1
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Hayashi T, Muguruma C, Okamoto Y. Calculation of the residual entropy of Ice Ih by Monte Carlo simulation with the combination of the replica-exchange Wang-Landau algorithm and multicanonical replica-exchange method. J Chem Phys 2021; 154:044503. [PMID: 33514077 DOI: 10.1063/5.0038157] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/02/2023] Open
Abstract
We estimated the residual entropy of Ice Ih by the recently developed simulation protocol, namely, the combination of the replica-exchange Wang-Landau algorithm and multicanonical replica-exchange method. We employed a model with the nearest neighbor interactions on the three-dimensional hexagonal lattice, which satisfied the ice rules in the ground state. The results showed that our estimate of the residual entropy is in accordance with various previous results. In this article, we not only give our latest estimate of the residual entropy of Ice Ih but also discuss the importance of the uniformity of a random number generator in Monte Carlo simulations.
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Affiliation(s)
- Takuya Hayashi
- Department of Physics, Graduate School of Science, Nagoya University, Nagoya, Aichi 464-8602, Japan
| | - Chizuru Muguruma
- Faculty of Liberal Arts and Sciences, Chukyo University, Toyota, Aichi 470-0393, Japan
| | - Yuko Okamoto
- Department of Physics, Graduate School of Science, Nagoya University, Nagoya, Aichi 464-8602, Japan
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2
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Rick SW, Schwing GJ, Summa CM. An Implementation of Replica Exchange with Dynamical Scaling for Efficient Large-Scale Simulations. J Chem Inf Model 2021; 61:810-818. [PMID: 33496583 DOI: 10.1021/acs.jcim.0c01236] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
An implementation of the replica exchange with dynamical scaling (REDS) method in the commonly used molecular dynamics program GROMACS is presented. REDS is a replica exchange method that requires fewer replicas than conventional replica exchange while still providing data over a range of temperatures and can be used in either constant volume or constant pressure ensembles. Details for running REDS simulations are given, and an application to the human islet amyloid polypeptide (hIAPP) 11-25 fragment shows that the model efficiently samples conformational space.
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Affiliation(s)
- Steven W Rick
- Department of Chemistry, University of New Orleans, New Orleans, Louisiana 70148, United States
| | - Gregory J Schwing
- Department of Computer Science, University of New Orleans, New Orleans, Louisiana 70148, United States
| | - Christopher M Summa
- Department of Computer Science, University of New Orleans, New Orleans, Louisiana 70148, United States
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3
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Timr S, Madern D, Sterpone F. Protein thermal stability. PROGRESS IN MOLECULAR BIOLOGY AND TRANSLATIONAL SCIENCE 2020; 170:239-272. [PMID: 32145947 DOI: 10.1016/bs.pmbts.2019.12.007] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Abstract
Proteins, in general, fold to a well-organized three-dimensional structure in order to function. The stability of this functional shape can be perturbed by external environmental conditions, such as temperature. Understanding the molecular factors underlying the resistance of proteins to the thermal stress has important consequences. First of all, it can aid the design of thermostable enzymes able to perform efficient catalysis in the high-temperature regime. Second, it is an essential brick of knowledge required to decipher the evolutionary pathways of life adaptation on Earth. Thanks to the development of atomistic simulations and ad hoc enhanced sampling techniques, it is now possible to investigate this problem in silico, and therefore provide support to experiments. After having described the methodological aspects, the chapter proposes an extended discussion on two problems. First, we focus on thermophilic proteins, a perfect model to address the issue of thermal stability and molecular evolution. Second, we discuss the issue of how protein thermal stability is affected by crowded in vivo-like conditions.
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Affiliation(s)
- Stepan Timr
- CNRS, Université de Paris, UPR 9080, Laboratoire de Biochimie Théorique, Paris, France; Institut de Biologie Physico-Chimique-Fondation Edmond de Rothschild, PSL Research University, Paris, France
| | | | - Fabio Sterpone
- CNRS, Université de Paris, UPR 9080, Laboratoire de Biochimie Théorique, Paris, France; Institut de Biologie Physico-Chimique-Fondation Edmond de Rothschild, PSL Research University, Paris, France.
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4
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Hayashi T, Okamoto Y. Efficient simulation protocol for determining the density of states: Combination of replica-exchange Wang-Landau method and multicanonical replica-exchange method. Phys Rev E 2019; 100:043304. [PMID: 31770876 DOI: 10.1103/physreve.100.043304] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/05/2019] [Indexed: 11/07/2022]
Abstract
By combining two generalized-ensemble algorithms, the replica-exchange Wang-Landau (REWL) method and the multicanonical replica-exchange method (MUCAREM), we propose an effective simulation protocol to determine the density of states with high accuracy. The new protocol is referred to as REWL-MUCAREM, and REWL is first performed and then MUCAREM is performed. In order to verify the effectiveness of our protocol, we performed simulations of a square-lattice Ising model using the three methods, namely REWL, MUCAREM, and REWL-MUCAREM. The results showed that the density of states obtained by REWL-MUCAREM is more accurate than that is estimated by the two methods separately.
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Affiliation(s)
- Takuya Hayashi
- Department of Physics, Graduate School of Science, Nagoya University, Nagoya, Aichi 464-8602, Japan
| | - Yuko Okamoto
- Department of Physics, Graduate School of Science, Nagoya University, Nagoya, Aichi 464-8602, Japan.,Structural Biology Research Center, Graduate School of Science, Nagoya University, Nagoya, Aichi 464-8602, Japan.,Center for Computational Science, Graduate School of Engineering, Nagoya University, Nagoya, Aichi 464-8603, Japan.,Information Technology Center, Nagoya University, Nagoya, Aichi 464-8601, Japan.,JST-CREST, Nagoya, Aichi 464-8602, Japan
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5
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Abstract
We report an embarrassingly parallel method for the evaluation of thermodynamic properties over an energy landscape exhibiting broken ergodicity, nested is the likelihood of the observed data D givenbasin-sampling (NBS). We also introduce the No Galilean U-Turn Sampler (NoGUTS), a new sampling scheme based on the No U-Turn Sampler (NUTS) introduced by Hoffman and Gelman (2014) that works with the Galilean Monte Carlo scheme introduced by Betancourt (2012) to aid the efficient generation of new live points. NoGUTS can be thought of as a form of reflective slice sampling with an automatic stopping criterion. We apply this approach to a benchmark atomic cluster of 31 Lennard-Jones atoms, which exhibits a low temperature solid-solid heat capacity peak. The calculated heat capacity is compared with results generated by parallel tempering (PT), basin-sampling parallel tempering (BSPT), and standard nested sampling (NS) simulations. NBS reproduces the full heat capacity curve predicted by PT and BSPT, while the NS calculation with similar computational cost fails to resolve the low-temperature solid-solid phase transition.
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Affiliation(s)
- Matthew Griffiths
- Department of Chemistry , University of Cambridge , Lensfield Road , Cambridge CB2 1EW , United Kingdom
| | - David J Wales
- Department of Chemistry , University of Cambridge , Lensfield Road , Cambridge CB2 1EW , United Kingdom
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6
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Stelter D, Keyes T. Simulation of fluid/gel phase equilibrium in lipid vesicles. SOFT MATTER 2019; 15:8102-8112. [PMID: 31588466 DOI: 10.1039/c9sm00854c] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Simulation of single component dipalmitoylphosphatidylcholine (DPPC) coarse-grained DRY-MARTINI lipid vesicles of diameter 10 nm (1350 lipids), 20 nm (5100 lipids) and 40 nm (17 600 lipids) is performed using statistical temperature molecular dynamics (STMD), to study finite size effects upon the order-disorder gel/fluid transition. STMD obtains enhanced sampling using a generalized ensemble, obtaining a flat energy distribution between upper and lower cutoffs, with little computational cost over canonical molecular dynamics. A single STMD trajectory of moderate length is sufficient to sample 20+ transition events, without trapping in the gel phase, and obtain well averaged properties. Phase transitions are analyzed via the energy-dependence of the statistical temperature, TS(U). The transition temperature decreases with decreasing diameter, in agreement with experiment, and the transition changes from first order to borderline first-second order. The size- and layer-dependence of the structure of both stable phases, and of the pathway of the phase transition, are determined. It is argued that the finite size effects are primarily caused by the disruption of the gel packing by curvature. Inhomogeneous states with faceted gel patches connected by unusual fluid seams are observed at high curvature, with visually different structure in the inner and outer layers due to the different curvatures. Thus a simple physical picture describes phase transitions in nanoscale finite systems far from the thermodynamic limit.
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Affiliation(s)
- David Stelter
- Boston University, Chemistry Department, 590 Commonwealth Avenue, Boston, MA 02215, USA.
| | - Tom Keyes
- Boston University, Chemistry Department, 590 Commonwealth Avenue, Boston, MA 02215, USA.
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7
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Oshima H, Re S, Sugita Y. Replica-Exchange Umbrella Sampling Combined with Gaussian Accelerated Molecular Dynamics for Free-Energy Calculation of Biomolecules. J Chem Theory Comput 2019; 15:5199-5208. [PMID: 31539245 DOI: 10.1021/acs.jctc.9b00761] [Citation(s) in RCA: 51] [Impact Index Per Article: 10.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
Abstract
We have developed an enhanced conformational sampling method combining replica-exchange umbrella sampling (REUS) with Gaussian accelerated molecular dynamics (GaMD). REUS enhances the sampling along predefined reaction coordinates, while GaMD accelerates the conformational dynamics by adding a boost potential to the system energy. The method, which we call GaREUS (Gaussian accelerated replica-exchange umbrella sampling), enhances the sampling more efficiently than REUS or GaMD, while the computational resource for GaREUS is the same as that required for REUS. The two-step reweighting procedure using the multistate Bennett acceptance ratio method and the cumulant expansion for the exponential average is applied to the simulation trajectories for obtaining the unbiased free-energy landscapes. We apply GaREUS to the calculations of free-energy landscapes for three different cases: conformational equilibria of N-glycan, folding of chignolin, and conformational change of adenyl kinase. We show that GaREUS speeds up the convergences of free-energy calculations using the same amount of computational resources as REUS. The free-energy landscapes reweighted from the trajectories of GaREUS agree with previously reported ones. GaREUS is applicable to free-energy calculations of various biomolecular dynamics and functions with reasonable computational costs.
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Affiliation(s)
- Hiraku Oshima
- Laboratory for Biomolecular Function Simulation , RIKEN Center for Biosystems Dynamics Research , Integrated Innovation Building N702, 6-7-1 Minatojima-minamimachi, Chuo-ku , Kobe , Hyogo 650-0047 , Japan
| | - Suyong Re
- Laboratory for Biomolecular Function Simulation , RIKEN Center for Biosystems Dynamics Research , Integrated Innovation Building N702, 6-7-1 Minatojima-minamimachi, Chuo-ku , Kobe , Hyogo 650-0047 , Japan
| | - Yuji Sugita
- Laboratory for Biomolecular Function Simulation , RIKEN Center for Biosystems Dynamics Research , Integrated Innovation Building N702, 6-7-1 Minatojima-minamimachi, Chuo-ku , Kobe , Hyogo 650-0047 , Japan.,Theoretical Molecular Science Laboratory , RIKEN Cluster for Pioneering Research , 2-1 Hirosawa, Wako-shi , Saitama 351-0198 , Japan.,Computational Biophysics Research Team , RIKEN Center for Computational Science , Integrated Innovation Building N702, 6-7-1 Minatojima-minamimachi, Chuo-ku , Kobe , Hyogo 650-0047 , Japan
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8
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Musiani F, Giorgetti A. Protein Aggregation and Molecular Crowding: Perspectives From Multiscale Simulations. INTERNATIONAL REVIEW OF CELL AND MOLECULAR BIOLOGY 2016; 329:49-77. [PMID: 28109331 DOI: 10.1016/bs.ircmb.2016.08.009] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/04/2023]
Abstract
Cells are extremely crowded environments, thus the use of diluted salted aqueous solutions containing a single protein is too simplistic to mimic the real situation. Macromolecular crowding might affect protein structure, folding, shape, conformational stability, binding of small molecules, enzymatic activity, interactions with cognate biomolecules, and pathological aggregation. The latter phenomenon typically leads to the formation of amyloid fibrils that are linked to several lethal neurodegenerative diseases, but that can also play a functional role in certain organisms. The majority of molecular simulations performed before the last few years were conducted in diluted solutions and were restricted both in the timescales and in the system dimensions by the available computational resources. In recent years, several computational solutions were developed to get close to physiological conditions. In this review we summarize the main computational techniques used to tackle the issue of protein aggregation both in a diluted and in a crowded environment.
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Affiliation(s)
- F Musiani
- Laboratory of Bioinorganic Chemistry, University of Bologna, Bologna, Italy.
| | - A Giorgetti
- Applied Bioinformatics Group, University of Verona, Verona, Italy.
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9
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Nagai T, Pantelopulos GA, Takahashi T, Straub JE. On the use of mass scaling for stable and efficient simulated tempering with molecular dynamics. J Comput Chem 2016; 37:2017-28. [PMID: 27338239 DOI: 10.1002/jcc.24430] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/12/2016] [Revised: 04/30/2016] [Accepted: 05/30/2016] [Indexed: 01/12/2023]
Abstract
Simulated tempering (ST) is a generalized-ensemble algorithm that employs trajectories exploring a range of temperatures to effectively sample rugged energy landscapes. When implemented using the molecular dynamics method, ST can require the use of short time steps for ensuring the stability of trajectories at high temperatures. To address this shortcoming, a mass-scaling ST (MSST) method is presented in which the particle mass is scaled in proportion to the temperature. Mass scaling in the MSST method leads to velocity distributions that are independent of temperature and eliminates the need for velocity scaling after the accepted temperature updates that are required in conventional ST simulations. The homogeneity in time scales with changing temperature improves the stability of simulations and allows for the use of longer time steps at high temperatures. As a result, the MSST is found to be more efficient than the standard ST method, particularly for cases in which a large temperature range is employed. © 2016 Wiley Periodicals, Inc.
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Affiliation(s)
- Tetsuro Nagai
- Department of Bioinformatics, College of Life Sciences, Ritsumeikan University, Kusatsu, Shiga 525-8577, Japan
| | | | - Takuya Takahashi
- Department of Bioinformatics, College of Life Sciences, Ritsumeikan University, Kusatsu, Shiga 525-8577, Japan
| | - John E Straub
- Department of Chemistry, Boston University, Boston, Massachusetts, 02215
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10
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Macdonald B, McCarley S, Noeen S, van Giessen AE. β-Hairpin Crowding Agents Affect α-Helix Stability in Crowded Environments. J Phys Chem B 2016; 120:650-9. [DOI: 10.1021/acs.jpcb.5b10575] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Affiliation(s)
- Bryanne Macdonald
- Department of Chemistry, Mount Holyoke College, South Hadley, Massachusetts 01075, United States
| | - Shannon McCarley
- Department of Chemistry, Mount Holyoke College, South Hadley, Massachusetts 01075, United States
| | - Sundus Noeen
- Department of Chemistry, Mount Holyoke College, South Hadley, Massachusetts 01075, United States
| | - Alan E. van Giessen
- Department of Chemistry, Mount Holyoke College, South Hadley, Massachusetts 01075, United States
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11
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Schierz P, Zierenberg J, Janke W. Molecular Dynamics and Monte Carlo simulations in the microcanonical ensemble: Quantitative comparison and reweighting techniques. J Chem Phys 2016; 143:134114. [PMID: 26450299 DOI: 10.1063/1.4931484] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023] Open
Abstract
Molecular Dynamics (MD) and Monte Carlo (MC) simulations are the most popular simulation techniques for many-particle systems. Although they are often applied to similar systems, it is unclear to which extent one has to expect quantitative agreement of the two simulation techniques. In this work, we present a quantitative comparison of MD and MC simulations in the microcanonical ensemble. For three test examples, we study first- and second-order phase transitions with a focus on liquid-gas like transitions. We present MD analysis techniques to compensate for conservation law effects due to linear and angular momentum conservation. Additionally, we apply the weighted histogram analysis method to microcanonical histograms reweighted from MD simulations. By this means, we are able to estimate the density of states from many microcanonical simulations at various total energies. This further allows us to compute estimates of canonical expectation values.
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Affiliation(s)
- Philipp Schierz
- Institut für Theoretische Physik, Universität Leipzig, Postfach 100 920, 04009 Leipzig, Germany
| | - Johannes Zierenberg
- Institut für Theoretische Physik, Universität Leipzig, Postfach 100 920, 04009 Leipzig, Germany
| | - Wolfhard Janke
- Institut für Theoretische Physik, Universität Leipzig, Postfach 100 920, 04009 Leipzig, Germany
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12
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Shea JE, Levine ZA. Studying the Early Stages of Protein Aggregation Using Replica Exchange Molecular Dynamics Simulations. Methods Mol Biol 2016; 1345:225-250. [PMID: 26453216 DOI: 10.1007/978-1-4939-2978-8_15] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
The simulation of protein aggregation poses several computational challenges due to the disparate time and lengths scales that are involved. This chapter focuses on the use of atomistically detailed simulations to probe the initial steps of aggregation, with an emphasis on the Tau peptide as a model system, run under a replica exchange molecular dynamics protocol.
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Affiliation(s)
- Joan-Emma Shea
- Department of Chemistry and Biochemistry, University of California Santa Barbara, Santa Barbara, CA, 93106, USA.
- Department of Physics, University of California Santa Barbara, Santa Barbara, CA, 93106, USA.
| | - Zachary A Levine
- Department of Chemistry and Biochemistry, University of California Santa Barbara, Santa Barbara, CA, 93106, USA
- Department of Physics, University of California Santa Barbara, Santa Barbara, CA, 93106, USA
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13
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Vogel T, Perez D. Towards an Optimal Flow: Density-of-States-Informed Replica-Exchange Simulations. PHYSICAL REVIEW LETTERS 2015; 115:190602. [PMID: 26588368 DOI: 10.1103/physrevlett.115.190602] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/13/2015] [Indexed: 06/05/2023]
Abstract
Replica exchange (RE) is one of the most popular enhanced-sampling simulations technique in use today. Despite widespread successes, RE simulations can sometimes fail to converge in practical amounts of time, e.g., when sampling around phase transitions, or when a few hard-to-find configurations dominate the statistical averages. We introduce a generalized RE scheme, density-of-states-informed RE, that addresses some of these challenges. The key feature of our approach is to inform the simulation with readily available, but commonly unused, information on the density of states of the system as the RE simulation proceeds. This enables two improvements, namely, the introduction of resampling moves that actively move the system towards equilibrium and the continual adaptation of the optimal temperature set. As a consequence of these two innovations, we show that the configuration flow in temperature space is optimized and that the overall convergence of RE simulations can be dramatically accelerated.
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Affiliation(s)
- Thomas Vogel
- Theoretical Division (T-1), Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Danny Perez
- Theoretical Division (T-1), Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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14
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Małolepsza E, Secor M, Keyes T. Isobaric Molecular Dynamics Version of the Generalized Replica Exchange Method (gREM): Liquid–Vapor Equilibrium. J Phys Chem B 2015; 119:13379-84. [DOI: 10.1021/acs.jpcb.5b07614] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Edyta Małolepsza
- Department of Chemistry, Boston University, Boston, Massachusetts 02215-2521, United States
| | - Maxim Secor
- Department of Chemistry, Boston University, Boston, Massachusetts 02215-2521, United States
| | - Tom Keyes
- Department of Chemistry, Boston University, Boston, Massachusetts 02215-2521, United States
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15
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Zang T, Yu L, Zhang C, Ma J. Parallel continuous simulated tempering and its applications in large-scale molecular simulations. J Chem Phys 2015; 141:044113. [PMID: 25084887 DOI: 10.1063/1.4890038] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022] Open
Abstract
In this paper, we introduce a parallel continuous simulated tempering (PCST) method for enhanced sampling in studying large complex systems. It mainly inherits the continuous simulated tempering (CST) method in our previous studies [C. Zhang and J. Ma, J. Chem. Phys. 130, 194112 (2009); C. Zhang and J. Ma, J. Chem. Phys. 132, 244101 (2010)], while adopts the spirit of parallel tempering (PT), or replica exchange method, by employing multiple copies with different temperature distributions. Differing from conventional PT methods, despite the large stride of total temperature range, the PCST method requires very few copies of simulations, typically 2-3 copies, yet it is still capable of maintaining a high rate of exchange between neighboring copies. Furthermore, in PCST method, the size of the system does not dramatically affect the number of copy needed because the exchange rate is independent of total potential energy, thus providing an enormous advantage over conventional PT methods in studying very large systems. The sampling efficiency of PCST was tested in two-dimensional Ising model, Lennard-Jones liquid and all-atom folding simulation of a small globular protein trp-cage in explicit solvent. The results demonstrate that the PCST method significantly improves sampling efficiency compared with other methods and it is particularly effective in simulating systems with long relaxation time or correlation time. We expect the PCST method to be a good alternative to parallel tempering methods in simulating large systems such as phase transition and dynamics of macromolecules in explicit solvent.
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Affiliation(s)
- Tianwu Zang
- Applied Physics Program and Department of Bioengineering, Rice University, Houston, Texas 77005, USA
| | - Linglin Yu
- Applied Physics Program and Department of Bioengineering, Rice University, Houston, Texas 77005, USA
| | - Chong Zhang
- Applied Physics Program and Department of Bioengineering, Rice University, Houston, Texas 77005, USA
| | - Jianpeng Ma
- Applied Physics Program and Department of Bioengineering, Rice University, Houston, Texas 77005, USA
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16
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Zhang T, Nguyen PH, Nasica-Labouze J, Mu Y, Derreumaux P. Folding Atomistic Proteins in Explicit Solvent Using Simulated Tempering. J Phys Chem B 2015; 119:6941-51. [PMID: 25985144 DOI: 10.1021/acs.jpcb.5b03381] [Citation(s) in RCA: 33] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Following a previous report on a coarse-grained protein model in implicit solvent, we applied simulated tempering (ST) with on-the-fly Helmholtz free energy (weight factors) determination to the folding or aggregation of seven proteins with the CHARMM, OPLS, and AMBER protein, and the SPC and TIP3P water force fields. For efficiency and reliability, we also performed replica exchange molecular dynamics (REMD) simulations on the alanine di- and deca-peptide, and the dimer of the Aβ16-22 Alzheimer's fragment, and used experimental data and previous simulation results on the chignolin, beta3s, Trp-cage, and WW domain peptides of 10-37 amino acids. The sampling with ST is found to be more efficient than with REMD for a much lower CPU cost. Starting from unfolded or extended conformations, the WW domain and the Trp-cage peptide fold to their NMR structures with a backbone RMSD of 2.0 and 1 Å. Remarkably, the ST simulation explores transient non-native topologies for Trp-cage that have been rarely discussed by other simulations. Our ST simulations also show that the CHARMM22* force field has limitations in describing accurately the beta3s peptide. Taken together, these results open the door to the study of the configurations of single proteins, protein aggregates, and any molecular systems at atomic details in explicit solvent using a single normal CPU. They also demonstrate that our ST scheme can be used with any force field ranging from quantum mechanics to coarse-grain and atomistic.
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Affiliation(s)
- Tong Zhang
- †Laboratoire de Biochimie Théorique, UPR 9080 CNRS, Université Denis Diderot, Sorbonne Paris Cité, IBPC, 13 rue Pierre et Marie Curie, 75005 Paris, France.,‡School of Biological Sciences, Nanyang Technological University, 60 Nanyang Drive, Singapore 637551, Singapore
| | - Phuong H Nguyen
- †Laboratoire de Biochimie Théorique, UPR 9080 CNRS, Université Denis Diderot, Sorbonne Paris Cité, IBPC, 13 rue Pierre et Marie Curie, 75005 Paris, France
| | - Jessica Nasica-Labouze
- †Laboratoire de Biochimie Théorique, UPR 9080 CNRS, Université Denis Diderot, Sorbonne Paris Cité, IBPC, 13 rue Pierre et Marie Curie, 75005 Paris, France.,§International School of Advanced Studies (SISSA), Via Bonomea, 265, 34126 Trieste, Italy
| | - Yuguang Mu
- ‡School of Biological Sciences, Nanyang Technological University, 60 Nanyang Drive, Singapore 637551, Singapore
| | - Philippe Derreumaux
- †Laboratoire de Biochimie Théorique, UPR 9080 CNRS, Université Denis Diderot, Sorbonne Paris Cité, IBPC, 13 rue Pierre et Marie Curie, 75005 Paris, France.,∥Institut Universitaire de France, 103 Boulevard Saint-Michel, 75005 Paris, France
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17
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Wales DJ. Perspective: Insight into reaction coordinates and dynamics from the potential energy landscape. J Chem Phys 2015; 142:130901. [DOI: 10.1063/1.4916307] [Citation(s) in RCA: 73] [Impact Index Per Article: 8.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2023] Open
Affiliation(s)
- D. J. Wales
- University Chemical Laboratories, Lensfield Road, Cambridge CB2 1EW, United Kingdom
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18
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Morriss-Andrews A, Shea JE. Computational Studies of Protein Aggregation: Methods and Applications. Annu Rev Phys Chem 2015; 66:643-66. [DOI: 10.1146/annurev-physchem-040513-103738] [Citation(s) in RCA: 132] [Impact Index Per Article: 14.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Affiliation(s)
| | - Joan-Emma Shea
- Department of Physics and
- Department of Chemistry, University of California, Santa Barbara, California 93106;
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19
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Exploiting the potential energy landscape to sample free energy. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2015. [DOI: 10.1002/wcms.1217] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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20
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Macdonald B, McCarley S, Noeen S, van Giessen AE. Protein–Protein Interactions Affect Alpha Helix Stability in Crowded Environments. J Phys Chem B 2015; 119:2956-67. [DOI: 10.1021/jp512630s] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Affiliation(s)
- Bryanne Macdonald
- Department of Chemistry, Mount Holyoke College, 50 College Street, South
Hadley, Massachusetts 01075, United States
| | - Shannon McCarley
- Department of Chemistry, Mount Holyoke College, 50 College Street, South
Hadley, Massachusetts 01075, United States
| | - Sundus Noeen
- Department of Chemistry, Mount Holyoke College, 50 College Street, South
Hadley, Massachusetts 01075, United States
| | - Alan E. van Giessen
- Department of Chemistry, Mount Holyoke College, 50 College Street, South
Hadley, Massachusetts 01075, United States
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Ballard AJ, Wales DJ. Superposition-Enhanced Estimation of Optimal Temperature Spacings for Parallel Tempering Simulations. J Chem Theory Comput 2014; 10:5599-5605. [PMID: 25512744 PMCID: PMC4262936 DOI: 10.1021/ct500797a] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/02/2014] [Indexed: 01/31/2023]
Abstract
Effective parallel tempering simulations rely crucially on a properly chosen sequence of temperatures. While it is desirable to achieve a uniform exchange acceptance rate across neighboring replicas, finding a set of temperatures that achieves this end is often a difficult task, in particular for systems undergoing phase transitions. Here we present a method for determination of optimal replica spacings, which is based upon knowledge of local minima in the potential energy landscape. Working within the harmonic superposition approximation, we derive an analytic expression for the parallel tempering acceptance rate as a function of the replica temperatures. For a particular system and a given database of minima, we show how this expression can be used to determine optimal temperatures that achieve a desired uniform acceptance rate. We test our strategy for two atomic clusters that exhibit broken ergodicity, demonstrating that our method achieves uniform acceptance as well as significant efficiency gains.
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Affiliation(s)
- Andrew J. Ballard
- University
Chemical Laboratories, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United
Kingdom
| | - David J. Wales
- University
Chemical Laboratories, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United
Kingdom
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22
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Junghans C, Perez D, Vogel T. Molecular Dynamics in the Multicanonical Ensemble: Equivalence of Wang-Landau Sampling, Statistical Temperature Molecular Dynamics, and Metadynamics. J Chem Theory Comput 2014; 10:1843-7. [PMID: 26580515 DOI: 10.1021/ct500077d] [Citation(s) in RCA: 37] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023]
Abstract
We show a direct formal relationship between the Wang-Landau iteration [PRL 86, 2050 (2001)], metadynamics [PNAS 99, 12562 (2002)], and statistical temperature molecular dynamics (STMD) [PRL 97, 050601 (2006)] that are the major work-horses for sampling from generalized ensembles. We demonstrate that STMD, itself derived from the Wang-Landau method, can be made indistinguishable from metadynamics. We also show that Gaussian kernels significantly improve the performance of STMD, highlighting the practical benefits of this improved formal understanding.
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Affiliation(s)
- Christoph Junghans
- Theoretical Division T-1, Los Alamos National Laboratory , Los Alamos, New Mexico 87545, United States
| | - Danny Perez
- Theoretical Division T-1, Los Alamos National Laboratory , Los Alamos, New Mexico 87545, United States
| | - Thomas Vogel
- Theoretical Division T-1, Los Alamos National Laboratory , Los Alamos, New Mexico 87545, United States
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Wales DJ. Surveying a complex potential energy landscape: Overcoming broken ergodicity using basin-sampling. Chem Phys Lett 2013. [DOI: 10.1016/j.cplett.2013.07.066] [Citation(s) in RCA: 54] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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Somani S, Wales DJ. Energy landscapes and global thermodynamics for alanine peptides. J Chem Phys 2013; 139:121909. [DOI: 10.1063/1.4813627] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Gai L, Vogel T, Maerzke KA, Iacovella CR, Landau DP, Cummings PT, McCabe C. Examining the phase transition behavior of amphiphilic lipids in solution using statistical temperature molecular dynamics and replica-exchange Wang-Landau methods. J Chem Phys 2013; 139:054505. [PMID: 23927268 DOI: 10.1063/1.4816520] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Two different techniques - replica-exchange Wang-Landau (REWL) and statistical temperature molecular dynamics (STMD) - were applied to systematically study the phase transition behavior of self-assembling lipids as a function of temperature using an off-lattice lipid model. Both methods allow the direct calculation of the density of states with improved efficiency compared to the original Wang-Landau method. A 3-segment model of amphiphilic lipids solvated in water has been studied with varied particle interaction energies (ε) and lipid concentrations. The phase behavior of the lipid molecules with respect to bilayer formation has been characterized through the calculation of the heat capacity as a function of temperature, in addition to various order parameters and general visual inspection. The simulations conducted by both methods can go to very low temperatures with the whole system exhibiting well-ordered structures. With optimized parameters, several bilayer phases are observed within the temperature range studied, including gel phase bilayers with frozen water, mixed water (i.e., frozen and liquid water), and liquid water, and a more fluid bilayer with liquid water. The results obtained from both methods, STMD and REWL, are consistently in excellent agreement with each other, thereby validating both the methods and the results.
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Affiliation(s)
- Lili Gai
- Department of Chemical and Biomolecular Engineering, Vanderbilt University, Nashville, Tennessee 37235, USA
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