Elastic Network Models are Robust to Variations in Formalism

Anisotropic Network Analysis of Open/Closed HCN4 Channel Advocates Asymmetric Subunit Cooperativity in cAMP Modulation of Gating

Hyperpolarization-activated cyclic nucleotide-modulated (HCN) channels are opened in an allosteric manner by membrane hyperpolarization and cyclic nucleotides such as cAMP. Because of conflicting reports from experimental studies on whether cAMP binding to the four available binding sites in the channel tetramer operates cooperatively in gating, we employ here a computational approach as a promising route to examine ligand-induced conformational changes after binding to individual sites. By combining an elastic network model (ENM) with linear response theory (LRT) for modeling the apo-holo transition of the cyclic nucleotide-binding domain (CNBD) in HCN channels, we observe a distinct pattern of cooperativity matching the "positive-negative-positive" cooperativity reported from functional studies. This cooperativity pattern is highly conserved among HCN subtypes (HCN4, HCN1), but only to a lesser extent visible in structurally related channels, which are only gated by voltage (KAT1) or cyclic nucleotides (TAX4). This suggests an inherent cooperativity between subunits in HCN channels as part of a ligand-triggered gating mechanism in these channels.

Predicting allosteric pockets in protein biological assemblages

MOTIVATION

Allostery enables changes to the dynamic behavior of a protein at distant positions induced by binding. Here, we present APOP, a new allosteric pocket prediction method, which perturbs the pockets formed in the structure by stiffening pairwise interactions in the elastic network across the pocket, to emulate ligand binding. Ranking the pockets based on the shifts in the global mode frequencies, as well as their mean local hydrophobicities, leads to high prediction success when tested on a dataset of allosteric proteins, composed of both monomers and multimeric assemblages.

RESULTS

Out of the 104 test cases, APOP predicts known allosteric pockets for 92 within the top 3 rank out of multiple pockets available in the protein. In addition, we demonstrate that APOP can also find new alternative allosteric pockets in proteins. Particularly interesting findings are the discovery of previously overlooked large pockets located in the centers of many protein biological assemblages; binding of ligands at these sites would likely be particularly effective in changing the protein's global dynamics.

AVAILABILITY AND IMPLEMENTATION

APOP is freely available as an open-source code (https://github.com/Ambuj-UF/APOP) and as a web server at https://apop.bb.iastate.edu/.

Surveying nonvisual arrestins reveals allosteric interactions between functional sites

Arrestins are important scaffolding proteins that are expressed in all vertebrate animals. They regulate cell-signaling events upon binding to active G-protein coupled receptors (GPCR) and trigger endocytosis of active GPCRs. While many of the functional sites on arrestins have been characterized, the question of how these sites interact is unanswered. We used anisotropic network modeling (ANM) together with our covariance compliment techniques to survey all the available structures of the nonvisual arrestins to map how structural changes and protein-binding affect their structural dynamics. We found that activation and clathrin binding have a marked effect on arrestin dynamics, and that these dynamics changes are localized to a small number of distant functional sites. These sites include α-helix 1, the lariat loop, nuclear localization domain, and the C-domain β-sheets on the C-loop side. Our techniques suggest that clathrin binding and/or GPCR activation of arrestin perturb the dynamics of these sites independent of structural changes.

Reconstructing data-driven governing equations for cell phenotypic transitions: integration of data science and systems biology

Cells with the same genome can exist in different phenotypes and can change between distinct phenotypes when subject to specific stimuli and microenvironments. Some examples include cell differentiation during development, reprogramming for induced pluripotent stem cells and transdifferentiation, cancer metastasis and fibrosis progression. The regulation and dynamics of cell phenotypic conversion is a fundamental problem in biology, and has a long history of being studied within the formalism of dynamical systems. A main challenge for mechanism-driven modeling studies is acquiring sufficient amount of quantitative information for constraining model parameters. Advances in quantitative experimental approaches, especially high throughput single-cell techniques, have accelerated the emergence of a new direction for reconstructing the governing dynamical equations of a cellular system from quantitative single-cell data, beyond the dominant statistical approaches. Here I review a selected number of recent studies using live- and fixed-cell data and provide my perspective on future development.

Reconstructing data-driven governing equations for cell phenotypic transitions: integration of data science and systems biology

Cells with the same genome can exist in different phenotypes and can change between distinct phenotypes when subject to specific stimuli and microenvironments. Some examples include cell differentiation during development, reprogramming for induced pluripotent stem cells and transdifferentiation, cancer metastasis and fibrosis progression. The regulation and dynamics of cell phenotypic conversion is a fundamental problem in biology, and has a long history of being studied within the formalism of dynamical systems. A main challenge for mechanism-driven modeling studies is acquiring sufficient amount of quantitative information for constraining model parameters. Advances in quantitative experimental approaches, especially high throughput single-cell techniques, have accelerated the emergence of a new direction for reconstructing the governing dynamical equations of a cellular system from quantitative single-cell data, beyond the dominant statistical approaches. Here I review a selected number of recent studies using live- and fixed-cell data and provide my perspective on future development.

Architecture and self-assembly of the jumbo bacteriophage nuclear shell

Bacteria encode myriad defences that target the genomes of infecting bacteriophage, including restriction-modification and CRISPR-Cas systems¹. In response, one family of large bacteriophages uses a nucleus-like compartment to protect its replicating genomes by excluding host defence factors^2-4. However, the principal composition and structure of this compartment remain unknown. Here we find that the bacteriophage nuclear shell assembles primarily from one protein, which we name chimallin (ChmA). Combining cryo-electron tomography of nuclear shells in bacteriophage-infected cells and cryo-electron microscopy of a minimal chimallin compartment in vitro, we show that chimallin self-assembles as a flexible sheet into closed micrometre-scale compartments. The architecture and assembly dynamics of the chimallin shell suggest mechanisms for its nucleation and growth, and its role as a scaffold for phage-encoded factors mediating macromolecular transport, cytoskeletal interactions, and viral maturation.

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.

Parameterizing elastic network models to capture the dynamics of proteins

Coarse-grained normal mode analyses of protein dynamics rely on the idea that the geometry of a protein structure contains enough information for computing its fluctuations around its equilibrium conformation. This geometry is captured in the form of an elastic network (EN), namely a network of edges between its residues. The normal modes of a protein are then identified with the normal modes of its EN. Different approaches have been proposed to construct ENs, focusing on the choice of the edges that they are comprised of, and on their parameterizations by the force constants associated with those edges. Here we propose new tools to guide choices on these two facets of EN. We study first different geometric models for ENs. We compare cutoff-based ENs, whose edges have lengths that are smaller than a cutoff distance, with Delaunay-based ENs and find that the latter provide better representations of the geometry of protein structures. We then derive an analytical method for the parameterization of the EN such that its dynamics leads to atomic fluctuations that agree with experimental B-factors. To limit overfitting, we attach a parameter referred to as flexibility constant to each atom instead of to each edge in the EN. The parameterization is expressed as a non-linear optimization problem whose parameters describe both rigid-body and internal motions. We show that this parameterization leads to improved ENs, whose dynamics mimic MD simulations better than ENs with uniform force constants, and reduces the number of normal modes needed to reproduce functional conformational changes.

Normal mode analysis of membrane protein dynamics using the vibrational subsystem analysis

The vibrational subsystem analysis is a useful approach that allows for evaluating the spectrum of modes of a given system by integrating out the degrees of freedom accessible to the environment. The approach could be utilized for exploring the collective dynamics of a membrane protein (system) coupled to the lipid bilayer (environment). However, the application to membrane proteins is limited due to high computational costs of modeling a sufficiently large membrane environment unbiased by end effects, which drastically increases the size of the investigated system. We derived a recursive formula for calculating the reduced Hessian of a membrane protein embedded in a lipid bilayer by decomposing the membrane into concentric cylindrical domains with the protein located at the center. The approach allows for the design of a time- and memory-efficient algorithm and a mathematical understanding of the convergence of the reduced Hessian with respect to increasing membrane sizes. The application to the archaeal aspartate transporter Glt_Ph illustrates its utility and efficiency in capturing the transporter's elevator-like movement during its transition between outward-facing and inward-facing states.

Persistent Protein Motions in a Rugged Energy Landscape Revealed by Normal Mode Ensemble Analysis

Proteins are allosteric machines that couple motions at distinct, often distant, sites to control biological function. Low-frequency structural vibrations are a mechanism of this long-distance connection and are often used computationally to predict correlations, but experimentally identifying the vibrations associated with specific motions has proved challenging. Spectroscopy is an ideal tool to explore these excitations, but measurements have been largely unable to identify important frequency bands. The result is at odds with some previous calculations and raises the question what methods could successfully characterize protein structural vibrations. Here we show the lack of spectral structure arises in part from the variations in protein structure as the protein samples the energy landscape. However, by averaging over the energy landscape as sampled using an aggregate 18.5 μs of all-atom molecular dynamics simulation of hen egg white lysozyme and normal-mode analyses, we find vibrations with large overlap with functional displacements are surprisingly concentrated in narrow frequency bands. These bands are not apparent in either the ensemble averaged vibrational density of states or isotropic absorption. However, in the case of the ensemble averaged anisotropic absorption, there is persistent spectral structure and overlap between this structure and the functional displacement frequency bands. We systematically lay out heuristics for calculating the spectra robustly, including the need for statistical sampling of the protein and inclusion of adequate water in the spectral calculation. The results show the congested spectrum of these complex molecules obscures important frequency bands associated with function and reveal a method to overcome this congestion by combining structurally sensitive spectroscopy with robust normal mode ensemble analysis.

Adaptability and specificity: how do proteins balance opposing needs to achieve function?

Many proteins select from a small repertoire of 3-dimensional folds retained over evolutional timescales and recruited for different functions, with changes in local structure and sequence to enable specificity. Recent studies have revealed the evolutionary constraints on protein dynamics to achieve function. The significance of protein dynamics in simultaneously satisfying conformational flexibility/malleability and stability/precision requirements becomes clear upon dissecting the spectrum of equilibrium motions accessible to fold families. Accessibility to highly conserved global modes of motions shared by family members, to low-to-intermediate-frequency modes that distinguish subfamilies and confer specificity, and to conserved high-frequency modes ensuring chemical precision and core stability underlies functional specialization while exploiting highly versatile folds. These design principles are illustrated for the family of PDZ domains.

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

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

Residue-Level Allostery Propagates through the Effective Coarse-Grained Hessian

The long-ranged coupling between residues that gives rise to allostery in a protein is built up from short-ranged physical interactions. Computational tools used to predict this coupling and its functional relevance have relied on the application of graph theoretical metrics to residue-level correlations measured from all-atom molecular dynamics simulations. The short-ranged interactions that yield these long-ranged residue-level correlations are quantified by the effective coarse-grained Hessian. Here we compute an effective harmonic coarse-grained Hessian from simulations of a benchmark allosteric protein, IGPS, and demonstrate the improved locality of this graph Laplacian over two other connectivity matrices. Additionally, two centrality metrics are developed that indicate the direct and indirect importance of each residue at producing the covariance between the effector binding pocket and the active site. The residue importance indicated by these two metrics is corroborated by previous mutagenesis experiments and leads to unique functional insights; in contrast to previous computational analyses, our results suggest that fP76-hK181 is the most important contact for conveying direct allosteric paths across the HisF-HisH interface. The connectivity around fD98 is found to be important at affecting allostery through indirect means.

Modulation of Toroidal Proteins Dynamics in Favor of Functional Mechanisms upon Ligand Binding

Toroidal proteins serve as molecular machines and play crucial roles in biological processes such as DNA replication and RNA transcription. Despite progress in the structural characterization of several toroidal proteins, we still lack a mechanistic understanding of the significance of their architecture, oligomerization states, and intermolecular interactions in defining their biological function. In this work, we analyze the collective dynamics of toroidal proteins with different oligomerization states, namely, dimeric and trimeric DNA sliding clamps, nucleocapsid proteins (4-, 5-, and 6-mers) and Trp RNA-binding attenuation proteins (11- and 12-mers). We observe common global modes, among which cooperative rolling stands out as a mechanism enabling DNA processivity, and clamshell motions as those underlying the opening/closure of the sliding clamps. Alterations in global dynamics due to complexation with DNA or the clamp loader are shown to assist in enhancing motions to enable robust function. The analysis provides new insights into the differentiation and enhancement of functional motions upon intersubunit and intermolecular interactions.

Essential site scanning analysis: A new approach for detecting sites that modulate the dispersion of protein global motions

Despite the wealth of methods developed for exploring the molecular basis of allostery in biomolecular systems, there is still a need for structure-based predictive tools that can efficiently detect susceptible sites for triggering allosteric responses. Toward this goal, we introduce here an elastic network model (ENM)-based method, Essential Site Scanning Analysis (ESSA). Essential sites are here defined as residues that would significantly alter the protein's global dynamics if bound to a ligand. To mimic the crowding induced upon substrate binding, the heavy atoms of each residue are incorporated as additional network nodes into the α-carbon-based ENM, and the resulting shifts in soft mode frequencies are used as a metric for evaluating the essentiality of each residue. Results on a dataset of monomeric proteins indicate the enrichment of allosteric and orthosteric binding sites, as well as global hinge regions among essential residues, highlighting the significant role of these sites in controlling the overall structural dynamics. Further integration of ESSA with information on predicted pockets and their local hydrophobicity density enables successful predictions of allosteric pockets for both ligand-bound and -unbound structures. ESSA can be efficiently applied to large multimeric systems. Three case studies, namely (i) G-protein binding to a GPCR, (ii) heterotrimeric assembly of the Ser/Thr protein phosphatase PP2A, and (iii) allo-targeting of AMPA receptor, demonstrate the utility of ESSA for identifying essential sites and narrowing down target allosteric sites identified by druggability simulations.

Analyzing Fluctuation Properties in Protein Elastic Networks with Sequence-Specific and Distance-Dependent Interactions

Simple protein elastic networks which neglect amino-acid information often yield reasonable predictions of conformational dynamics and are broadly used. Recently, model variants which incorporate sequence-specific and distance-dependent interactions of residue pairs have been constructed and demonstrated to improve agreement with experimental data. We have applied the new variants in a systematic study of protein fluctuation properties and compared their predictions with those of conventional anisotropic network models. We find that the quality of predictions is frequently linked to poor estimations in highly flexible protein regions. An analysis of a large set of protein structures shows that fluctuations of very weakly connected network residues are intrinsically prone to be significantly overestimated by all models. This problem persists in the new models and is not resolved by taking into account sequence information. The effect becomes even enhanced in the model variant which takes into account very soft long-ranged residue interactions. Beyond these shortcomings, we find that model predictions are largely insensitive to the integration of chemical information, at least regarding the fluctuation properties of individual residues. One can furthermore conclude that the inherent drawbacks may present a serious hindrance when improvement of elastic network models are attempted.

Characterization of Differential Dynamics, Specificity, and Allostery of Lipoxygenase Family Members

Accurate modeling of structural dynamics of proteins and their differentiation across different species can help us understand generic mechanisms of function shared by family members and the molecular basis of the specificity of individual members. We focused here on the family of lipoxygenases, enzymes that catalyze lipid oxidation, the mammalian and bacterial structures of which have been elucidated. We present a systematic method of approach for characterizing the sequence, structure, dynamics, and allosteric signaling properties of these enzymes using a combination of structure-based models and methods and bioinformatics tools applied to a data set of 88 structures. The analysis elucidates the signature dynamics of the lipoxygenase family and its differentiation among members, as well as key sites that enable its adaptation to specific substrate binding and allosteric activity.

Chemically Accurate Relative Folding Stability of RNA Hairpins from Molecular Simulations

To benchmark RNA force fields, we compared the folding stabilities of three 12-nucleotide hairpin stem loops estimated by simulation to stabilities determined by experiment. We used umbrella sampling and a reaction coordinate of end-to-end (5' to 3' hydroxyl oxygen) distance to estimate the free energy change of the transition from the native conformation to a fully extended conformation with no hydrogen bonds between non-neighboring bases. Each simulation was performed four times using the AMBER FF99+bsc0+χ_OL3 force field, and each window, spaced at 1 Å intervals, was sampled for 1 μs, for a total of 552 μs of simulation. We compared differences in the simulated free energy changes to analogous differences in free energies from optical melting experiments using thermodynamic cycles where the free energy change between stretched and random coil sequences is assumed to be sequence-independent. The differences between experimental and simulated ΔΔ G° are, on average, 0.98 ± 0.66 kcal/mol, which is chemically accurate and suggests that analogous simulations could be used predictively. We also report a novel method to identify where replica free energies diverge along a reaction coordinate, thus indicating where additional sampling would most improve convergence. We conclude by discussing methods to more economically perform these simulations.

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.

Computational Exploration of Conformational Transitions in Protein Drug Targets

Protein drug targets vary from highly structured to completely disordered; either way dynamics governs function. Hence, understanding the dynamical aspects of how protein targets function can enable improved interventions with drug molecules. Computational approaches offer highly detailed structural models of protein dynamics which are becoming more predictive as model quality and sampling power improve. However, the most advanced and popular models still have errors owing to imperfect parameter sets and often cannot access longer timescales of many crucial biological processes. Experimental approaches offer more certainty but can struggle to detect and measure lightly populated conformations of target proteins and subtle allostery. An emerging solution is to integrate available experimental data into advanced molecular simulations. In the future, molecular simulation in combination with experimental data may be able to offer detailed models of important drug targets such that improved functional mechanisms or selectivity can be accessed.

Elastic network model of learned maintained contacts to predict protein motion

We present a novel elastic network model, lmcENM, to determine protein motion even for localized functional motions that involve substantial changes in the protein's contact topology. Existing elastic network models assume that the contact topology remains unchanged throughout the motion and are thus most appropriate to simulate highly collective function-related movements. lmcENM uses machine learning to differentiate breaking from maintained contacts. We show that lmcENM accurately captures functional transitions unexplained by the classical ENM and three reference ENM variants, while preserving the simplicity of classical ENM. We demonstrate the effectiveness of our approach on a large set of proteins covering different motion types. Our results suggest that accurately predicting a "deformation-invariant" contact topology offers a promising route to increase the general applicability of ENMs. We also find that to correctly predict this contact topology a combination of several features seems to be relevant which may vary slightly depending on the protein. Additionally, we present case studies of two biologically interesting systems, Ferric Citrate membrane transporter FecA and Arachidonate 15-Lipoxygenase.

Jumping between protein conformers using normal modes

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

Effect of Dimerization on the Dynamics of Neurotransmitter:Sodium Symporters

Dimerization is a common feature among the members of the neurotransmitter:sodium symporter (NSS) family of membrane proteins. Yet, the effect of dimerization on the mechanism of action of NSS members is not fully understood. In this study, we examined the collective dynamics of two members of the family, leucine transporter (LeuT) and dopamine transporter (DAT), to assess the significance of dimerization in modulating the functional motions of the monomers. We used to this aim the anisotropic network model (ANM), an efficient and robust method for modeling the intrinsic motions of proteins and their complexes. Transporters belonging to the NSS family are known to alternate between outward-facing (OF) and inward-facing (IF) states, which enables the uptake and release of their substrate (neurotransmitter) respectively, as the substrate is transported from the exterior to the interior of the cell. In both LeuT and DAT, dimerization is found to alter the collective motions intrinsically accessible to the individual monomers in favor of the functional transitions (OF ↔ IF), suggesting that dimerization may play a role in facilitating transport.

Comparative Normal Mode Analysis of the Dynamics of DENV and ZIKV Capsids

Key steps in the life cycle of a virus, such as the fusion event as the virus infects a host cell and its maturation process, relate to an intricate interplay between the structure and the dynamics of its constituent proteins, especially those that define its capsid, much akin to an envelope that protects its genomic material. We present a comprehensive, comparative analysis of such interplay for the capsids of two viruses from the flaviviridae family, Dengue (DENV) and Zika (ZIKV). We use for that purpose our own software suite, DD-NMA, which is based on normal mode analysis. We describe the elements of DD-NMA that are relevant to the analysis of large systems, such as virus capsids. In particular, we introduce our implementation of simplified elastic networks and justify their parametrization. Using DD-NMA, we illustrate the importance of packing interactions within the virus capsids on the dynamics of the E proteins of DENV and ZIKV. We identify differences between the computed atomic fluctuations of the E proteins in DENV and ZIKV and relate those differences to changes observed in their high resolution structures. We conclude with a discussion on additional analyses that are needed to fully characterize the dynamics of the two viruses.

A multi-resolution model to capture both global fluctuations of an enzyme and molecular recognition in the ligand-binding site

In multi-resolution simulations, different system components are simultaneously modeled at different levels of resolution, these being smoothly coupled together. In the case of enzyme systems, computationally expensive atomistic detail is needed in the active site to capture the chemistry of ligand binding. Global properties of the rest of the protein also play an essential role, determining the structure and fluctuations of the binding site; however, these can be modeled on a coarser level. Similarly, in the most computationally efficient scheme only the solvent hydrating the active site requires atomistic detail. We present a methodology to couple atomistic and coarse-grained protein models, while solvating the atomistic part of the protein in atomistic water. This allows a free choice of which protein and solvent degrees of freedom to include atomistically. This multi-resolution methodology can successfully model stable ligand binding, and we further confirm its validity by exploring the reproduction of system properties relevant to enzymatic function. In addition to a computational speedup, such an approach can allow the identification of the essential degrees of freedom playing a role in a given process, potentially yielding new insights into biomolecular function. Proteins 2016; 84:1902-1913. © 2016 Wiley Periodicals, Inc.

iGNM 2.0: the Gaussian network model database for biomolecular structural dynamics

Gaussian network model (GNM) is a simple yet powerful model for investigating the dynamics of proteins and their complexes. GNM analysis became a broadly used method for assessing the conformational dynamics of biomolecular structures with the development of a user-friendly interface and database, iGNM, in 2005. We present here an updated version, iGNM 2.0 http://gnmdb.csb.pitt.edu/, which covers more than 95% of the structures currently available in the Protein Data Bank (PDB). Advanced search and visualization capabilities, both 2D and 3D, permit users to retrieve information on inter-residue and inter-domain cross-correlations, cooperative modes of motion, the location of hinge sites and energy localization spots. The ability of iGNM 2.0 to provide structural dynamics data on the large majority of PDB structures and, in particular, on their biological assemblies makes it a useful resource for establishing the bridge between structure, dynamics and function.

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.

Structure-Encoded Global Motions and Their Role in Mediating Protein-Substrate Interactions

Recent structure-based computational studies suggest that, in contrast to the classical description of equilibrium fluctuations as wigglings and jigglings, proteins have access to well-defined spectra of collective motions, called intrinsic dynamics, encoded by their structure under native state conditions. In particular, the global modes of motions (at the low frequency end of the spectrum) are shown by multiple studies to be highly robust to minor differences in the structure or to detailed interactions at the atomic level. These modes, encoded by the overall fold, usually define the mechanisms of interactions with substrates. They can be estimated by low-resolution models such as the elastic network models (ENMs) exclusively based on interresidue contact topology. The ability of ENMs to efficiently assess the global motions intrinsically favored by the overall fold as well as the relevance of these predictions to the dominant changes in structure experimentally observed for a given protein in the presence of different substrates suggest that the intrinsic dynamics plays a role in mediating protein-substrate interactions. These observations underscore the functional significance of structure-encoded dynamics, or the importance of the predisposition to favor functional global modes in the evolutionary selection of structures.

Aldolases Utilize Different Oligomeric States To Preserve Their Functional Dynamics

Aldolases are essential enzymes in the glycolysis pathway and catalyze the reaction cleaving fructose/tagatose 1,6-bisphosphate into dihydroxyacetone phosphate and glyceraldehyde 3-phosphate. To determine how the aldolase motions relate to its catalytic process, we studied the dynamics of three different class II aldolase structures through simulations. We employed coarse-grained elastic network normal-mode analyses to investigate the dynamics of Escherichia coli fructose 1,6-bisphosphate aldolase, E. coli tagatose 1,6-bisphosphate aldolase, and Thermus aquaticus fructose 1,6-bisphosphate aldolase and compared their motions in different oligomeric states. The first one is a dimer, and the second and third are tetramers. Our analyses suggest that oligomerization not only stabilizes the aldolase structures, showing fewer fluctuations at the subunit interfaces, but also allows the enzyme to achieve the required dynamics for its functional loops. The essential mobility of these loops in the functional oligomeric states can facilitate the enzymatic mechanism, substrate recruitment in the open state, bringing the catalytic residues into their required configuration in the closed bound state, and moving back to the open state to release the catalytic products and repositioning the enzyme for its next catalytic cycle. These findings suggest that the aldolase global motions are conserved among aldolases having different oligomeric states to preserve its catalytic mechanism. The coarse-grained approaches taken permit an unprecedented view of the changes in the structural dynamics and how these relate to the critical structural stabilities essential for catalysis. The results are supported by experimental findings from many previous studies.

Fe protein-independent substrate reduction by nitrogenase MoFe protein variants

The reduction of substrates catalyzed by nitrogenase normally requires nucleotide-dependent Fe protein delivery of electrons to the MoFe protein, which contains the active site FeMo cofactor. Here, it is reported that independent substitution of three amino acids (β-98(Tyr→His), α-64(Tyr→His), and β-99(Phe→His)) located between the P cluster and FeMo cofactor within the MoFe protein endows it with the ability to reduce protons to H2, azide to ammonia, and hydrazine to ammonia without the need for Fe protein or ATP. Instead, electrons can be provided by the low-potential reductant polyaminocarboxylate-ligated Eu(II) (Em values of -1.1 to -0.84 V vs the normal hydrogen electrode). The crystal structure of the β-98(Tyr→His) variant MoFe protein was determined, revealing only small changes near the amino acid substitution that affect the solvent structure and the immediate vicinity between the P cluster and the FeMo cofactor, with no global conformational changes observed. Computational normal-mode analysis of the nitrogenase complex reveals coupling in the motions of the Fe protein and the region of the MoFe protein with these three amino acids, which suggests a possible mechanism for how Fe protein might communicate subtle changes deep within the MoFe protein that profoundly affect intramolecular electron transfer and substrate reduction.

Lightweight object oriented structure analysis: tools for building tools to analyze molecular dynamics simulations

LOOS (Lightweight Object Oriented Structure-analysis) is a C++ library designed to facilitate making novel tools for analyzing molecular dynamics simulations by abstracting out the repetitive tasks, allowing developers to focus on the scientifically relevant part of the problem. LOOS supports input using the native file formats of most common biomolecular simulation packages, including CHARMM, NAMD, Amber, Tinker, and Gromacs. A dynamic atom selection language based on the C expression syntax is included and is easily accessible to the tool-writer. In addition, LOOS is bundled with over 140 prebuilt tools, including suites of tools for analyzing simulation convergence, three-dimensional histograms, and elastic network models. Through modern C++ design, LOOS is both simple to develop with (requiring knowledge of only four core classes and a few utility functions) and is easily extensible. A python interface to the core classes is also provided, further facilitating tool development.

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.

Structure-based simulations reveal concerted dynamics of GPCR activation

G protein-coupled receptors (GPCRs) are a vital class of proteins that transduce biological signals across the cell membrane. However, their allosteric activation mechanism is not fully understood; crystal structures of active and inactive receptors have been reported, but the functional pathway between these two states remains elusive. Here, we use structure-based (Gō-like) models to simulate activation of two GPCRs, rhodopsin and the β₂ adrenergic receptor (β₂AR). We used data-derived reaction coordinates that capture the activation mechanism for both proteins, showing that activation proceeds through quantitatively different paths in the two systems. Both reaction coordinates are determined from the dominant concerted motions in the simulations so the technique is broadly applicable. There were two surprising results. First, the main structural changes in the simulations were distributed throughout the transmembrane bundle, and not localized to the obvious areas of interest, such as the intracellular portion of Helix 6. Second, the activation (and deactivation) paths were distinctly nonmonotonic, populating states that were not simply interpolations between the inactive and active structures. These transitions also suggest a functional explanation for β₂AR's basal activity: it can proceed through a more broadly defined path during the observed transitions.

Elastic Network Models of Nucleic Acids Flexibility

Elastic network models (ENMs) are a useful tool for describing large scale motions in protein systems. While they are well validated in the context of proteins, relatively little is known about their applicability to nucleic acids, whose different architecture does not necessarily warrant comparable performance. In this study we thoroughly evaluate and optimize the efficiency of popular ENMs for capturing RNA and DNA flexibility. We also introduce two alternative models in which the strength of elastic connections at a coarse-grained level is governed by distance distribution at atomic resolution. For each of the considered ENMs we report the optimal length of spring connections as well as the scaling of elastic force constants that provides the best agreement of vibrational frequencies with normal modes based on atomic force field. In order to determine the absolute values of force constants we introduce a novel method based on the overlap of pseudoinverse of Hessian matrices.

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.

Effective harmonic potentials: insights into the internal cooperativity and sequence-specificity of protein dynamics

The proper biological functioning of proteins often relies on the occurrence of coordinated fluctuations around their native structure, or on their ability to perform wider and sometimes highly elaborated motions. Hence, there is considerable interest in the definition of accurate coarse-grained descriptions of protein dynamics, as an alternative to more computationally expensive approaches. In particular, the elastic network model, in which residue motions are subjected to pairwise harmonic potentials, is known to capture essential aspects of conformational dynamics in proteins, but has so far remained mostly phenomenological, and unable to account for the chemical specificities of amino acids. We propose, for the first time, a method to derive residue- and distance-specific effective harmonic potentials from the statistical analysis of an extensive dataset of NMR conformational ensembles. These potentials constitute dynamical counterparts to the mean-force statistical potentials commonly used for static analyses of protein structures. In the context of the elastic network model, they yield a strongly improved description of the cooperative aspects of residue motions, and give the opportunity to systematically explore the influence of sequence details on protein dynamics.

The interplay of structure and dynamics: insights from a survey of HIV-1 reverse transcriptase crystal structures

HIV-1 reverse transcriptase (RT) is a critical drug target for HIV treatment, and understanding the exact mechanisms of its function and inhibition would significantly accelerate the development of new anti-HIV drugs. It is well known that structure plays a critical role in protein function, but for RT, structural information has proven to be insufficient-despite enormous effort-to explain the mechanism of inhibition and drug resistance of non-nucleoside RT inhibitors. We hypothesize that the missing link is dynamics, information about the motions of the system. However, many of the techniques that give the best information about dynamics, such as solution nuclear magnetic resonance and molecular dynamics simulations, cannot be easily applied to a protein as large as RT. As an alternative, we combine elastic network modeling with simultaneous hierarchical clustering of structural and dynamic data. We present an extensive survey of the dynamics of RT bound to a variety of ligands and with a number of mutations, revealing a novel mechanism for drug resistance to non-nucleoside RT inhibitors. Hydrophobic core mutations restore active-state motion to multiple functionally significant regions of HIV-1 RT. This model arises out of a combination of structural and dynamic information, rather than exclusively from one or the other.

Robust Heterogeneous Anisotropic Elastic Network Model Precisely Reproduces the Experimental B-factors of Biomolecules

A computational method called the progressive fluctuation matching (PFM) is developed for constructing robust heterogeneous anisotropic network models (HANMs) for biomolecular systems. An HANM derived through the PFM approach consists of harmonic springs with realistic positive force constants, and yields the calculated B-factors that are basically identical to the experimental ones. For the four tested protein systems including crambin, trypsin inhibitor, HIV-1 protease, and lysozyme, the root-mean-square deviations between the experimental and the computed B-factors are only 0.060, 0.095, 0.247, and 0.049 Å(2), respectively, and the correlation coefficients are 0.99 for all. By comparing the HANM/ANM normal modes to their counterparts derived from both an atomistic force field and an NMR structure ensemble, it is found that HANM may provide more accurate results on protein dynamics.

Thermodynamics of ideal proteinogenic homopolymer chains as a function of the energy spectrum E, helical propensity ω and enthalpic energy barrier

A reformulation and generalization of the Zwanzig model (ZW model) for ideal homopolymer chains poly-X, where X represents any of the twenty naturally occurring proteinogenic amino acid residues is presented. This reformulation and generalization provides a direct connection between coarse-grained parameters originally proposed in the ZW model with variables from the Lifson-Roig (LR) theory, such as the helical propensity per residue ω, and new variables introduced here, such as the energy gap Δ between unfolded and folded structures, as well as the ratio f of the energy scales involved. This enables us to discover the relevance of the energy spectrum E to the onset of configurational phase transitions. From the configurational partition function Q, thermodynamic properties such as the configurational entropy S, specific heat v and average energy <E> are calculated in terms of the number of residues K, temperature T, helical propensity ω and energy barrier ΔH for different poly-X chains in vacuo. Results obtained here provide substantial evidence that configurational phase transitions for ideal poly-X chains correspond to first-order phase transitions. An anomalous behavior of the thermodynamic functions <E>, Cv, S with respect to the number K of residues is also highlighted. On-going methods of solution are outlined.

Multiscale Coarse-Graining via Normal Mode Analysis

A multiscale coarse-graining method called the normal-mode analysis based fluctuation matching (NMA-FM) is developed for constructing coarse-grained models of biomolecular systems. In the framework of normal-mode analysis, an arbitrary fine-grained model can be systematically converted to a more coarse-grained model, while the crucial low-frequency motions of the fine-grained system are able to be reproduced in the coarse-grained modeling. The method relies on the technique of fluctuation matching that has been devised earlier for parametrizing heterogeneous elastic network models based on data from atomistic molecular dynamics simulations. The new approach is quite efficient since it avoids expensive atomistic molecular dynamics simulations and can start from already coarse-grained elastic network models. In the practical aspect, the method is suitable for conformational analyses of large biomacromolecules and calculations of mechanical properties of biomaterials, which is demonstrated by the studied systems including an amyloid dimer, lysozyme and adenylate kinase proteins, and the S2 subdomain of myosin.