement of Candida antarctica lipase B by flexibility modulation in helix region surrounding the active site

The activity of Candida antarctica lipase B was improved by mutation of the area surrounding the active site. We changed the edges of four helices surrounding the active site to flexible amino acids. Two mutants, V139E and I255E, obtained as a result of Pichia pastoris expression, showed enhanced specific activity of 9.9 and 8.1 U/mg while that of wild type was 2.3 U/mg for p-nitrophenyl caprylate hydrolysis. It was nearly 5.4-fold and 3.5-fold, respectively. The stability of both mutants on organic solvent was slightly decreased but almost similar with that of wild type. In the kinetic assay, k(cat) values were shown as dominant factor for the enhancement of catalytic efficiency, k(cat)/K(m), since it was 4.1-fold and 3.8-fold, respectively.

Stability and rigidity/flexibility-two sides of the same coin?

Protein molecules require both flexibility and rigidity for functioning. The fast and accurate prediction of protein rigidity/flexibility is one of the important problems in protein science. We have determined flexible regions for four homologous pairs from thermophilic and mesophilic organisms by two methods: the fast FoldUnfold which uses amino acid sequence and the time consuming MDFirst which uses three-dimensional structures. We demonstrate that both methods allow determining flexible regions in protein structure. For three of the four thermophile-mesophile pairs of proteins, FoldUnfold predicts practically the same flexible regions which have been found by the MD/First method. As expected, molecular dynamics simulations show that thermophilic proteins are more rigid in comparison to their mesophilic homologues. Analysis of rigid clusters and their decomposition provides new insights into protein stability. It has been found that the local networks of salt bridges and hydrogen bonds in thermophiles render their structure more stable with respect to fluctuations of individual contacts. Such network includes salt bridge triads Agr-Glu-Lys and Arg-Glu-Arg, or salt bridges (such as Arg-Glu) connected with hydrogen bonds. This ionic network connects alpha helices and rigidifies the structure. Mesophiles can be characterized by stand alone salt bridges and hydrogen bonds or small ionic clusters. Such difference in the network of salt bridges results in different flexibility of homologous proteins. Combining both approaches allows characterizing structural features in atomic detail that determine the rigidity/flexibility of a protein structure. This article is a part of a Special Issue entitled: The emerging dynamic view of proteins: Protein plasticity in allostery, evolution and self-assembly.

Structure fluctuations and conformational changes in protein binding

Structure fluctuations and conformational changes accompany all biological processes involving macromolecules. The paper presents a classification of protein residues based on the normalized equilibrium fluctuations of the residue centers of mass in proteins and a statistical analysis of conformation changes in the side-chains upon binding. Normal mode analysis and an elastic network model were applied to a set of protein complexes to calculate the residue fluctuations and develop the residue classification. Comparison with a classification based on normalized B-factors suggests that the B-factors may underestimate protein flexibility in solvent. Our classification shows that protein loops and disordered fragments are enriched with highly fluctuating residues and depleted with weakly fluctuating residues. Strategies for engineering thermostable proteins are discussed. To calculate the dihedral angles distribution functions, the configuration space was divided into cells by a cubic grid. The effect of protein association on the distribution functions depends on the amino acid type and a grid step in the dihedral angles space. The changes in the dihedral angles increase from the near-backbone dihedral angle to the most distant one, for most residues. On average, one fifth of the interface residues change the rotamer state upon binding, whereas the rest of the interface residues undergo local readjustments within the same rotamer.

Using rigidity analysis to probe mutation-induced structural changes in proteins

Predicting the effect of a single amino acid substitution on the stability of a protein structure is a fundamental task in macromolecular modeling. It has relevance to drug design and understanding of disease-causing protein variants. We present KINARI-Mutagen, a web server for performing in silico mutation experiments on protein structures from the Protein Data Bank. Our rigidity-theoretical approach permits fast evaluation of the effects of mutations that may not be easy to perform in vitro, because it is not always possible to express a protein with a specific amino acid substitution. We use KINARI-Mutagen to identify critical residues, and we show that our predictions correlate with destabilizing mutations to glycine. In two in-depth case studies we show that the mutated residues identified by KINARI-Mutagen as critical correlate with experimental data, and would not have been identified by other methods such as Solvent Accessible Surface Area measurements or residue ranking by contributions to stabilizing interactions. We also generate 48 mutants for 14 proteins, and compare our rigidity-based results against experimental mutation stability data. KINARI-Mutagen is available at http://kinari.cs.umass.edu.

Response of rotation-translation blocked proteins using Langevin dynamics on a locally harmonic landscape

Langevin dynamics is used to compute the time evolution of the nonequilibrium motion of the atomic coordinates of a protein in response to ligand dissociation. The protein potential energy surface (PES) is approximated by a harmonic basin about the minimum of the unliganded state. Upon ligand dissociation, the protein undergoes relaxation from the bound to the unbound state. A coarse graining scheme based on rotation translation blocks (RTB) is applied to the relaxation of the two domain iron transport protein, ferric binding protein. This scheme provides a natural and efficient way to freeze out the small amplitude, high frequency motions within each rigid fragment, thereby allowing for the number of dynamical degrees of freedom to be reduced. The results obtained from all flexible atom (constraint free) dynamics are compared to those obtained using RTB-Langevin dynamics. To assess the impact of the assumed rigid fragment clustering on the temporal relaxation dynamics of the protein molecule, three distinct rigid block decompositions were generated and their responses compared. Each of the decompositions was a variant of the one-block-per-residue grouping, with their force and friction matrices being derived from their fully flexible counterpart. Monitoring the time evolution of the distance separating a selected pair of amino acids, the response curves of the blocked decompositions were similar in shape to each other and to the control system in which all atomic degrees of freedom are fully independent. The similar shape of the blocked responses showed that the variations in grouping had only a minor impact on the kinematics. Compared with the all atom responses, however, the blocked responses were faster as a result of the instantaneous transmission of force throughout each rigid block. This occurred because rigid blocking does not permit any intrablock deformation that could store or divert energy. It was found, however, that this accelerated response could be successfully corrected by scaling each eigenvalue in the appropriate propagation matrix by the least-squares fitted slope of the blocked vs nonblocked eigenvalue spectra. The RTB responses for each test system were dominated by small eigenvalue overdamped Langevin modes. The large eigenvalue members of each response dissipated within the first 5 ps, after which the long time response was dominated by a modest set of low energy, overdamped normal modes, that were characterized by highly cooperative, functionally relevant displacements. The response assuming that the system is in the overdamped limit was compared to the full phase space Langevin dynamics results. The responses after the first 5 ps were nearly identical, confirming that the inertial components were significant only in the initial stages of the relaxation. Since the propagator matrix in the overdamped formulation is real-symmetric and does not require the inertial component in the propagator, the computation time and memory footprint was reduced by 1 order of magnitude.

Inhibition of HIV-1 protease: the rigidity perspective

MOTIVATION

HIV-1 protease is a key drug target due to its role in the life cycle of the HIV-1 virus. Rigidity analysis using the software First is a computationally inexpensive method for inferring functional information from protein crystal structures. We evaluate the rigidity of 206 high-resolution (2 Å or better) X-ray crystal structures of HIV-1 protease and compare the effects of different inhibitors binding to the enzyme.

RESULTS

Inhibitor binding has little effect on the overall rigidity of the protein homodimer, including the rigidity of the active site. The principal effect of inhibitor binding on rigidity is to constrain the flexibility of the β-hairpin flaps, which move to allow access to the active site of the enzyme. We show that commercially available antiviral drugs which target HIV-1 protease can be divided into two classes, those which significantly affect flap rigidity and those which do not. The non-peptidic inhibitor tipranavir is distinctive in its consistently strong effect on flap rigidity.

CONTACT

jack.heal@warwick.ac.uk; r.roemer@warwick.ac.uk

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Changes in Lysozyme Flexibility upon Mutation Are Frequent, Large and Long-Ranged

We investigate changes in human c-type lysozyme flexibility upon mutation via a Distance Constraint Model, which gives a statistical mechanical treatment of network rigidity. Specifically, two dynamical metrics are tracked. Changes in flexibility index quantify differences within backbone flexibility, whereas changes in the cooperativity correlation quantify differences within pairwise mechanical couplings. Regardless of metric, the same general conclusions are drawn. That is, small structural perturbations introduced by single point mutations have a frequent and pronounced affect on lysozyme flexibility that can extend over long distances. Specifically, an appreciable change occurs in backbone flexibility for 48% of the residues, and a change in cooperativity occurs in 42% of residue pairs. The average distance from mutation to a site with a change in flexibility is 17–20 Å. Interestingly, the frequency and scale of the changes within single point mutant structures are generally larger than those observed in the hen egg white lysozyme (HEWL) ortholog, which shares 61% sequence identity with human lysozyme. For example, point mutations often lead to substantial flexibility increases within the β-subdomain, which is consistent with experimental results indicating that it is the nucleation site for amyloid formation. However, β-subdomain flexibility within the human and HEWL orthologs is more similar despite the lowered sequence identity. These results suggest compensating mutations in HEWL reestablish desired properties.

The functional importance of protein dynamics is universally accepted, making the study of dynamical similarities and differences among proteins of the same function an intriguing problem. While some metrics are likely to be conserved across family, differences are also very common. In previous works we have used a Distance Constraint Model to quantify flexibility differences across sets of orthologous proteins, which reproduce this diversity. In the same manner, this work investigates changes occurring upon individual point mutations. Somewhat surprisingly, the small structural perturbations caused by mutation lead to changes throughout the protein. These changes can be quite large, actually surpassing the scale for differences between ortholog pairs. Moreover, changes in flexibility frequently occur at sites far from the mutation site. These results underscore the sensitivity of protein dynamics in connection with allostery, and help explain why differences across protein families are so common.

Exploring the energy landscapes of protein folding simulations with Bayesian computation

Nested sampling is a Bayesian sampling technique developed to explore probability distributions localized in an exponentially small area of the parameter space. The algorithm provides both posterior samples and an estimate of the evidence (marginal likelihood) of the model. The nested sampling algorithm also provides an efficient way to calculate free energies and the expectation value of thermodynamic observables at any temperature, through a simple post processing of the output. Previous applications of the algorithm have yielded large efficiency gains over other sampling techniques, including parallel tempering. In this article, we describe a parallel implementation of the nested sampling algorithm and its application to the problem of protein folding in a Gō-like force field of empirical potentials that were designed to stabilize secondary structure elements in room-temperature simulations. We demonstrate the method by conducting folding simulations on a number of small proteins that are commonly used for testing protein-folding procedures. A topological analysis of the posterior samples is performed to produce energy landscape charts, which give a high-level description of the potential energy surface for the protein folding simulations. These charts provide qualitative insights into both the folding process and the nature of the model and force field used.

Integrating structure-based and ligand-based approaches for computational drug design

Methods utilized in computer-aided drug design can be classified into two major categories: structure based and ligand based, using information on the structure of the protein or on the biological and physicochemical properties of bound ligands, respectively. In recent years there has been a trend towards integrating these two methods in order to enhance the reliability and efficiency of computer-aided drug-design approaches by combining information from both the ligand and the protein. This trend resulted in a variety of methods that include: pseudoreceptor methods, pharmacophore methods, fingerprint methods and approaches integrating docking with similarity-based methods. In this article, we will describe the concepts behind each method and selected applications.

The elastic network model reveals a consistent picture on intrinsic functional dynamics of type II restriction endonucleases

The vibrational dynamics of various type II restriction endonucleases, in complex with cognate/non-cognate DNA and in the apo form, are investigated with the elastic network model in order to reveal common functional mechanisms in this enzyme family. Scissor-like and tong-like motions observed in the slowest modes of all enzymes and their complexes point to common DNA recognition and cleavage mechanisms. Normal mode analysis further points out that the scissor-like motion has an important role in differentiating between cognate and non-cognate sequences at the recognition site, thus implying its catalytic relevance. Flexible regions observed around the DNA-binding site of the enzyme usually concentrate on the highly conserved β-strands, especially after DNA binding. These β-strands may have a structurally stabilizing role in functional dynamics for target site recognition and cleavage. In addition, hot spot residues based on high-frequency modes reveal possible communication pathways between the two distant cleavage sites in the enzyme family. Some of these hot spots also exist on the shortest path between the catalytic sites and are highly conserved.

KINARI-Web: a server for protein rigidity analysis

KINARI-Web is an interactive web server for performing rigidity analysis and visually exploring rigidity properties of proteins. It also provides tools for pre-processing the input data, such as selecting relevant chains from PDB files, adding hydrogen atoms and identifying stabilizing interactions. KINARI-Web offers a quick-start option for beginners, and highly customizable features for the experienced user. Chains, residues or atoms, as well as stabilizing constraints can be selected, removed or added, and the user can designate how different chemical interactions should be modeled during rigidity analysis. The enhanced Jmol-based visualizer allows for zooming in, highlighting or investigating different calculated rigidity properties of a molecular structure. KINARI-Web is freely available at http://kinari.cs.umass.edu.

Significant enhancement of docking sensitivity using implicit ligand sampling

The efficient and accurate quantification of protein-ligand interactions using computational methods is still a challenging task. Two factors strongly contribute to the failure of docking methods to predict free energies of binding accurately: the insufficient incorporation of protein flexibility coupled to ligand binding and the neglected dynamics of the protein-ligand complex in current scoring schemes. We have developed a new methodology, named the 'ligand-model' concept, to sample protein conformations that are relevant for binding structurally diverse sets of ligands. In the ligand-model concept, molecular-dynamics (MD) simulations are performed with a virtual ligand, represented by a collection of functional groups that binds to the protein and dynamically changes its shape and properties during the simulation. The ligand model essentially represents a large ensemble of different chemical species binding to the same target protein. Representative protein structures were obtained from the MD simulation, and docking was performed into this ensemble of protein conformation. Similar binding poses were clustered, and the averaged score was utilized to rerank the poses. We demonstrate that the ligand-model approach yields significant improvements in predicting native-like binding poses and quantifying binding affinities compared to static docking and ensemble docking simulations into protein structures generated from an apo MD simulation.

Learning probabilistic models of hydrogen bond stability from molecular dynamics simulation trajectories

Background

Hydrogen bonds (H-bonds) play a key role in both the formation and stabilization of protein structures. They form and break while a protein deforms, for instance during the transition from a non-functional to a functional state. The intrinsic strength of an individual H-bond has been studied from an energetic viewpoint, but energy alone may not be a very good predictor.

Methods

This paper describes inductive learning methods to train protein-independent probabilistic models of H-bond stability from molecular dynamics (MD) simulation trajectories of various proteins. The training data contains 32 input attributes (predictors) that describe an H-bond and its local environment in a conformation c and the output attribute is the probability that the H-bond will be present in an arbitrary conformation of this protein achievable from c within a time duration Δ. We model dependence of the output variable on the predictors by a regression tree.

Results

Several models are built using 6 MD simulation trajectories containing over 4000 distinct H-bonds (millions of occurrences). Experimental results demonstrate that such models can predict H-bond stability quite well. They perform roughly 20% better than models based on H-bond energy alone. In addition, they can accurately identify a large fraction of the least stable H-bonds in a conformation. In most tests, about 80% of the 10% H-bonds predicted as the least stable are actually among the 10% truly least stable. The important attributes identified during the tree construction are consistent with previous findings.

Conclusions

We use inductive learning methods to build protein-independent probabilistic models to study H-bond stability, and demonstrate that the models perform better than H-bond energy alone.

Flexibility and mobility in mesophilic and thermophilic homologous proteins from molecular dynamics and FoldUnfold method

To function properly protein molecules require both flexibility and rigidity, therefore fast and accurate prediction of protein rigidity/flexibility is one of the important problems in protein science. In this work we used two theoretical approaches to determine flexible regions in four homologous pairs of proteins from thermophilic and mesophilic organisms. Protein pairs chosen in this study were selected to represent four typical folding classes. Our first approach, FoldUnfold, uses amino acid sequence and statistical information on the density of contacts of amino acids in tertiary structures of known globular proteins. The main advantages of such knowledge-based methodology are its computational speed and ability to make predictions in the absence of three-dimensional (3D) structure of a protein. The second approach uses a graph theory-based rigid cluster decomposition termed FIRST, applied together with Molecular Dynamics (MD) simulations of proteins with known structure. While MD simulations are time-consuming, they are the most direct way of studying physical properties of proteins, including their rigidity/flexibility. Flexible regions predicted by both methods in this work were in good agreement with each other. We also showed that high mobility of a site is not necessarily indicative of its high flexibility and vice versa. In our simulations thermophile proteins were less flexible than their mesophilic homologues. Longer flexible loops were found in mesophilic proteins of all classes.

Rationale for more diverse inhibitors in competition with substrates in HIV-1 protease

The structural fluctuations of HIV-1 protease in interaction with its substrates versus inhibitors were analyzed using the anisotropic network model. The directions of fluctuations in the most cooperative functional modes differ mainly around the dynamically key regions, i.e., the hinge axes, which appear to be more flexible in substrate complexes. The flexibility of HIV-1 protease is likely optimized for the substrates' turnover, resulting in substrate complexes being dynamic. In contrast, in an inhibitor complex, the inhibitor should bind and lock down to inactivate the active site. Protease and ligands are not independent. Substrates are also more flexible than inhibitors and have the potential to meet the dynamic distributions that are inherent in the protease. This may suggest a rationale and guidelines for designing inhibitors that can better fit the ensemble of binding sites that are dynamically accessible to the protease.

Allostery and conformational free energy changes in human tryptophanyl-tRNA synthetase from essential dynamics and structure networks

The interdependence of the concept of allostery and enzymatic catalysis, and they being guided by conformational mobility is gaining increased prominence. However, to gain a molecular level understanding of allostery and hence of enzymatic catalysis, it is of utter importance that the networks of amino acids participating in allostery be deciphered. Our lab has been exploring the methods of network analysis combined with molecular dynamics simulations to understand allostery at molecular level. Earlier we had outlined methods to obtain communication paths and then to map the rigid/flexible regions of proteins through network parameters like the shortest correlated paths, cliques, and communities. In this article, we advance the methodology to estimate the conformational populations in terms of cliques/communities formed by interactions including the side-chains and then to compute the ligand-induced population shift. Finally, we obtain the free-energy landscape of the protein in equilibrium, characterizing the free-energy minima accessed by the protein complexes. We have chosen human tryptophanyl-tRNA synthetase (hTrpRS), a protein responsible for charging tryptophan to its cognate tRNA during protein biosynthesis for this investigation. This is a multidomain protein exhibiting excellent allosteric communication. Our approach has provided valuable structural as well as functional insights into the protein. The methodology adopted here is highly generalized to illuminate the linkage between protein structure networks and conformational mobility involved in the allosteric mechanism in any protein with known structure.

Union of geometric constraint-based simulations with molecular dynamics for protein structure prediction

Although proteins are a fundamental unit in biology, the mechanism by which proteins fold into their native state is not well understood. In this work, we explore the assembly of secondary structure units via geometric constraint-based simulations and the effect of refinement of assembled structures using reservoir replica exchange molecular dynamics. Our approach uses two crucial features of these methods: i), geometric simulations speed up the search for nativelike topologies as there are no energy barriers to overcome; and ii), molecular dynamics identifies the low free energy structures and further refines these structures toward the actual native conformation. We use eight alpha-, beta-, and alpha/beta-proteins to test our method. The geometric simulations of our test set result in an average RMSD from native of 3.7 A and this further reduces to 2.7 A after refinement. We also explore the question of robustness of assembly for inaccurate (shifted and shortened) secondary structure. We find that the RMSD from native is highly dependent on the accuracy of secondary structure input, and even slightly shifting the location of secondary structure along the amino acid sequence can lead to a rapid decrease in RMSD to native due to incorrect packing.

Visualization of macromolecular structures

Structural biology is rapidly accumulating a wealth of detailed information about protein function, binding sites, RNA, large assemblies and molecular motions. These data are increasingly of interest to a broader community of life scientists, not just structural experts. Visualization is a primary means for accessing and using these data, yet visualization is also a stumbling block that prevents many life scientists from benefiting from three-dimensional structural data. In this review, we focus on key biological questions where visualizing three-dimensional structures can provide insight and describe available methods and tools.

In Pursuit of Fully Flexible Protein-Ligand Docking: Modeling the Bilateral Mechanism of Binding

Modern structure-based drug design aims at accounting for the intrinsic flexibility of therapeutic relevant targets. Over the last few years a considerable amount of docking approaches that encounter this challenging problem has emerged. Here we provide the readership with an overview of established methods for fully flexible protein-ligand docking and current developments in the field. All methods are based on one of two fundamental models which describe the dynamic behavior of proteins upon ligand binding. Methods for ensemble docking (ED) model the protein conformational change before the ligand is placed, whereas induced-fit docking (IFD) optimizes the protein structure afterwards. A third category of docking approaches is formed by recent approaches that follow both concepts. This categorization allows to comprehensively discover strengths and weaknesses of the individual processes and to extract information for their applicability in real world docking scenarios.

Thermostability in rubredoxin and its relationship to mechanical rigidity

The source of increased stability in proteins from organisms that thrive in extreme thermal environments is not well understood. Previous experimental and theoretical studies have suggested many different features possibly responsible for such thermostability. Many of these thermostabilizing mechanisms can be accounted for in terms of structural rigidity. Thus a plausible hypothesis accounting for this remarkable stability in thermophilic enzymes states that these enzymes have enhanced conformational rigidity at temperatures below their native, functioning temperature. Experimental evidence exists to both support and contradict this supposition. We computationally investigate the relationship between thermostability and rigidity using rubredoxin as a case study. The mechanical rigidity is calculated using atomic models of homologous rubredoxin structures from the hyperthermophile Pyrococcus furiosus and mesophile Clostridium pasteurianum using the FIRST software. A global increase in structural rigidity (equivalently a decrease in flexibility) corresponds to an increase in thermostability. Locally, rigidity differences (between mesophilic and thermophilic structures) agree with differences in protection factors.

Design and characterization of a mutation outside the active site of human thymidylate synthase that affects ligand binding

Owing to its central role in DNA synthesis, human thymidylate synthase (hTS) is a well-established target for chemotherapeutic agents, such as fluoropyrimidines. The use of hTS inhibitors in cancer therapy is limited by their toxicity and the development of cellular drug resistance. Here, with the aim of shedding light on the structural role of the A-helix in fluoropyrimidine resistance, we have created a fluoropyrimidine-resistant mutant by making a single point mutation, Glu30Trp. We postulated that residue 30, which is located in the A-helix, close to but outside the enzyme active site, could have a long-range effect on inhibitor binding. The mutant shows 100 times lower specific activity with respect to the wild-type hTS and is resistant to the classical inhibitor, FdUMP, as shown by a 6-fold higher inhibition constant. Circular dichroism experiments show that the mutant is folded. The results of molecular modeling and simulation suggest that the Glu30Trp mutation gives rise to resistance by altering the hydrogen-bond network between residue 30 and the active site.