Coarse-grained description of protein internal dynamics: an optimal strategy for decomposing proteins in rigid subunits

Surveying the energy landscape of coarse-grained mappings

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

Fast, Accurate, and System-Specific Variable-Resolution Modeling of Proteins

In recent years, a few multiple-resolution modeling strategies have been proposed, in which functionally relevant parts of a biomolecule are described with atomistic resolution, with the remainder of the system being concurrently treated using a coarse-grained model. In most cases, the parametrization of the latter requires lengthy reference all-atom simulations and/or the usage of off-shelf coarse-grained force fields, whose interactions have to be refined to fit the specific system under examination. Here, we overcome these limitations through a novel multiresolution modeling scheme for proteins, dubbed coarse-grained anisotropic network model for variable resolution simulations, or CANVAS. This scheme enables a user-defined modulation of the resolution level throughout the system structure; a fast parametrization of the potential without the necessity of reference simulations; and the straightforward usage of the model on the most commonly used molecular dynamics platforms. The method is presented and validated with two case studies, the enzyme adenylate kinase and the therapeutic antibody pembrolizumab, by comparing the results obtained with the CANVAS model against fully atomistic simulations. The modeling software, implemented in Python, is made freely available for the community on a collaborative github repository.

Assignment of structural domains in proteins using diffusion kernels on graphs

Though proposing algorithmic approaches for protein domain decomposition has been of high interest, the inherent ambiguity to the problem makes it still an active area of research. Besides, accurate automated methods are in high demand as the number of solved structures for complex proteins is on the rise. While majority of the previous efforts for decomposition of 3D structures are centered on the developing clustering algorithms, employing enhanced measures of proximity between the amino acids has remained rather uncharted. If there exists a kernel function that in its reproducing kernel Hilbert space, structural domains of proteins become well separated, then protein structures can be parsed into domains without the need to use a complex clustering algorithm. Inspired by this idea, we developed a protein domain decomposition method based on diffusion kernels on protein graphs. We examined all combinations of four graph node kernels and two clustering algorithms to investigate their capability to decompose protein structures. The proposed method is tested on five of the most commonly used benchmark datasets for protein domain assignment plus a comprehensive non-redundant dataset. The results show a competitive performance of the method utilizing one of the diffusion kernels compared to four of the best automatic methods. Our method is also able to offer alternative partitionings for the same structure which is in line with the subjective definition of protein domain. With a competitive accuracy and balanced performance for the simple and complex structures despite relying on a relatively naive criterion to choose optimal decomposition, the proposed method revealed that diffusion kernels on graphs in particular, and kernel functions in general are promising measures to facilitate parsing proteins into domains and performing different structural analysis on proteins. The size and interconnectedness of the protein graphs make them promising targets for diffusion kernels as measures of affinity between amino acids. The versatility of our method allows the implementation of future kernels with higher performance. The source code of the proposed method is accessible at https://github.com/taherimo/kludo . Also, the proposed method is available as a web application from https://cbph.ir/tools/kludo .

From System Modeling to System Analysis: The Impact of Resolution Level and Resolution Distribution in the Computer-Aided Investigation of Biomolecules

The ever increasing computer power, together with the improved accuracy of atomistic force fields, enables researchers to investigate biological systems at the molecular level with remarkable detail. However, the relevant length and time scales of many processes of interest are still hardly within reach even for state-of-the-art hardware, thus leaving important questions often unanswered. The computer-aided investigation of many biological physics problems thus largely benefits from the usage of coarse-grained models, that is, simplified representations of a molecule at a level of resolution that is lower than atomistic. A plethora of coarse-grained models have been developed, which differ most notably in their granularity; this latter aspect determines one of the crucial open issues in the field, i.e. the identification of an optimal degree of coarsening, which enables the greatest simplification at the expenses of the smallest information loss. In this review, we present the problem of coarse-grained modeling in biophysics from the viewpoint of system representation and information content. In particular, we discuss two distinct yet complementary aspects of protein modeling: on the one hand, the relationship between the resolution of a model and its capacity of accurately reproducing the properties of interest; on the other hand, the possibility of employing a lower resolution description of a detailed model to extract simple, useful, and intelligible information from the latter.

A journey through mapping space: characterising the statistical and metric properties of reduced representations of macromolecules

ABSTRACT

A mapping of a macromolecule is a prescription to construct a simplified representation of the system in which only a subset of its constituent atoms is retained. As the specific choice of the mapping affects the analysis of all-atom simulations as well as the construction of coarse-grained models, the characterisation of the mapping space has recently attracted increasing attention. We here introduce a notion of scalar product and distance between reduced representations, which allows the study of the metric and topological properties of their space in a quantitative manner. Making use of a Wang-Landau enhanced sampling algorithm, we exhaustively explore such space, and examine the qualitative features of mappings in terms of their squared norm. A one-to-one correspondence with an interacting lattice gas on a finite volume leads to the emergence of discontinuous phase transitions in mapping space, which mark the boundaries between qualitatively different reduced representations of the same molecule.

An Information-Theory-Based Approach for Optimal Model Reduction of Biomolecules

In theoretical modeling of a physical system, a crucial step consists of the identification of those degrees of freedom that enable a synthetic yet informative representation of it. While in some cases this selection can be carried out on the basis of intuition and experience, straightforward discrimination of the important features from the negligible ones is difficult for many complex systems, most notably heteropolymers and large biomolecules. We here present a thermodynamics-based theoretical framework to gauge the effectiveness of a given simplified representation by measuring its information content. We employ this method to identify those reduced descriptions of proteins, in terms of a subset of their atoms, that retain the largest amount of information from the original model; we show that these highly informative representations share common features that are intrinsically related to the biological properties of the proteins under examination, thereby establishing a bridge between protein structure, energetics, and function.

Ligand-protein interactions in lysozyme investigated through a dual-resolution model

A fully atomistic (AT) modeling of biological macromolecules at relevant length- and time-scales is often cumbersome or not even desirable, both in terms of computational effort required and a posteriori analysis. This difficulty can be overcome with the use of multiresolution models, in which different regions of the same system are concurrently described at different levels of detail. In enzymes, computationally expensive AT detail is crucial in the modeling of the active site in order to capture, for example, the chemically subtle process of ligand binding. In contrast, important yet more collective properties of the remainder of the protein can be reproduced with a coarser description. In the present work, we demonstrate the effectiveness of this approach through the calculation of the binding free energy of hen egg white lysozyme with the inhibitor di-N-acetylchitotriose. Particular attention is payed to the impact of the mapping, that is, the selection of AT and coarse-grained residues, on the binding free energy. It is shown that, in spite of small variations of the binding free energy with respect to the active site resolution, the separate contributions coming from different energetic terms (such as electrostatic and van der Waals interactions) manifest a stronger dependence on the mapping, thus pointing to the existence of an optimal level of intermediate resolution.

Large-Scale Conformational Changes and Protein Function: Breaking the in silico Barrier

Large-scale conformational changes are essential to link protein structures with their function at the cell and organism scale, but have been elusive both experimentally and computationally. Over the past few years developments in cryo-electron microscopy and crystallography techniques have started to reveal multiple snapshots of increasingly large and flexible systems, deemed impossible only short time ago. As structural information accumulates, theoretical methods become central to understand how different conformers interconvert to mediate biological function. Here we briefly survey current in silico methods to tackle large conformational changes, reviewing recent examples of cross-validation of experiments and computational predictions, which show how the integration of different scale simulations with biological information is already starting to break the barriers between the in silico, in vitro, and in vivo worlds, shedding new light onto complex biological problems inaccessible so far.

Ligand Binding, Unbinding, and Allosteric Effects: Deciphering Small-Molecule Modulation of HSP90

The molecular chaperone HSP90 oversees the functional activation of a large number of client proteins. Because of its role in multiple pathways linked to cancer and neurodegeneration, drug discovery targeting HSP90 has been actively pursued. Yet, a number of inhibitors failed to meet expectations due to induced toxicity problems. In this context, allosteric perturbation has emerged as an alternative strategy for the pharmacological modulation of HSP90 functions. Specifically, novel allosteric stimulators showed the interesting capability of accelerating HSP90 closure dynamics and ATPase activities while inducing tumor cell death. Here, we gain atomistic insight into the mechanisms of allosteric ligand recognition and their consequences on the functional dynamics of HSP90, starting from the fully unbound state. We integrate advanced computational sampling methods based on FunnelMetadynamics, with the analysis of internal dynamics of the structural ensembles visited during the simulations. We observe several binding/unbinding events, and from these, we derive an accurate estimation of the absolute binding free energy. Importantly, we show that different binding poses induce different dynamics states. Our work for the first time explicitly correlates HSP90 responses to binding/unbinding of an allosteric ligand to the modulation of functionally oriented protein motions.

A deep learning approach to the structural analysis of proteins

Deep learning (DL) algorithms hold great promise for applications in the field of computational biophysics. In fact, the vast amount of available molecular structures, as well as their notable complexity, constitutes an ideal context in which DL-based approaches can be profitably employed. To express the full potential of these techniques, though, it is a prerequisite to express the information contained in a molecule’s atomic positions and distances in a set of input quantities that the network can process. Many of the molecular descriptors devised so far are effective and manageable for relatively small structures, but become complex and cumbersome for larger ones. Furthermore, most of them are defined locally, a feature that could represent a limit for those applications where global properties are of interest. Here, we build a DL architecture capable of predicting non-trivial and intrinsically global quantities, that is, the eigenvalues of a protein’s lowest-energy fluctuation modes. This application represents a first, relatively simple test bed for the development of a neural network approach to the quantitative analysis of protein structures, and demonstrates unexpected use in the identification of mechanically relevant regions of the molecule.

Optimal Coarse-Grained Site Selection in Elastic Network Models of Biomolecules

Elastic network models, simple structure-based representations of biomolecules where atoms interact via short-range harmonic potentials, provide great insight into a molecule's internal dynamics and mechanical properties at extremely low computational cost. Their efficiency and effectiveness have made them a pivotal instrument in the computer-aided study of proteins and, since a few years, also of nucleic acids. In general, the coarse-grained sites, i.e. those effective force centers onto which the all-atom structure is mapped, are constructed based on intuitive rules: a typical choice for proteins is to retain only the C _α atoms of each amino acid. However, a mapping strategy relying only on the atom type and not the local properties of its embedding can be suboptimal compared to a more careful selection. Here, we present a strategy in which the subset of atoms, each of which is mapped onto a unique coarse-grained site of the model, is selected in a stochastic search aimed at optimizing a cost function. The latter is taken to be a simple measure of the consistency between the harmonic approximation of an elastic network model and the harmonic model obtained through exact integration of the discarded degrees of freedom. The method is applied to two representatives of structurally very different types of biomolecules: the protein adenylate kinase and the RNA molecule adenine riboswitch. Our analysis quantifies the substantial impact that an algorithm-driven selection of coarse-grained sites can have on a model's properties.

Modeling of Protein Structural Flexibility and Large-Scale Dynamics: Coarse-Grained Simulations and Elastic Network Models

Fluctuations of protein three-dimensional structures and large-scale conformational transitions are crucial for the biological function of proteins and their complexes. Experimental studies of such phenomena remain very challenging and therefore molecular modeling can be a good alternative or a valuable supporting tool for the investigation of large molecular systems and long-time events. In this minireview, we present two alternative approaches to the coarse-grained (CG) modeling of dynamic properties of protein systems. We discuss two CG representations of polypeptide chains used for Monte Carlo dynamics simulations of protein local dynamics and conformational transitions, and highly simplified structure-based elastic network models of protein flexibility. In contrast to classical all-atom molecular dynamics, the modeling strategies discussed here allow the quite accurate modeling of much larger systems and longer-time dynamic phenomena. We briefly describe the main features of these models and outline some of their applications, including modeling of near-native structure fluctuations, sampling of large regions of the protein conformational space, or possible support for the structure prediction of large proteins and their complexes.

A novel phylogenetic tree based on the presence of protein domains in selected actinobacteria

Protein functional domains are semi-autonomous parts of proteins capable of functioning independently. One protein may contain several domains and one domain may be present in different protein sequences. Thus, protein domains represent the niche specific adaptive nature of an organism. We hypothesized that the presence and absence of protein domains in an organism could be used to make a phylogenetic tree, which may better depict the biotope (niche). Here, we selected 100 actinobacteria and built a phylogenetic tree depending upon the presence and absence of protein domains. Strains of different genera from the same niche were found to cluster together suggesting niche specific domain acquisition among selected strains. Thus, the domain based phylogeny clustered the selected actinobacteria mainly according to their niche rather than their taxonomic classification.

Protein dynamic communities from elastic network models align closely to the communities defined by molecular dynamics

Dynamic communities in proteins comprise the cohesive structural units that individually exhibit rigid body motions. These can correspond to structural domains, but are usually smaller parts that move with respect to one another in a protein's internal motions, key to its functional dynamics. Previous studies emphasized their importance to understand the nature of ligand-induced allosteric regulation. These studies reported that mutations to key community residues can hinder transmission of allosteric signals among the communities. Usually molecular dynamic (MD) simulations (~ 100 ns or longer) have been used to identify the communities-a demanding task for larger proteins. In the present study, we propose that dynamic communities obtained from MD simulations can also be obtained alternatively with simpler models-the elastic network models (ENMs). To verify this premise, we compare the specific communities obtained from MD and ENMs for 44 proteins. We evaluate the correspondence in communities from the two methods and compute the extent of agreement in the dynamic cross-correlation data used for community detection. Our study reveals a strong correspondence between the communities from MD and ENM and also good agreement for the residue cross-correlations. Importantly, we observe that the dynamic communities from MD can be closely reproduced with ENMs. With ENMs, we also compare the community structures of stable and unstable mutant forms of T4 Lysozyme with its wild-type. We find that communities for unstable mutants show substantially poorer agreement with the wild-type communities than do stable mutants, suggesting such ENM-based community structures can serve as a means to rapidly identify deleterious mutants.

Molecular modeling and molecular dynamic simulation of the effects of variants in the TGFBR2 kinase domain as a paradigm for interpretation of variants obtained by next generation sequencing

Variants in the TGFBR2 kinase domain cause several human diseases and can increase propensity for cancer. The widespread application of next generation sequencing within the setting of Individualized Medicine (IM) is increasing the rate at which TGFBR2 kinase domain variants are being identified. However, their clinical relevance is often uncertain. Consequently, we sought to evaluate the use of molecular modeling and molecular dynamics (MD) simulations for assessing the potential impact of variants within this domain. We documented the structural differences revealed by these models across 57 variants using independent MD simulations for each. Our simulations revealed various mechanisms by which variants may lead to functional alteration; some are revealed energetically, while others structurally or dynamically. We found that the ATP binding site and activation loop dynamics may be affected by variants at positions throughout the structure. This prediction cannot be made from the linear sequence alone. We present our structure-based analyses alongside those obtained using several commonly used genomics-based predictive algorithms. We believe the further mechanistic information revealed by molecular modeling will be useful in guiding the examination of clinically observed variants throughout the exome, as well as those likely to be discovered in the near future by clinical tests leveraging next-generation sequencing through IM efforts.

Unifying view of mechanical and functional hotspots across class A GPCRs

G protein-coupled receptors (GPCRs) are the largest superfamily of signaling proteins. Their activation process is accompanied by conformational changes that have not yet been fully uncovered. Here, we carry out a novel comparative analysis of internal structural fluctuations across a variety of receptors from class A GPCRs, which currently has the richest structural coverage. We infer the local mechanical couplings underpinning the receptors’ functional dynamics and finally identify those amino acids whose virtual deletion causes a significant softening of the mechanical network. The relevance of these amino acids is demonstrated by their overlap with those known to be crucial for GPCR function, based on static structural criteria. The differences with the latter set allow us to identify those sites whose functional role is more clearly detected by considering dynamical and mechanical properties. Of these sites with a genuine mechanical/dynamical character, the top ranking is amino acid 7x52, a previously unexplored, and experimentally verifiable key site for GPCR conformational response to ligand binding.

The biological functionality of several receptors and enzymes depends on their capability to sustain large-scale structural fluctuations and adopt different conformational states in response to ligand binding. This is the case for G protein-coupled receptors (GPCRs), the largest superfamily of signaling proteins in mammals and a primary pharmaceutical target. To better understand the functional dynamics of GPCRs, we have analysed the inter-residue distance variations across the available structures for several receptors of the rhodopsin-like family (class A). We first reconstructed the network of mechanical, rigid-like couplings between nearby amino acids and then identified those acting as dynamical/mechanical hubs. These were the sites whose virtual removal led to a significant softening of the overall mechanical network. After validating the biological relevance of these sites by comparison against known key functional sites, we singled out those regions which emerge as prominent mechanical hubs and yet have an otherwise still unknown functional role. The most relevant of such novel putative functional sites, which could be probed by mutagenesis experiments, is at interface of two transmembrane helices and we expect it to be crucial for assisting GPCRs conformational response to agonist binding.

DNA Polymerase Conformational Dynamics and the Role of Fidelity-Conferring Residues: Insights from Computational Simulations

Herein we investigate the molecular bases of DNA polymerase I conformational dynamics that underlie the replication fidelity of the enzyme. Such fidelity is determined by conformational changes that promote the rejection of incorrect nucleotides before the chemical ligation step. We report a comprehensive atomic resolution study of wild type and mutant enzymes in different bound states and starting from different crystal structures, using extensive molecular dynamics (MD) simulations that cover a total timespan of ~5 ms. The resulting trajectories are examined via a combination of novel methods of internal dynamics and energetics analysis, aimed to reveal the principal molecular determinants for the (de)stabilization of a certain conformational state. Our results show that the presence of fidelity-decreasing mutations or the binding of incorrect nucleotides in ternary complexes tend to favor transitions from closed toward open structures, passing through an ensemble of semi-closed intermediates. The latter ensemble includes the experimentally observed ajar conformation which, consistent with previous experimental observations, emerges as a molecular checkpoint for the selection of the correct nucleotide to incorporate. We discuss the implications of our results for the understanding of the relationships between the structure, dynamics, and function of DNA polymerase I at the atomistic level.

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.

Domain motions and electron transfer dynamics in 2Fe-superoxide reductase

Theoretical studies on 2Fe-superoxide reductase provide mechanistic insights into structural dynamics and electron transfer efficiencies.

ResiCon: a method for the identification of dynamic domains, hinges and interfacial regions in proteins

MOTIVATION

Structure of most proteins is flexible. Identification and analysis of intramolecular motions is a complex problem. Breaking a structure into relatively rigid parts, the so-called dynamic domains, may help comprehend the complexity of protein's mobility. We propose a new approach called ResiCon (Residue Contacts analysis), which performs this task by applying a data-mining analysis of an ensemble of protein configurations and recognizes dynamic domains, hinges and interfacial regions, by considering contacts between residues.

RESULTS

Dynamic domains found by ResiCon are more compact than those identified by two other popular methods: PiSQRD and GeoStaS. The current analysis was carried out using a known reference set of 30 NMR protein structures, as well as molecular dynamics simulation data of flap opening events in HIV-1 protease. The more detailed analysis of HIV-1 protease dataset shows that ResiCon identified dynamic domains involved in structural changes of functional importance.

AVAILABILITY AND IMPLEMENTATION

The ResiCon server is available at URL: http://dworkowa.imdik.pan.pl/EP/ResiCon.

CONTACT

pawel@bioexploratorium.pl

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Systematic methods for defining coarse-grained maps in large biomolecules

Large biomolecules are involved in many important biological processes. It would be difficult to use large-scale atomistic molecular dynamics (MD) simulations to study the functional motions of these systems because of the computational expense. Therefore various coarse-grained (CG) approaches have attracted rapidly growing interest, which enable simulations of large biomolecules over longer effective timescales than all-atom MD simulations. The first issue in CG modeling is to construct CG maps from atomic structures. In this chapter, we review the recent development of a novel and systematic method for constructing CG representations of arbitrarily complex biomolecules, in order to preserve large-scale and functionally relevant essential dynamics (ED) at the CG level. In this ED-CG scheme, the essential dynamics can be characterized by principal component analysis (PCA) on a structural ensemble, or elastic network model (ENM) of a single atomic structure. Validation and applications of the method cover various biological systems, such as multi-domain proteins, protein complexes, and even biomolecular machines. The results demonstrate that the ED-CG method may serve as a very useful tool for identifying functional dynamics of large biomolecules at the CG level.

Dynamical insights into the differential characteristics of Mycobacterium avium subsp. paratuberculosis peptide binding to HLA-DRB1 proteins associated with multiple sclerosis

Differential properties of MAP binding to HLA proteins in Sardinian MS patients.

Molecular dynamics simulations identify time scale of conformational changes responsible for conformational selection in molecular recognition of HIV-1 transactivation responsive RNA

The HIV-1 Tat protein and several small molecules bind to HIV-1 transactivation responsive RNA (TAR) by selecting sparsely populated but pre-existing conformations. Thus, a complete characterization of TAR conformational ensemble and dynamics is crucial to understand this paradigmatic system and could facilitate the discovery of new antivirals targeting this essential regulatory element. We show here that molecular dynamics simulations can be effectively used toward this goal by bridging the gap between functionally relevant time scales that are inaccessible to current experimental techniques. Specifically, we have performed several independent microsecond long molecular simulations of TAR based on one of the most advanced force fields available for RNA, the parmbsc0 AMBER. Our simulations are first validated against available experimental data, yielding an excellent agreement with measured residual dipolar couplings and order parameter S(2). This contrast with previous molecular dynamics simulations (Salmon et al., J. Am. Chem. Soc. 2013 135, 5457-5466) based on the CHARMM36 force field, which could achieve only modest accord with the experimental RDC values. Next, we direct the computation toward characterizing the internal dynamics of TAR over the microsecond time scale. We show that the conformational fluctuations observed over this previously elusive time scale have a strong functionally oriented character in that they are primed to sustain and assist ligand binding.

Temperature-accelerated molecular dynamics gives insights into globular conformations sampled in the free state of the AC catalytic domain

The catalytic domain of the adenyl cyclase (AC) toxin from Bordetella pertussis is activated by interaction with calmodulin (CaM), resulting in cAMP overproduction in the infected cell. In the X-ray crystallographic structure of the complex between AC and the C terminal lobe of CaM, the toxin displays a markedly elongated shape. As for the structure of the isolated protein, experimental results support the hypothesis that more globular conformations are sampled, but information at atomic resolution is still lacking. Here, we use temperature-accelerated molecular dynamics (TAMD) simulations to generate putative all-atom models of globular conformations sampled by CaM-free AC. As collective variables, we use centers of mass coordinates of groups of residues selected from the analysis of standard molecular dynamics (MD) simulations. Results show that TAMD allows extended conformational sampling and generates AC conformations that are more globular than in the complexed state. These structures are then refined via energy minimization and further unrestrained MD simulations to optimize inter-domain packing interactions, thus resulting in the identification of a set of hydrogen bonds present in the globular conformations.

Enhancing the activity of Bacillus circulans xylanase by modulating the flexibility of the hinge region

Enzymes undergo multiple conformational changes in solution, and these dynamics are considered to play a critical role in enzyme activity. Hinge-bending motions, resulting from reciprocal movements of dynamical quasi-rigid bodies, are thought to be related to turnover rate and are affected by the physical properties of the hinge regions. In this study, hinge identification and flexibility modification of the regions by mutagenesis were conducted to explore the relationship between hinge flexibility and catalytic activity. Bacillus circulans xylanase was selected for the identification and mutation of the hinge regions. As a result, turnover rate (V(max)) was improved approximately twofold in mutants that have more rigid hinge structure, despite the decrease in K(m) and V(max)/K(m). This result indicates that the rigidly mutated hinge has positive effects on B. circulans xylanase activity.

Perspective: Coarse-grained models for biomolecular systems

By focusing on essential features, while averaging over less important details, coarse-grained (CG) models provide significant computational and conceptual advantages with respect to more detailed models. Consequently, despite dramatic advances in computational methodologies and resources, CG models enjoy surging popularity and are becoming increasingly equal partners to atomically detailed models. This perspective surveys the rapidly developing landscape of CG models for biomolecular systems. In particular, this review seeks to provide a balanced, coherent, and unified presentation of several distinct approaches for developing CG models, including top-down, network-based, native-centric, knowledge-based, and bottom-up modeling strategies. The review summarizes their basic philosophies, theoretical foundations, typical applications, and recent developments. Additionally, the review identifies fundamental inter-relationships among the diverse approaches and discusses outstanding challenges in the field. When carefully applied and assessed, current CG models provide highly efficient means for investigating the biological consequences of basic physicochemical principles. Moreover, rigorous bottom-up approaches hold great promise for further improving the accuracy and scope of CG models for biomolecular systems.

Mechanical and assembly units of viral capsids identified via quasi-rigid domain decomposition

Key steps in a viral life-cycle, such as self-assembly of a protective protein container or in some cases also subsequent maturation events, are governed by the interplay of physico-chemical mechanisms involving various spatial and temporal scales. These salient aspects of a viral life cycle are hence well described and rationalised from a mesoscopic perspective. Accordingly, various experimental and computational efforts have been directed towards identifying the fundamental building blocks that are instrumental for the mechanical response, or constitute the assembly units, of a few specific viral shells. Motivated by these earlier studies we introduce and apply a general and efficient computational scheme for identifying the stable domains of a given viral capsid. The method is based on elastic network models and quasi-rigid domain decomposition. It is first applied to a heterogeneous set of well-characterized viruses (CCMV, MS2, STNV, STMV) for which the known mechanical or assembly domains are correctly identified. The validated method is next applied to other viral particles such as L-A, Pariacoto and polyoma viruses, whose fundamental functional domains are still unknown or debated and for which we formulate verifiable predictions. The numerical code implementing the domain decomposition strategy is made freely available.

The genetic material of viruses is packaged inside capsids constituted from a few tens to thousands of proteins. The latter can organize in multimers that serve as fundamental blocks for the viral shell assembly or that control the capsid conformational transitions and response to mechanical stress. In this work, we introduce and apply a computational scheme that identifies the fundamental protein blocks from the structural fluctuations of the capsids in thermal equilibrium. These can be derived from phenomenological elastic network models with minimal computational expenditure. Accordingly, the basic functional protein units of a capsid can be obtained from the sole input of the capsid crystal structure. The method is applied to a heterogeneous set of viruses of various size and geometries. These include well-characterised instances for validation purposes, as well as debated ones for which predictions are formulated.

Elucidating the interacting domains of chandipura virus nucleocapsid protein

The nucleocapsid (N) protein of Chandipura virus (CHPV) plays a crucial role in viral life cycle, besides being an important structural component of the virion through proper organization of its interactions with other viral proteins. In a recent study, the authors had mapped the associations among CHPV proteins and shown that N protein interacts with four of the viral proteins: N, phosphoprotein (P), matrix protein (M), and glycoprotein (G). The present study aimed to distinguish the regions of CHPV N protein responsible for its interactions with other viral proteins. In this direction, we have generated the structure of CHPV N protein by homology modeling using SWISS-MODEL workspace and Accelrys Discovery Studio client 2.55 and mapped the domains of N protein using PiSQRD. The interactions of N protein fragments with other proteins were determined by ZDOCK rigid-body docking method and validated by yeast two-hybrid and ELISA. The study revealed a unique binding site, comprising of amino acids 1–30 at the N terminus of the nucleocapsid protein (N1) that is instrumental in its interactions with N, P, M, and G proteins. It was also observed that N2 associates with N and G proteins while N3 interacts with N, P, and M proteins.

Molecular dynamics studies on the conformational transitions of adenylate kinase: a computational evidence for the conformational selection mechanism

Escherichia coli adenylate kinase (ADK) is a monomeric phosphotransferase enzyme that catalyzes reversible transfer of phosphoryl group from ATP to AMP with a large-scale domain motion. The detailed mechanism for this conformational transition remains unknown. In the current study, we performed long time-scale molecular dynamics simulations on both open and closed states of ADK. Based on the structural analyses of the simulation trajectories, we detected over 20 times conformational transitions between the open and closed states of ADK and identified two novel conformations as intermediate states in the catalytic processes. With these findings, we proposed a possible mechanism for the large-scale domain motion of Escherichia coli ADK and its catalytic process: (1) the substrate free ADK adopted an open conformation; (2) ATP bound with LID domain closure; (3) AMP bound with NMP domain closure; (4) phosphoryl transfer occurred with ATP, and AMP converted into two ADPs, and no conformational transition was detected in the enzyme; (5) LID domain opened with one ADP released; (6) another ADP released with NMP domain open. As both open and closed states sampled a wide range of conformation transitions, our simulation strongly supported the conformational selection mechanism for Escherichia coli ADK.

Conformational fluctuations of UreG, an intrinsically disordered enzyme

UreG proteins are small GTP binding (G) proteins that catalyze the hydrolysis of GTP necessary for the maturation of urease, a virulence factor in bacterial pathogenesis. UreG proteins are the first documented cases of intrinsically disordered enzymes. The comprehension of the dynamics of folding-unfolding events occurring in this protein could shed light on the enzymatic mechanism of UreG. Here, we used the recently developed replica exchange with solute tempering (REST2) computational methodology to explore the conformational space of UreG from Helicobacter pylori (HpUreG) and to identify its structural fluctuations. The same simulation and analysis protocol has been applied to HypB from Methanocaldococcus jannaschii (MjHypB), which is closely related to UreG in both sequence and function, even though it is not intrinsically disordered. A comparison of the two systems reveals that both HpUreG and MjHypB feature a substantial rigidity of the protein regions involved in catalysis, justifying its residual catalytic activity. On the other hand, HpUreG tends to unfold more than MjHypB in portions involved in protein-protein interactions with metallochaperones necessary for the formation of multiprotein complexes known to be involved in urease activation.

Thermodynamics of strongly allosteric inhibition: a model study of HIV-1 protease

Protein inhibitors that shift the thermodynamic equilibrium towards a denatured state escape, in general, the straightforward framework of competitive or allosteric inhibitors. The equilibrium properties of peptides which compete with the folding, or more precisely destabilize the native state, of the human immunodeficiency virus (HIV)-1 protease monomer are studied within a structure-based model. The effect of peptides that disrupt the hydrophobic core of the protein can still be summarized in terms of an inhibition constant, which depends on the thermal stability of the protein. The state of the protein denatured by such a peptide is more structured than its intrinsic denatured state, but displays the same degree of compactness. Peptides that target less buried regions of the protein are less efficient and display a more complex thermodynamics that cannot be captured in a simple way.

Comparing proteins by their internal dynamics: exploring structure-function relationships beyond static structural alignments

The growing interest for comparing protein internal dynamics owes much to the realisation that protein function can be accompanied or assisted by structural fluctuations and conformational changes. Analogously to the case of functional structural elements, those aspects of protein flexibility and dynamics that are functionally oriented should be subject to evolutionary conservation. Accordingly, dynamics-based protein comparisons or alignments could be used to detect protein relationships that are more elusive to sequence and structural alignments. Here we provide an account of the progress that has been made in recent years towards developing and applying general methods for comparing proteins in terms of their internal dynamics and advance the understanding of the structure-function relationship.

Combining coarse-grained nonbonded and atomistic bonded interactions for protein modeling

A hybrid coarse-grained (CG) and atomistic (AT) model for protein simulations and rapid searching and refinement of peptide-protein complexes has been developed. In contrast to other hybrid models that typically represent spatially separate parts of a protein by either a CG or an AT force field model, the present approach simultaneously represents the protein by an AT (united atom) and a CG model. The interactions of the protein main chain are described based on the united atom force field allowing a realistic representation of protein secondary structures. In addition, the AT description of all other bonded interactions keeps the protein compatible with a realistic bonded geometry. Nonbonded interactions between side chains and side chains and main chain are calculated at the level of a CG model using a knowledge-based potential. Unrestrained molecular dynamics simulations on several test proteins resulted in trajectories in reasonable agreement with the corresponding experimental structures. Applications to the refinement of docked peptide-protein complexes resulted in improved complex structures. Application to the rapid refinement of docked protein-protein complex is also possible but requires further optimization of force field parameters.

Corresponding functional dynamics across the Hsp90 Chaperone family: insights from a multiscale analysis of MD simulations

Understanding how local protein modifications, such as binding small-molecule ligands, can trigger and regulate large-scale motions of large protein domains is a major open issue in molecular biology. We address various aspects of this problem by analyzing and comparing atomistic simulations of Hsp90 family representatives for which crystal structures of the full length protein are available: mammalian Grp94, yeast Hsp90 and E.coli HtpG. These chaperones are studied in complex with the natural ligands ATP, ADP and in the Apo state. Common key aspects of their functional dynamics are elucidated with a novel multi-scale comparison of their internal dynamics. Starting from the atomic resolution investigation of internal fluctuations and geometric strain patterns, a novel analysis of domain dynamics is developed. The results reveal that the ligand-dependent structural modulations mostly consist of relative rigid-like movements of a limited number of quasi-rigid domains, shared by the three proteins. Two common primary hinges for such movements are identified. The first hinge, whose functional role has been demonstrated by several experimental approaches, is located at the boundary between the N-terminal and Middle-domains. The second hinge is located at the end of a three-helix bundle in the Middle-domain and unfolds/unpacks going from the ATP- to the ADP-state. This latter site could represent a promising novel druggable allosteric site common to all chaperones.

Understanding the connections between structure, binding, dynamics and function in proteins is one of the most fascinating problems in biology and is actively investigated experimentally and computationally. In the latter context, significant advancements are possible by exposing the causal link between the fine atomic-scale protein-ligand interactions and the large-scale protein motions. One ideal avenue to explore this relationship is given by proteins of the Hsp90 chaperones family. Their dynamics is regulated by ATP binding and hydrolysis, which activates the onset of large-scale, functional conformational changes. Herein, we concentrated on three homologs with markedly different structural organization—mammalian Grp94, yeast Hsp90 and prokaryotic HtpG—and developed a novel computational multiscale approach to detect and characterize the salient traits of the functionally-oriented internal dynamics of the three chaperones. The comparative analysis, which exploits a novel highly simplified, yet viable, description of the protein internal dynamics, highlights fundamental mechanical aspects that preside the ligand-dependent conformational arrangements in all chaperones. For the three molecules, two corresponding regions are singled out as ligand-susceptible hinges for the large-scale internal motion. On the basis of this and other evidence it is suggested that these regions represent functionally relevant druggable substructures in the discovery of novel allosteric modulators.

Identification of domains in protein structures from the analysis of intramolecular interactions

The subdivision of protein structures into smaller and independent structural domains has a fundamental importance in understanding protein evolution and function and in the development of protein classification methods as well as in the interpretation of experimental data. Due to the rapid growth in the number of solved protein structures, the need for devising new accurate algorithmic methods has become more and more urgent. In this paper, we propose a new computational approach that is based on the concept of domain as a compact and independent folding unit and on the analysis of the residue-residue energy interactions obtainable through classical all-atom force field calculations. In particular, starting from the analysis of the nonbonded interaction energy matrix associated with a protein, our method filters out and selects only those specific subsets of interactions that define possible independent folding nuclei within a complex protein structure. This allows grouping different protein fragments into energy clusters that are found to correspond to structural domains. The strategy has been tested using proper benchmark data sets, and the results have shown that the new approach is fast and reliable in determining the number of domains in a totally ab initio manner and without making use of any training set or knowledge of the systems in exam. Moreover, our method, identifying the most relevant residues for the stabilization of each domain, may complement the results given by other classification techniques and may provide useful information to design and guide new experiments.

Structural distributions from single-molecule measurements as a tool for molecular mechanics

A mechanical view provides an attractive alternative for predicting the behavior of complex systems since it circumvents the resource-intensive requirements of atomistic models; however, it remains extremely challenging to characterize the mechanical responses of a system at the molecular level. Here, the structural distribution is proposed to be an effective means to extracting the molecular mechanical properties. End-to-end distance distributions for a series of short poly-L-proline peptides with the sequence P(n)CG(3)K-biotin (n = 8, 12, 15 and 24) were used to experimentally illustrate this new approach. High-resolution single-molecule Förster-type resonance energy transfer (FRET) experiments were carried out and the conformation-resolving power was characterized and discussed in the context of the conventional constant-time binning procedure for FRET data analysis. It was shown that the commonly adopted theoretical polymer models-including the worm-like chain, the freely jointed chain, and the self-avoiding chain-could not be distinguished by the averaged end-to-end distances, but could be ruled out using the molecular details gained by conformational distribution analysis because similar polymers of different sizes could respond to external forces differently. Specifically, by fitting the molecular conformational distribution to a semi-flexible polymer model, the effective persistence lengths for the series of short poly-L-proline peptides were found to be size-dependent with values of ~190 Å, ~67 Å, ~51 Å, and ~76 Å for n = 8, 12, 15, and 24, respectively. A comprehensive computational modeling was carried out to gain further insights for this surprising discovery. It was found that P(8) exists as the extended all-trans isomaer whereas P(12) and P(15) predominantly contained one proline residue in the cis conformation. P(24) exists as a mixture of one-cis (75%) and two-cis (25%) isomers where each isomer contributes to an experimentally resolvable conformational mode. This work demonstrates the resolving power of the distribution-based approach, and the capacity of integrating high-resolution single-molecule FRET experiments with molecular modeling to reveal detailed structural information about the conformation of molecules on the length scales relevant to the study of biological molecules.

Optimal number of coarse-grained sites in different components of large biomolecular complexes

The computational study of large biomolecular complexes (molecular machines, cytoskeletal filaments, etc.) is a formidable challenge facing computational biophysics and biology. To achieve biologically relevant length and time scales, coarse-grained (CG) models of such complexes usually must be built and employed. One of the important early stages in this approach is to determine an optimal number of CG sites in different constituents of a complex. This work presents a systematic approach to this problem. First, a universal scaling law is derived and numerically corroborated for the intensity of the intrasite (intradomain) thermal fluctuations as a function of the number of CG sites. Second, this result is used for derivation of the criterion for the optimal number of CG sites in different parts of a large multibiomolecule complex. In the zeroth-order approximation, this approach validates the empirical rule of taking one CG site per fixed number of atoms or residues in each biomolecule, previously widely used for smaller systems (e.g., individual biomolecules). The first-order corrections to this rule are derived and numerically checked by the case studies of the Escherichia coli ribosome and Arp2/3 actin filament junction. In different ribosomal proteins, the optimal number of amino acids per CG site is shown to differ by a factor of 3.5, and an even wider spread may exist in other large biomolecular complexes. Therefore, the method proposed in this paper is valuable for the optimal construction of CG models of such complexes.

Key intermolecular interactions in the E. coli 70S ribosome revealed by coarse-grained analysis

The ribosome is a very large complex that consists of many RNA and protein molecules and plays a central role in protein biosynthesis in all organisms. Extensive interactions between different molecules are critical to ribosomal functional dynamics. In this work, intermolecular interactions in the Escherichia coli 70S ribosome are investigated by coarse-grained (CG) analysis. CG models are defined to preserve dynamic domains in RNAs and proteins and to capture functional motions in the ribosome, and then the CG sites are connected by harmonic springs, and spring constants are obtained by matching the computed fluctuations to those of an all-atom molecular dynamics (MD) simulation. Those spring constants indicate how strong the interactions are between the ribosomal components, and they are in good agreement with various experimental data. Nearly all the bridges between the small and large ribosomal subunits are indicated by CG interactions with large spring constants. The head of the small subunit is very mobile because it has minimal CG interactions with the rest of the subunit; however, a large number of small subunit proteins bind to maintain the internal structure of the head. The results show a clear connection between the intermolecular interactions and the structural and functional properties of the ribosome because of the reduced complexity in domain-based CG models. The present approach also provides a useful strategy to map interactions between molecules within large biomolecular complexes since it is not straightforward to investigate these by either atomistic MD simulations or residue-based elastic network models.

Fluctuation dynamics analysis of gp120 envelope protein reveals a topologically based communication network

Human Immunodeficiency Virus (HIV) infection is initiated by binding of the viral glycoprotein gp120, to the cellular receptor CD4. On CD4 binding, gp120 undergoes conformational change, permitting binding to the chemokine receptor. Crystal structures of gp120 ternary complex reveal the CD4 bound conformation of gp120. We report here the application of the Gaussian network model (GNM) to the crystal structures of gp120 bound to CD4 or CD4 mimic and 17b, to study the collective motions of the gp120 core and determine the communication propensities of the residue network. The GNM fluctuation profiles identify residues in the inner domain and outer domain that may facilitate conformational change or stability, respectively. Communication propensities delineate a residue network that is topologically suited for signal propagation from the Phe43 cavity throughout the gp120 outer domain. These results provide a new context for interpreting gp120 core envelope structure-function relationships.