An analysis of core deformations in protein superfamilies

Physical effects of learning

Interacting many-body physical systems ranging from neural networks in the brain to folding proteins to self-modifying electrical circuits can learn to perform diverse tasks. This learning, both in nature and in engineered systems, can occur through evolutionary selection or through dynamical rules that drive active learning from experience. Here, we show that learning in linear physical networks with weak input signals leaves architectural imprints on the Hessian of a physical system. Compared to a generic organization of the system components, (a) the effective physical dimension of the response to inputs decreases, (b) the response of physical degrees of freedom to random perturbations (or system "susceptibility") increases, and (c) the low-eigenvalue eigenvectors of the Hessian align with the task. Overall, these effects embody the typical scenario for learning processes in physical systems in the weak input regime, suggesting ways of discovering whether a physical network may have been trained.

Activation Loop Plasticity and Active Site Coupling in the MAP Kinase, ERK2

Previous studies of the protein kinase, ERK2, using NMR and hydrogen-exchange measurements have shown changes in dynamics accompanying its activation by phosphorylation. However, knowledge about the conformational motions involved is incomplete. Here, we examined ERK2 using long conventional molecular dynamics (MD) simulations starting from crystal structures of phosphorylated (2P) and unphosphorylated (0P) forms. Individual trajectories were run for (5 to 25) μs, totaling 727 μs. The results show unexpected flexibility of the A-loop, with multiple long-lived (>5 μs) conformational states in both 2P- and 0P-ERK2. Differential contact network and principal component analyses reveal coupling between the A-loop fold and active site dynamics, with evidence for conformational selection in the kinase core of 2P-ERK2 but not 0P-ERK2. Simulations of 2P-ERK2 show A-loop states corresponding to restrained dynamics within the N-lobe, including regions around catalytic residues. One A-loop conformer forms lasting interactions with the L16 segment, leading to reduced RMSF and greater compaction in the active site. By contrast, simulations of 0P-ERK2 reveal excursions of A-loop residues away from the C-lobe, leading to greater active site mobility. Thus, the A-loop in ERK2 switches between distinct conformations that reflect coupling with the active site, possibly via the L16 segment. Crystal packing interactions suggest that lattice contacts with the A-loop may restrain its structural variation in X-ray structures of ERK2. The novel conformational states identified by MD expand our understanding of ERK2 regulation, by linking the activated state of the kinase to reduced dynamics and greater compaction surrounding the catalytic site.

The Boltzmann distributions of molecular structures predict likely changes through random mutations

New folded molecular structures can only evolve after arising through mutations. This aspect is modeled using genotype-phenotype maps, which connect sequence changes through mutations to changes in molecular structures. Previous work has shown that the likelihood of appearing through mutations can differ by orders of magnitude from structure to structure and that this can affect the outcomes of evolutionary processes. Thus, we focus on the phenotypic mutation probabilities φqp, i.e., the likelihood that a random mutation changes structure p into structure q. For both RNA secondary structures and the HP protein model, we show that a simple biophysical principle can explain and predict how this likelihood depends on the new structure q: φqp is high if sequences that fold into p as the minimum-free-energy structure are likely to have q as an alternative structure with high Boltzmann frequency. This generalizes the existing concept of plastogenetic congruence from individual sequences to the entire neutral spaces of structures. Our result helps us understand why some structural changes are more likely than others, may be useful for estimating these likelihoods via sampling and makes a connection to alternative structures with high Boltzmann frequency, which could be relevant in evolutionary processes.

Telescoping-Solvation-Box Protocol-Based Umbrella Sampling Method for Potential Mean Force Estimation

Previously, it was shown that the telescoping box scheme, in combination with adaptive steered molecule dynamics (ASMD), can be used to estimate the potential of mean force (PMF) with a decrease in computational cost associated with large solvation boxes. Since ASMD reduces to umbrella sampling (US) in the limit of infinitely slow pulling velocity, a hypothesis was made that the telescoping box scheme can be extended to include the US method. The hypothesis was tested using the unfolding pathway of a polyalanine peptide in a water box and translocation of α-tocopherol through the human membrane. Two different approaches were tried: telescoping US (TELUS), in which the number of solvent molecules was linearly coupled to the reaction coordinate, and Block-TELUS, which was a compromise between the fixed solvation box of the US and the window-wise variable solvation box of TELUS. In the case of polyalanine peptide in a water box, both approaches gave overlapping potential of mean force (PMF) concerning the benchmark US-PMF. Window-wise comparison of properties like root-mean-square inner product, Ramachandran plot, α-helix content, and hydrogen bond formation was used to verify that both approaches captured the same dynamics as the US method. Applying the Block-TELUS protocol in the system with diffusing α-tocopherol through the bilayer resulted in overlapping PMF to its US benchmark. A comparison between the window-wise orientation of the chromanol headgroup also produced almost identical results. This study concluded that with the careful application of telescoping solvation boxes, a less computationally expensive US could be performed for systems where the effect of distant solvent molecules on the configurational space sampled in the window depends on the value of the reaction coordinate.

Combining Protein Conformational Diversity and Phylogenetic Information Using CoDNaS and CoDNaS-Q

CoDNaS (http://ufq.unq.edu.ar/codnas/) and CoDNaS-Q (http://ufq.unq.edu.ar/codnasq) are repositories of proteins with different degrees of conformational diversity. Following the ensemble nature of the native state, conformational diversity represents the structural differences between the conformers in the ensemble. Each entry in CoDNaS and CoDNaS-Q contains a redundant collection of experimentally determined conformers obtained under different conditions. These conformers represent snapshots of the protein dynamism. While CoDNaS contains examples of conformational diversity at the tertiary level, a recent development, CoDNaS-Q, contains examples at the quaternary level. In the emerging age of accurate protein structure prediction by machine learning approaches, many questions remain open regarding the characterization of protein dynamism. In this context, most bioinformatics resources take advantage of distinct features derived from protein alignments, however, the complexity and heterogeneity of information makes it difficult to recover reliable biological signatures. Here we present five protocols to explore tertiary and quaternary conformational diversity at the individual protein level as well as for the characterization of the distribution of conformational diversity at the protein family level in a phylogenetic context. These protocols can provide curated protein families with experimentally known conformational diversity, facilitating the exploration of sequence determinants of protein dynamism. © 2023 Wiley Periodicals LLC. Basic Protocol 1: Assessing conformational diversity with CoDNaS Alternate Protocol 1: Assessing conformational diversity at the quaternary level with CoDNaS-Q Basic Protocol 2: Exploring conformational diversity in a protein family Alternate Protocol 2: Exploring quaternary conformational diversity in a protein family Basic Protocol 3: Representing conformational diversity in a phylogenetic context.

Statistical Learning of Protein Elastic Network from Positional Covariance Matrix

Positional fluctuation and covariance during protein dynamics are key observables for understanding the molecular origin of biological functions. A frequently employed potential energy function for describing protein structural variation at the coarse-gained level is elastic network model (ENM). A long-standing issue in biomolecular simulation is thus the parametrization of ENM spring constants from the components of positional covariance matrix (PCM). Based on sensitivity analysis of PCM, the direct-coupling statistics of each spring, which is a specific combination of position fluctuation and covariance, is found to exhibit prominent signal of parameter dependence. This finding provides the basis for devising the objective function and the scheme of running through the effective one-dimensional optimization of every spring by self-consistent iteration. Formal derivation of the positional covariance statistical learning (PCSL) method also motivates the necessary data regularization for stable calculations. Robust convergence of PCSL is achieved in taking an all-atom molecular dynamics trajectory or an ensemble of homologous structures as input data. The PCSL framework can also be generalized with mixed objective functions to capture specific property such as the residue flexibility profile. Such physical chemistry-based statistical learning thus provides a useful platform for integrating the mechanical information encoded in various experimental or computational data.

The community-function landscape of microbial consortia

Quantitatively linking the composition and function of microbial communities is a major aspiration of microbial ecology. Microbial community functions emerge from a complex web of molecular interactions between cells, which give rise to population-level interactions among strains and species. Incorporating this complexity into predictive models is highly challenging. Inspired by a similar problem in genetics of predicting quantitative phenotypes from genotypes, an ecological community-function (or structure-function) landscape could be defined that maps community composition and function. In this piece, we present an overview of our current understanding of these community landscapes, their uses, limitations, and open questions. We argue that exploiting the parallels between both landscapes could bring powerful predictive methodologies from evolution and genetics into ecology, providing a boost to our ability to engineer and optimize microbial consortia.

AlphaFold2 models indicate that protein sequence determines both structure and dynamics

AlphaFold 2 (AF2) has placed Molecular Biology in a new era where we can visualize, analyze and interpret the structures and functions of all proteins solely from their primary sequences. We performed AF2 structure predictions for various protein systems, including globular proteins, a multi-domain protein, an intrinsically disordered protein (IDP), a randomized protein, two larger proteins (> 1000 AA), a heterodimer and a homodimer protein complex. Our results show that along with the three dimensional (3D) structures, AF2 also decodes protein sequences into residue flexibilities via both the predicted local distance difference test (pLDDT) scores of the models, and the predicted aligned error (PAE) maps. We show that PAE maps from AF2 are correlated with the distance variation (DV) matrices from molecular dynamics (MD) simulations, which reveals that the PAE maps can predict the dynamical nature of protein residues. Here, we introduce the AF2-scores, which are simply derived from pLDDT scores and are in the range of [0, 1]. We found that for most protein models, including large proteins and protein complexes, the AF2-scores are highly correlated with the root mean square fluctuations (RMSF) calculated from MD simulations. However, for an IDP and a randomized protein, the AF2-scores do not correlate with the RMSF from MD, especially for the IDP. Our results indicate that the protein structures predicted by AF2 also convey information of the residue flexibility, i.e., protein dynamics.

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.

GTP Cyclohydrolase I as a Potential Drug Target: New Insights into Its Allosteric Modulation via Normal Mode Analysis

Guanosine triphosphate (GTP) cyclohydrolase I (GCH1) catalyzes the conversion of GTP into dihydroneopterin triphosphate (DHNP). DHNP is the first intermediate of the folate de novo biosynthesis pathway in prokaryotic and lower eukaryotic microorganisms and the tetrahydrobiopterin (BH4) biosynthesis pathway in higher eukaryotes. The de novo folate biosynthesis provides essential cofactors for DNA replication, cell division, and synthesis of key amino acids in rapidly replicating pathogen cells, such as Plasmodium falciparum (P. falciparum), a causative agent of malaria. In eukaryotes, the product of the BH4 biosynthesis pathway is essential for the production of nitric oxide and several neurotransmitter precursors. An increased copy number of the malaria parasite P. falciparum GCH1 gene has been reported to influence antimalarial antifolate drug resistance evolution, whereas mutations in the human GCH1 are associated with neuropathic and inflammatory pain disorders. Thus, GCH1 stands as an important and attractive drug target for developing therapeutics. The GCH1 intrinsic dynamics that modulate its activity remains unclear, and key sites that exert allosteric effects across the structure are yet to be elucidated. This study employed the anisotropic network model to analyze the intrinsic motions of the GCH1 structure alone and in complex with its regulatory partner protein. We showed that the GCH1 tunnel-gating mechanism is regulated by a global shear motion and an outward expansion of the central five-helix bundle. We further identified hotspot residues within sites of structural significance for the GCH1 intrinsic allosteric modulation. The obtained results can provide a solid starting point to design novel antineuropathic treatments for humans and novel antimalarial drugs against the malaria parasite P. falciparum GCH1 enzyme.

Dynamics-Evolution Correspondence in Protein Structures

The genotype-phenotype mapping of proteins is a fundamental question in structural biology. In this Letter, with the analysis of a large dataset of proteins from hundreds of protein families, we quantitatively demonstrate the correlations between the noise-induced protein dynamics and mutation-induced variations of native structures, indicating the dynamics-evolution correspondence of proteins. Based on the investigations of the linear responses of native proteins, the origin of such a correspondence is elucidated. It is essential that the noise- and mutation-induced deformations of the proteins are restricted on a common low-dimensional subspace, as confirmed from the data. These results suggest an evolutionary mechanism of the proteins gaining both dynamical flexibility and evolutionary structural variability.

The variation among sites of protein structure divergence is shaped by mutation and scaled by selection

Protein structures do not evolve uniformly, but the degree of structure divergence varies among sites. The resulting site-dependent structure divergence patterns emerge from a process that involves mutation and selection, which may both, in principle, influence the emergent pattern. In contrast with sequence divergence patterns, which are known to be mainly determined by selection, the relative contributions of mutation and selection to structure divergence patterns is unclear. Here, studying 6 protein families with a mechanistic biophysical model of protein evolution, we untangle the effects of mutation and selection. We found that even in the absence of selection, structure divergence varies from site to site because the mutational sensitivity is not uniform. Selection scales the profile, increasing its amplitude, without changing its shape. This scaling effect follows from the similarity between mutational sensitivity and sequence variability profiles.

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The degree of evolutionary divergence of protein structures varies among sites.

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A Mutation-Selection model (MSM) of protein structure evolution with selection for stability is developed.

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Even in the case of no selection, the sensitivity of the structure to random mutations varies among sites. Selection amplifies this variation but it does not affect its shape.

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This scaling effect of selection follows from the similarity between the selection-independent mutational sensitivity and the selection-dependent sequence divergence, the two contributions that are combined to produce the observed structural divergence profile.

The NRGTEN Python package: an extensible toolkit for coarse-grained normal mode analysis of proteins, nucleic acids, small molecules and their complexes

SUMMARY

The Najmanovich Research Group Toolkit for Elastic Networks (NRGTEN) is a Python toolkit that implements four different NMA models in addition to popular and novel metrics to benchmark and measure properties from these models. Furthermore, the toolkit is available as a public Python package and is easily extensible for the development or implementation of additional NMA models. The inclusion of the ENCoM model (Elastic Network Contact Model) developed in our group within NRGTEN is noteworthy, owing to its account for the specific chemical nature of atomic interactions.

AVAILABILITY AND IMPLEMENTATION

https://github.com/gregorpatof/nrgten_package/.

Using normal mode analysis on protein structural models. How far can we go on our predictions?

Normal mode analysis (NMA) is a fast and inexpensive approach that is largely used to gain insight into functional protein motions, and more recently to create conformations for further computational studies. However, when the protein structure is unknown, the use of computational models is necessary. Here, we analyze the capacity of NMA in internal coordinate space to predict protein motion, its intrinsic flexibility, and atomic displacements, using protein models instead of native structures, and the possibility to use it for model refinement. Our results show that NMA is quite insensitive to modeling errors, but that calculations are strictly reliable only for very accurate models. Our study also suggests that internal NMA is a more suitable tool for the improvement of structural models, and for integrating them with experimental data or in other computational techniques, such as protein docking or more refined molecular dynamics simulations.

A Coarse-Grained Methodology Identifies Intrinsic Mechanisms That Dissociate Interacting Protein Pairs

We address the problem of triggering dissociation events between proteins that have formed a complex. We have collected a set of 25 non-redundant, functionally diverse protein complexes having high-resolution three-dimensional structures in both the unbound and bound forms. We unify elastic network models with perturbation response scanning (PRS) methodology as an efficient approach for predicting residues that have the propensity to trigger dissociation of an interacting protein pair, using the three-dimensional structures of the bound and unbound proteins as input. PRS reveals that while for a group of protein pairs, residues involved in the conformational shifts are confined to regions with large motions, there are others where they originate from parts of the protein unaffected structurally by binding. Strikingly, only a few of the complexes have interface residues responsible for dissociation. We find two main modes of response: In one mode, remote control of dissociation in which disruption of the electrostatic potential distribution along protein surfaces play the major role; in the alternative mode, mechanical control of dissociation by remote residues prevail. In the former, dissociation is triggered by changes in the local environment of the protein, e.g., pH or ionic strength, while in the latter, specific perturbations arriving at the controlling residues, e.g., via binding to a third interacting partner is required for decomplexation. We resolve the observations by relying on an electromechanical coupling model which reduces to the usual elastic network result in the limit of the lack of coupling. We validate the approach by illustrating the biological significance of top residues selected by PRS on select cases where we show that the residues whose perturbation leads to the observed conformational changes correspond to either functionally important or highly conserved residues in the complex.

Physical Constraints on Epistasis

Living systems evolve one mutation at a time, but a single mutation can alter the effect of subsequent mutations. The underlying mechanistic determinants of such epistasis are unclear. Here, we demonstrate that the physical dynamics of a biological system can generically constrain epistasis. We analyze models and experimental data on proteins and regulatory networks. In each, we find that if the long-time physical dynamics is dominated by a slow, collective mode, then the dimensionality of mutational effects is reduced. Consequently, epistatic coefficients for different combinations of mutations are no longer independent, even if individually strong. Such epistasis can be summarized as resulting from a global nonlinearity applied to an underlying linear trait, that is, as global epistasis. This constraint, in turn, reduces the ruggedness of the sequence-to-function map. By providing a generic mechanistic origin for experimentally observed global epistasis, our work suggests that slow collective physical modes can make biological systems evolvable.

Predicted dynamical couplings of protein residues characterize catalysis, transport and allostery

MOTIVATION

Protein function is intrinsically linked to native dynamics, but the systematic characterization of functionally relevant dynamics remains elusive besides specific examples. Here we exhaustively characterize three types of dynamical couplings between protein residues: co-directionality (moving along collinear directions), coordination (small fluctuations of the interatomic distance) and deformation (the extent by which perturbations applied at one residue modify the local structure of the other one), which we analytically compute through the torsional network model.

RESULTS

We find that ligand binding sites are characterized by large within-site coordination and co-directionality, much larger than expected for generic sets of residues with equivalent sequence distances. In addition, catalytic sites are characterized by high coordination couplings with other residues in the protein, supporting the view that the overall protein structure facilitates the catalytic dynamics. The binding sites of allosteric effectors are characterized by comparably smaller coordination and higher within-site deformation than other ligands, which supports their dynamic nature. Allosteric inhibitors are coupled to the active site more frequently through deformation than through coordination, while the contrary holds for activators. We characterize the dynamical couplings of the sodium-dependent Leucine transporter protein (LeuT). The couplings between and within sites progress consistently along the transport cycle, providing a mechanistic description of the coupling between the uptake and release of ions and substrate, and they highlight qualitative differences between the wild-type and a mutant for which chloride is necessary for transport.

AVAILABILITY AND IMPLEMENTATION

The program tnm is freely available at https://github.com/ugobas/tnm.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Exploring the conformational transition between the fully folded and locally unfolded substates of Escherichia coli thiol peroxidase

Temporal acquisition of the fully folded conformational substate of the Escherichia coli thiol peroxidase by accelerated molecular dynamics simulations.

Dynamics fingerprints of active conformers of epidermal growth factor receptor kinase

Epidermal growth factor receptor (EGFR) is a prototypical cell-surface receptor that plays a key role in the regulation of cellular signaling, proliferation and differentiation. Mutations of its kinase domain have been associated with the development of a variety of cancers and, therefore, it has been the target of drug design. Single amino acid substitutions (SASs) in this domain have been proven to alter the equilibrium of pre-existing conformer populations. Despite the advances in structural descriptions of its so-called active and inactive conformations, the associated dynamics aspects that characterize them have not been thoroughly studied yet. As the dynamic behaviors and molecular motions of proteins are important for a complete understanding of their structure-function relationships we present a novel procedure, using (or based on) normal mode analysis, to identify the collective dynamics shared among different conformers in EGFR kinase. The method allows the comparison of patterns of low-frequency vibrational modes defining representative directions of motions. Our procedure is able to emphasize the main similarities and differences between the collective dynamics of different conformers. In the case of EGFR kinase, two representative directions of motions have been found as dynamics fingerprints of the active conformers. Protein motion along both directions reveals to have a significant impact on the cavity volume of the main pocket of the active site. Otherwise, the inactive conformers exhibit a more heterogeneous distribution of collective motions. © 2018 Wiley Periodicals, Inc.

Concerted motions and large-scale structural fluctuations of Trichoderma reesei Cel7A cellobiohydrolase

Cellobiohydrolases (CBHs) are key enzymes for the saccharification of cellulose and play major roles in industrial settings for biofuel production. The catalytic core domain of these enzymes exhibits a long and narrow binding tunnel capable of binding glucan chains from crystalline cellulose and processively hydrolyze them. The binding cleft is topped by a set of loops, which are believed to play key roles in substrate binding and cleavage processivity. Here, we present an analysis of the loop motions of the Trichoderma reesei Cel7A catalytic core domain (TrCel7A) using conventional and accelerated molecular dynamics simulations. We observe that the loops exhibit highly coupled fluctuations and cannot move independently of each other. In the absence of a substrate, the characteristic large amplitude dynamics of TrCel7A consists of breathing motions, where the loops undergo open-and-close fluctuations. Upon substrate binding, the open-close fluctuations of the loops are quenched and one of the loops moves parallel to the binding site, possibly to allow processive motion along the glucan chain. Using microsecond accelerated molecular dynamics, we observe large-scale fluctuations of the loops (up to 37 Å) and the entire exposure of the TrCel7A binding site in the absence of the substrate, resembling an endoglucanase. These results suggest that the initial CBH-substrate contact and substrate recognition by the enzyme are similar to that of endoglucanases and, once bound to the substrate, the loops remain closed for proper enzymatic activity.

JED: a Java Essential Dynamics Program for comparative analysis of protein trajectories

BACKGROUND

Essential Dynamics (ED) is a common application of principal component analysis (PCA) to extract biologically relevant motions from atomic trajectories of proteins. Covariance and correlation based PCA are two common approaches to determine PCA modes (eigenvectors) and their eigenvalues. Protein dynamics can be characterized in terms of Cartesian coordinates or internal distance pairs. In understanding protein dynamics, a comparison of trajectories taken from a set of proteins for similarity assessment provides insight into conserved mechanisms. Comprehensive software is needed to facilitate comparative-analysis with user-friendly features that are rooted in best practices from multivariate statistics.

RESULTS

We developed a Java based Essential Dynamics toolkit called JED to compare the ED from multiple protein trajectories. Trajectories from different simulations and different proteins can be pooled for comparative studies. JED implements Cartesian-based coordinates (cPCA) and internal distance pair coordinates (dpPCA) as options to construct covariance (Q) or correlation (R) matrices. Statistical methods are implemented for treating outliers, benchmarking sampling adequacy, characterizing the precision of Q and R, and reporting partial correlations. JED output results as text files that include transformed coordinates for aligned structures, several metrics that quantify protein mobility, PCA modes with their eigenvalues, and displacement vector (DV) projections onto the top principal modes. Pymol scripts together with PDB files allow movies of individual Q- and R-cPCA modes to be visualized, and the essential dynamics occurring within user-selected time scales. Subspaces defined by the top eigenvectors are compared using several statistical metrics to quantify similarity/overlap of high dimensional vector spaces. Free energy landscapes can be generated for both cPCA and dpPCA.

CONCLUSIONS

JED offers a convenient toolkit that encourages best practices in applying multivariate statistics methods to perform comparative studies of essential dynamics over multiple proteins. For each protein, Cartesian coordinates or internal distance pairs can be employed over the entire structure or user-selected parts to quantify similarity/differences in mobility and correlations in dynamics to develop insight into protein structure/function relationships.

Similarity in Shape Dictates Signature Intrinsic Dynamics Despite No Functional Conservation in TIM Barrel Enzymes

The conservation of the intrinsic dynamics of proteins emerges as we attempt to understand the relationship between sequence, structure and functional conservation. We characterise the conservation of such dynamics in a case where the structure is conserved but function differs greatly. The triosephosphate isomerase barrel fold (TBF), renowned for its 8 β-strand-α-helix repeats that close to form a barrel, is one of the most diverse and abundant folds found in known protein structures. Proteins with this fold have diverse enzymatic functions spanning five of six Enzyme Commission classes, and we have picked five different superfamily candidates for our analysis using elastic network models. We find that the overall shape is a large determinant in the similarity of the intrinsic dynamics, regardless of function. In particular, the β-barrel core is highly rigid, while the α-helices that flank the β-strands have greater relative mobility, allowing for the many possibilities for placement of catalytic residues. We find that these elements correlate with each other via the loops that link them, as opposed to being directly correlated. We are also able to analyse the types of motions encoded by the normal mode vectors of the α-helices. We suggest that the global conservation of the intrinsic dynamics in the TBF contributes greatly to its success as an enzymatic scaffold both through evolution and enzyme design.

Evolutionary Conserved Positions Define Protein Conformational Diversity

Conformational diversity of the native state plays a central role in modulating protein function. The selection paradigm sustains that different ligands shift the conformational equilibrium through their binding to highest-affinity conformers. Intramolecular vibrational dynamics associated to each conformation should guarantee conformational transitions, which due to its importance, could possibly be associated with evolutionary conserved traits. Normal mode analysis, based on a coarse-grained model of the protein, can provide the required information to explore these features. Herein, we present a novel procedure to identify key positions sustaining the conformational diversity associated to ligand binding. The method is applied to an adequate refined dataset of 188 paired protein structures in their bound and unbound forms. Firstly, normal modes most involved in the conformational change are selected according to their corresponding overlap with structural distortions introduced by ligand binding. The subspace defined by these modes is used to analyze the effect of simulated point mutations on preserving the conformational diversity of the protein. We find a negative correlation between the effects of mutations on these normal mode subspaces associated to ligand-binding and position-specific evolutionary conservations obtained from multiple sequence-structure alignments. Positions whose mutations are found to alter the most these subspaces are defined as key positions, that is, dynamically important residues that mediate the ligand-binding conformational change. These positions are shown to be evolutionary conserved, mostly buried aliphatic residues localized in regular structural regions of the protein like β-sheets and α-helix.

E-pharmacophore filtering and molecular dynamics simulation studies in the discovery of potent drug-like molecules for chronic kidney disease

Chronic kidney disease (CKD) is a prominent health issue reported globally. The level of the vitamin D receptor (VDR) and cytochrome P450 enzyme 24-hydroxylase (CYP24A1) are crucial in the pathogenesis of secondary hyperparathyroidism (sHPT) in CKD. An elevated expression of the CYP24A1 leads to the deficiency of vitamin D and resistance to vitamin D therapy. Hence, VDR agonists and CYP24A1 antagonists are suggested to CKD patients for the management of biochemical complications. CTA-018 is a recently reported analog and acts as a potent CYP24A1 inhibitor. It inhibits CYP24A1 with an IC₅₀ 27 ± 6 nM, about 10 times more potentially than the non-selective inhibitor ketoconazole (253 ± 20 nM), and it is also been reported to induce the VDR expression. Thus, CTA-018 is under clinical trial among CKD patients. In this study, combined molecular docking and pharmacophore filtering were employed to identify compounds better than CTA-018. A huge set of 9127 compounds from Sweet Lead database were docked into the active site of VDR using Glide XP program. E-pharmacophore was developed from both the targets along with CTA-018. The compounds retrieved from the two different pharmacophore-based screening were re-docked into the active site of CYP24A1. The hits that bind well at both the active sites and matched with the pharmacophore models were considered as possible dual functional molecules against VDR and CYP24A1. Further, molecular dynamics simulation and subsequent energy decomposition analyses were also performed to study the role of specific amino acids in the active site of both VDR and CYP24A1.

Revealing an outward-facing open conformational state in a CLC Cl(-)/H(+) exchange transporter

CLC secondary active transporters exchange Cl^- for H⁺. Crystal structures have suggested that the conformational change from occluded to outward-facing states is unusually simple, involving only the rotation of a conserved glutamate (Glu_ex) upon its protonation. Using ¹⁹F NMR, we show that as [H⁺] is increased to protonate Glu_ex and enrich the outward-facing state, a residue ~20 Å away from Glu_ex, near the subunit interface, moves from buried to solvent-exposed. Consistent with functional relevance of this motion, constriction via inter-subunit cross-linking reduces transport. Molecular dynamics simulations indicate that the cross-link dampens extracellular gate-opening motions. In support of this model, mutations that decrease steric contact between Helix N (part of the extracellular gate) and Helix P (at the subunit interface) remove the inhibitory effect of the cross-link. Together, these results demonstrate the formation of a previously uncharacterized 'outward-facing open' state, and highlight the relevance of global structural changes in CLC function.

DOI:http://dx.doi.org/10.7554/eLife.11189.001

Cells have transporter proteins on their surface to carry molecules in and out of the cell. For example, the CLC family of transporters move two chloride ions in one direction at the same time as moving one hydrogen ion in the opposite direction.

To be able to move these ions in opposite directions, transporters have to cycle through a series of shapes in which the ions can only access alternate sides of the membrane. First, the transporter adopts an 'outward-facing' shape when the ions first bind to the transporter, then it switches into the 'occluded' shape to move the ions through the membrane. Finally, the transporter takes on the 'inward-facing' shape to release the ions on the other side of the membrane. However, structural studies of CLCs suggest that the structures of these proteins do not change much while they are moving ions, which suggests that they might work in a different way.

Khantwal, Abraham et al. have now used techniques called “nuclear magnetic resonance” and "double electron-electron resonance" to investigate how a CLC from a bacterium moves ions. The experiments suggest that when the transporter adopts the outward-facing shape, points on the protein known as Y419 and D417 shift their positions. Chemically linking two regions of the CLC prevented this movement and inhibited the transport of chloride ions across the membrane.

Khantwal, Abraham et al. then used a computer simulation to model how the protein changes shape in more detail. This model predicts that two regions of the transporter undergo major rearrangements resulting in a gate-opening motion that widens a passage to allow the chloride ions to bind to the protein. Khantwal, Abraham et al.’s findings will prompt future studies to reveal the other shapes and how CLCs transition between them.

DOI:http://dx.doi.org/10.7554/eLife.11189.002

New generation of elastic network models

The intrinsic flexibility of proteins and nucleic acids can be grasped from remarkably simple mechanical models of particles connected by springs. In recent decades, Elastic Network Models (ENMs) combined with Normal Model Analysis widely confirmed their ability to predict biologically relevant motions of biomolecules and soon became a popular methodology to reveal large-scale dynamics in multiple structural biology scenarios. The simplicity, robustness, low computational cost, and relatively high accuracy are the reasons behind the success of ENMs. This review focuses on recent advances in the development and application of ENMs, paying particular attention to combinations with experimental data. Successful application scenarios include large macromolecular machines, structural refinement, docking, and evolutionary conservation.

Molecular dynamics simulations: advances and applications

Molecular dynamics simulations have evolved into a mature technique that can be used effectively to understand macromolecular structure-to-function relationships. Present simulation times are close to biologically relevant ones. Information gathered about the dynamic properties of macromolecules is rich enough to shift the usual paradigm of structural bioinformatics from studying single structures to analyze conformational ensembles. Here, we describe the foundations of molecular dynamics and the improvements made in the direction of getting such ensemble. Specific application of the technique to three main issues (allosteric regulation, docking, and structure refinement) is discussed.

Comparison of the Internal Dynamics of Metalloproteases Provides New Insights on Their Function and Evolution

Metalloproteases have evolved in a vast number of biological systems, being one of the most diverse types of proteases and presenting a wide range of folds and catalytic metal ions. Given the increasing understanding of protein internal dynamics and its role in enzyme function, we are interested in assessing how the structural heterogeneity of metalloproteases translates into their dynamics. Therefore, the dynamical profile of the clan MA type protein thermolysin, derived from an Elastic Network Model of protein structure, was evaluated against those obtained from a set of experimental structures and molecular dynamics simulation trajectories. A close correspondence was obtained between modes derived from the coarse-grained model and the subspace of functionally-relevant motions observed experimentally, the later being shown to be encoded in the internal dynamics of the protein. This prompted the use of dynamics-based comparison methods that employ such coarse-grained models in a representative set of clan members, allowing for its quantitative description in terms of structural and dynamical variability. Although members show structural similarity, they nonetheless present distinct dynamical profiles, with no apparent correlation between structural and dynamical relatedness. However, previously unnoticed dynamical similarity was found between the relevant members Carboxypeptidase Pfu, Leishmanolysin, and Botulinum Neurotoxin Type A, despite sharing no structural similarity. Inspection of the respective alignments shows that dynamical similarity has a functional basis, namely the need for maintaining proper intermolecular interactions with the respective substrates. These results suggest that distinct selective pressure mechanisms act on metalloproteases at structural and dynamical levels through the course of their evolution. This work shows how new insights on metalloprotease function and evolution can be assessed with comparison schemes that incorporate information on protein dynamics. The integration of these newly developed tools, if applied to other protein families, can lead to more accurate and descriptive protein classification systems.

Adaptability of protein structures to enable functional interactions and evolutionary implications

Several studies in recent years have drawn attention to the ability of proteins to adapt to intermolecular interactions by conformational changes along structure-encoded collective modes of motions. These so-called soft modes, primarily driven by entropic effects, facilitate, if not enable, functional interactions. They represent excursions on the conformational space along principal low-ascent directions/paths away from the original free energy minimum, and they are accessible to the protein even before protein-protein/ligand interactions. An emerging concept from these studies is the evolution of structures or modular domains to favor such modes of motion that will be recruited or integrated for enabling functional interactions. Structural dynamics, including the allosteric switches in conformation that are often stabilized upon formation of complexes and multimeric assemblies, emerge as key properties that are evolutionarily maintained to accomplish biological activities, consistent with the paradigm sequence→structure→dynamics→function where 'dynamics' bridges structure and function.

Comparison of intrinsic dynamics of cytochrome p450 proteins using normal mode analysis

Cytochrome P450 enzymes are hemeproteins that catalyze the monooxygenation of a wide-range of structurally diverse substrates of endogenous and exogenous origin. These heme monooxygenases receive electrons from NADH/NADPH via electron transfer proteins. The cytochrome P450 enzymes, which constitute a diverse superfamily of more than 8,700 proteins, share a common tertiary fold but < 25% sequence identity. Based on their electron transfer protein partner, cytochrome P450 proteins are classified into six broad classes. Traditional methods of pro are based on the canonical paradigm that attributes proteins' function to their three-dimensional structure, which is determined by their primary structure that is the amino acid sequence. It is increasingly recognized that protein dynamics play an important role in molecular recognition and catalytic activity. As the mobility of a protein is an intrinsic property that is encrypted in its primary structure, we examined if different classes of cytochrome P450 enzymes display any unique patterns of intrinsic mobility. Normal mode analysis was performed to characterize the intrinsic dynamics of five classes of cytochrome P450 proteins. The present study revealed that cytochrome P450 enzymes share a strong dynamic similarity (root mean squared inner product > 55% and Bhattacharyya coefficient > 80%), despite the low sequence identity (< 25%) and sequence similarity (< 50%) across the cytochrome P450 superfamily. Noticeable differences in Cα atom fluctuations of structural elements responsible for substrate binding were noticed. These differences in residue fluctuations might be crucial for substrate selectivity in these enzymes.

WEBnm@ v2.0: Web server and services for comparing protein flexibility

BACKGROUND

Normal mode analysis (NMA) using elastic network models is a reliable and cost-effective computational method to characterise protein flexibility and by extension, their dynamics. Further insight into the dynamics-function relationship can be gained by comparing protein motions between protein homologs and functional classifications. This can be achieved by comparing normal modes obtained from sets of evolutionary related proteins.

RESULTS

We have developed an automated tool for comparative NMA of a set of pre-aligned protein structures. The user can submit a sequence alignment in the FASTA format and the corresponding coordinate files in the Protein Data Bank (PDB) format. The computed normalised squared atomic fluctuations and atomic deformation energies of the submitted structures can be easily compared on graphs provided by the web user interface. The web server provides pairwise comparison of the dynamics of all proteins included in the submitted set using two measures: the Root Mean Squared Inner Product and the Bhattacharyya Coefficient. The Comparative Analysis has been implemented on our web server for NMA, WEBnm@, which also provides recently upgraded functionality for NMA of single protein structures. This includes new visualisations of protein motion, visualisation of inter-residue correlations and the analysis of conformational change using the overlap analysis. In addition, programmatic access to WEBnm@ is now available through a SOAP-based web service. Webnm@ is available at http://apps.cbu.uib.no/webnma .

CONCLUSION

WEBnm@ v2.0 is an online tool offering unique capability for comparative NMA on multiple protein structures. Along with a convenient web interface, powerful computing resources, and several methods for mode analyses, WEBnm@ facilitates the assessment of protein flexibility within protein families and superfamilies. These analyses can give a good view of how the structures move and how the flexibility is conserved over the different structures.

Evolution of oligomeric state through allosteric pathways that mimic ligand binding

Evolution and design of protein complexes are almost always viewed through the lens of amino acid mutations at protein interfaces. We showed previously that residues not involved in the physical interaction between proteins make important contributions to oligomerization by acting indirectly or allosterically. In this work, we sought to investigate the mechanism by which allosteric mutations act, using the example of the PyrR family of pyrimidine operon attenuators. In this family, a perfectly sequence-conserved helix that forms a tetrameric interface is exposed as solvent-accessible surface in dimeric orthologs. This means that mutations must be acting from a distance to destabilize the interface. We identified 11 key mutations controlling oligomeric state, all distant from the interfaces and outside ligand-binding pockets. Finally, we show that the key mutations introduce conformational changes equivalent to the conformational shift between the free versus nucleotide-bound conformations of the proteins.

Comparing the intrinsic dynamics of multiple protein structures using elastic network models

BACKGROUND

Elastic network models (ENMs) are based on the simple idea that a protein can be described as a set of particles connected by springs, which can then be used to describe its intrinsic flexibility using, for example, normal mode analysis. Since the introduction of the first ENM by Monique Tirion in 1996, several variants using coarser protein models have been proposed and their reliability for the description of protein intrinsic dynamics has been widely demonstrated. Lately an increasing number of studies have focused on the meaning of slow dynamics for protein function and its potential conservation through evolution. This leads naturally to comparisons of the intrinsic dynamics of multiple protein structures with varying levels of similarity.

SCOPE OF REVIEW

We describe computational strategies for calculating and comparing intrinsic dynamics of multiple proteins using elastic network models, as well as a selection of examples from the recent literature.

MAJOR CONCLUSIONS

The increasing interest for comparing dynamics across protein structures with various levels of similarity, has led to the establishment and validation of reliable computational strategies using ENMs. Comparing dynamics has been shown to be a viable way for gaining greater understanding for the mechanisms employed by proteins for their function. Choices of ENM parameters, structure alignment or similarity measures will likely influence the interpretation of the comparative analysis of protein motion.

GENERAL SIGNIFICANCE

Understanding the relation between protein function and dynamics is relevant to the fundamental understanding of protein structure-dynamics-function relationship. This article is part of a Special Issue entitled Recent developments of molecular dynamics.

Elastic network models capture the motions apparent within ensembles of RNA structures

The role of structure and dynamics in mechanisms for RNA becomes increasingly important. Computational approaches using simple dynamics models have been successful at predicting the motions of proteins and are often applied to ribonucleo-protein complexes but have not been thoroughly tested for well-packed nucleic acid structures. In order to characterize a true set of motions, we investigate the apparent motions from 16 ensembles of experimentally determined RNA structures. These indicate a relatively limited set of motions that are captured by a small set of principal components (PCs). These limited motions closely resemble the motions computed from low frequency normal modes from elastic network models (ENMs), either at atomic or coarse-grained resolution. Various ENM model types, parameters, and structure representations are tested here against the experimental RNA structural ensembles, exposing differences between models for proteins and for folded RNAs. Differences in performance are seen, depending on the structure alignment algorithm used to generate PCs, modulating the apparent utility of ENMs but not significantly impacting their ability to generate functional motions. The loss of dynamical information upon coarse-graining is somewhat larger for RNAs than for globular proteins, indicating, perhaps, the lower cooperativity of the less densely packed RNA. However, the RNA structures show less sensitivity to the elastic network model parameters than do proteins. These findings further demonstrate the utility of ENMs and the appropriateness of their application to well-packed RNA-only structures, justifying their use for studying the dynamics of ribonucleo-proteins, such as the ribosome and regulatory RNAs.

A theoretical view of protein dynamics

Proteins are fascinating supramolecular structures, which are able to recognize ligands transforming binding information into chemical signals. They can transfer information across the cell, can catalyse complex chemical reactions, and are able to transform energy into work with much more efficiency than any human engine. The unique abilities of proteins are tightly coupled with their dynamic properties, which are coded in a complex way in the sequence and carefully refined by evolution. Despite its importance, our experimental knowledge of protein dynamics is still rather limited, and mostly derived from theoretical calculations. I will review here, in a systematic way, the current state-of-the-art theoretical approaches to the study of protein dynamics, emphasizing the most recent advances, examples of use and the expected lines of development in the near future.

Phylogenetic and biological significance of evolutionary elements from metazoan mitochondrial genomes

The evolutionary history of living species is usually inferred through the phylogenetic analysis of molecular and morphological information using various mathematical models. New challenges in phylogenetic analysis are centered mostly on the search for accurate and efficient methods to handle the huge amounts of sequence data generated from newer genome sequencing. The next major challenge is the determination of relationships between the evolution of structural elements and their functional implementation, which is largely ignored in previous analyses. Here, we described the discovery of structural elements in metazoan mitochondrial genomes, termed key K-strings, that can serve as a basis for phylogenetic tree construction. Although comprising only a small fraction (0.73%) of all K-strings, these key K-strings are pivotal to the tree construction because they allow for a significant reduction in the computational time required to construct phylogenetic trees, and more importantly, they make significant improvement to the results of phylogenetic inference. The trees constructed from the key K-strings were consistent overall to our current view of metazoan phylogeny and exhibited a more rational topology than the trees constructed by using other conventional methods. Surprisingly, the key K-strings tended to accumulate in the conserved regions of the original sequences, which were most likely due to strong selection pressure. Furthermore, the special structural features of the key K-strings should have some potential applications in the study of the structures and functions relationship of proteins and in the determination of evolutionary trajectory of species. The novelty and potential importance of key K-strings lead us to believe that they are essential evolutionary elements. As such, they may play important roles in the process of species evolution and their physical existence. Further studies could lead to discoveries regarding the relationship between evolution and processes of speciation.

Principal component analysis: a method for determining the essential dynamics of proteins

It has become commonplace to employ principal component analysis to reveal the most important motions in proteins. This method is more commonly known by its acronym, PCA. While most popular molecular dynamics packages inevitably provide PCA tools to analyze protein trajectories, researchers often make inferences of their results without having insight into how to make interpretations, and they are often unaware of limitations and generalizations of such analysis. Here we review best practices for applying standard PCA, describe useful variants, discuss why one may wish to make comparison studies, and describe a set of metrics that make comparisons possible. In practice, one will be forced to make inferences about the essential dynamics of a protein without having the desired amount of samples. Therefore, considerable time is spent on describing how to judge the significance of results, highlighting pitfalls. The topic of PCA is reviewed from the perspective of many practical considerations, and useful recipes are provided.

The critical role of the loops of triosephosphate isomerase for its oligomerization, dynamics, and functionality

Triosephosphate isomerase (TIM) catalyzes the reaction to convert dihydroxyacetone phosphate into glyceraldehyde 3-phosphate, and vice versa. In most organisms, its functional oligomeric state is a homodimer; however, tetramer formation in hyperthermophiles is required for functional activity. The tetrameric TIM structure also provides added stability to the structure, enabling it to function at more extreme temperatures. We apply Principal Component Analysis to find that the TIM structure space is clearly divided into two groups--the open and the closed TIM structures. The distribution of the structures in the open set is much sparser than that in the closed set, showing a greater conformational diversity of the open structures. We also apply the Elastic Network Model to four different TIM structures--an engineered monomeric structure, a dimeric structure from a mesophile--Trypanosoma brucei, and two tetrameric structures from hyperthermophiles Thermotoga maritima and Pyrococcus woesei. We find that dimerization not only stabilizes the structures, it also enhances their functional dynamics. Moreover, tetramerization of the hyperthermophilic structures increases their functional loop dynamics, enabling them to function in the destabilizing environment of extreme temperatures. Computations also show that the functional loop motions, especially loops 6 and 7, are highly coordinated. In summary, our computations reveal the underlying mechanism of the allosteric regulation of the functional loops of the TIM structures, and show that tetramerization of the structure as found in the hyperthermophilic organisms is required to maintain the coordination of the functional loops at a level similar to that in the dimeric mesophilic structure.

Evaluation of Protein Elastic Network Models Based on an Analysis of Collective Motions

Elastic network models (ENMs) are valuable tools for investigating collective motions of proteins, and a rich variety of simple models have been proposed over the past decade. A good representation of the collective motions requires a good approximation of the covariances between the fluctuations of the individual atoms. Nevertheless, most studies have validated such models only by the magnitudes of the single-atom fluctuations they predict. In the present study, we have quantified the agreement between the covariance structure predicted by molecular dynamics (MD) simulations and those predicted by a representative selection of proposed coarse-grained ENMs. We then contrast this approach with the comparison to MD-predicted atomic fluctuations and comparison to crystallographic B-factors. While all the ENMs yield approximations to the MD-predicted covariance structure, we report large and consistent differences between proposed models. We also find that the ability of the ENMs to predict atomic fluctuations is correlated with their ability to capture the covariance structure. In contrast, we find that the models that agree best with B-factors model collective motions less reliably and recommend against using B-factors as a benchmark.

Exploration of conformational transition pathways from coarse-grained simulations

MOTIVATION

A new algorithm to trace conformational transitions in proteins is presented. The method uses discrete molecular dynamics as engine to sample protein conformational space. A multiple minima Go-like potential energy function is used in combination with several enhancing sampling strategies, such as metadynamics, Maxwell Demon molecular dynamics and essential dynamics. The method, which shows an unprecedented computational efficiency, is able to trace a wide range of known experimental transitions. Contrary to simpler methods our strategy does not introduce distortions in the chemical structure of the protein and is able to reproduce well complex non-linear conformational transitions. The method, called GOdMD, can easily introduce additional restraints to the transition (presence of ligand, known intermediate, known maintained contacts, …) and is freely distributed to the community through the Spanish National Bioinformatics Institute (http://mmb.irbbarcelona.org/GOdMD).

AVAILABILITY

Freely available on the web at http://mmb.irbbarcelona.org/GOdMD.