Allosteric transitions of supramolecular systems explored by network models: application to chaperonin GroEL

Insights into Activation Dynamics and Functional Sites of Inwardly Rectifying Potassium Channel Kir3.2 by an Elastic Network Model Combined with Perturbation Methods

The inwardly rectifying potassium channel Kir3.2, a member of the inward rectifier potassium (Kir) channel family, exerts important biological functions through transporting potassium ions outside of the cell, during which a large-scale synergistic movement occurs among its different domains. Currently, it is not fully understood how the binding of the ligand to the Kir3.2 channel leads to the structural changes and which key residues are responsible for the channel gating and allosteric dynamics. Here, we construct the Gaussian network model (GNM) of the Kir3.2 channel with the secondary structure and covalent interaction information considered (sscGNM), which shows a better performance in reproducing the channel's flexibility compared with the traditional GNM. In addition, the sscANM-based perturbation method is used to simulate the channel's conformational transition caused by the activator PIP2's binding. By applying certain forces to the PIP2 binding pocket, the coarse-grained calculations generate the similar conformational changes to the experimental observation, suggesting that the topology structure as well as PIP2 binding are crucial to the allosteric activation of the Kir3.2 channel. We also utilize the sscGNM-based thermodynamic cycle method developed by us to identify the key residues whose mutations significantly alter the channel's binding free energy with PIP2. We identify not only the residues important for the specific binding but also the ones critical for the allosteric transition coupled with PIP2 binding. This study is helpful for understanding the working mechanism of Kir3.2 channels and can provide important information for related drug design.

Study on the allosteric activation mechanism of SHP2 via elastic network models and neural relational inference molecular dynamics simulation

As a ubiquitous protein tyrosine phosphatase, SHP2 is involved in PD-1/PD-L1 mediated tumor immune escape and undergoes substantial conformational changes. Therefore, it is considered an ideal target for tumor intervention. However, the allosteric mechanisms of SHP2 binding PD-1 intracellular ITIM/ITSM phosphopeptides remain unclear, which greatly hinders the development of novel structure-based anticancer allosteric inhibitors. In this work, the open and closed structural models of SHP2 are first constructed based on this knowledge; next their motion modes are investigated via elastic network models such as the Gaussian network model (GNM), anisotropic network model (ANM) and adaptive anisotropic network model (aANM); and finally, a possible allosteric signaling pathway is proposed using a neural relational inference molecular dynamics (NRI-MD) simulation embedded with an artificial intelligence (AI) strategy. In GNM and ANM, the N-SH2, C-SH2 and PTP domains all exhibit distinct dynamics partitions, and the N-SH2/C-SH2 regions show a rigid rotation relative to PTP. According to a series of intermediate snapshots given by aANM, N-SH2 is first identified with pY223 specifically, inducing a D'E-loop to change from β-sheets to random coils, and then, C-SH2 serves as a fulcrum to drive N-SH2 to rotate 110° completely away from the original active sites of PTP. Finally, a possible allosteric signaling-transfer path for SHP2, namely R220-R138-T108-R32, is proposed based on NRI-MD sampling. This work provides a possible allosteric mechanism of SHP2, which is helpful for the following design of novel allosteric inhibitors and is expected to be used in clinical synergies with PD-1 monoclonal antibody.

Identifying a Feasible Transition Pathway between Two Conformational States for a Protein

Proteins usually need to transit between different conformational states to fulfill their biological functions. In the mechanistic study of such transition processes by molecular dynamics simulations, identification of the minimum free energy path (MFEP) can substantially reduce the sampling space, thus enabling rigorous thermodynamic evaluation of the process. Conventionally, the MFEP is derived by iterative local optimization from an initial path, which is typically generated by simple brute force techniques like the targeted molecular dynamics (tMD). Therefore, the quality of the initial path determines the successfulness of MFEP estimation. In this work, we propose a method to improve derivation of the initial path. Through iterative relaxation-biasing simulations in a bidirectional manner, this method can construct a feasible transition pathway connecting two known states for a protein. Evaluation on small, fast-folding proteins against long equilibrium trajectories supports the good sampling efficiency of our method. When applied to larger proteins including the catalytic domain of human c-Src kinase as well as the converter domain of myosin VI, the paths generated by our method deviate significantly from those computed with the generic tMD approach. More importantly, free energy profiles and intermediate states obtained from our paths exhibit remarkable improvements over those from tMD paths with respect to both physical rationality and consistency with a priori knowledge.

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

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

Protein dynamics developments for the large scale and cryoEM: case study of ProDy 2.0

New computational biophysics pipelines for analysing the global dynamics of structural ensembles and large, dynamic complexes resolved by cryoEM are reviewed.

Cryo-electron microscopy (cryoEM) has become a well established technique with the potential to produce structures of large and dynamic supramolecular complexes that are not amenable to traditional approaches for studying structure and dynamics. The size and low resolution of such molecular systems often make structural modelling and molecular dynamics simulations challenging and computationally expensive. This, together with the growing wealth of structural data arising from cryoEM and other structural biology methods, has driven a trend in the computational biophysics community towards the development of new pipelines for analysing global dynamics using coarse-grained models and methods. At the centre of this trend has been a return to elastic network models, normal mode analysis (NMA) and ensemble analyses such as principal component analysis, and the growth of hybrid simulation methodologies that make use of them. Here, this field is reviewed with a focus on ProDy, the Python application programming interface for protein dynamics, which has been developed over the last decade. Two key developments in this area are highlighted: (i) ensemble NMA towards extracting and comparing the signature dynamics of homologous structures, aided by the recent SignDy pipeline, and (ii) pseudoatom fitting for more efficient global dynamics analyses of large and low-resolution supramolecular assemblies from cryoEM, revisited in the CryoDy pipeline. It is believed that such a renewal and extension of old models and methods in new pipelines will be critical for driving the field forward into the next cryoEM revolution.

Allosteric and transport modulation of human concentrative nucleoside transporter 3 at the atomic scale

Nucleosides are important precursors of nucleotide synthesis in cells, and nucleoside transporters play an important role in many physiological processes by mediating transmembrane transport and absorption. During nucleoside transport, such proteins undergo a significant conformational transition between the outward- and inward-facing states, which leads to alternating access of the substrate-binding site to either side of the membrane. In this work, a variety of molecular simulation methods have been applied to comparatively investigate the motion modes of human concentrative nucleoside transporter 3 (hCNT3) in three states, as well as global and local cavity conformational changes; and finally, a possible elevator-like transport mechanism consistent with experimental data was proposed. The results of the Gaussian network model (GNM) and anisotropic network model (ANM) show that hCNT3 as a whole tends to contract inwards and shift towards a membrane inside, exhibiting an allosteric process that is more energetically favorable than the rigid conversion. To reveal the complete allosteric process of hCNT3 in detail, a series of intermediate conformations were obtained by an adaptive anisotropic network model (aANM). One of the simulated intermediate states is similar to that of a crystal structure, which indicates that the allosteric process is reliable; the state with lower energy is slightly inclined to the inward-facing structure rather than the expected intermediate crystal structure. The final HOLE analysis showed that except for the outward-facing state, the transport channels were gradually enlarged, which was conductive to the directional transport of nucleosides. Our work provides a theoretical basis for the multistep elevator-like transportation mechanism of nucleosides, which helps to further understand the dynamic recognition between nucleoside substrates and hCNT3 as well as the design of nucleoside anticancer drugs.

Approximating deformation fields for the analysis of continuous heterogeneity of biological macromolecules by 3D Zernike polynomials

Structural biology has evolved greatly due to the advances introduced in fields like electron microscopy. This image-capturing technique, combined with improved algorithms and current data processing software, allows the recovery of different conformational states of a macromolecule, opening new possibilities for the study of its flexibility and dynamic events. However, the ensemble analysis of these different conformations, and in particular their placement into a common variable space in which the differences and similarities can be easily recognized, is not an easy matter. To simplify the analysis of continuous heterogeneity data, this work proposes a new automatic algorithm that relies on a mathematical basis defined over the sphere to estimate the deformation fields describing conformational transitions among different structures. Thanks to the approximation of these deformation fields, it is possible to describe the forces acting on the molecules due to the presence of different motions. It is also possible to represent and compare several structures in a low-dimensional mapping, which summarizes the structural characteristics of different states. All these analyses are integrated into a common framework, providing the user with the ability to combine them seamlessly. In addition, this new approach is a significant step forward compared with principal component analysis and normal mode analysis of cryo-electron microscopy maps, avoiding the need to select components or modes and producing localized analysis.

Novel cryo-EM structure of an ADP-bound GroEL-GroES complex

The GroEL–GroES chaperonin complex is a bacterial protein folding system, functioning in an ATP-dependent manner. Upon ATP binding and hydrolysis, it undergoes multiple stages linked to substrate protein binding, folding and release. Structural methods helped to reveal several conformational states and provide more information about the chaperonin functional cycle. Here, using cryo-EM we resolved two nucleotide-bound structures of the bullet-shaped GroEL–GroES₁ complex at 3.4 Å resolution. The main difference between them is the relative orientation of their apical domains. Both structures contain nucleotides in cis and trans GroEL rings; in contrast to previously reported bullet-shaped complexes where nucleotides were only present in the cis ring. Our results suggest that the bound nucleotides correspond to ADP, and that such a state appears at low ATP:ADP ratios.

State-dependent sequential allostery exhibited by chaperonin TRiC/CCT revealed by network analysis of Cryo-EM maps

The eukaryotic chaperonin TRiC/CCT plays a major role in assisting the folding of many proteins through an ATP-driven allosteric cycle. Recent structures elucidated by cryo-electron microscopy provide a broad view of the conformations visited at various stages of the chaperonin cycle, including a sequential activation of its subunits in response to nucleotide binding. But we lack a thorough mechanistic understanding of the structure-based dynamics and communication properties that underlie the TRiC/CCT machinery. In this study, we present a computational methodology based on elastic network models adapted to cryo-EM density maps to gain a deeper understanding of the structure-encoded allosteric dynamics of this hexadecameric machine. We have analysed several structures of the chaperonin resolved in different states toward mapping its conformational landscape. Our study indicates that the overall architecture intrinsically favours cooperative movements that comply with the structural variabilities observed in experiments. Furthermore, the individual subunits CCT1-CCT8 exhibit state-dependent sequential events at different states of the allosteric cycle. For example, in the ATP-bound state, subunits CCT5 and CCT4 selectively initiate the lid closure motions favoured by the overall architecture; whereas in the apo form of the heteromer, the subunit CCT7 exhibits the highest predisposition to structural change. The changes then propagate through parallel fluxes of allosteric signals to neighbours on both rings. The predicted state-dependent mechanisms of sequential activation provide new insights into TRiC/CCT intra- and inter-ring signal transduction events.

Identification of potential allosteric binding sites in cathepsin K based on intramolecular communication

Network theory methods and molecular dynamics (MD) simulations are accepted tools to study allosteric regulation. Indeed, dynamic networks built upon correlation analysis of MD trajectories provide detailed information about communication paths between distant sites. In this context, we aimed to understand whether the efficiency of intramolecular communication could be used to predict the allosteric potential of a given site. To this end, we performed MD simulations and network theory analyses in cathepsin K (catK), whose allosteric sites are well defined. To obtain a quantitative measure of the efficiency of communication, we designed a new protocol that enables the comparison between properties related to ensembles of communication paths obtained from different sites. Further, we applied our strategy to evaluate the allosteric potential of different catK cavities not yet considered for drug design. Our predictions of the allosteric potential based on intramolecular communication correlate well with previous catK experimental and theoretical data. We also discuss the possibility of applying our approach to other proteins from the same family.

Towards gaining sight of multiscale events: utilizing network models and normal modes in hybrid methods

With the explosion of normal mode analyses (NMAs) based on elastic network models (ENMs) in the last decade, and the proven precision of MD simulations for visualizing interactions at atomic scale, many hybrid methods have been proposed in recent years. These aim at exploiting the best of both worlds: the atomic precision of MD that often fall short of exploring time and length scales of biological interest, and the capability of ENM-NMA to predict the cooperative and often functional rearrangements of large structures and assemblies, albeit at low resolution. We present an overview of recent progress in the field with examples of successful applications highlighting the utility of such hybrid methods and pointing to emerging future directions guided by advances in experimental characterization of biomolecular systems structure and dynamics.

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.

Integrated Computational Approaches and Tools forAllosteric Drug Discovery

Understanding molecular mechanisms underlying the complexity of allosteric regulationin proteins has attracted considerable attention in drug discovery due to the benefits and versatilityof allosteric modulators in providing desirable selectivity against protein targets while minimizingtoxicity and other side effects. The proliferation of novel computational approaches for predictingligand-protein interactions and binding using dynamic and network-centric perspectives has ledto new insights into allosteric mechanisms and facilitated computer-based discovery of allostericdrugs. Although no absolute method of experimental and in silico allosteric drug/site discoveryexists, current methods are still being improved. As such, the critical analysis and integration ofestablished approaches into robust, reproducible, and customizable computational pipelines withexperimental feedback could make allosteric drug discovery more efficient and reliable. In this article,we review computational approaches for allosteric drug discovery and discuss how these tools can beutilized to develop consensus workflows for in silico identification of allosteric sites and modulatorswith some applications to pathogen resistance and precision medicine. The emerging realization thatallosteric modulators can exploit distinct regulatory mechanisms and can provide access to targetedmodulation of protein activities could open opportunities for probing biological processes and insilico design of drug combinations with improved therapeutic indices and a broad range of activities.

Intrinsic dynamics is evolutionarily optimized to enable allosteric behavior

Allosteric behavior is central to the function of many proteins, enabling molecular machinery, metabolism, signaling and regulation. Recent years have shown that the intrinsic dynamics of allosteric proteins defined by their 3-dimensional architecture or by the topology of inter-residue contacts favors cooperative motions that bear close similarity to structural changes they undergo during their allosteric actions. These conformational motions are usually driven by energetically favorable or soft modes at the low frequency end of the mode spectrum, and they are evolutionarily conserved among orthologs. These observations brought into light evolutionary adaptation mechanisms that help maintain, optimize or regulate allosteric behavior as the evolution from bacterial to higher organisms introduces sequential heterogeneities and structural complexities.

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.

Simple mechanics of protein machines

While belonging to the nanoscale, protein machines are so complex that tracing even a small fraction of their cycle requires weeks of calculations on supercomputers. Surprisingly, many aspects of their operation can be however already reproduced by using very simple mechanical models of elastic networks. The analysis suggests that, similar to other self-organized complex systems, functional collective dynamics in such proteins is effectively reduced to a low-dimensional attractive manifold.

Ligand binding effects on the activation of the EGFR extracellular domain

The epidermal growth factor receptor (EGFR) is one of the most common target proteins in anti-cancer therapy. The binding of the EGF ligand to the EGFR extracellular domain (EGFR-ECD) promotes its inactive-to-active conformational transition (activation) but the relevant detailed mechanism remains elusive still. Here, the structural characterization and energetics of the EGFR-ECD conformational transition with and without the binding of the EGF are quantitatively explored using an innovative enhanced sampling MD simulation method. Intriguingly, the EGF offers hydrophobic interactions (e.g., EGF residues of Tyr44 and Leu47) and electrostatic interactions (e.g., the EGF residues of Glu5, Asp11, Asp17, and Arg41) to play a dominant role in dragging domain III to close the ligand binding domain gap. Subsequently, the correlation between domains III and II is enhanced through salt-bridges among Glu376, Arg403, and Arg405 from domain III and Glu293, Glu295, and Arg300 from domain II. Finally, the structural bending of domain II is regulated to facilitate the disengagement of domain II from domain IV. In this regard, the functional conformational transition of EGFR-ECD is a consequence of the cooperative motion of protein domains driven by the EGF ligand binding. The present study shows a detailed scenario of the EGF induced activation of EGFR-ECD and provides valuable information for drug discovery targeting the EGFR.

Shared dynamics of LeuT superfamily members and allosteric differentiation by structural irregularities and multimerization

The LeuT-fold superfamily includes secondary active transporters from different functional families, which share a common tertiary structure, despite having a remarkably low sequence similarity. By identifying the common structural and dynamical features upon principal component analysis of a comprehensive ensemble of 90 experimentally resolved structures and anisotropic network model evaluation of collective motions, we provide a unified point of view for understanding the reasons why this particular fold has been selected by evolution to accomplish such a broad spectrum of functions. The parallel identification of conserved sequence features, localized at specific sites of transmembrane helices, sheds light on the role of broken helices (TM1 and TM6 in LeuT) in promoting ion/substrate binding and allosteric interconversion between the outward- and inward-facing conformations of transporters. Finally, the determination of the dynamics landscape for the structural ensemble provides a promising framework for the classification of transporters based on their dynamics, and the characterization of the collective movements that favour multimerization.This article is part of a discussion meeting issue 'Allostery and molecular machines'.

Allosteric mechanism of the circadian protein Vivid resolved through Markov state model and machine learning analysis

The fungal circadian clock photoreceptor Vivid (VVD) contains a photosensitive allosteric light, oxygen, voltage (LOV) domain that undergoes a large N-terminal conformational change. The mechanism by which a blue-light driven covalent bond formation leads to a global conformational change remains unclear, which hinders the further development of VVD as an optogenetic tool. We answered this question through a novel computational platform integrating Markov state models, machine learning methods, and newly developed community analysis algorithms. Applying this new integrative approach, we provided a quantitative evaluation of the contribution from the covalent bond to the protein global conformational change, and proposed an atomistic allosteric mechanism leading to the discovery of the unexpected importance of A'α/Aβ and previously overlooked Eα/Fα loops in the conformational change. This approach could be applicable to other allosteric proteins in general to provide interpretable atomistic representations of their otherwise elusive allosteric mechanisms.

Survey of the analysis of continuous conformational variability of biological macromolecules by electron microscopy

Single-particle analysis by electron microscopy is a well established technique for analyzing the three-dimensional structures of biological macromolecules. Besides its ability to produce high-resolution structures, it also provides insights into the dynamic behavior of the structures by elucidating their conformational variability. Here, the different image-processing methods currently available to study continuous conformational changes are reviewed.

Designed Elastic Networks: Models of Complex Protein Machinery

Recently, the design of mechanical networks with protein-inspired responses has become increasingly popular. Here, we review contributions which were motivated by studies of protein dynamics employing coarse-grained elastic network models. First, the concept of evolutionary optimization that we developed to design network structures which execute prescribed tasks is explained. We then review what presumably marks the origin of the idea to design complex functional networks which encode protein-inspired behavior, namely the design of an elastic network structure which emulates the cycles of ATP-powered conformational motion in protein machines. Two recent applications are reviewed. First, the construction of a model molecular motor, whose operation incorporates both the tight coupling power stroke as well as the loose coupling Brownian ratchet mechanism, is discussed. Second, the evolutionary design of network structures which encode optimal long-range communication between remote sites and represent mechanical models of allosteric proteins is presented. We discuss the prospects of designed protein-mimicking elastic networks as model systems to elucidate the design principles and functional signatures underlying the operation of complex protein machinery.

Design of Elastic Networks with Evolutionary Optimized Long-Range Communication as Mechanical Models of Allosteric Proteins

Allosteric effects often underlie the activity of proteins, and elucidating generic design aspects and functional principles unique to allosteric phenomena represent a major challenge. Here an approach consisting of the in silico design of synthetic structures, which, as the principal element of allostery, encode dynamical long-range coupling among two sites, is presented. The structures are represented by elastic networks, similar to coarse-grained models of real proteins. A strategy of evolutionary optimization was implemented to iteratively improve allosteric coupling. In the designed structures, allosteric interactions were analyzed in terms of strain propagation, and simple pathways that emerged during evolution were identified as signatures through which long-range communication was established. Moreover, robustness of allosteric performance with respect to mutations was demonstrated. As it turned out, the designed prototype structures reveal dynamical properties resembling those found in real allosteric proteins. Hence, they may serve as toy models of complex allosteric systems, such as proteins. Application of the developed modeling scheme to the allosteric transition in the myosin V molecular motor was also demonstrated.

Directional Force Originating from ATP Hydrolysis Drives the GroEL Conformational Change

Protein functional mechanisms usually require conformational changes, and often there are known structures for the different conformational states. However, usually neither the origin of the driving force nor the underlying pathways for these conformational transitions is known. Exothermic chemical reactions may be an important source of forces that drive conformational changes. Here we investigate this type of force originating from ATP hydrolysis in the chaperonin GroEL, by applying forces originating from the chemical reaction. Specifically, we apply directed forces to drive the GroEL conformational changes and learn that there is a highly specific direction for applied forces to drive the closed form to the open form. For this purpose, we utilize coarse-grained elastic network models. Principal component analysis on 38 GroEL experimental structures yields the most important motions, and these are used in structural interpolation for the construction of a coarse-grained free energy landscape. In addition, we investigate a more random application of forces with a Monte Carlo method and demonstrate pathways for the closed-open conformational transition in both directions by computing trajectories that are shown upon the free energy landscape. Initial root mean square deviation (RMSD) between the open and closed forms of the subunit is 14.7 Å and final forms from our simulations reach an average RMSD of 3.6 Å from the target forms, closely matching the level of resolution of the coarse-grained model.

Minimum action transition paths connecting minima on an energy surface

Dynamics is essential to the biological functions of many bio-molecules, yet our knowledge of dynamics remains fragmented. Experimental techniques for studying bio-molecules either provide high resolution information on static conformations of the molecule or provide low-resolution, ensemble information that does not shed light on single molecule dynamics. In parallel, bio-molecular dynamics occur at time scale that are not yet attainable through detailed simulation methods. These limitations are especially noticeable when studying transition paths. To address this issue, we report in this paper two methods that derive meaningful trajectories for proteins between two of their conformations. The first method, MinActionPath, uses approximations of the potential energy surface for the molecule to derive an analytical solution of the equations of motion related to the concept of minimum action path. The second method, RelaxPath, follows the same principle of minimum action path but implements a more sophisticated potential, including a mixed elastic potential and a collision term to alleviate steric clashes. Using this new potential, the equations of motion cannot be solved analytically. We have introduced a relaxation method for solving those equations. We describe both the theories behind the two methods and their implementations, focusing on the specific techniques we have used that make those implementations amenable to study large molecular systems. We have illustrated the performance of RelaxPath on simple 2D systems. We have also compared MinActionPath and RelaxPath to other methods for generating transition paths on a well suited test set of large proteins, for which the end points of the trajectories as well as an intermediate conformation between those end points are known. We have shown that RelaxPath outperforms those other methods, including MinActionPath, in its ability to generate trajectories that get close to the known intermediates. We have also shown that the structures along the RelaxPath trajectories remain protein-like. Open source versions of the two programs MinActionPath and RelaxPath are available by request.

Prediction and validation of protein intermediate states from structurally rich ensembles and coarse-grained simulations

Protein conformational changes are at the heart of cell functions, from signalling to ion transport. However, the transient nature of the intermediates along transition pathways hampers their experimental detection, making the underlying mechanisms elusive. Here we retrieve dynamic information on the actual transition routes from principal component analysis (PCA) of structurally-rich ensembles and, in combination with coarse-grained simulations, explore the conformational landscapes of five well-studied proteins. Modelling them as elastic networks in a hybrid elastic-network Brownian dynamics simulation (eBDIMS), we generate trajectories connecting stable end-states that spontaneously sample the crystallographic motions, predicting the structures of known intermediates along the paths. We also show that the explored non-linear routes can delimit the lowest energy passages between end-states sampled by atomistic molecular dynamics. The integrative methodology presented here provides a powerful framework to extract and expand dynamic pathway information from the Protein Data Bank, as well as to validate sampling methods in general.

Protein conformational changes are key to a wide range of cellular functions but remain difficult to access experimentally. Here the authors describe eBDIMS, a novel approach to predict intermediates observed in structural transition pathways from experimental ensembles.

Conformational shift in the closed state of GroEL induced by ATP-binding triggers a transition to the open state

We investigated the effect of ATP binding to GroEL and elucidated a role of ATP in the conformational change of GroEL. GroEL is a tetradecamer chaperonin that helps protein folding by undergoing a conformational change from a closed state to an open state. This conformational change requires ATP, but does not require the hydrolysis of the ATP. The following three types of conformations are crystalized and the atomic coordinates are available; closed state without ATP, closed state with ATP and open state with ADP. We conducted simulations of the conformational change using Elastic Network Model from the closed state without ATP targeting at the open state, and from the closed state with ATP targeting at the open state. The simulations emphasizing the lowest normal mode showed that the one started with the closed state with ATP, rather than the one without ATP, reached a conformation closer to the open state. This difference was mainly caused by the changes in the positions of residues in the initial structure rather than the changes in "connectivity" of residues within the subunit. Our results suggest that ATP should behave as an insulator to induce conformation population shift in the closed state to the conformation that has a pathway leading to the open state.

Principles and Overview of Sampling Methods for Modeling Macromolecular Structure and Dynamics

Investigation of macromolecular structure and dynamics is fundamental to understanding how macromolecules carry out their functions in the cell. Significant advances have been made toward this end in silico, with a growing number of computational methods proposed yearly to study and simulate various aspects of macromolecular structure and dynamics. This review aims to provide an overview of recent advances, focusing primarily on methods proposed for exploring the structure space of macromolecules in isolation and in assemblies for the purpose of characterizing equilibrium structure and dynamics. In addition to surveying recent applications that showcase current capabilities of computational methods, this review highlights state-of-the-art algorithmic techniques proposed to overcome challenges posed in silico by the disparate spatial and time scales accessed by dynamic macromolecules. This review is not meant to be exhaustive, as such an endeavor is impossible, but rather aims to balance breadth and depth of strategies for modeling macromolecular structure and dynamics for a broad audience of novices and experts.

Controlling Allosteric Networks in Proteins

Allosteric transition, defined as conformational changes induced by ligand binding, is one of the fundamental properties of proteins. Allostery has been observed and characterized in many proteins, and has been recently utilized to control protein function via regulation of protein activity. Here, we review the physical and evolutionary origin of protein allostery, as well as its importance to protein regulation, drug discovery, and biological processes in living systems. We describe recently developed approaches to identify allosteric pathways, connected sets of pairwise interactions that are responsible for propagation of conformational change from the ligand-binding site to a distal functional site. We then present experimental and computational protein engineering approaches for control of protein function by modulation of allosteric sites. As an example of application of these approaches, we describe a synergistic computational and experimental approach to rescue the cystic-fibrosis-associated protein cystic fibrosis transmembrane conductance regulator, which upon deletion of a single residue misfolds and causes disease. This example demonstrates the power of allosteric manipulation in proteins to both elucidate mechanisms of molecular function and to develop therapeutic strategies that rescue those functions. Allosteric control of proteins provides a tool to shine a light on the complex cascades of cellular processes and facilitate unprecedented interrogation of biological systems.

Allosteric Mechanisms in Chaperonin Machines

Chaperonins are nanomachines that facilitate protein folding by undergoing energy (ATP)-dependent movements that are coordinated in time and space owing to complex allosteric regulation. They consist of two back-to-back stacked oligomeric rings with a cavity at each end where protein substrate folding can take place. Here, we focus on the GroEL/GroES chaperonin system from Escherichia coli and, to a lesser extent, on the more poorly characterized eukaryotic chaperonin CCT/TRiC. We describe their various functional (allosteric) states and how they are affected by substrates and allosteric effectors that include ATP, ADP, nonfolded protein substrates, potassium ions, and GroES (in the case of GroEL). We also discuss the pathways of intra- and inter-ring allosteric communication by which they interconvert and the coupling between allosteric transitions and protein folding reactions.

A modified PATH algorithm rapidly generates transition states comparable to those found by other well established algorithms

PATH rapidly computes a path and a transition state between crystal structures by minimizing the Onsager-Machlup action. It requires input parameters whose range of values can generate different transition-state structures that cannot be uniquely compared with those generated by other methods. We outline modifications to estimate these input parameters to circumvent these difficulties and validate the PATH transition states by showing consistency between transition-states derived by different algorithms for unrelated protein systems. Although functional protein conformational change trajectories are to a degree stochastic, they nonetheless pass through a well-defined transition state whose detailed structural properties can rapidly be identified using PATH.

Enhanced conformational sampling technique provides an energy landscape view of large-scale protein conformational transitions

A novel in silico approach (NMA–ITS) is introduced to rapidly and effectively sample the configuration space and give quantitative data for exploring the conformational changes of proteins.

Cofilin reduces the mechanical properties of actin filaments: approach with coarse-grained methods

An actin filament is an essential cytoskeleton protein in a cell. Various proteins bind to actin for cell functions such as migration, division, and shape control. ADF/cofilin is a protein that severs actin filaments and is related to their dynamics. Actin is known to have excellent mechanical properties. Binding cofilin reduces its mechanical properties, and is related to the severing process. In this research, we applied a coarse-grained molecular dynamics simulation (CGMD) method to obtain actin filaments and cofilin-bound actin (cofilactin) filaments. Using these two obtained models, we constructed an elastic network model-based structure and conducted a normal mode analysis. Based on the low-frequency normal modes of the filament structure, we applied the continuum beam theory to calculate the mechanical properties of the actin and cofilactin filaments. The CGMD method provided structurally accurate actin and cofilactin filaments in relation to the mechanical properties, which showed good agreement with the established experimental results.

Bridging between NMA and Elastic Network Models: Preserving All-Atom Accuracy in Coarse-Grained Models

Dynamics can provide deep insights into the functional mechanisms of proteins and protein complexes. For large protein complexes such as GroEL/GroES with more than 8,000 residues, obtaining a fine-grained all-atom description of its normal mode motions can be computationally prohibitive and is often unnecessary. For this reason, coarse-grained models have been used successfully. However, most existing coarse-grained models use extremely simple potentials to represent the interactions within the coarse-grained structures and as a result, the dynamics obtained for the coarse-grained structures may not always be fully realistic. There is a gap between the quality of the dynamics of the coarse-grained structures given by all-atom models and that by coarse-grained models. In this work, we resolve an important question in protein dynamics computations—how can we efficiently construct coarse-grained models whose description of the dynamics of the coarse-grained structures remains as accurate as that given by all-atom models? Our method takes advantage of the sparseness of the Hessian matrix and achieves a high efficiency with a novel iterative matrix projection approach. The result is highly significant since it can provide descriptions of normal mode motions at an all-atom level of accuracy even for the largest biomolecular complexes. The application of our method to GroEL/GroES offers new insights into the mechanism of this biologically important chaperonin, such as that the conformational transitions of this protein complex in its functional cycle are even more strongly connected to the first few lowest frequency modes than with other coarse-grained models.

Proteins and other biomolecules are not static but are constantly in motion. Moreover, they possess intrinsic collective motion patterns that are tightly linked to their functions. Thus, an accurate and detailed description of their motions can provide deep insights into their functional mechanisms. For large protein complexes with hundreds of thousands of atoms or more, an atomic level description of the motions can be computationally prohibitive, and so coarse-grained models with fewer structural details are often used instead. However, there can be a big gap between the quality of motions derived from atomic models and those from coarse-grained models. In this work, we solve an important problem in protein dynamics studies: how to preserve the atomic-level accuracy in describing molecular motions while using coarse-grained models? We accomplish this by developing a novel iterative matrix projection method that dramatically speeds up the computations. This method is significant since it promises accurate descriptions of protein motions approaching an all-atom level even for the largest biomolecular complexes. Results shown here for a large molecular chaperonin demonstrate how this can provide new insights into its functional process.

Dynamic Transmission of Protein Allostery without Structural Change: Spatial Pathways or Global Modes?

We examine the contrast between mechanisms for allosteric signaling that involve structural change, and those that do not, from the perspective of allosteric pathways. In particular we treat in detail the case of fluctuation-allostery by which amplitude modulation of the thermal fluctuations of the elastic normal modes conveys the allosteric signal, and address the question of what an allosteric pathway means in this case. We find that a perturbation theory of thermal elastic solids and nonperturbative approach (by super-coarse-graining elasticity into internal bending modes) have opposite signatures in their structure of correlated pathways. We illustrate the effect from analysis of previous results from GlxR of Corynebacterium glutamicum, an example of the CRP/FNR transcription family of allosteric homodimers. We find that the visibility of both correlated pathways and disconnected sites of correlated motion in this protein suggests that mechanisms of local elastic stretch and bend are recruited for the purpose of creating and controlling allosteric cooperativity.

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.

Features of large hinge-bending conformational transitions. Prediction of closed structure from open state

We performed a detailed analysis of conformational transition pathways for a set of 10 proteins, which undergo large hinge-bending-type motions with 4-12 Å RMSD (root mean-square distance) between open and closed crystal structures. Anisotropic network model-Monte Carlo (ANM-MC) algorithm generates a targeted pathway between two conformations, where the collective modes from the ANM are used for deformation at each iteration and the conformational energy of the deformed structure is minimized via an MC algorithm. The target structure was approached successfully with an RMSD of 0.9-4.1 Å when a relatively low cutoff radius of 10 Å was used in ANM. Even though one predominant mode (first or second) directed the open-to-closed conformational transition, changes in the dominant mode character were observed for most cases along the transition. By imposing radius of gyration constraint during mode selection, it was possible to predict the closed structure for eight out of 10 proteins (with initial 4.1-7.1 Å and final 1.7-2.9 Å RMSD to target). Deforming along a single mode leads to most successful predictions. Based on the previously reported free energy surface of adenylate kinase, deformations along the first mode produced an energetically favorable path, which was interestingly facilitated by a change in mode shape (resembling second and third modes) at key points. Pathway intermediates are provided in our database of conformational transitions (http://safir.prc.boun.edu.tr/anmmc/method/1).