Coarse-Grained Protein Models and Their Applications

Multiscale simulation of the interaction of calreticulin-thrombospondin-1 complex with a model membrane microdomain

Cell surface calreticulin (CRT) binding to thrombospondin-1 (TSP1), regulates cell adhesion, migration, anoikis resistance, and collagen production. Due to the essential role of membrane microdomains in CRT-mediated focal adhesion disassembly, we previously studied the effect of raft-like bilayers on TSP1-CRT interactions with all-atom molecular dynamics (AAMD) simulations. However, the simulated systems of protein on the surface of the bilayer(s) in the explicit solvent are too large for long timescale AAMD simulations due to computational expense. In this study, we adopted a multiscale modeling approach of combining AAMD, coarse-grained molecule dynamics (CGMD), and reversed AAMD (REV AAMD) simulations to investigate the interactions of single CRT or of the TSP1-CRT complex with a membrane microdomain at microsecond timescale. Results showed that CRT conformational stabilization by binding of TSP1 in AAMD simulation was undetectable in CGMD simulation, but it was recovered in REV AAMD simulation. Similarly, interactions of the CRT N-domain and TSP1 with the membrane microdomain were lost in CGMD simulations but they were re-gained in the REV AAMD simulations. There was the higher coordination of the CRT P-domain in the TSP1-CRT complex with the lipid components of membrane microdomain compared to that of single CRT, which could directly affect the conformation of CRT and further mediate CRT recruitment of LDL receptor-related protein for signaling events. This study provides structural and molecular insights into TSP1-CRT interactions in a membrane microdomain environment and demonstrates the feasibility of using multiscale simulations to investigate the interactions between protein and membrane microdomains at a long timescale.

Finding the needle in the haystack: towards solving the protein-folding problem computationally

Prediction of protein tertiary structures from amino acid sequence and understanding the mechanisms of how proteins fold, collectively known as "the protein folding problem," has been a grand challenge in molecular biology for over half a century. Theories have been developed that provide us with an unprecedented understanding of protein folding mechanisms. However, computational simulation of protein folding is still difficult, and prediction of protein tertiary structure from amino acid sequence is an unsolved problem. Progress toward a satisfying solution has been slow due to challenges in sampling the vast conformational space and deriving sufficiently accurate energy functions. Nevertheless, several techniques and algorithms have been adopted to overcome these challenges, and the last two decades have seen exciting advances in enhanced sampling algorithms, computational power and tertiary structure prediction methodologies. This review aims at summarizing these computational techniques, specifically conformational sampling algorithms and energy approximations that have been frequently used to study protein-folding mechanisms or to de novo predict protein tertiary structures. We hope that this review can serve as an overview on how the protein-folding problem can be studied computationally and, in cases where experimental approaches are prohibitive, help the researcher choose the most relevant computational approach for the problem at hand. We conclude with a summary of current challenges faced and an outlook on potential future directions.

Solution x-ray scattering and structure formation in protein dynamics

We propose a computationally effective approach that builds on Landau mean-field theory in combination with modern nonequilibrium statistical mechanics to model and interpret protein dynamics and structure formation in small- to wide-angle x-ray scattering (S/WAXS) experiments. We develop the methodology by analyzing experimental data in the case of Engrailed homeodomain protein as an example. We demonstrate how to interpret S/WAXS data qualitatively with a good precision and over an extended temperature range. We explain experimental observations in terms of protein phase structure, and we make predictions for future experiments and for how to analyze data at different ambient temperature values. We conclude that the approach we propose has the potential to become a highly accurate, computationally effective, and predictive tool for analyzing S/WAXS data. For this, we compare our results with those obtained previously in an all-atom molecular dynamics simulation.

Refining amino acid hydrophobicity for dynamics simulation of membrane proteins

Coarse-grained (CG) models have been successful in simulating the chemical properties of lipid bilayers, but accurate treatment of membrane proteins and lipid-protein molecular interactions remains a challenge. The CgProt force field, original developed with the multiscale coarse graining method, is assessed by comparing the potentials of mean force for sidechain insertion in a DOPC bilayer to results reported for atomistic molecular dynamics simulations. Reassignment of select CG sidechain sites from the apolar to polar site type was found to improve the attractive interfacial behavior of tyrosine, phenylalanine and asparagine as well as charged lysine and arginine residues. The solvation energy at membrane depths of 0, 1.3 and 1.7 nm correlates with experimental partition coefficients in aqueous mixtures of cyclohexane, octanol and POPC, respectively, for sidechain analogs and Wimley-White peptides. These experimental values serve as important anchor points in choosing between alternate CG models based on their observed permeation profiles, particularly for Arg, Lys and Gln residues where the all-atom OPLS solvation energy does not agree well with experiment. Available partitioning data was also used to reparameterize the representation of the peptide backbone, which needed to be made less attractive for the bilayer hydrophobic core region. The newly developed force field, CgProt 2.4, correctly predicts the global energy minimum in the potentials of mean force for insertion of the uncharged membrane-associated peptides LS3 and WALP23. CgProt will find application in studies of lipid-protein interactions and the conformational properties of diverse membrane protein systems.

Towards a coarse-grained model of the peptoid backbone: the case of N,N-dimethylacetamide

Coarse-grained model of DMA, containing the basic motif of the peptoid backbone, based on short ranged many-body ranged interactions.

Probing the cooperative mechanism of the μ–δ opioid receptor heterodimer by multiscale simulation

The activation-cooperativity of the μ–δ opioid receptor heterodimer was probed by multiscale simulation coupled with a protein structure network.

Selecting Conformational Ensembles Using Residual Electron and Anomalous Density (READ)

Heterogeneous and dynamic biomolecular complexes play a central role in many cellular processes but are poorly understood due to experimental challenges in characterizing their structural ensembles. To address these difficulties, we developed a hybrid methodology that combines X-ray crystallography with ensemble selections typically used in NMR studies to determine structural ensembles of heterogeneous biomolecular complexes. The method, termed READ, for residual electron and anomalous density, enables the visualization of heterogeneous conformational ensembles of complexes within crystals. Here we present a detailed protocol for performing the ensemble selections to construct READ ensembles. From a diverse pool of binding poses, a selection scheme is used to determine a subset of conformations that maximizes agreement with the X-ray data. Overall, READ is a general approach for obtaining a high-resolution view of dynamic protein-protein complexes.

HyRes: a coarse-grained model for multi-scale enhanced sampling of disordered protein conformations

Efficient coarse-grained (CG) models can be coupled with atomistic force fields to accelerate the sampling of atomistic energy landscapes in the multi-scale enhanced sampling (MSES) framework. This approach may be particularly suitable for generating atomistic conformational ensembles of intrinsically disordered proteins (IDPs). While MSES is relatively robust to inherent CG artifacts, achieving optimal sampling efficiency requires CG modeling to generate the local and long-range fluctuations that are largely consistent with those at the atomistic level. Here, we describe a new hybrid resolution CG model (HyRes) for MSES simulations of disordered protein states, which is specifically designed to provide semi-quantitative secondary structure propensities together with a qualitative description of long-range nonspecific interactions. The HyRes model contains an atomistic description of the backbone with intermediate resolution side chains. The secondary structure propensities are tuned by adjusting the backbone hydrogen-bonding strength and the ϕ/ψ torsion profile. The sizes and covalent geometries of the side chains are parameterized to reproduce distributions derived from atomistic simulations. Lennard-Jones parameters for sidechain beads are assigned to reproduce statistical potentials derived from the protein structural database, and then globally parameterized with nonspecific electrostatic interactions to reproduce the free energy profiles of pair wise interactions and the key conformational properties of model peptides. Application of HyRes to MSES simulations of small IDPs suggests that it is capable of driving faster structural transitions at the atomistic level and increasing the convergence rate compared to the Cα-only Gō-like models previously utilized. With further optimization, we believe that the new CG model could greatly improve the efficiency of MSES simulations of the larger and more complex IDPs frequently involved in cellular signalling and regulation.

Molecular simulations of cellular processes

It is, nowadays, possible to simulate biological processes in conditions that mimic the different cellular compartments. Several groups have performed these calculations using molecular models that vary in performance and accuracy. In many cases, the atomistic degrees of freedom have been eliminated, sacrificing both structural complexity and chemical specificity to be able to explore slow processes. In this review, we will discuss the insights gained from computer simulations on macromolecule diffusion, nuclear body formation, and processes involving the genetic material inside cell-mimicking spaces. We will also discuss the challenges to generate new models suitable for the simulations of biological processes on a cell scale and for cell-cycle-long times, including non-equilibrium events such as the co-translational folding, misfolding, and aggregation of proteins. A prominent role will be played by the wise choice of the structural simplifications and, simultaneously, of a relatively complex energetic description. These challenging tasks will rely on the integration of experimental and computational methods, achieved through the application of efficient algorithms. Graphical abstract.

Prediction of protein disorder based on IUPred

Many proteins contain intrinsically disordered regions (IDRs), functional polypeptide segments that in isolation adopt a highly flexible conformational ensemble instead of a single, well-defined structure. Disorder prediction methods, which can discriminate ordered and disordered regions from the amino acid sequence, have contributed significantly to our current understanding of the distinct properties of intrinsically disordered proteins by enabling the characterization of individual examples as well as large-scale analyses of these protein regions. One popular method, IUPred provides a robust prediction of protein disorder based on an energy estimation approach that captures the fundamental difference between the biophysical properties of ordered and disordered regions. This paper reviews the energy estimation method underlying IUPred and the basic properties of the web server. Through an example, it also illustrates how the prediction output can be interpreted in a more complex case by taking into account the heterogeneous nature of IDRs. Various applications that benefited from IUPred to provide improved disorder predictions, complementing domain annotations and aiding the identification of functional short linear motifs are also described here. IUPred is freely available for noncommercial users through the web server (http://iupred.enzim.hu and http://iupred.elte.hu) . The program can also be downloaded and installed locally for large-scale analyses.

OPUS-CSF: A C-atom-based scoring function for ranking protein structural models

We report a C‐atom‐based scoring function, named OPUS‐CSF, for ranking protein structural models. Rather than using traditional Boltzmann formula, we built a scoring function (CSF score) based on the native distributions (derived from the entire PDB) of coordinate components of mainchain C (carbonyl) atoms on selected residues of peptide segments of 5, 7, 9, and 11 residues in length. In testing OPUS‐CSF on decoy recognition, it maximally recognized 257 native structures out of 278 targets in 11 commonly used decoy sets, significantly outperforming other popular all‐atom empirical potentials. The average correlation coefficient with TM‐score was also comparable with those of other potentials. OPUS‐CSF is a highly coarse‐grained scoring function, which only requires input of partial mainchain information, and very fast. Thus, it is suitable for applications at early stage of structural building.

Shielding effect in protein folding

One of the most important interactions responsible for protein folding and stability are hydrogen bonds between peptide groups. There is a constant competition between the water molecules and peptide groups in a hydrogen bond formation. Also side-chains take part in this process by reducing hydration of peptide group (shielding effect) that promotes the protein folding. In this paper, a new approach to take into account a shielding effect is presented. A modification of the energy function is derived and incorporated into the UNited RESidue (UNRES) force field. Canonical Molecular Dynamics and Replica Exchange Molecular Dynamics with UNRES force field is applied to study the influence of this effect on protein structure, folding kinetics and free energy landscapes. The results of test calculations suggest that even small contribution of this effect into energy function changes force field behavior as well as speeds up the folding process significantly.

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.

Theoretical approaches for dynamical ordering of biomolecular systems

BACKGROUND

Living systems are characterized by the dynamic assembly and disassembly of biomolecules. The dynamical ordering mechanism of these biomolecules has been investigated both experimentally and theoretically. The main theoretical approaches include quantum mechanical (QM) calculation, all-atom (AA) modeling, and coarse-grained (CG) modeling. The selected approach depends on the size of the target system (which differs among electrons, atoms, molecules, and molecular assemblies). These hierarchal approaches can be combined with molecular dynamics (MD) simulation and/or integral equation theories for liquids, which cover all size hierarchies.

SCOPE OF REVIEW

We review the framework of quantum mechanical/molecular mechanical (QM/MM) calculations, AA MD simulations, CG modeling, and integral equation theories. Applications of these methods to the dynamical ordering of biomolecular systems are also exemplified.

MAJOR CONCLUSIONS

The QM/MM calculation enables the study of chemical reactions. The AA MD simulation, which omits the QM calculation, can follow longer time-scale phenomena. By reducing the number of degrees of freedom and the computational cost, CG modeling can follow much longer time-scale phenomena than AA modeling. Integral equation theories for liquids elucidate the liquid structure, for example, whether the liquid follows a radial distribution function.

GENERAL SIGNIFICANCE

These theoretical approaches can analyze the dynamic behaviors of biomolecular systems. They also provide useful tools for exploring the dynamic ordering systems of biomolecules, such as self-assembly. This article is part of a Special Issue entitled "Biophysical Exploration of Dynamical Ordering of Biomolecular Systems" edited by Dr. Koichi Kato.

Effects of Periplasmic Chaperones and Membrane Thickness on BamA-Catalyzed Outer-Membrane Protein Folding

The biogenesis of outer-membrane proteins (OMPs) in gram-negative bacteria involves delivery by periplasmic chaperones to the β-barrel assembly machinery (BAM), which catalyzes OMP insertion into the outer membrane. Here, we examine the effects of membrane thickness, the Escherichia coli periplasmic chaperones Skp and SurA, and BamA, the central subunit of the BAM complex, on the folding kinetics of a model OMP (tOmpA) using fluorescence spectroscopy, native mass spectrometry, and molecular dynamics simulations. We show that prefolded BamA promotes the release of tOmpA from Skp despite the nM affinity of the Skp:tOmpA complex. This activity is located in the BamA β-barrel domain, but is greater when full-length BamA is present, indicating that both the β-barrel and polypeptide transport-associated (POTRA) domains are required for maximal activity. By contrast, SurA is unable to release tOmpA from Skp, providing direct evidence against a sequential chaperone model. By varying lipid acyl chain length in synthetic liposomes we show that BamA has a greater catalytic effect on tOmpA folding in thicker bilayers, suggesting that BAM catalysis involves lowering of the kinetic barrier imposed by the hydrophobic thickness of the membrane. Consistent with this, molecular dynamics simulations reveal that increases in membrane thinning/disorder by the transmembrane domain of BamA is greatest in thicker bilayers. Finally, we demonstrate that cross-linking of the BamA barrel does not affect tOmpA folding kinetics in 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) liposomes, suggesting that lateral gating of the BamA barrel and/or hybrid barrel formation is not required, at least for the assembly of a small 8-stranded OMP in vitro.

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Mechanisms of OMP periplasmic transport and folding by BAM are poorly understood.

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BamA catalyzes folding by reducing the kinetic barrier imposed by membrane thickness.

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BamA proteoliposomes promote folding of Skp-bound tOmpA.

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Lateral gating is not required for BamA-catalyzed folding of tOmpA in DMPC bilayers.

Multi-scale simulations of biological systems using the OPEP coarse-grained model

Biomolecules are complex machines that are optimized by evolution to properly fulfill or contribute to a variety of biochemical tasks in the cellular environment. Computer simulations based on quantum mechanics and atomistic force fields have been proven to be a powerful microscope for obtaining valuable insights into many biological, physical, and chemical processes. Many interesting phenomena involve, however, a time scale and a number of degrees of freedom, notably if crowding is considered, that cannot be explored at an atomistic resolution. To bridge the gap between reality and simulation, many different advanced computational techniques and coarse-grained (CG) models have been developed. Here, we report some applications of the CG OPEP protein model to amyloid fibril formation, the response of catch-bond proteins to two types of fluid flow, and interactive simulations to fold peptides with well-defined 3D structures or with intrinsic disorder.

OPUS-DOSP: A Distance- and Orientation-Dependent All-Atom Potential Derived from Side-Chain Packing

We report a new distance- and orientation-dependent, all-atom statistical potential derived from side-chain packing, named OPUS-DOSP, for protein structure modeling. The framework of OPUS-DOSP is based on OPUS-PSP, previously developed by us [JMB (2008), 376, 288-301], with refinement and new features. In particular, distance or orientation contribution is considered depending on the range of contact distance. A new auxiliary function in energy function is also introduced, in addition to the traditional Boltzmann term, in order to adjust the contributions of extreme cases. OPUS-DOSP was tested on 11 decoy sets commonly used for statistical potential benchmarking. Among 278 native structures, 239 and 249 native structures were recognized by OPUS-DOSP without and with the auxiliary function, respectively. The results show that OPUS-DOSP has an increased decoy recognition capability comparing with those of other relevant potentials to date.

A protocol for CABS-dock protein-peptide docking driven by side-chain contact information

Background

The characterization of protein–peptide interactions is a challenge for computational molecular docking. Protein–peptide docking tools face at least two major difficulties: (1) efficient sampling of large-scale conformational changes induced by binding and (2) selection of the best models from a large set of predicted structures. In this paper, we merge an efficient sampling technique with external information about side-chain contacts to sample and select the best possible models.

Methods

In this paper we test a new protocol that uses information about side-chain contacts in CABS-dock protein–peptide docking. As shown in our recent studies, CABS-dock enables efficient modeling of large-scale conformational changes without knowledge about the binding site. However, the resulting set of binding sites and poses is in many cases highly diverse and difficult to score.

Results

As we demonstrate here, information about a single side-chain contact can significantly improve the prediction accuracy. Importantly, the imposed constraints for side-chain contacts are quite soft. Therefore, the developed protocol does not require precise contact information and ensures large-scale peptide flexibility in the broad contact area.

Conclusions

The demonstrated protocol provides the extension of the CABS-dock method that can be practically used in the structure prediction of protein–peptide complexes guided by the knowledge of the binding interface.

Modeling EphB4-EphrinB2 protein-protein interaction using flexible docking of a short linear motif

Background

Many protein–protein interactions are mediated by a short linear motif. Usually, amino acid sequences of those motifs are known or can be predicted. It is much harder to experimentally characterize or predict their structure in the bound form. In this work, we test a possibility of using flexible docking of a short linear motif to predict the interaction interface of the EphB4-EphrinB2 complex (a system extensively studied for its significance in tumor progression).

Methods

In the modeling, we only use knowledge about the motif sequence and experimental structures of EphB4-EphrinB2 complex partners. The proposed protocol enables efficient modeling of significant conformational changes in the short linear motif fragment during molecular docking simulation. For the docking simulations, we use the CABS-dock method for docking fully flexible peptides to flexible protein receptors (available as a server at http://biocomp.chem.uw.edu.pl/CABSdock/). Based on the docking result, the protein–protein complex is reconstructed and refined.

Results

Using this novel protocol, we obtained an accurate EphB4-EphrinB2 interaction model.

Conclusions

The results show that the CABS-dock method may be useful as the primary docking tool in specific protein–protein docking cases similar to EphB4-EphrinB2 complex—that is, where a short linear motif fragment can be identified.

Molecular modeling to predict peptide accessibility for peptide-functionalized hydrogels

Peptide-functionalized (PF) hydrogels are being widely investigated by the tissue engineering and regenerative medicine communities for a broad range of applications because of their unique potential to mimic the natural extracellular matrix and promote tissue regeneration. In order for these complex material systems to perform their intended bioactive function (e.g., cell signaling), the peptides that are tethered to the hydrogel matrix must be accessible at the hydrogel surface for cell-receptor binding. The factors influencing the surface accessibility of the tethered peptide mainly include the length of the tethers, the loading (i.e., concentration) of the peptide, and the association between the tethered peptide and the hydrogel matrix. In the present work, the authors developed coarse-grained molecular models based on the all-atom polymer consistent force field for a type of poly(ethylene glycol)-based PF hydrogel and conducted molecular simulations to investigate the distribution of the peptide within the hydrogel and its surface accessibility as a function of tether length and peptide concentration. The calculated results of the effects of these design parameters on the surface accessibility of the peptide agree very well with corresponding experimental measurements in which peptide accessibility was quantified by the number of cells attached to the hydrogel surface per unit area. The developed modeling methods are able to provide unique insights into the molecular behavior of PF hydrogels and the distribution of the tethered peptides, which can serve as a guide for hydrogel design optimization.

Computational Biochemistry-Enzyme Mechanisms Explored

Understanding enzyme mechanisms is a major task to achieve in order to comprehend how living cells work. Recent advances in biomolecular research provide huge amount of data on enzyme kinetics and structure. The analysis of diverse experimental results and their combination into an overall picture is, however, often challenging. Microscopic details of the enzymatic processes are often anticipated based on several hints from macroscopic experimental data. Computational biochemistry aims at creation of a computational model of an enzyme in order to explain microscopic details of the catalytic process and reproduce or predict macroscopic experimental findings. Results of such computations are in part complementary to experimental data and provide an explanation of a biochemical process at the microscopic level. In order to evaluate the mechanism of an enzyme, a structural model is constructed which can be analyzed by several theoretical approaches. Several simulation methods can and should be combined to get a reliable picture of the process of interest. Furthermore, abstract models of biological systems can be constructed combining computational and experimental data. In this review, we discuss structural computational models of enzymatic systems. We first discuss various models to simulate enzyme catalysis. Furthermore, we review various approaches how to characterize the enzyme mechanism both qualitatively and quantitatively using different modeling approaches.

Sequence statistics of tertiary structural motifs reflect protein stability

The Protein Data Bank (PDB) has been a key resource for learning general rules of sequence-structure relationships in proteins. Quantitative insights have been gained by defining geometric descriptors of structure (e.g., distances, dihedral angles, solvent exposure, etc.) and observing their distributions and sequence preferences. Here we argue that as the PDB continues to grow, it may become unnecessary to reduce structure into a set of elementary descriptors. Instead, it could be possible to deduce quantitative sequence-structure relationships in the context of precisely-defined complex structural motifs by mining the PDB for closely matching backbone geometries. To validate this idea, we turned to the the task of predicting changes in protein stability upon amino-acid substitution—a difficult problem of broad significance. We defined non-contiguous tertiary motifs (TERMs) around a protein site of interest and extracted sequence preferences from ensembles of closely-matching substructures in the PDB to predict mutational stability changes at the site, ΔΔG_m. We demonstrate that these ensemble statistics predict ΔΔG_m on par with state-of-the-art statistical and machine-learning methods on large thermodynamic datasets, and outperform these, along with a leading structure-based modeling approach, when tested in the context of unbiased diverse mutations. Further, we show that the performance of the TERM-based method is directly related to the amount of available relevant structural data, automatically improving with the growing PDB. This enables a means of estimating prediction accuracy. Our results clearly demonstrate that: 1) statistics of non-contiguous structural motifs in the PDB encode fundamental sequence-structure relationships related to protein thermodynamic stability, and 2) the PDB is now large enough that such statistics are already useful in practice, with their accuracy expected to continue increasing as the database grows. These observations suggest new ways of using structural data towards addressing problems of computational structural biology.

Modeling disordered protein interactions from biophysical principles

Disordered protein-protein interactions (PPIs), those involving a folded protein and an intrinsically disordered protein (IDP), are prevalent in the cell, including important signaling and regulatory pathways. IDPs do not adopt a single dominant structure in isolation but often become ordered upon binding. To aid understanding of the molecular mechanisms of disordered PPIs, it is crucial to obtain the tertiary structure of the PPIs. However, experimental methods have difficulty in solving disordered PPIs and existing protein-protein and protein-peptide docking methods are not able to model them. Here we present a novel computational method, IDP-LZerD, which models the conformation of a disordered PPI by considering the biophysical binding mechanism of an IDP to a structured protein, whereby a local segment of the IDP initiates the interaction and subsequently the remaining IDP regions explore and coalesce around the initial binding site. On a dataset of 22 disordered PPIs with IDPs up to 69 amino acids, successful predictions were made for 21 bound and 18 unbound receptors. The successful modeling provides additional support for biophysical principles. Moreover, the new technique significantly expands the capability of protein structure modeling and provides crucial insights into the molecular mechanisms of disordered PPIs.

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.

The Renormalization Group and Its Applications to Generating Coarse-Grained Models of Large Biological Molecular Systems

Understanding the dynamics of biomolecules is the key to understanding their biological activities. Computational methods ranging from all-atom molecular dynamics simulations to coarse-grained normal-mode analyses based on simplified elastic networks provide a general framework to studying these dynamics. Despite recent successes in studying very large systems with up to a 100,000,000 atoms, those methods are currently limited to studying small- to medium-sized molecular systems due to computational limitations. One solution to circumvent these limitations is to reduce the size of the system under study. In this paper, we argue that coarse-graining, the standard approach to such size reduction, must define a hierarchy of models of decreasing sizes that are consistent with each other, i.e., that each model contains the information of the dynamics of its predecessor. We propose a new method, Decimate, for generating such a hierarchy within the context of elastic networks for normal-mode analysis. This method is based on the concept of the renormalization group developed in statistical physics. We highlight the details of its implementation, with a special focus on its scalability to large systems of up to millions of atoms. We illustrate its application on two large systems, the capsid of a virus and the ribosome translation complex. We show that highly decimated representations of those systems, containing down to 1% of their original number of atoms, still capture qualitatively and quantitatively their dynamics. Decimate is available as an OpenSource resource.

Combining the MARTINI and Structure-Based Coarse-Grained Approaches for the Molecular Dynamics Studies of Conformational Transitions in Proteins

The application of coarse-grained (CG) models in biology is essential to access large length and time scales required for the description of many biological processes. The ELNEDIN protein model is based on the well-known MARTINI CG force-field and incorporates additionally harmonic bonds of a certain spring constant within a defined cutoff distance between pairs of residues, in order to preserve the native structure of the protein. In this case, the use of unbreakable harmonic bonds hinders the study of unfolding and folding processes. To overcome this barrier we have replaced the harmonic bonds with Lennard-Jones interactions based on the contact map of the native protein structure as is done in Go̅-like models. This model exhibits very good agreement with all-atom simulations and the ELNEDIN. Moreover, it can capture the structural motion linked to particular catalytic activity in the Man5B protein, in agreement with all-atom simulations. In addition, our model is based on the van der Waals radii, instead of a cutoff distance, which results in a smaller contact map. In conclusion, we anticipate that our model will provide further possibilities for studying biological systems based on the MARTINI CG force-field by using advanced-sampling methods, such as parallel tempering and metadynamics.

Performance Comparison of Systematic Methods for Rigorous Definition of Coarse-Grained Sites of Large Biomolecules

Construction of coarse-grained (CG) models for large biomolecules used for multiscale simulations demands a rigorous definition of CG sites for them. Several coarse-graining methods such as the simulated annealing and steepest descent (SASD) based on the essential dynamics coarse-graining (ED-CG) or the stepwise local iterative optimization (SLIO) based on the fluctuation maximization coarse-graining (FM-CG), were developed to do it. However, the practical applications of these methods such as SASD based on ED-CG are subject to limitations because they are too expensive. In this work, we extend the applicability of ED-CG by combining it with the SLIO algorithm. A comprehensive comparison of optimized results and accuracy of various algorithms based on ED-CG show that SLIO is the fastest as well as the most accurate algorithm among them. ED-CG combined with SLIO could give converged results as the number of CG sites increases, which demonstrates that it is another efficient method for coarse-graining large biomolecules. The construction of CG sites for Ras protein by using MD fluctuations demonstrates that the CG sites derived from FM-CG can reflect the fluctuation properties of secondary structures in Ras accurately.

Metal Ion Modeling Using Classical Mechanics

Metal ions play significant roles in numerous fields including chemistry, geochemistry, biochemistry, and materials science. With computational tools increasingly becoming important in chemical research, methods have emerged to effectively face the challenge of modeling metal ions in the gas, aqueous, and solid phases. Herein, we review both quantum and classical modeling strategies for metal ion-containing systems that have been developed over the past few decades. This Review focuses on classical metal ion modeling based on unpolarized models (including the nonbonded, bonded, cationic dummy atom, and combined models), polarizable models (e.g., the fluctuating charge, Drude oscillator, and the induced dipole models), the angular overlap model, and valence bond-based models. Quantum mechanical studies of metal ion-containing systems at the semiempirical, ab initio, and density functional levels of theory are reviewed as well with a particular focus on how these methods inform classical modeling efforts. Finally, conclusions and future prospects and directions are offered that will further enhance the classical modeling of metal ion-containing systems.

Simple Physics-Based Analytical Formulas for the Potentials of Mean Force of the Interaction of Amino Acid Side Chains in Water. VII. Charged-Hydrophobic/Polar and Polar-Hydrophobic/Polar Side Chains

The physics-based potentials of side-chain-side-chain interactions corresponding to pairs composed of charged and polar, polar and polar, charged and hydrophobic, and hydrophobic and hydrophobic side chains have been determined. A total of 144 four-dimensional potentials of mean force (PMFs) of all possible pairs of molecules modeling these pairs were determined by umbrella-sampling molecular dynamics simulations in explicit water as functions of distance and orientation, and the analytical expressions were then fitted to the PMFs. Depending on the type of interacting sites, the analytical approximation to the PMF is a sum of terms corresponding to van der Waals interactions and cavity-creation involving the nonpolar sections of the side chains and van der Waals, cavity-creation, and electrostatic (charge-dipole or dipole-dipole) interaction energies and polarization energies involving the charged or polar sections of the side chains. The model used in this work reproduces all features of the interacting pairs. The UNited RESidue force field with the new side-chain-side-chain interaction potentials was preliminarily tested with the N-terminal part of the B-domain of staphylococcal protein A (PDBL 1BDD ; a three-α-helix bundle) and UPF0291 protein YnzC from Bacillus subtilis (PDB: 2HEP ; an α-helical hairpin).

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.

Highly Flexible Protein-Peptide Docking Using CABS-Dock

Protein-peptide molecular docking is a difficult modeling problem. It is even more challenging when significant conformational changes that may occur during the binding process need to be predicted. In this chapter, we demonstrate the capabilities and features of the CABS-dock server for flexible protein-peptide docking. CABS-dock allows highly efficient modeling of full peptide flexibility and significant flexibility of a protein receptor. During CABS-dock docking, the peptide folding and binding process is explicitly simulated and no information about the peptide binding site or its structure is used. This chapter presents a successful CABS-dock use for docking a potentially therapeutic peptide to a protein target. Moreover, simulation contact maps, a new CABS-dock feature, are described and applied to the docking test case. Finally, a tutorial for running CABS-dock from the command line or command line scripts is provided. The CABS-dock web server is available from http://biocomp.chem.uw.edu.pl/CABSdock/ .

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

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