Backbone building from quadrilaterals: a fast and accurate algorithm for protein backbone reconstruction from alpha carbon coordinates

Evaluation of Essential Dynamics and Fixed-Length Coarse Graining for Multidomain Proteins

For multiscale modeling of biomolecules, reliable coarse-grained (CG) models can offer great potential to simulate larger temporal and spatial scales than traditional all-atom (AA) models. In this study, we explore the essential dynamics coarse graining (EDCG) and fixed-length coarse graining (FLCG) approaches for constructing highly coarse-grained models for multidomain proteins (MDPs), with 1 to 10 amino acid residues per CG site. In the studies of 13 MDPs, our data indicate that both EDCG and FLCG can preserve the protein dynamics of MDPs. FLCG, which restricts an equal number of residues in each CG site, represents an excellent approximation to EDCG and a straightforward approach for coarse-graining MDPs. Furthermore, FLCG is tested with a class B G-protein-coupled receptor protein, and the agreement with prior experiments suggests its general application to various MDPs in different environments or conditions. Finally, we demonstrate another application of FLCG through progressive backmapping, showcasing the ability to recover from lower-resolution CG models (6 residues/CG site) to higher-resolution ones (1 residue/CG site). These promising outcomes underscore the broad applicability of FLCG to construct highly or ultra-coarse-grained models of complex biomolecules for multiscale simulations.

Genome-wide mapping and cryo-EM structural analyses of the overlapping tri-nucleosome composed of hexasome-hexasome-octasome moieties

The nucleosome is a fundamental unit of chromatin in which about 150 base pairs of DNA are wrapped around a histone octamer. The overlapping di-nucleosome has been proposed as a product of chromatin remodeling around the transcription start site, and previously found as a chromatin unit, in which about 250 base pairs of DNA continuously bind to the histone core composed of a hexamer and an octamer. In the present study, our genome-wide analysis of human cells suggests another higher nucleosome stacking structure, the overlapping tri-nucleosome, which wraps about 300-350 base-pairs of DNA in the region downstream of certain transcription start sites of actively transcribed genes. We determine the cryo-electron microscopy (cryo-EM) structure of the overlapping tri-nucleosome, in which three subnucleosome moieties, hexasome, hexasome, and octasome, are associated by short connecting DNA segments. Small angle X-ray scattering and coarse-grained molecular dynamics simulation analyses reveal that the cryo-EM structure of the overlapping tri-nucleosome may reflect its structure in solution. Our findings suggest that nucleosome stacking structures composed of hexasome and octasome moieties may be formed by nucleosome remodeling factors around transcription start sites for gene regulation.

Energy landscapes of Aβ monomers are sculpted in accordance with Ostwald's rule of stages

The transition from a disordered to an assembly-competent monomeric state (N*) in amyloidogenic sequences is a crucial event in the aggregation cascade. Using a well-calibrated model for intrinsically disordered proteins (IDPs), we show that the N* states, which bear considerable resemblance to the polymorphic fibril structures found in experiments, not only appear as excitations in the free energy landscapes of Aβ40 and Aβ42, but also initiate the aggregation cascade. For Aβ42, the transitions to the different N* states are in accord with Ostwald's rule of stages, with the least stable structures forming ahead of thermodynamically favored ones. The Aβ40 and Aβ42 monomer landscapes exhibit different extents of local frustration, which we show have profound implications in dictating subsequent self-assembly. Using kinetic transition networks, we illustrate that the most favored dimerization routes proceed via N* states. We argue that Ostwald's rule also holds for the aggregation of fused in sarcoma and polyglutamine proteins.

3D-BMPP: 3D Beta-Barrel Membrane Protein Predictor

β-barrel membrane proteins (βMPs), found in the outer membrane of gram-negative bacteria, mitochondria, and chloroplasts, play important roles in membrane anchoring, pore formation, and enzyme activities. However, it is often difficult to determine their structures experimentally, and the knowledge of their structures is currently limited. We have developed a method to predict the 3D architectures of βMPs. We can accurately construct transmembrane domains of βMPs by predicting their strand registers, from which full 3D atomic structures are derived. Using 3D Beta-barrel Membrane Protein Predictor (3D-BMPP), we can further accurately model the extended beta barrels and loops in non-TM regions with overall greater structure prediction coverage. 3DBMPP is a general technique that can be applied to protein families with limited sequences as well as proteins with novel folds. Applications of 3DBMPP can be broadly applied to genome-wide βMPs structure prediction.

Automated Protein Secondary Structure Assignment from Cα Positions Using Neural Networks

The assignment of secondary structure elements in protein conformations is necessary to interpret a protein model that has been established by computational methods. The process essentially involves labeling the amino acid residues with H (Helix), E (Strand), or C (Coil, also known as Loop). When particular atoms are absent from an input protein structure, the procedure becomes more complicated, especially when only the alpha carbon locations are known. Various techniques have been tested and applied to this problem during the last forty years. The application of machine learning techniques is the most recent trend. This contribution presents the HECA classifier, which uses neural networks to assign protein secondary structure types. The technique exclusively employs Cα coordinates. The Keras (TensorFlow) library was used to implement and train the neural network model. The BioShell toolkit was used to calculate the neural network input features from raw coordinates. The study’s findings show that neural network-based methods may be successfully used to take on structure assignment challenges when only Cα trace is available. Thanks to the careful selection of input features, our approach’s accuracy (above 97%) exceeded that of the existing methods.

Kinematic Reconstruction of Cyclic Peptides and Protein Backbones from Partial Data

We present an algorithm, QBKR (Quaternary Backbone Kinematic Reconstruction), a fast analytical method for an all-atom backbone reconstruction of proteins and linear or cyclic peptide chains from C_α coordinate traces. Unlike previous analytical methods for deriving all-atom representations from coarse-grained models that rely on canonical geometry with planar peptides in the trans conformation, our de novo kinematic model incorporates noncanonical, cis-trans, geometry naturally. Perturbations to this geometry can be effected with ease in our formulation, for example, to account for a continuous change from cis to trans geometry. A simple optimization of a spring-based objective function is employed for C_α-C_α distance variations that extend beyond the cis-trans limit. The kinematic construction produces a linked chain of peptide units, C_α-C-N-C_α, hinged at the C_α atoms spanning all possible planar and nonplanar peptide conformations. We have combined our method with a ring closure algorithm for the case of ring peptides and missing loops in a protein structure. Here, the reconstruction proceeding from both the N and C termini of the protein backbone (or in both directions from a starting position for rings) requires freedom in the position of one C_α atom (a capstone) to achieve a successful loop or ring closure. A salient feature of our reconstruction method is the ability to enrich conformational ensembles to produce alternative feasible conformations in which H-bond forming C-O or N-H pairs in the backbone can reverse orientations, thus addressing a well-known shortcoming in C_α-based RMSD structure comparison, wherein very close structures may lead to significantly different overall H-bond behavior. We apply the fixed C_α-based design to the reverse reconstruction from noisy Cryo-EM data, a posteriori to the optimization. Our method can be applied to speed up the process of an all-atom description from voluminous experimental data or subpar electron density maps.

Accurate Estimation of Solvent Accessible Surface Area for Coarse-Grained Biomolecular Structures with Deep Learning

Coarse-grained (CG) models of biomolecules have been widely used in protein/ribonucleic acid (RNA) three-dimensional structure prediction, docking, drug design, and molecular simulations due to their superiority in computational efficiency. Most of these applications strongly depend on the reasonable estimation of solvation free energy, which requires the accurate calculation of solvent accessible surface area (SASA). Although algorithms for SASA calculations with all-atom protein and RNA structures have been well-established, accurately estimating the SASA based on CG structures is extremely challenging. In this work, we developed a deep learning-based SASA estimator (DeepCGSA), which can provide almost perfect SASA estimation based on CG structures of protein and RNA molecules. Extensive testing analysis showed that for three types of widely used CG protein models, including the Cα-based, Cα-Cβ, and Martini models, the correlation coefficients between the predicted values and the reference values can be as high as 0.95-0.99, which perform dramatically better than available methods. In addition, the new method can be used for CG RNA structures and unfolded protein structures with much improved accuracy. We anticipate that DeepCGSA will be highly useful in the protein/RNA structure prediction, drug design, and other applications, in which accurate estimations of SASA for CG biomolecular structures are critically important.

ESCASA: Analytical estimation of atomic coordinates from coarse-grained geometry for nuclear-magnetic-resonance-assisted protein structure modeling. I. Backbone and Hβ protons

A method for the estimation of coordinates of atoms in proteins from coarse-grained geometry by simple analytical formulas (ESCASA), for use in nuclear-magnetic-resonance (NMR) data-assisted coarse-grained simulations of proteins is proposed. In this paper, the formulas for the backbone H^α and amide (H^N ) protons, and the side-chain H^β protons, given the C^α -trace, have been derived and parameterized, by using the interproton distances calculated from a set of 140 high-resolution non-homologous protein structures. The mean standard deviation over all types of proton pairs in the set was 0.44 Å after fitting. Validation against a set of 41 proteins with NMR-determined structures, which were not considered in parameterization, resulted in average standard deviation from average proton-proton distances of the NMR-determined structures of 0.25 Å, compared to 0.21 Å obtained with the PULCHRA all-atom-chain reconstruction algorithm and to the 0.12 Å standard deviation of the average-structure proton-proton distance of NMR-determined ensembles. The formulas provide analytical forces and can, therefore, be used in coarse-grained molecular dynamics.

Generative Adversarial Learning of Protein Tertiary Structures

Protein molecules are inherently dynamic and modulate their interactions with different molecular partners by accessing different tertiary structures under physiological conditions. Elucidating such structures remains challenging. Current momentum in deep learning and the powerful performance of generative adversarial networks (GANs) in complex domains, such as computer vision, inspires us to investigate GANs on their ability to generate physically-realistic protein tertiary structures. The analysis presented here shows that several GAN models fail to capture complex, distal structural patterns present in protein tertiary structures. The study additionally reveals that mechanisms touted as effective in stabilizing the training of a GAN model are not all effective, and that performance based on loss alone may be orthogonal to performance based on the quality of generated datasets. A novel contribution in this study is the demonstration that Wasserstein GAN strikes a good balance and manages to capture both local and distal patterns, thus presenting a first step towards more powerful deep generative models for exploring a possibly very diverse set of structures supporting diverse activities of a protein molecule in the cell.

Double-Well Ultra-Coarse-Grained Model to Describe Protein Conformational Transitions

The double-well model is usually used to describe the conformational transition between two states of a protein. Since conformational changes usually occur within a relatively large time scale, coarse-grained models are often used to accelerate the dynamic process due to their inexpensive computational cost. In this work, we develop a double-well ultra-coarse-grained (DW-UCG) model to describe the conformational transitions of the adenylate kinase, glutamine-binding protein, and lactoferrin. The coarse-grained simulation results show that the DW-UCG model of adenylate kinase captures the crucial intermediate states in the LID-closing and NMP-closing pathways, reflecting the key secondary structural changes in the conformational transition. A comparison of the different DW-UCG models of adenylate kinase indicates that an appropriate choice of bead resolution could generate the free energy landscape that is comparable to that from the residue-based model. The coarse-grained simulations for the glutamine-binding protein and lactoferrin also demonstrate that the DW-UCG model is valid in reproducing the correct two-state behavior for their functional study, which indicates the potential application of the DW-UCG model in investigating the mechanism of conformational changes of large proteins.

Computational reconstruction of atomistic protein structures from coarse-grained models

Three-dimensional protein structures, whether determined experimentally or theoretically, are often too low resolution. In this mini-review, we outline the computational methods for protein structure reconstruction from incomplete coarse-grained to all atomistic models. Typical reconstruction schemes can be divided into four major steps. Usually, the first step is reconstruction of the protein backbone chain starting from the C-alpha trace. This is followed by side-chains rebuilding based on protein backbone geometry. Subsequently, hydrogen atoms can be reconstructed. Finally, the resulting all-atom models may require structure optimization. Many methods are available to perform each of these tasks. We discuss the available tools and their potential applications in integrative modeling pipelines that can transfer coarse-grained information from computational predictions, or experiment, to all atomistic structures.

Gō model revisited

This review discusses Gō models broadly used in biomolecular simulations. I start with a brief description of the original lattice model study by Nobuhiro Gō. Then, the theory of protein folding behind Gō model, free energy approaches, and off-lattice Gō models are reviewed. I also mention a stringent test for the assumption in Gō models given from all-atom molecular dynamics simulations. Subsequently, I move to application of Gō models to protein dynamical functions. Various extension of Gō models is also reviewed. Finally, some publicly available tools to use Gō models are listed.

Modeling of Disordered Protein Structures Using Monte Carlo Simulations and Knowledge-Based Statistical Force Fields

The description of protein disordered states is important for understanding protein folding mechanisms and their functions. In this short review, we briefly describe a simulation approach to modeling protein interactions, which involve disordered peptide partners or intrinsically disordered protein regions, and unfolded states of globular proteins. It is based on the CABS coarse-grained protein model that uses a Monte Carlo (MC) sampling scheme and a knowledge-based statistical force field. We review several case studies showing that description of protein disordered states resulting from CABS simulations is consistent with experimental data. The case studies comprise investigations of protein⁻peptide binding and protein folding processes. The CABS model has been recently made available as the simulation engine of multiscale modeling tools enabling studies of protein⁻peptide docking and protein flexibility. Those tools offer customization of the modeling process, driving the conformational search using distance restraints, reconstruction of selected models to all-atom resolution, and simulation of large protein systems in a reasonable computational time. Therefore, CABS can be combined in integrative modeling pipelines incorporating experimental data and other modeling tools of various resolution.

Stabilizing Effect of Inherent Knots on Proteins Revealed by Molecular Dynamics Simulations

A growing number of proteins have been identified as knotted in their native structures, with such entangled topological features being expected to play stabilizing roles maintaining both the global fold and the nature of proteins. However, the molecular mechanism underlying the stabilizing effect is ambiguous. Here, we combine unbiased and mechanical atomistic molecular dynamics simulations to investigate how a protein is stabilized by an inherent knot by directly comparing chemical, thermal, and mechanical denaturing properties of two proteins having the same sequence and secondary structures but differing in the presence or absence of an inherent knot. One protein is YbeA from Escherichia coli, containing a deep trefoil knot within the sequence, and the other is the modified protein with the knot of YbeA being removed. Under certain chemical denaturing conditions, the unknotted protein fully unfolds whereas the knotted protein does not, suggesting a higher intrinsic stability for the protein having a knot. Both proteins unfold under enhanced thermal fluctuations but at different rates and with distinct pathways. Opening the hydrophobic core via separation between two α-helices is identified as a crucial step initiating the protein unfolding, which, however, is restrained for the knotted protein by topological and geometrical frustrations. Energy barriers for denaturing the protein are reduced by removing the knot, as evidenced by mechanical unfolding simulations. Finally, yet importantly, no obvious change in size or location of the knot was observed during denaturing processes, indicating that YbeA may remain knotted for a relatively long time during and after denaturation.

Structure-Guided Protein Transition Modeling with a Probabilistic Roadmap Algorithm

Proteins are macromolecules in perpetual motion, switching between structural states to modulate their function. A detailed characterization of the precise yet complex relationship between protein structure, dynamics, and function requires elucidating transitions between functionally-relevant states. Doing so challenges both wet and dry laboratories, as protein dynamics involves disparate temporal scales. In this paper, we present a novel, sampling-based algorithm to compute transition paths. The algorithm exploits two main ideas. First, it leverages known structures to initialize its search and define a reduced conformation space for rapid sampling. This is key to address the insufficient sampling issue suffered by sampling-based algorithms. Second, the algorithm embeds samples in a nearest-neighbor graph where transition paths can be efficiently computed via queries. The algorithm adapts the probabilistic roadmap framework that is popular in robot motion planning. In addition to efficiently computing lowest-cost paths between any given structures, the algorithm allows investigating hypotheses regarding the order of experimentally-known structures in a transition event. This novel contribution is likely to open up new venues of research. Detailed analysis is presented on multiple-basin proteins of relevance to human disease. Multiscaling and the AMBER ff14SB force field are used to obtain energetically-credible paths at atomistic detail.

De novo design of a fluorescence-activating β-barrel

The regular arrangements of β-strands around a central axis in β-barrels and of α-helices in coiled coils contrast with the irregular tertiary structures of most globular proteins, and have fascinated structural biologists since they were first discovered. Simple parametric models have been used to design a wide range of α-helical coiled-coil structures, but to date there has been no success with β-barrels. Here we show that accurate de novo design of β-barrels requires considerable symmetry-breaking to achieve continuous hydrogen-bond connectivity and eliminate backbone strain. We then build ensembles of β-barrel backbone models with cavity shapes that match the fluorogenic compound DFHBI, and use a hierarchical grid-based search method to simultaneously optimize the rigid-body placement of DFHBI in these cavities and the identities of the surrounding amino acids to achieve high shape and chemical complementarity. The designs have high structural accuracy and bind and fluorescently activate DFHBI in vitro and in Escherichia coli, yeast and mammalian cells. This de novo design of small-molecule binding activity, using backbones custom-built to bind the ligand, should enable the design of increasingly sophisticated ligand-binding proteins, sensors and catalysts that are not limited by the backbone geometries available in known protein structures.

Protein structure prediction

Predicting 3D structure of protein from its amino acid sequence is one of the most important unsolved problems in biophysics and computational biology. This paper attempts to give a comprehensive introduction of the most recent effort and progress on protein structure prediction. Following the general flowchart of structure prediction, related concepts and methods are presented and discussed. Moreover, brief introductions are made to several widely-used prediction methods and the community-wide critical assessment of protein structure prediction (CASP) experiments.

A general method for the derivation of the functional forms of the effective energy terms in coarse-grained energy functions of polymers. I. Backbone potentials of coarse-grained polypeptide chains

A general and systematic method for the derivation of the functional expressions for the effective energy terms in coarse-grained force fields of polymer chains is proposed. The method is based on the expansion of the potential of mean force of the system studied in the cluster-cumulant series and expanding the all-atom energy in the Taylor series in the squares of interatomic distances about the squares of the distances between coarse-grained centers, to obtain approximate analytical expressions for the cluster cumulants. The primary degrees of freedom to average about are the angles for collective rotation of the atoms contained in the coarse-grained interaction sites about the respective virtual-bond axes. The approach has been applied to the revision of the virtual-bond-angle, virtual-bond-torsional, and backbone-local-and-electrostatic correlation potentials for the UNited RESidue (UNRES) model of polypeptide chains, demonstrating the strong dependence of the torsional and correlation potentials on virtual-bond angles, not considered in the current UNRES. The theoretical considerations are illustrated with the potentials calculated from the ab initiopotential-energysurface of terminally blocked alanine by numerical integration and with the statistical potentials derived from known protein structures. The revised torsional potentials correctly indicate that virtual-bond angles close to 90° result in the preference for the turn and helical structures, while large virtual-bond angles result in the preference for polyproline II and extended backbone geometry. The revised correlation potentials correctly reproduce the preference for the formation of β-sheet structures for large values of virtual-bond angles and for the formation of α-helical structures for virtual-bond angles close to 90°.

From Optimization to Mapping: An Evolutionary Algorithm for Protein Energy Landscapes

Stochastic search is often the only viable option to address complex optimization problems. Recently, evolutionary algorithms have been shown to handle challenging continuous optimization problems related to protein structure modeling. Building on recent work in our laboratories, we propose an evolutionary algorithm for efficiently mapping the multi-basin energy landscapes of dynamic proteins that switch between thermodynamically stable or semi-stable structural states to regulate their biological activity in the cell. The proposed algorithm balances computational resources between exploration and exploitation of the nonlinear, multimodal landscapes that characterize multi-state proteins via a novel combination of global and local search to generate a dynamically-updated, information-rich map of a protein's energy landscape. This new mapping-oriented EA is applied to several dynamic proteins and their disease-implicated variants to illustrate its ability to map complex energy landscapes in a computationally feasible manner. We further show that, given the availability of such maps, comparison between the maps of wildtype and variants of a protein allows for the formulation of a structural and thermodynamic basis for the impact of sequence mutations on dysfunction that may prove useful in guiding further wet-laboratory investigations of dysfunction and molecular interventions.

Reconstruction of Atomistic Structures from Coarse-Grained Models for Protein-DNA Complexes

While coarse-grained (CG) simulations have widely been used to accelerate structure sampling of large biomolecular complexes, they are unavoidably less accurate and thus the reconstruction of all-atom (AA) structures and the subsequent refinement is desirable. In this study we developed an efficient method to reconstruct AA structures from sampled CG protein-DNA complex models, which attempts to model the protein-DNA interface accurately. First we developed a method to reconstruct atomic details of DNA structures from a three-site per nucleotide CG model, which uses a DNA fragment library. Next, for the protein-DNA interface, we referred to the side chain orientations in the known structure of the target interface when available. The other parts are modeled by existing tools. We confirmed the accuracy of the protocol in various aspects including the structure deviation in the self-reproduction, the base pair reproducibility, atomic contacts at the protein-DNA interface, and feasibility of the posterior AA simulations.

High-resolution structure prediction of β-barrel membrane proteins

[Formula: see text]-Barrel membrane proteins ([Formula: see text]MPs) play important roles, but knowledge of their structures is limited. We have developed a method to predict their 3D structures. We predict strand registers and construct transmembrane (TM) domains of [Formula: see text]MPs accurately, including proteins for which no prediction has been attempted before. Our method also accurately predicts structures from protein families with a limited number of sequences and proteins with novel folds. An average main-chain rmsd of 3.48 Å is achieved between predicted and experimentally resolved structures of TM domains, which is a significant improvement ([Formula: see text]3 Å) over a recent study. For [Formula: see text]MPs with NMR structures, the deviation between predictions and experimentally solved structures is similar to the difference among the NMR structures, indicating excellent prediction accuracy. Moreover, we can now accurately model the extended [Formula: see text]-barrels and loops in non-TM domains, increasing the overall coverage of structure prediction by [Formula: see text]%. Our method is general and can be applied to genome-wide structural prediction of [Formula: see text]MPs.

SURPASS Low-Resolution Coarse-Grained Protein Modeling

Coarse-grained modeling of biomolecules has a very important role in molecular biology. In this work we present a novel SURPASS (Single United Residue per Pre-Averaged Secondary Structure fragment) model of proteins that can be an interesting alternative for existing coarse-grained models. The design of the model is unique and strongly supported by the statistical analysis of structural regularities characteristic for protein systems. Coarse-graining of protein chain structures assumes a single center of interactions per residue and accounts for preaveraged effects of four adjacent residue fragments. Knowledge-based statistical potentials encode complex interaction patterns of these fragments. Using the Replica Exchange Monte Carlo sampling scheme and a generic version of the SURPASS force field we performed test simulations of a representative set of single-domain globular proteins. The method samples a significant part of conformational space and reproduces protein structures, including native-like, with surprisingly good accuracy. Future extension of the SURPASS model on large biomacromolecular systems is briefly discussed.

Piecing Together the Allosteric Patterns of Chaperonin GroEL

Despite considerable efforts, elucidating the allostery of large macromolecular assemblies at a molecular level in solution remains technically challenging due to its structural complexity. Here we have employed an approach combining amide backbone hydrogen/deuterium exchange coupled with mass spectrometry, fluorescence spectroscopy, and molecular simulations to characterize allosteric patterns of chaperonin GroEL, an ∼800 kDa tetradecamer from E. coli. Using available crystal structures of GroEL, we quantitatively map out GroEL allosteric changes in solution by resolving exchange behaviors of 133 overlapping proteolytic peptides with more than 95% sequence coverage. This comprehensive analysis gives a refined resolution down to five residues to pilot the GroEL allosteric determinants, of which the localized dynamics is monitored by tryptophan-mutated GroEL. Furthermore, the GroEL conformational transition is evaluated by molecular dynamics simulations with an atomic-interaction-based coarse-grained model. Collectively, we provide a practical methodology to analyze GroEL allostery in solution.

One-Dimensional Structural Properties of Proteins in the Coarse-Grained CABS Model

Despite the significant increase in computational power, molecular modeling of protein structure using classical all-atom approaches remains inefficient, at least for most of the protein targets in the focus of biomedical research. Perhaps the most successful strategy to overcome the inefficiency problem is multiscale modeling to merge all-atom and coarse-grained models. This chapter describes a well-established CABS coarse-grained protein model. The CABS (C-Alpha, C-Beta, and Side chains) model assumes a 2-4 united-atom representation of amino acids, knowledge-based force field (derived from the statistical regularities seen in known protein sequences and structures) and efficient Monte Carlo sampling schemes (MC dynamics, MC replica-exchange, and combinations). A particular emphasis is given to the unique design of the CABS force-field, which is largely defined using one-dimensional structural properties of proteins, including protein secondary structure. This chapter also presents CABS-based modeling methods, including multiscale tools for de novo structure prediction, modeling of protein dynamics and prediction of protein-peptide complexes. CABS-based tools are freely available at http://biocomp.chem.uw.edu.pl/tools.

Computing energy landscape maps and structural excursions of proteins

BACKGROUND

Structural excursions of a protein at equilibrium are key to biomolecular recognition and function modulation. Protein modeling research is driven by the need to aid wet laboratories in characterizing equilibrium protein dynamics. In principle, structural excursions of a protein can be directly observed via simulation of its dynamics, but the disparate temporal scales involved in such excursions make this approach computationally impractical. On the other hand, an informative representation of the structure space available to a protein at equilibrium can be obtained efficiently via stochastic optimization, but this approach does not directly yield information on equilibrium dynamics.

METHODS

We present here a novel methodology that first builds a multi-dimensional map of the energy landscape that underlies the structure space of a given protein and then queries the computed map for energetically-feasible excursions between structures of interest. An evolutionary algorithm builds such maps with a practical computational budget. Graphical techniques analyze a computed multi-dimensional map and expose interesting features of an energy landscape, such as basins and barriers. A path searching algorithm then queries a nearest-neighbor graph representation of a computed map for energetically-feasible basin-to-basin excursions.

RESULTS

Evaluation is conducted on intrinsically-dynamic proteins of importance in human biology and disease. Visual statistical analysis of the maps of energy landscapes computed by the proposed methodology reveals features already captured in the wet laboratory, as well as new features indicative of interesting, unknown thermodynamically-stable and semi-stable regions of the equilibrium structure space. Comparison of maps and structural excursions computed by the proposed methodology on sequence variants of a protein sheds light on the role of equilibrium structure and dynamics in the sequence-function relationship.

CONCLUSIONS

Applications show that the proposed methodology is effective at locating basins in complex energy landscapes and computing basin-basin excursions of a protein with a practical computational budget. While the actual temporal scales spanned by a structural excursion cannot be directly obtained due to the foregoing of simulation of dynamics, hypotheses can be formulated regarding the impact of sequence mutations on protein function. These hypotheses are valuable in instigating further research in wet laboratories.

Mechanism of Folding and Binding of an Intrinsically Disordered Protein As Revealed by ab Initio Simulations

A complex of the phosphorylated kinase-inducible domain (pKID) with its interacting domain (KIX) is a model system for studies of mechanisms by which intrinsically unfolded proteins perform their functions. These mechanisms are not fully understood. Using an efficient coarse-grained model, ab initio simulations were performed of the coupled folding and binding of the pKID to the KIX. The simulations start from an unbound, randomly positioned and disordered pKID structure. During the simulations the pKID chain and its position remain completely unrestricted, while the KIX backbone is limited to near-native fluctuations. Ab initio simulations of such large-scale conformational transitions, unaffected by any knowledge about the bound pKID structure, remain inaccessible to classical simulations. Our simulations recover an ensemble of transient encounter complexes in good agreement with experimental results. We find that a key folding and binding step is linked to the formation of weak native interactions between a preformed nativelike fragment of a pKID helix and KIX surface. Once that nucleus forms, the pKID chain may condense from a largely disordered encounter ensemble to a natively bound and ordered conformation. The observed mechanism is reminiscent of a nucleation-condensation model, a common scenario for folding of globular proteins.

Mapping the Conformation Space of Wildtype and Mutant H-Ras with a Memetic, Cellular, and Multiscale Evolutionary Algorithm

An important goal in molecular biology is to understand functional changes upon single-point mutations in proteins. Doing so through a detailed characterization of structure spaces and underlying energy landscapes is desirable but continues to challenge methods based on Molecular Dynamics. In this paper we propose a novel algorithm, SIfTER, which is based instead on stochastic optimization to circumvent the computational challenge of exploring the breadth of a protein's structure space. SIfTER is a data-driven evolutionary algorithm, leveraging experimentally-available structures of wildtype and variant sequences of a protein to define a reduced search space from where to efficiently draw samples corresponding to novel structures not directly observed in the wet laboratory. The main advantage of SIfTER is its ability to rapidly generate conformational ensembles, thus allowing mapping and juxtaposing landscapes of variant sequences and relating observed differences to functional changes. We apply SIfTER to variant sequences of the H-Ras catalytic domain, due to the prominent role of the Ras protein in signaling pathways that control cell proliferation, its well-studied conformational switching, and abundance of documented mutations in several human tumors. Many Ras mutations are oncogenic, but detailed energy landscapes have not been reported until now. Analysis of SIfTER-computed energy landscapes for the wildtype and two oncogenic variants, G12V and Q61L, suggests that these mutations cause constitutive activation through two different mechanisms. G12V directly affects binding specificity while leaving the energy landscape largely unchanged, whereas Q61L has pronounced, starker effects on the landscape. An implementation of SIfTER is made available at http://www.cs.gmu.edu/~ashehu/?q=OurTools. We believe SIfTER is useful to the community to answer the question of how sequence mutations affect the function of a protein, when there is an abundance of experimental structures that can be exploited to reconstruct an energy landscape that would be computationally impractical to do via Molecular Dynamics.

Structural Model of the Bilitranslocase Transmembrane Domain Supported by NMR and FRET Data

We present a 3D model of the four transmembrane (TM) helical regions of bilitranslocase (BTL), a structurally uncharacterized protein that transports organic anions across the cell membrane. The model was computed by considering helix-helix interactions as primary constraints, using Monte Carlo simulations. The interactions between the TM2 and TM3 segments have been confirmed by Förster resonance energy transfer (FRET) spectroscopy and nuclear magnetic resonance (NMR) spectroscopy, increasing our confidence in the model. Several insights into the BTL transport mechanism were obtained by analyzing the model. For example, the observed cis-trans Leu-Pro peptide bond isomerization in the TM3 fragment may indicate a key conformational change during anion transport by BTL. Our structural model of BTL may facilitate further studies, including drug discovery.

A Data-Driven Evolutionary Algorithm for Mapping Multibasin Protein Energy Landscapes

Evidence is emerging that many proteins involved in proteinopathies are dynamic molecules switching between stable and semistable structures to modulate their function. A detailed understanding of the relationship between structure and function in such molecules demands a comprehensive characterization of their conformation space. Currently, only stochastic optimization methods are capable of exploring conformation spaces to obtain sample-based representations of associated energy surfaces. These methods have to address the fundamental but challenging issue of balancing computational resources between exploration (obtaining a broad view of the space) and exploitation (going deep in the energy surface). We propose a novel algorithm that strikes an effective balance by employing concepts from evolutionary computation. The algorithm leverages deposited crystal structures of wildtype and variant sequences of a protein to define a reduced, low-dimensional search space from where to rapidly draw samples. A multiscale technique maps samples to local minima of the all-atom energy surface of a protein under investigation. Several novel algorithmic strategies are employed to avoid premature convergence to particular minima and obtain a broad view of a possibly multibasin energy surface. Analysis of applications on different proteins demonstrates the broad utility of the algorithm to map multibasin energy landscapes and advance modeling of multibasin proteins. In particular, applications on wildtype and variant sequences of proteins involved in proteinopathies demonstrate that the algorithm makes an important first step toward understanding the impact of sequence mutations on misfunction by providing the energy landscape as the intermediate explanatory link between protein sequence and function.

Modeling of protein-peptide interactions using the CABS-dock web server for binding site search and flexible docking

Protein-peptide interactions play essential functional roles in living organisms and their structural characterization is a hot subject of current experimental and theoretical research. Computational modeling of the structure of protein-peptide interactions is usually divided into two stages: prediction of the binding site at a protein receptor surface, and then docking (and modeling) the peptide structure into the known binding site. This paper presents a comprehensive CABS-dock method for the simultaneous search of binding sites and flexible protein-peptide docking, available as a user's friendly web server. We present example CABS-dock results obtained in the default CABS-dock mode and using its advanced options that enable the user to increase the range of flexibility for chosen receptor fragments or to exclude user-selected binding modes from docking search. Furthermore, we demonstrate a strategy to improve CABS-dock performance by assessing the quality of models with classical molecular dynamics. Finally, we discuss the promising extensions and applications of the CABS-dock method and provide a tutorial appendix for the convenient analysis and visualization of CABS-dock results. The CABS-dock web server is freely available at http://biocomp.chem.uw.edu.pl/CABSdock/.

Structure prediction of the second extracellular loop in G-protein-coupled receptors

G-protein-coupled receptors (GPCRs) play key roles in living organisms. Therefore, it is important to determine their functional structures. The second extracellular loop (ECL2) is a functionally important region of GPCRs, which poses significant challenge for computational structure prediction methods. In this work, we evaluated CABS, a well-established protein modeling tool for predicting ECL2 structure in 13 GPCRs. The ECL2s (with between 13 and 34 residues) are predicted in an environment of other extracellular loops being fully flexible and the transmembrane domain fixed in its x-ray conformation. The modeling procedure used theoretical predictions of ECL2 secondary structure and experimental constraints on disulfide bridges. Our approach yielded ensembles of low-energy conformers and the most populated conformers that contained models close to the available x-ray structures. The level of similarity between the predicted models and x-ray structures is comparable to that of other state-of-the-art computational methods. Our results extend other studies by including newly crystallized GPCRs.

Multiscale approach to the determination of the photoactive yellow protein signaling state ensemble

The nature of the optical cycle of photoactive yellow protein (PYP) makes its elucidation challenging for both experiment and theory. The long transition times render conventional simulation methods ineffective, and yet the short signaling-state lifetime makes experimental data difficult to obtain and interpret. Here, through an innovative combination of computational methods, a prediction and analysis of the biological signaling state of PYP is presented. Coarse-grained modeling and locally scaled diffusion map are first used to obtain a rough bird's-eye view of the free energy landscape of photo-activated PYP. Then all-atom reconstruction, followed by an enhanced sampling scheme; diffusion map-directed-molecular dynamics are used to focus in on the signaling-state region of configuration space and obtain an ensemble of signaling state structures. To the best of our knowledge, this is the first time an all-atom reconstruction from a coarse grained model has been performed in a relatively unexplored region of molecular configuration space. We compare our signaling state prediction with previous computational and more recent experimental results, and the comparison is favorable, which validates the method presented. This approach provides additional insight to understand the PYP photo cycle, and can be applied to other systems for which more direct methods are impractical.

Many protein systems of biological interest undergo dynamical changes on a time scale too long to be modeled using standard computational methods. One example is photoactive yellow protein (PYP), found in several bacterial species. Blue light, potentially harmful for DNA, triggers several structural changes in PYP, eventually resulting in a conformation that changes the swimming behavior of bacteria. This conformation is difficult to investigate, as it is too short lived. In addition, understanding this “signaling state” is computationally difficult because of the long timescale of the transition. We overcome this by constructing a coarse-grained model to rapidly induce transitions to the signaling state. We then reconstruct and further sample the all-atom configurations from these coarse-grained representations. Our results are consistent with all available experimental and computational evidence.

Designability landscape reveals sequence features that define axial helix rotation in four-helical homo-oligomeric antiparallel coiled-coil structures

Coiled coils are widespread protein domains comprising α-helices wound around each other in a regular fashion. Owing to their regularity, coiled-coil structures can be fully described by parametric equations. This in turn makes them an excellent model for studying sequence-structure relationships in proteins. Here, we used computational design to identify sequence features that determine the degree of helix axial rotation in four-helical homo-oligomeric antiparallel coiled coils. We designed 135,000 artificial sequences for a repertoire of backbone models representing all theoretically possible axial rotation states. Analysis of the designed sequences revealed features that precisely define the rotation of the helices. Based on these features we implemented a bioinformatic tool, which given a coiled-coil sequence, predicts the rotation of the helices in its structure. Moreover, we showed that another structural parameter, helix axial shift, is coupled to helix axial rotation and that dependence between these two parameters narrows the number of possible axial rotation states.

A structure-based model fails to probe the mechanical unfolding pathways of the titin I27 domain

We discuss the use of a structure based Cα-Go model and Langevin dynamics to study in detail the mechanical properties and unfolding pathway of the titin I27 domain. We show that a simple Go-model does detect correctly the origin of the mechanical stability of this domain. The unfolding free energy landscape parameters x(u) and ΔG(‡), extracted from dependencies of unfolding forces on pulling speeds, are found to agree reasonably well with experiments. We predict that above v = 10(4) nm/s the additional force-induced intermediate state is populated at an end-to-end extension of about 75 Å. The force-induced switch in the unfolding pathway occurs at the critical pulling speed v(crit) ≈ 10(6)-10(7) nm/s. We argue that this critical pulling speed is an upper limit of the interval where Bell's theory works. However, our results suggest that the Go-model fails to reproduce the experimentally observed mechanical unfolding pathway properly, yielding an incomplete picture of the free energy landscape. Surprisingly, the experimentally observed intermediate state with the A strand detached is not populated in Go-model simulations over a wide range of pulling speeds. The discrepancy between simulation and experiment is clearly seen from the early stage of the unfolding process which shows the limitation of the Go model in reproducing unfolding pathways and deciphering the complete picture of the free energy landscape.

Protocols for efficient simulations of long-time protein dynamics using coarse-grained CABS model

Coarse-grained (CG) modeling is a well-acknowledged simulation approach for getting insight into long-time scale protein folding events at reasonable computational cost. Depending on the design of a CG model, the simulation protocols vary from highly case-specific-requiring user-defined assumptions about the folding scenario-to more sophisticated blind prediction methods for which only a protein sequence is required. Here we describe the framework protocol for the simulations of long-term dynamics of globular proteins, with the use of the CABS CG protein model and sequence data. The simulations can start from a random or a selected (e.g., native) structure. The described protocol has been validated using experimental data for protein folding model systems-the prediction results agreed well with the experimental results.

Validating a Coarse-Grained Potential Energy Function through Protein Loop Modelling

Coarse-grained (CG) methods for sampling protein conformational space have the potential to increase computational efficiency by reducing the degrees of freedom. The gain in computational efficiency of CG methods often comes at the expense of non-protein like local conformational features. This could cause problems when transitioning to full atom models in a hierarchical framework. Here, a CG potential energy function was validated by applying it to the problem of loop prediction. A novel method to sample the conformational space of backbone atoms was benchmarked using a standard test set consisting of 351 distinct loops. This method used a sequence-independent CG potential energy function representing the protein using -carbon positions only and sampling conformations with a Monte Carlo simulated annealing based protocol. Backbone atoms were added using a method previously described and then gradient minimised in the Rosetta force field. Despite the CG potential energy function being sequence-independent, the method performed similarly to methods that explicitly use either fragments of known protein backbones with similar sequences or residue-specific /-maps to restrict the search space. The method was also able to predict with sub-Angstrom accuracy two out of seven loops from recently solved crystal structures of proteins with low sequence and structure similarity to previously deposited structures in the PDB. The ability to sample realistic loop conformations directly from a potential energy function enables the incorporation of additional geometric restraints and the use of more advanced sampling methods in a way that is not possible to do easily with fragment replacement methods and also enable multi-scale simulations for protein design and protein structure prediction. These restraints could be derived from experimental data or could be design restraints in the case of computational protein design. C++ source code is available for download from http://www.sbg.bio.ic.ac.uk/phyre2/PD2/.

CABS-fold: Server for the de novo and consensus-based prediction of protein structure

The CABS-fold web server provides tools for protein structure prediction from sequence only (de novo modeling) and also using alternative templates (consensus modeling). The web server is based on the CABS modeling procedures ranked in previous Critical Assessment of techniques for protein Structure Prediction competitions as one of the leading approaches for de novo and template-based modeling. Except for template data, fragmentary distance restraints can also be incorporated into the modeling process. The web server output is a coarse-grained trajectory of generated conformations, its Jmol representation and predicted models in all-atom resolution (together with accompanying analysis). CABS-fold can be freely accessed at http://biocomp.chem.uw.edu.pl/CABSfold.

High-quality protein backbone reconstruction from alpha carbons using Gaussian mixture models

Coarse-grained protein structure models offer increased efficiency in structural modeling, but these must be coupled with fast and accurate methods to revert to a full-atom structure. Here, we present a novel algorithm to reconstruct mainchain models from C traces. This has been parameterized by fitting Gaussian mixture models (GMMs) to short backbone fragments centered on idealized peptide bonds. The method we have developed is statistically significantly more accurate than several competing methods, both in terms of RMSD values and dihedral angle differences. The method produced Ramachandran dihedral angle distributions that are closer to that observed in real proteins and better Phaser molecular replacement log-likelihood gains. Amino acid residue sidechain reconstruction accuracy using SCWRL4 was found to be statistically significantly correlated to backbone reconstruction accuracy. Finally, the PD2 method was found to produce significantly lower energy full-atom models using Rosetta which has implications for multiscale protein modeling using coarse-grained models. A webserver and C++ source code is freely available for noncommercial use from: http://www.sbg.bio.ic.ac.uk/phyre2/PD2_ca2main/.

Combining coarse-grained protein models with replica-exchange all-atom molecular dynamics

We describe a combination of all-atom simulations with CABS, a well-established coarse-grained protein modeling tool, into a single multiscale protocol. The simulation method has been tested on the C-terminal beta hairpin of protein G, a model system of protein folding. After reconstructing atomistic details, conformations derived from the CABS simulation were subjected to replica-exchange molecular dynamics simulations with OPLS-AA and AMBER99sb force fields in explicit solvent. Such a combination accelerates system convergence several times in comparison with all-atom simulations starting from the extended chain conformation, demonstrated by the analysis of melting curves, the number of native-like conformations as a function of time and secondary structure propagation. The results strongly suggest that the proposed multiscale method could be an efficient and accurate tool for high-resolution studies of protein folding dynamics in larger systems.

CABS-flex: Server for fast simulation of protein structure fluctuations

The CABS-flex server (http://biocomp.chem.uw.edu.pl/CABSflex) implements CABS-model–based protocol for the fast simulations of near-native dynamics of globular proteins. In this application, the CABS model was shown to be a computationally efficient alternative to all-atom molecular dynamics—a classical simulation approach. The simulation method has been validated on a large set of molecular dynamics simulation data. Using a single input (user-provided file in PDB format), the CABS-flex server outputs an ensemble of protein models (in all-atom PDB format) reflecting the flexibility of the input structure, together with the accompanying analysis (residue mean-square-fluctuation profile and others). The ensemble of predicted models can be used in structure-based studies of protein functions and interactions.

Ranking models of transmembrane β-barrel proteins using Z-coordinate predictions

Motivation: Transmembrane β-barrels exist in the outer membrane of gram-negative bacteria as well as in chloroplast and mitochondria. They are often involved in transport processes and are promising antimicrobial drug targets. Structures of only a few β-barrel protein families are known. Therefore, a method that could automatically generate such models would be valuable. The symmetrical arrangement of the barrels suggests that an approach based on idealized geometries may be successful.

Results: Here, we present tobmodel; a method for generating 3D models of β-barrel transmembrane proteins. First, alternative topologies are obtained from the BOCTOPUS topology predictor. Thereafter, several 3D models are constructed by using different angles of the β-sheets. Finally, the best model is selected based on agreement with a novel predictor, ZPRED3, which predicts the distance from the center of the membrane for each residue, i.e. the Z-coordinate. The Z-coordinate prediction has an average error of 1.61 Å. Tobmodel predicts the correct topology for 75% of the proteins in the dataset which is a slight improvement over BOCTOPUS alone. More importantly, however, tobmodel provides a Cα template with an average RMSD of 7.24 Å from the native structure.

Availability: Tobmodel is freely available as a web server at: http://tobmodel.cbr.su.se/. The datasets used for training and evaluations are also available from this site.

Contact:arne@bioinfo.se

Mining tertiary structural motifs for assessment of designability

The observation of a limited secondary-structural alphabet in native proteins, with significant sequence preferences, has profoundly influenced the fields of protein design and structure prediction (Simons, Kooperberg, Huang, & Baker, 1997; Verschueren et al., 2011). In the era of structural genomics, as the size of the structural dataset continues to grow rapidly, it is becoming possible to extend this analysis to tertiary structural motifs and their sequences. For a hypothetical tertiary motif, the rate of its utilization in natural proteins may be used to assess its designability-the ease with which the motif can be realized with natural amino acids. This requires a structural similarity search methodology, which rather than looking for global topological agreement (more appropriate for categorization of full proteins or domains), identifies detailed geometric matches. In this chapter, we introduce such a method, called MaDCaT, and demonstrate its use by assessing the designability landscapes of two tertiary structural motifs. We also show that such analysis can establish structure/sequence links by providing the sequence constraints necessary to encode designable motifs. As logical extension of their secondary-structure counterparts, tertiary structural preferences will likely prove extremely useful in de novo protein design and structure prediction.

Knowledge-based potential for positioning membrane-associated structures and assessing residue-specific energetic contributions

The complex hydrophobic and hydrophilic milieus of membrane-associated proteins pose experimental and theoretical challenges to their understanding. Here, we produce a nonredundant database to compute knowledge-based asymmetric cross-membrane potentials from the per-residue distributions of C(β), C(γ) and functional group atoms. We predict transmembrane and peripherally associated regions from genomic sequence and position peptides and protein structures relative to the bilayer (available at http://www.degradolab.org/ez). The pseudo-energy topological landscapes underscore positional stability and functional mechanisms demonstrated here for antimicrobial peptides, transmembrane proteins, and viral fusion proteins. Moreover, experimental effects of point mutations on the relative ratio changes of dual-topology proteins are quantitatively reproduced. The functional group potential and the membrane-exposed residues display the largest energetic changes enabling to detect native-like structures from decoys. Hence, focusing on the uniqueness of membrane-associated proteins and peptides, we quantitatively parameterize their cross-membrane propensity, thus facilitating structural refinement, characterization, prediction, and design.

Assessing protein conformational sampling methods based on bivariate lag-distributions of backbone angles

Despite considerable progress in the past decades, protein structure prediction remains one of the major unsolved problems in computational biology. Angular-sampling-based methods have been extensively studied recently due to their ability to capture the continuous conformational space of protein structures. The literature has focused on using a variety of parametric models of the sequential dependencies between angle pairs along the protein chains. In this article, we present a thorough review of angular-sampling-based methods by assessing three main questions: What is the best distribution type to model the protein angles? What is a reasonable number of components in a mixture model that should be considered to accurately parameterize the joint distribution of the angles? and What is the order of the local sequence-structure dependency that should be considered by a prediction method? We assess the model fits for different methods using bivariate lag-distributions of the dihedral/planar angles. Moreover, the main information across the lags can be extracted using a technique called Lag singular value decomposition (LagSVD), which considers the joint distribution of the dihedral/planar angles over different lags using a nonparametric approach and monitors the behavior of the lag-distribution of the angles using singular value decomposition. As a result, we developed graphical tools and numerical measurements to compare and evaluate the performance of different model fits. Furthermore, we developed a web-tool (http://www.stat.tamu.edu/∼madoliat/LagSVD) that can be used to produce informative animations.

Structural informatics, modeling, and design with an open-source Molecular Software Library (MSL)

We present the Molecular Software Library (MSL), a C++ library for molecular modeling. MSL is a set of tools that supports a large variety of algorithms for the design, modeling, and analysis of macromolecules. Among the main features supported by the library are methods for applying geometric transformations and alignments, the implementation of a rich set of energy functions, side chain optimization, backbone manipulation, calculation of solvent accessible surface area, and other tools. MSL has a number of unique features, such as the ability of storing alternative atomic coordinates (for modeling) and multiple amino acid identities at the same backbone position (for design). It has a straightforward mechanism for extending its energy functions and can work with any type of molecules. Although the code base is large, MSL was created with ease of developing in mind. It allows the rapid implementation of simple tasks while fully supporting the creation of complex applications. Some of the potentialities of the software are demonstrated here with examples that show how to program complex and essential modeling tasks with few lines of code. MSL is an ongoing and evolving project, with new features and improvements being introduced regularly, but it is mature and suitable for production and has been used in numerous protein modeling and design projects. MSL is open-source software, freely downloadable at http://msl-libraries.org. We propose it as a common platform for the development of new molecular algorithms and to promote the distribution, sharing, and reutilization of computational methods.

Simulation of the opening and closing of Hsp70 chaperones by coarse-grained molecular dynamics

Heat-shock proteins 70 (Hsp70s) are key molecular chaperones which assist in the folding and refolding/disaggregation of proteins. Hsp70s, which consist of a nucleotide-binding domain (NBD, consisting of NBD-I and NBD-II subdomains) and a substrate-binding domain [SBD, further split into the β-sheet (SBD-β) and α-helical (SBD-α) subdomains], occur in two major conformations having (a) a closed SBD, in which the SBD and NBD domains do not interact, (b) an open SBD, in which SBD-α interacts with NBD-I and SBD-β interacts with the top parts of NBD-I and NBD-II. In the SBD-closed conformation, SBD is bound to a substrate protein, with release occurring after transition to the open conformation. While the transition from the closed to the open conformation is triggered efficiently by binding of adenosine triphosphate (ATP) to the NBD, it also occurs, although less frequently, in the absence of ATP. The reverse transition occurs after ATP hydrolysis. Here, we report canonical and multiplexed replica exchange simulations of the conformational dynamics of Hsp70s using a coarse-grained molecular dynamics approach with the UNRES force field. The simulations were run in the following three modes: (i) with the two halves of the NBD unrestrained relative to each other, (ii) with the two halves of the NBD restrained in an "open" geometry as in the SBD-closed form of DnaK (2KHO), and (iii) the two halves of NBD restrained in a "closed" geometry as in known experimental structures of ATP-bound NBD forms of Hsp70. Open conformations, in which the SBD interacted strongly with the NBD, formed spontaneously during all simulations; the number of transitions was largest in simulations carried out with the "closed" NBD domain, and smallest in those carried out with the "open" NBD domain; this observation is in agreement with the experimentally-observed influence of ATP-binding on the transition of Hsp70's from the SBD-closed to the SBD-open form. Two kinds of open conformations were observed: one in which SBD-α interacts with NBD-I and SBD-β interacts with the top parts of NBD-I and NBD-II (as observed in the structures of nucleotide exchange factors), and another one in which this interaction pattern is swapped. A third type of motion, in which SBD-α binds to NBD without dissociating from SBD-β was also observed. It was found that the first stage of interdomain communication (approach of SBD-β, to NBD) is coupled with the rotation of the long axes of NBD-I and NBD-II towards each other. To the best of our knowledge, this is the first successful simulation of the full transition of an Hsp70 from the SBD-closed to the SBD-open conformation.

Coarse-grained molecular simulations of large biomolecules

Recently, we saw a dramatic increase in the number of researches that rely on coarse-grained (CG) simulations for large biomolecules. Here, first, we briefly describe recently developed and used CG models for proteins and nucleic acids. Balance between structure-based and physico-chemical terms is a key issue. We also discuss the multiscale algorithms used to derive CG parameters. Next, we comment on the dynamics used in CG simulations with an emphasis on the importance of hydrodynamic interactions. We then discuss the pros and cons of CG simulations. Finally, we overview recent exciting applications of CG simulations. Publicly available tools and software for CG simulations are also summarized.