Application of biasing-potential replica-exchange simulations for loop modeling and refinement of proteins in explicit solvent: Biasing Potential Replica Exchange

Using Local Protein Model Quality Estimates to Guide a Molecular Dynamics-Based Refinement Strategy

The refinement of predicted 3D models aims to bring them closer to the native structure by fixing errors including unusual bonds and torsion angles and irregular hydrogen bonding patterns. Refinement approaches based on molecular dynamics (MD) simulations using different types of restraints have performed well since CASP10. ReFOLD, developed by the McGuffin group, was one of the many MD-based refinement approaches, which were tested in CASP 12. When the performance of the ReFOLD method in CASP12 was evaluated, it was observed that ReFOLD suffered from the absence of a reliable guidance mechanism to reach consistent improvement for the quality of predicted 3D models, particularly in the case of template-based modelling (TBM) targets. Therefore, here we propose to utilize the local quality assessment score produced by ModFOLD6 to guide the MD-based refinement approach to further increase the accuracy of the predicted 3D models. The relative performance of the new local quality assessment guided MD-based refinement protocol and the original MD-based protocol ReFOLD are compared utilizing many different official scoring methods. By using the per-residue accuracy (or local quality) score to guide the refinement process, we are able to prevent the refined models from undesired structural deviations, thereby leading to more consistent improvements. This chapter will include a detailed analysis of the performance of the local quality assessment guided MD-based protocol versus that deployed in the original ReFOLD method.

Methods for the Refinement of Protein Structure 3D Models

The refinement of predicted 3D protein models is crucial in bringing them closer towards experimental accuracy for further computational studies. Refinement approaches can be divided into two main stages: The sampling and scoring stages. Sampling strategies, such as the popular Molecular Dynamics (MD)-based protocols, aim to generate improved 3D models. However, generating 3D models that are closer to the native structure than the initial model remains challenging, as structural deviations from the native basin can be encountered due to force-field inaccuracies. Therefore, different restraint strategies have been applied in order to avoid deviations away from the native structure. For example, the accurate prediction of local errors and/or contacts in the initial models can be used to guide restraints. MD-based protocols, using physics-based force fields and smart restraints, have made significant progress towards a more consistent refinement of 3D models. The scoring stage, including energy functions and Model Quality Assessment Programs (MQAPs) are also used to discriminate near-native conformations from non-native conformations. Nevertheless, there are often very small differences among generated 3D models in refinement pipelines, which makes model discrimination and selection problematic. For this reason, the identification of the most native-like conformations remains a major challenge.

FF12MC: A revised AMBER forcefield and new protein simulation protocol

Specialized to simulate proteins in molecular dynamics (MD) simulations with explicit solvation, FF12MC is a combination of a new protein simulation protocol employing uniformly reduced atomic masses by tenfold and a revised AMBER forcefield FF99 with (i) shortened CH bonds, (ii) removal of torsions involving a nonperipheral sp(3) atom, and (iii) reduced 1-4 interaction scaling factors of torsions ϕ and ψ. This article reports that in multiple, distinct, independent, unrestricted, unbiased, isobaric-isothermal, and classical MD simulations FF12MC can (i) simulate the experimentally observed flipping between left- and right-handed configurations for C14-C38 of BPTI in solution, (ii) autonomously fold chignolin, CLN025, and Trp-cage with folding times that agree with the experimental values, (iii) simulate subsequent unfolding and refolding of these miniproteins, and (iv) achieve a robust Z score of 1.33 for refining protein models TMR01, TMR04, and TMR07. By comparison, the latest general-purpose AMBER forcefield FF14SB locks the C14-C38 bond to the right-handed configuration in solution under the same protein simulation conditions. Statistical survival analysis shows that FF12MC folds chignolin and CLN025 in isobaric-isothermal MD simulations 2-4 times faster than FF14SB under the same protein simulation conditions. These results suggest that FF12MC may be used for protein simulations to study kinetics and thermodynamics of miniprotein folding as well as protein structure and dynamics. Proteins 2016; 84:1490-1516. © 2016 The Authors Proteins: Structure, Function, and Bioinformatics Published by Wiley Periodicals, Inc.

Use of multiple picosecond high-mass molecular dynamics simulations to predict crystallographic B-factors of folded globular proteins

Predicting crystallographic B-factors of a protein from a conventional molecular dynamics simulation is challenging, in part because the B-factors calculated through sampling the atomic positional fluctuations in a picosecond molecular dynamics simulation are unreliable, and the sampling of a longer simulation yields overly large root mean square deviations between calculated and experimental B-factors. This article reports improved B-factor prediction achieved by sampling the atomic positional fluctuations in multiple picosecond molecular dynamics simulations that use uniformly increased atomic masses by 100-fold to increase time resolution. Using the third immunoglobulin-binding domain of protein G, bovine pancreatic trypsin inhibitor, ubiquitin, and lysozyme as model systems, the B-factor root mean square deviations (mean ± standard error) of these proteins were 3.1 ± 0.2–9 ± 1 Ų for Cα and 7.3 ± 0.9–9.6 ± 0.2 Ų for Cγ, when the sampling was done for each of these proteins over 20 distinct, independent, and 50-picosecond high-mass molecular dynamics simulations with AMBER forcefield FF12MC or FF14SB. These results suggest that sampling the atomic positional fluctuations in multiple picosecond high-mass molecular dynamics simulations may be conducive to a priori prediction of crystallographic B-factors of a folded globular protein.

Unconstrained Enhanced Sampling for Free Energy Calculations of Biomolecules: A Review

Free energy calculations are central to understanding the structure, dynamics and function of biomolecules. Yet insufficient sampling of biomolecular configurations is often regarded as one of the main sources of error. Many enhanced sampling techniques have been developed to address this issue. Notably, enhanced sampling methods based on biasing collective variables (CVs), including the widely used umbrella sampling, adaptive biasing force and metadynamics, have been discussed in a recent excellent review (Abrams and Bussi, Entropy, 2014). Here, we aim to review enhanced sampling methods that do not require predefined system-dependent CVs for biomolecular simulations and as such do not suffer from the hidden energy barrier problem as encountered in the CV-biasing methods. These methods include, but are not limited to, replica exchange/parallel tempering, self-guided molecular/Langevin dynamics, essential energy space random walk and accelerated molecular dynamics. While it is overwhelming to describe all details of each method, we provide a summary of the methods along with the applications and offer our perspectives. We conclude with challenges and prospects of the unconstrained enhanced sampling methods for accurate biomolecular free energy calculations.

Conformational sampling of oligosaccharides using Hamiltonian replica exchange with two-dimensional dihedral biasing potentials and the weighted histogram analysis method (WHAM)

Oligosaccharides and polysaccharides exert numerous functional roles in biology through their structural diversity and conformational properties. To investigate their conformational properties using computational methods, Hamiltonian replica exchange (H-REX) combined with two-dimensional grid-based correction maps as biasing potentials (bpCMAP) significantly improves the sampling efficiency about glycosidic linkages. In the current study, we extend the application of H-REX with bpCMAP to complex saccharides and establish systematic procedures for bpCMAP construction, determination of replica distribution, and data analysis. Our main findings are that (1) the bpCMAP for each type of glycosidic linkage can be constructed from the corresponding disaccharide using gas-phase umbrella sampling simulations, (2) the replica distribution can be conveniently determined following the exact definition of the average acceptance ratio based on the assigned distribution of biasing potentials, and (3) the extracted free energy surface (or potential of mean force (PMF)) can be improved using the weighted histogram analysis method (WHAM) allowing for the inclusion of data from the excited state replicas in the calculated probability distribution. The method is applied to a branched N-glycan found on the HIV gp120 protein, and a linear N-glycan. Considering the general importance of N-glycans and the wide appreciation of the sampling problem, the present method represents an efficient procedure for the conformational sampling of complex oligo- and polysaccharides under explicit solvent conditions. More generally, the use of WHAM is anticipated to be of general utility for the calculation of PMFs from H-REX simulations in a wide range of macromolecular systems.

Exploring biomolecular dynamics and interactions using advanced sampling methods

Molecular dynamics (MD) and Monte Carlo (MC) simulations have emerged as a valuable tool to investigate statistical mechanics and kinetics of biomolecules and synthetic soft matter materials. However, major limitations for routine applications are due to the accuracy of the molecular mechanics force field and due to the maximum simulation time that can be achieved in current simulations studies. For improving the sampling a number of advanced sampling approaches have been designed in recent years. In particular, variants of the parallel tempering replica-exchange methodology are widely used in many simulation studies. Recent methodological advancements and a discussion of specific aims and advantages are given. This includes improved free energy simulation approaches and conformational search applications.

Protein-ligand docking using hamiltonian replica exchange simulations with soft core potentials

Molecular dynamics (MD) simulations in explicit solvent allow studying receptor-ligand binding processes including full flexibility of the binding partners and an explicit inclusion of solvation effects. However, in MD simulations, the search for an optimal ligand-receptor complex geometry is frequently trapped in locally stable non-native binding geometries. A Hamiltonian replica-exchange (H-REMD)-based protocol has been designed to enhance the sampling of putative ligand-receptor complexes. It is based on softening nonbonded ligand-receptor interactions along the replicas and one reference replica under the control of the original force field. The efficiency of the method has been evaluated on two receptor-ligand systems and one protein-peptide complex. Starting from misplaced initial docking geometries, the H-REMD method reached in each case the known binding geometry significantly faster than a standard MD simulation. The approach could also be useful to identify and evaluate alternative binding geometries in a given binding region with small relative differences in binding free energy.

Enhanced conformational sampling of carbohydrates by Hamiltonian replica-exchange simulation

Knowledge of the structure and conformational flexibility of carbohydrates in an aqueous solvent is important to improving our understanding of how carbohydrates function in biological systems. In this study, we extend a variant of the Hamiltonian replica-exchange molecular dynamics (MD) simulation to improve the conformational sampling of saccharides in an explicit solvent. During the simulations, a biasing potential along the glycosidic-dihedral linkage between the saccharide monomer units in an oligomer is applied at various levels along the replica runs to enable effective transitions between various conformations. One reference replica runs under the control of the original force field. The method was tested on disaccharide structures and further validated on biologically relevant blood group B, Lewis X and Lewis A trisaccharides. The biasing potential-based replica-exchange molecular dynamics (BP-REMD) method provided a significantly improved sampling of relevant conformational states compared with standard continuous MD simulations, with modest computational costs. Thus, the proposed BP-REMD approach adds a new dimension to existing carbohydrate conformational sampling approaches by enhancing conformational sampling in the presence of solvent molecules explicitly at relatively low computational cost.

Effect of Ser392 phosphorylation on the structure and dynamics of the polybasic domain of ADP ribosylation factor nucleotide site opener protein: a molecular simulation study

ADP ribosylation factor nucleotide site opener (ARNO) as a guanine nucleotide exchange factor (GEF) activates small GTPases called ADP ribosylation factors (Arfs), which function as molecular switches and regulate a variety of cell biological events. ARNO directly interacts with the transmembrane a2-subunit isoform of the proton-pumping vacuolar ATPase in an acidification-dependent manner, and this interaction plays a crucial role in the regulation of the protein degradation pathway. A recent study reported specific interactions of a2N with the ARNO375-400 peptide corresponding to the polybasic (PB) domain of ARNO, which is a crucial regulatory element in the autoregulation and modulation of Arf-GEF activity. Interestingly, phosphorylation of Ser392 completely abolishes this interaction, and the experimental structure shows significant structural rearrangements. To investigate the effect of Ser392 phosphorylation on the structure and dynamics of the ARNO375-400 peptide, we employed all atom molecular dynamics (MD) simulations of the phosphorylated and unphosphorylated PB domain of the ARNO protein. A Hamiltonian-based replica exchange method called biasing potential replica exchange MD was used to enhance conformational sampling. Simulations predicted that the isolated PB domain is highly flexible, with the C-terminal region of the unphosphorylated state being unstable. In contrast, Ser392 phosphorylation increases the overall stability of the peptide. In agreement with experimental results, our simulations further support the hypothesis that phosphorylation induces disorder to order transitions and provide new insights into the structural dynamics of the PB domain. Phosphorylation of Ser392 appears to stabilize the C-terminal α-helix via formation of salt bridges between phospho-Ser392 and Arg390, Lys395, and Lys396.

Reliable oligonucleotide conformational ensemble generation in explicit solvent for force field assessment using reservoir replica exchange molecular dynamics simulations

Molecular dynamics force field development and assessment requires a reliable means for obtaining a well-converged conformational ensemble of a molecule in both a time-efficient and cost-effective manner. This remains a challenge for RNA because its rugged energy landscape results in slow conformational sampling and accurate results typically require explicit solvent which increases computational cost. To address this, we performed both traditional and modified replica exchange molecular dynamics simulations on a test system (alanine dipeptide) and an RNA tetramer known to populate A-form-like conformations in solution (single-stranded rGACC). A key focus is on providing the means to demonstrate that convergence is obtained, for example, by investigating replica RMSD profiles and/or detailed ensemble analysis through clustering. We found that traditional replica exchange simulations still require prohibitive time and resource expenditures, even when using GPU accelerated hardware, and our results are not well converged even at 2 μs of simulation time per replica. In contrast, a modified version of replica exchange, reservoir replica exchange in explicit solvent, showed much better convergence and proved to be both a cost-effective and reliable alternative to the traditional approach. We expect this method will be attractive for future research that requires quantitative conformational analysis from explicitly solvated simulations.

Advanced replica-exchange sampling to study the flexibility and plasticity of peptides and proteins

Molecular dynamics (MD) simulations are ideally suited to investigate protein and peptide plasticity and flexibility simultaneously at high spatial (atomic) and high time resolution. However, the applicability is still limited by the force field accuracy and by the maximum simulation time that can be routinely achieved in current MD simulations. In order to improve the sampling the replica-exchange (REMD) methodology has become popular and is now the most widely applied advanced sampling approach. Many variants of the REMD method have been designed to reduce the computational demand or to enhance sampling along specific sets of conformational variables. An overview on recent methodological advances and discussion of specific aims and advantages of the approaches will be given. Applications in the area of free energy simulations and advanced sampling of intrinsically disordered peptides and proteins will also be discussed. This article is part of a Special Issue entitled: The emerging dynamic view of proteins: Protein plasticity in allostery, evolution and self-assembly.

Refinement of protein structure homology models via long, all-atom molecular dynamics simulations

Accurate computational prediction of protein structure represents a longstanding challenge in molecular biology and structure-based drug design. Although homology modeling techniques are widely used to produce low-resolution models, refining these models to high resolution has proven difficult. With long enough simulations and sufficiently accurate force fields, molecular dynamics (MD) simulations should in principle allow such refinement, but efforts to refine homology models using MD have for the most part yielded disappointing results. It has thus far been unclear whether MD-based refinement is limited primarily by accessible simulation timescales, force field accuracy, or both. Here, we examine MD as a technique for homology model refinement using all-atom simulations, each at least 100 μs long-more than 100 times longer than previous refinement simulations-and a physics-based force field that was recently shown to successfully fold a structurally diverse set of fast-folding proteins. In MD simulations of 24 proteins chosen from the refinement category of recent Critical Assessment of Structure Prediction (CASP) experiments, we find that in most cases, simulations initiated from homology models drift away from the native structure. Comparison with simulations initiated from the native structure suggests that force field accuracy is the primary factor limiting MD-based refinement. This problem can be mitigated to some extent by restricting sampling to the neighborhood of the initial model, leading to structural improvement that, while limited, is roughly comparable to the leading alternative methods.

Protein Loop Modeling with Optimized Backbone Potential Functions

We represented protein backbone potential as a Fourier series. The parameters of the backbone dihedral potential were initialized to random values and optimized by Monte Carlo simulations so that generated native-like loop decoys had a lower energy than non-native decoys. The low energy regions of the optimized backbone potential were consistent with observed Ramachandran plots derived from crystal structures. The backbone potential was then used for the prediction of loop conformations (OSCAR-loop) combining with the previously described OSCAR force field, which has been shown to be very accurate in side chain modeling. As a result, the accuracy of OSCAR-loop was improved by local energy minimization based on the complete force field. The average accuracies were 0.40, 0.70, 1.10, 2.08, and 3.58 Å for 4, 6, 8, 10, and 12-residue loops, respectively, with each size being represented by 325 to 2809 targets. The accuracy was better than that of other loop modeling algorithms for short loops (<10 residues). For longer loops, the prediction accuracy was improved by concurrently sampling with a fragment-based method, Spanner. OSCAR-loop is available for download at http://sysimm.ifrec.osaka-u.ac.jp/OSCAR/ .

Density of states-based molecular simulations

One of the central problems in statistical mechanics is that of finding the density of states of a system. Knowledge of the density of states of a system is equivalent to knowledge of its fundamental equation, from which all thermodynamic quantities can be obtained. Over the past several years molecular simulations have made considerable strides in their ability to determine the density of states of complex fluids and materials. In this review we discuss some of the more promising approaches proposed in the recent literature along with their advantages and limitations.

Structural modelling and dynamics of proteins for insights into drug interactions

Proteins are the workhorses of biomolecules and their function is affected by their structure and their structural rearrangements during ligand entry, ligand binding and protein-protein interactions. Hence, the knowledge of protein structure and, importantly, the dynamic behaviour of the structure are critical for understanding how the protein performs its function. The predictions of the structure and the dynamic behaviour can be performed by combinations of structure modelling and molecular dynamics simulations. The simulations also need to be sensitive to the constraints of the environment in which the protein resides. Standard computational methods now exist in this field to support the experimental effort of solving protein structures. This review presents a comprehensive overview of the basis of the calculations and the well-established computational methods used to generate and understand protein structure and function and the study of their dynamic behaviour with the reference to lung-related targets.

Force fields for homology modeling

Accurate all-atom energy functions are crucial for successful high-resolution protein structure prediction. In this chapter, we review both physics-based force fields and knowledge-based potentials used in protein modeling. Because it is important to calculate the energy as accurately as possible given the limitations imposed by sampling convergence, different components of the energy, and force fields representing them to varying degrees of detail and complexity are discussed. Force fields using Cartesian as well as torsion angle representations of protein geometry are covered. Since solvent is important for protein energetics, different aqueous and membrane solvation models for protein simulations are also described. Finally, we summarize recent progress in protein structure refinement using new force fields.

A lightweight, flow-based toolkit for parallel and distributed bioinformatics pipelines

Background

Bioinformatic analyses typically proceed as chains of data-processing tasks. A pipeline, or 'workflow', is a well-defined protocol, with a specific structure defined by the topology of data-flow interdependencies, and a particular functionality arising from the data transformations applied at each step. In computer science, the dataflow programming (DFP) paradigm defines software systems constructed in this manner, as networks of message-passing components. Thus, bioinformatic workflows can be naturally mapped onto DFP concepts.

Results

To enable the flexible creation and execution of bioinformatics dataflows, we have written a modular framework for parallel pipelines in Python ('PaPy'). A PaPy workflow is created from re-usable components connected by data-pipes into a directed acyclic graph, which together define nested higher-order map functions. The successive functional transformations of input data are evaluated on flexibly pooled compute resources, either local or remote. Input items are processed in batches of adjustable size, all flowing one to tune the trade-off between parallelism and lazy-evaluation (memory consumption). An add-on module ('NuBio') facilitates the creation of bioinformatics workflows by providing domain specific data-containers (e.g., for biomolecular sequences, alignments, structures) and functionality (e.g., to parse/write standard file formats).

Conclusions

PaPy offers a modular framework for the creation and deployment of parallel and distributed data-processing workflows. Pipelines derive their functionality from user-written, data-coupled components, so PaPy also can be viewed as a lightweight toolkit for extensible, flow-based bioinformatics data-processing. The simplicity and flexibility of distributed PaPy pipelines may help users bridge the gap between traditional desktop/workstation and grid computing. PaPy is freely distributed as open-source Python code at http://muralab.org/PaPy, and includes extensive documentation and annotated usage examples.