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Vymětal J, Vondrášek J. Iterative Landmark-Based Umbrella Sampling (ILBUS) Protocol for Sampling of Conformational Space of Biomolecules. J Chem Inf Model 2022; 62:4783-4798. [PMID: 36122323 DOI: 10.1021/acs.jcim.2c00370] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Computer simulations of biomolecules such as molecular dynamics often suffer from insufficient sampling. Due to limited computational resources, insufficient sampling prevents obtaining proper equilibrium distributions of observed properties. To deal with this problem, we proposed a simulation protocol for efficient resampling of collected off-equilibrium trajectories. These trajectories are utilized for the initial mapping of the conformational space, which is later properly resampled by the introduced Iterative Landmark-Based Umbrella Sampling (ILBUS) method. Reconstruction of static equilibrium properties is achieved by the multistate Bennett acceptance ratio (MBAR) method, which enables efficient use of simulated data. The ILBUS protocol is geometry-based and does not demand any additional collective variable or a dimensional-reduction technique. The only requirement is a set of suitably spaced reference conformations, which serve as landmarks in the mapped conformational space. Additionally, the ILBUS protocol encompasses an iterative process that optimizes the force constant used in the umbrella sampling simulation. Such tuning is an inherent feature of the protocol and does not need to be performed by the user in advance. Furthermore, even the simulations with suboptimal force constants can be used in estimates by MBAR. We demonstrate the feasibility and the performance of this approach in the study of the conformational landscape of the alanine dipeptide, met-enkephalin, and adenylate kinase.
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Affiliation(s)
- Jiří Vymětal
- Institute of Organic Chemistry and Biochemistry of the Czech Academy of Sciences, Flemingovo náměstí 542/2, 160 00 Praha 6, Czech Republic
| | - Jiří Vondrášek
- Institute of Organic Chemistry and Biochemistry of the Czech Academy of Sciences, Flemingovo náměstí 542/2, 160 00 Praha 6, Czech Republic
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Yamauchi M, Okumura H. Replica sub-permutation method for molecular dynamics and monte carlo simulations. J Comput Chem 2019; 40:2694-2711. [PMID: 31365132 DOI: 10.1002/jcc.26030] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/07/2019] [Revised: 06/03/2019] [Accepted: 06/21/2019] [Indexed: 11/12/2022]
Abstract
We propose an improvement of the replica-exchange and replica-permutation methods, which we call the replica sub-permutation method (RSPM). Instead of considering all permutations, this method uses a new algorithm referred to as sub-permutation to perform parameter transition. The RSPM succeeds in reducing the number of combinations between replicas and parameters without the loss of sampling efficiency. For comparison, we applied the replica sub-permutation, replica-permutation, and replica-exchange methods to a β-hairpin mini protein, chignolin, in explicit water. We calculated the transition ratio and number of tunneling events in the parameter space, the number of folding-unfolding events, the autocorrelation function, and the autocorrelation time as measures of sampling efficiency. The results indicate that among the three methods, the proposed RSPM is the most efficient in both parameter and conformational spaces. © 2019 Wiley Periodicals, Inc.
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Affiliation(s)
- Masataka Yamauchi
- Department of Structural Molecular Science, SOKENDAI (The Graduate University for Advanced Studies), Okazaki, Aichi, 444-8585, Japan.,Exploratory Research Center on Life and Living Systems (ExCELLS), National Institutes of Natural Sciences, Okazaki, Aichi, 444-8787, Japan.,Institute for Molecular Science (IMS), National Institutes of Natural Sciences, Okazaki, Aichi, 444-8585, Japan
| | - Hisashi Okumura
- Department of Structural Molecular Science, SOKENDAI (The Graduate University for Advanced Studies), Okazaki, Aichi, 444-8585, Japan.,Exploratory Research Center on Life and Living Systems (ExCELLS), National Institutes of Natural Sciences, Okazaki, Aichi, 444-8787, Japan.,Institute for Molecular Science (IMS), National Institutes of Natural Sciences, Okazaki, Aichi, 444-8585, Japan
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Enhanced conformational sampling to visualize a free-energy landscape of protein complex formation. Biochem J 2017; 473:1651-62. [PMID: 27288028 PMCID: PMC4901360 DOI: 10.1042/bcj20160053] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/04/2016] [Accepted: 02/29/2016] [Indexed: 01/23/2023]
Abstract
We introduce various, recently developed, generalized ensemble methods, which are useful to sample various molecular configurations emerging in the process of protein-protein or protein-ligand binding. The methods introduced here are those that have been or will be applied to biomolecular binding, where the biomolecules are treated as flexible molecules expressed by an all-atom model in an explicit solvent. Sampling produces an ensemble of conformations (snapshots) that are thermodynamically probable at room temperature. Then, projection of those conformations to an abstract low-dimensional space generates a free-energy landscape. As an example, we show a landscape of homo-dimer formation of an endothelin-1-like molecule computed using a generalized ensemble method. The lowest free-energy cluster at room temperature coincided precisely with the experimentally determined complex structure. Two minor clusters were also found in the landscape, which were largely different from the native complex form. Although those clusters were isolated at room temperature, with rising temperature a pathway emerged linking the lowest and second-lowest free-energy clusters, and a further temperature increment connected all the clusters. This exemplifies that the generalized ensemble method is a powerful tool for computing the free-energy landscape, by which one can discuss the thermodynamic stability of clusters and the temperature dependence of the cluster networks.
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Zhang BW, Dai W, Gallicchio E, He P, Xia J, Tan Z, Levy RM. Simulating Replica Exchange: Markov State Models, Proposal Schemes, and the Infinite Swapping Limit. J Phys Chem B 2016; 120:8289-301. [PMID: 27079355 DOI: 10.1021/acs.jpcb.6b02015] [Citation(s) in RCA: 29] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2023]
Abstract
Replica exchange molecular dynamics is a multicanonical simulation technique commonly used to enhance the sampling of solvated biomolecules on rugged free energy landscapes. While replica exchange is relatively easy to implement, there are many unanswered questions about how to use this technique most efficiently, especially because it is frequently the case in practice that replica exchange simulations are not fully converged. A replica exchange cycle consists of a series of molecular dynamics steps of a set of replicas moving under different Hamiltonians or at different thermodynamic states followed by one or more replica exchange attempts to swap replicas among the different states. How the replica exchange cycle is constructed affects how rapidly the system equilibrates. We have constructed a Markov state model of replica exchange (MSMRE) using long molecular dynamics simulations of a host-guest binding system as an example, in order to study how different implementations of the replica exchange cycle can affect the sampling efficiency. We analyze how the number of replica exchange attempts per cycle, the number of MD steps per cycle, and the interaction between the two parameters affects the largest implied time scale of the MSMRE simulation. The infinite swapping limit is an important concept in replica exchange. We show how to estimate the infinite swapping limit from the diagonal elements of the exchange transition matrix constructed from MSMRE "simulations of simulations" as well as from relatively short runs of the actual replica exchange simulations.
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Affiliation(s)
- Bin W Zhang
- Center for Biophysics and Computational Biology, Department of Chemistry and Institute for Computational Molecular Science, Temple University , Philadelphia, Pennsylvania 19122, United States
| | - Wei Dai
- Department of Physics and Astronomy, Rutgers, the State University of New Jersey , Piscataway, New Jersey 08854, United States
| | - Emilio Gallicchio
- Department of Chemistry, Brooklyn College of the City University of New York , Brooklyn, New York 11210, United States
| | - Peng He
- Center for Biophysics and Computational Biology, Department of Chemistry and Institute for Computational Molecular Science, Temple University , Philadelphia, Pennsylvania 19122, United States
| | - Junchao Xia
- Center for Biophysics and Computational Biology, Department of Chemistry and Institute for Computational Molecular Science, Temple University , Philadelphia, Pennsylvania 19122, United States
| | - Zhiqiang Tan
- Department of Statistics, Rutgers, the State University of New Jersey , Piscataway, New Jersey 08854, United States
| | - Ronald M Levy
- Center for Biophysics and Computational Biology, Department of Chemistry and Institute for Computational Molecular Science, Temple University , Philadelphia, Pennsylvania 19122, United States
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Ikebe J, Umezawa K, Higo J. Enhanced sampling simulations to construct free-energy landscape of protein-partner substrate interaction. Biophys Rev 2016; 8:45-62. [PMID: 28510144 PMCID: PMC5425738 DOI: 10.1007/s12551-015-0189-z] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/01/2015] [Accepted: 12/07/2015] [Indexed: 01/08/2023] Open
Abstract
Molecular dynamics (MD) simulations using all-atom and explicit solvent models provide valuable information on the detailed behavior of protein-partner substrate binding at the atomic level. As the power of computational resources increase, MD simulations are being used more widely and easily. However, it is still difficult to investigate the thermodynamic properties of protein-partner substrate binding and protein folding with conventional MD simulations. Enhanced sampling methods have been developed to sample conformations that reflect equilibrium conditions in a more efficient manner than conventional MD simulations, thereby allowing the construction of accurate free-energy landscapes. In this review, we discuss these enhanced sampling methods using a series of case-by-case examples. In particular, we review enhanced sampling methods conforming to trivial trajectory parallelization, virtual-system coupled multicanonical MD, and adaptive lambda square dynamics. These methods have been recently developed based on the existing method of multicanonical MD simulation. Their applications are reviewed with an emphasis on describing their practical implementation. In our concluding remarks we explore extensions of the enhanced sampling methods that may allow for even more efficient sampling.
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Affiliation(s)
- Jinzen Ikebe
- Molecular Modeling and Simulation Group, Japan Atomic Energy Agency, 8-1-7 Umemidai, Kizugawa, Kyoto, 619-0215, Japan
| | - Koji Umezawa
- Department of Pure and Applied Physics, Waseda University, Okubo 3-4-1, Shinjuku-Ku, Tokyo, 169-8555, Japan
| | - Junichi Higo
- Institute for Protein Research, Osaka University, Suita, Osaka, 565-0871, Japan.
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Galvelis R, Sugita Y. Replica state exchange metadynamics for improving the convergence of free energy estimates. J Comput Chem 2015; 36:1446-55. [DOI: 10.1002/jcc.23945] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/25/2015] [Revised: 04/23/2015] [Accepted: 04/27/2015] [Indexed: 12/20/2022]
Affiliation(s)
- Raimondas Galvelis
- RIKEN Theoretical Molecular Science Laboratory; 2-1 Hirosawa Wako Saitama 351-0198 Japan
- RIKEN Advance Institute for Computational Science; 7-1-26 Minatojimaminamimachi Chuo-ku Kobe Hyogo 650-0047 Japan
| | - Yuji Sugita
- RIKEN Theoretical Molecular Science Laboratory; 2-1 Hirosawa Wako Saitama 351-0198 Japan
- RIKEN Advance Institute for Computational Science; 7-1-26 Minatojimaminamimachi Chuo-ku Kobe Hyogo 650-0047 Japan
- RIKEN iTHES; 2-1 Hirosawa Wako Saitama 351-0198 Japan
- RIKEN Quantitative Biology Center; IMDA 6F, 1-6-5 Minatojimaminamimachi Chuo-ku Kobe Hyogo 650-0047 Japan
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Yamagishi J, Okimoto N, Morimoto G, Taiji M. A new set of atomic radii for accurate estimation of solvation free energy by Poisson-Boltzmann solvent model. J Comput Chem 2014; 35:2132-9. [PMID: 25220475 PMCID: PMC4263261 DOI: 10.1002/jcc.23728] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/14/2014] [Revised: 07/04/2014] [Accepted: 08/20/2014] [Indexed: 01/16/2023]
Abstract
The Poisson-Boltzmann implicit solvent (PB) is widely used to estimate the solvation free energies of biomolecules in molecular simulations. An optimized set of atomic radii (PB radii) is an important parameter for PB calculations, which determines the distribution of dielectric constants around the solute. We here present new PB radii for the AMBER protein force field to accurately reproduce the solvation free energies obtained from explicit solvent simulations. The presented PB radii were optimized using results from explicit solvent simulations of the large systems. In addition, we discriminated PB radii for N- and C-terminal residues from those for nonterminal residues. The performances using our PB radii showed high accuracy for the estimation of solvation free energies at the level of the molecular fragment. The obtained PB radii are effective for the detailed analysis of the solvation effects of biomolecules.
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Affiliation(s)
- Junya Yamagishi
- Department of Computational Biology, Graduate School of Frontier Sciences, The University of Tokyo5-15 Kashiwanoha, Kashiwa, Chiba, 277-8561, Japan
| | - Noriaki Okimoto
- Department of Computational Biology, Graduate School of Frontier Sciences, The University of Tokyo5-15 Kashiwanoha, Kashiwa, Chiba, 277-8561, Japan
| | - Gentaro Morimoto
- Department of Computational Biology, Graduate School of Frontier Sciences, The University of Tokyo5-15 Kashiwanoha, Kashiwa, Chiba, 277-8561, Japan
| | - Makoto Taiji
- Department of Computational Biology, Graduate School of Frontier Sciences, The University of Tokyo5-15 Kashiwanoha, Kashiwa, Chiba, 277-8561, Japan
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Hédin F, Plattner N, Doll JD, Meuwly M. Spatial Averaging: Sampling Enhancement for Exploring Configurational Space of Atomic Clusters and Biomolecules. J Chem Theory Comput 2014; 10:4284-96. [DOI: 10.1021/ct500529w] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/08/2023]
Affiliation(s)
- Florent Hédin
- Department
of Chemistry, University of Basel, Klingelbergstrasse 80, CH-4056 Basel, Switzerland
| | - Nuria Plattner
- Department
of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, D-14195 Berlin, Germany
| | - J. D. Doll
- Department
of Chemistry, Brown University, Providence, Rhode Island 02912, United States
| | - Markus Meuwly
- Department
of Chemistry, University of Basel, Klingelbergstrasse 80, CH-4056 Basel, Switzerland
- Department
of Chemistry, Brown University, Providence, Rhode Island 02912, United States
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Zhang W, Chen J. Replica exchange with guided annealing for accelerated sampling of disordered protein conformations. J Comput Chem 2014; 35:1682-9. [PMID: 24995857 DOI: 10.1002/jcc.23675] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/13/2014] [Revised: 06/02/2014] [Accepted: 06/15/2014] [Indexed: 11/10/2022]
Abstract
We critically examine a recently proposed convective replica exchange (cRE) method for enhanced sampling of protein conformation based on theoretical and numerical analysis. The results demonstrate that cRE and related replica exchange with guided annealing (RE-GA) schemes lead to unbalanced exchange attempt probabilities and break detailed balance whenever the system undergoes slow conformational transitions (relative to the temperature diffusion timescale). Nonetheless, numerical simulations suggest that approximate canonical ensembles can be generated for systems with small conformational transition barriers. This suggests that RE-GA maybe suitable for simulating intrinsically disordered proteins, an important class of newly recognized functional proteins. The efficacy of RE-GA is demonstrated by calculating the conformational ensembles of intrinsically disordered kinase inducible domain protein. The results show that RE-GA helps the protein to escape nonspecific compact states more efficiently and provides several fold speedups in generating converged and largely correct ensembles compared to the standard temperature RE.
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Affiliation(s)
- Weihong Zhang
- Department of Biochemistry and Molecular Biophysics, Kansas State University, Manhattan, Kansas, 66506
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