1
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Mitsuta Y, Asada T. Parameter Optimization Method in Multidimensional Umbrella Sampling. J Chem Theory Comput 2024. [PMID: 39101750 DOI: 10.1021/acs.jctc.4c00282] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/06/2024]
Abstract
Umbrella sampling (US) is an effective method for calculating free-energy landscapes (FELs). However, the complexity of controlling the sampling positions complicates multidimensional FEL calculations. In this study, we proposed a method for controlling sampling by optimizing the US parameters. This method comprises the introduction of a target point and the optimization of the parameters to sample a window around this point. We approximated each window to normal distributions using an umbrella integration method and calculated the divergences between the window distributions and the state distributed at the target position by a variationally enhanced sampling method. Thus, the minimization of the divergence facilitated sampling around the target point, after which the parameters could be optimized on the fly while performing equilibration simulation. In practice, our method employs bias potentials with off-diagonal terms, ensuring a more efficient calculation of multidimensional FEL. Additionally, we developed an algorithm for determining the target point for automated FEL search; the algorithm samples in a specified direction while controlling the overlap of distributions. We performed three different FEL calculations as examples: (1) the calculation of the permeation of a water molecule through a lipid bilayer (one-dimensional FEL), (2) the calculation of the internal structural changes in alanine dipeptide in water (two-dimensional FEL), and (3) the calculation of the internal structural changes from a β-strand structure to an α-helix structure in alanine decapeptide (Ala10, 16-dimensional FEL). These results confirmed that our method could control the number of US windows and calculate the high-dimensional FELs that could not be evaluated by the conventional US method.
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Affiliation(s)
- Yuki Mitsuta
- Department of Chemistry, Osaka Metropolitan University, 3-3-138, Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan
- RIMED, Osaka Metropolitan University, 3-3-138, Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan
| | - Toshio Asada
- Department of Chemistry, Osaka Metropolitan University, 3-3-138, Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan
- RIMED, Osaka Metropolitan University, 3-3-138, Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan
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2
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Semelak JA, Zeida A, Foglia NO, Estrin DA. Minimum Free Energy Pathways of Reactive Processes with Nudged Elastic Bands. J Chem Theory Comput 2023; 19:6273-6293. [PMID: 37647166 DOI: 10.1021/acs.jctc.3c00366] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/01/2023]
Abstract
The determination of minimum free energy pathways (MFEP) is one of the most widely used strategies to study reactive processes. For chemical reactions in complex environments, the combination of quantum mechanics (QM) with a molecular mechanics (MM) representation is usually necessary in a hybrid QM/MM framework. However, even within the QM/MM approximation, the affordable sampling of the phase space is, in general, quite restricted. To reduce drastically the computational cost of the simulations, several methods such as umbrella sampling require performing a priori a selection of a reaction coordinate. The quality of the computed results, in an affordable computational time, is intimately related to the reaction coordinate election which is, in general, a nontrivial task. In this work, we provide an approach to model reactive processes in complex environments that does not require the a priori selection of a reaction coordinate. The proposed methodology combines QM/MM simulations with an extrapolation of the nudged elastic bands (NEB) method to the free energy surface (FENEB). We present and apply our own FENEB scheme to optimize MFEP in different reactive processes, using QM/MM frameworks at semiempirical and density functional theory levels. Our implementation is based on performing the FENEB optimization by uncoupling the optimization of the band in a perpendicular and tangential direction. In each step, a full optimization with the spring force is performed, which guarantees that the images remain evenly distributed. The robustness of the method and the influence of sampling on the quality of the optimized MFEP and its associated free energy barrier are studied. We show that the FENEB method provides a good estimation of the reaction barrier even with relatively short simulation times, supporting that its combination with QM/MM frameworks provides an adequate tool to study chemical processes in complex environments.
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Affiliation(s)
- Jonathan A Semelak
- Facultad de Ciencias Exactas y Naturales, Departamento de Química Inorgánica, Analítica y Química Física, Universidad de Buenos Aires, Buenos Aires C1428EHA, Argentina
- Instituto de Química Física de los Materiales, Medio Ambiente y Energía (INQUIMAE), CONICET-Universidad de Buenos Aires, Buenos Aires C1428EHA, Argentina
| | - Ari Zeida
- Departamento de Bioquímica, Facultad de Medicina, Universidad de la República, Montevideo 11800, Uruguay
- Centro de Investigaciones Biomédicas (CEINBIO), Universidad de la República, Montevideo 11800, Uruguay
| | - Nicolás O Foglia
- Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, Mülheim an der Ruhr 45470, Germany
| | - Darío A Estrin
- Facultad de Ciencias Exactas y Naturales, Departamento de Química Inorgánica, Analítica y Química Física, Universidad de Buenos Aires, Buenos Aires C1428EHA, Argentina
- Instituto de Química Física de los Materiales, Medio Ambiente y Energía (INQUIMAE), CONICET-Universidad de Buenos Aires, Buenos Aires C1428EHA, Argentina
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3
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Mitsuta Y, Asada T. Curvature-weighted nudged elastic band method using the Riemann curvature. J Comput Chem 2023; 44:662-669. [PMID: 36380703 DOI: 10.1002/jcc.27030] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/24/2022] [Revised: 10/03/2022] [Accepted: 10/08/2022] [Indexed: 11/17/2022]
Abstract
The nudged elastic band (NEB) method is utilized to find reaction paths (RPs) using discretized intermediate structures called "images" between a reactant and a product. In fact, NEB calculations do not always converge because of the bent of RPs. Mathematically, more images are needed for complex curves, and here, we focused on the curvature. In this study, we propose a new method for calculating the curvature of the RPs as well as a method for weighting the spring constant of the NEB with the curvature, which we named the curvature weighted NEB (CW-NEB) method. In addition, we will propose the CW-NEB method with the climbing image (CI) method (CW-CI-NEB). To show the efficiency of our method, calculations for the ene-reaction of the CW-CI-NEB method were performed and compared with those of the CI-NEB methods. The CW-CI-NEB methods converged in shorter iteration times than the CI-NEB calculation, which was found by gathering the bent of RPs.
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Affiliation(s)
- Yuki Mitsuta
- Graduate School of Science, Osaka Metropolitan University, Osaka, Japan.,RIMED, Osaka Prefecture University, Osaka, Japan
| | - Toshio Asada
- Graduate School of Science, Osaka Metropolitan University, Osaka, Japan.,RIMED, Osaka Prefecture University, Osaka, Japan
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4
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Hayami T, Higo J, Nakamura H, Kasahara K. Multidimensional virtual-system coupled canonical molecular dynamics to compute free-energy landscapes of peptide multimer assembly. J Comput Chem 2019; 40:2453-2463. [PMID: 31282023 DOI: 10.1002/jcc.26020] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/26/2019] [Revised: 05/26/2019] [Accepted: 06/17/2019] [Indexed: 11/05/2022]
Abstract
An enhanced-sampling method termed multidimensional virtual-system coupled canonical molecular dynamics (mD-VcMD) method is developed. In many cases, generalized-ensemble methods realizing enhanced sampling, for example, adaptive umbrella sampling, apply an effective potential, which is derived from temporarily assumed canonical distribution as a function of one or more arbitrarily defined reaction coordinates. However, it is not straightforward to estimate the appropriate canonical distribution, especially for cases applying multiple reaction coordinates. The current method, mD-VcMD, does not rely on the form of the canonical distribution. Therefore, it is practically useful to explore a high-dimensional reaction-coordinate space. In this article, formulation of mD-VcMD and its evaluation with the simple molecular models consisting of three or four alanine peptides are presented. We confirmed that mD-VcMD efficiently searched 2D and 3D reaction-coordinate spaces defined as interpeptide distances. Direct comparisons with results of long-term canonical MD simulations revealed that mD-VcMD produces correct canonical ensembles. © 2019 Wiley Periodicals, Inc.
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Affiliation(s)
- Tomonori Hayami
- Institute for Protein Research, Osaka University, 3-2 Yamada-oka, Suita, Osaka, 565-0871, Japan
| | - Junichi Higo
- Institute for Protein Research, Osaka University, 3-2 Yamada-oka, Suita, Osaka, 565-0871, Japan
| | - Haruki Nakamura
- Institute for Protein Research, Osaka University, 3-2 Yamada-oka, Suita, Osaka, 565-0871, Japan
| | - Kota Kasahara
- College of Life Sciences, Ritsumeikan University, 1-1-1 Noji-higashi, Kusatsu, Shiga, 525-8577, Japan
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5
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Mitsuta Y, Kästner J, Yamanaka S, Kawakami T, Okumura M. Free energy reaction root mapping of alanine tripeptide in water. Mol Phys 2018. [DOI: 10.1080/00268976.2018.1537525] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
Affiliation(s)
- Yuki Mitsuta
- Department of Chemistry, Osaka University, Osaka, Japan
| | - Johannes Kästner
- Institute for Theoretical Chemistry, University of Stuttgart, Stuttgart, Germany
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6
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Higo J, Kasahara K, Nakamura H. Multi-dimensional virtual system introduced to enhance canonical sampling. J Chem Phys 2018; 147:134102. [PMID: 28987097 DOI: 10.1063/1.4986129] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
When an important process of a molecular system occurs via a combination of two or more rare events, which occur almost independently to one another, computational sampling for the important process is difficult. Here, to sample such a process effectively, we developed a new method, named the "multi-dimensional Virtual-system coupled Monte Carlo (multi-dimensional-VcMC)" method, where the system interacts with a virtual system expressed by two or more virtual coordinates. Each virtual coordinate controls sampling along a reaction coordinate. By setting multiple reaction coordinates to be related to the corresponding rare events, sampling of the important process can be enhanced. An advantage of multi-dimensional-VcMC is its simplicity: Namely, the conformation moves widely in the multi-dimensional reaction coordinate space without knowledge of canonical distribution functions of the system. To examine the effectiveness of the algorithm, we introduced a toy model where two molecules (receptor and its ligand) bind and unbind to each other. The receptor has a deep binding pocket, to which the ligand enters for binding. Furthermore, a gate is set at the entrance of the pocket, and the gate is usually closed. Thus, the molecular binding takes place via the two events: ligand approach to the pocket and gate opening. In two-dimensional (2D)-VcMC, the two molecules exhibited repeated binding and unbinding, and an equilibrated distribution was obtained as expected. A conventional canonical simulation, which was 200 times longer than 2D-VcMC, failed in sampling the binding/unbinding effectively. The current method is applicable to various biological systems.
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Affiliation(s)
- Junichi Higo
- Institute for Protein Research, Osaka University, 3-2 Yamada-oka, Suita, Osaka 565-0871, Japan
| | - Kota Kasahara
- College of Life Sciences, Ritsumeikan University, 1-1-1 Noji-higashi, Kusatsu, Shiga 525-8577, Japan
| | - Haruki Nakamura
- Institute for Protein Research, Osaka University, 3-2 Yamada-oka, Suita, Osaka 565-0871, Japan
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7
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Mitsuta Y, Kawakami T, Okumura M, Yamanaka S. Automated Exploration of Free Energy Landscapes Based on Umbrella Integration. Int J Mol Sci 2018; 19:ijms19040937. [PMID: 29561821 PMCID: PMC5979611 DOI: 10.3390/ijms19040937] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/28/2018] [Revised: 03/19/2018] [Accepted: 03/21/2018] [Indexed: 12/15/2022] Open
Abstract
We present a new approach for automated exploration of free energy landscapes on the basis of the umbrella integration (UI) method. The method to search points in the landscape relies on the normal distributions and gradients of the potential of mean force (PMF) obtained from UI calculations. We applied this approach to the alanine dipeptide in solution and demonstrated that the equilibrium and the transition states were efficiently found in the ascending order of the PMF values.
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Affiliation(s)
- Yuki Mitsuta
- Graduate School of Science, Osaka University, Osaka 565-0871, Japan.
| | - Takashi Kawakami
- Graduate School of Science, Osaka University, Osaka 565-0871, Japan.
| | - Mitsutaka Okumura
- Graduate School of Science, Osaka University, Osaka 565-0871, Japan.
| | - Shusuke Yamanaka
- Graduate School of Science, Osaka University, Osaka 565-0871, Japan.
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8
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Hayami T, Kasahara K, Nakamura H, Higo J. Molecular dynamics coupled with a virtual system for effective conformational sampling. J Comput Chem 2018; 39:1291-1299. [PMID: 29464736 DOI: 10.1002/jcc.25196] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/03/2017] [Revised: 02/01/2018] [Accepted: 02/02/2018] [Indexed: 11/12/2022]
Abstract
An enhanced conformational sampling method is proposed: virtual-system coupled canonical molecular dynamics (VcMD). Although VcMD enhances sampling along a reaction coordinate, this method is free from estimation of a canonical distribution function along the reaction coordinate. This method introduces a virtual system that does not necessarily obey a physical law. To enhance sampling the virtual system couples with a molecular system to be studied. Resultant snapshots produce a canonical ensemble. This method was applied to a system consisting of two short peptides in an explicit solvent. Conventional molecular dynamics simulation, which is ten times longer than VcMD, was performed along with adaptive umbrella sampling. Free-energy landscapes computed from the three simulations mutually converged well. The VcMD provided quicker association/dissociation motions of peptides than the conventional molecular dynamics did. The VcMD method is applicable to various complicated systems because of its methodological simplicity. © 2018 Wiley Periodicals, Inc.
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Affiliation(s)
- Tomonori Hayami
- Institute for Protein Research, Osaka University, 3-2 Yamadaoka, Suita, Osaka, 565-0871, Japan
| | - Kota Kasahara
- College of Life Sciences, Ritsumeikan University, 1-1-1 Noji-higashi, Kusatsu, Shiga, 525-8577, Japan
| | - Haruki Nakamura
- Institute for Protein Research, Osaka University, 3-2 Yamadaoka, Suita, Osaka, 565-0871, Japan
| | - Junichi Higo
- Institute for Protein Research, Osaka University, 3-2 Yamadaoka, Suita, Osaka, 565-0871, Japan
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9
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Mecklenfeld A, Raabe G. Efficient solvation free energy simulations: impact of soft-core potential and a new adaptive λ-spacing method. Mol Phys 2017. [DOI: 10.1080/00268976.2017.1292008] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Affiliation(s)
- Andreas Mecklenfeld
- Institut für Thermodynamik, Technische Universität Braunschweig, Braunschweig, Germany
- Center of Pharmaceutical Engineering, Technische Universität Braunschweig, Braunschweig, Germany
| | - Gabriele Raabe
- Institut für Thermodynamik, Technische Universität Braunschweig, Braunschweig, Germany
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10
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Higo J, Kasahara K, Dasgupta B, Nakamura H. Enhancement of canonical sampling by virtual-state transitions. J Chem Phys 2017; 146:044104. [DOI: 10.1063/1.4974087] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Junichi Higo
- Institute for Protein Research, Osaka University, 3-2 Yamada-oka, Suita, Osaka 565-0871,
Japan
| | - Kota Kasahara
- College of Life Sciences, Ritsumeikan University, 1-1-1 Noji-higashi, Kusatsu, Shiga 525-8577,
Japan
| | - Bhaskar Dasgupta
- Institute for Protein Research, Osaka University, 3-2 Yamada-oka, Suita, Osaka 565-0871,
Japan
- Technology Research Association for Next Generation Natural Products Chemistry, 2-3-26 Aomi, Koto-ku, Tokyo
135-0064, Japan
| | - Haruki Nakamura
- Institute for Protein Research, Osaka University, 3-2 Yamada-oka, Suita, Osaka 565-0871,
Japan
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11
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Zinovjev K, Tuñón I. Transition state ensemble optimization for reactions of arbitrary complexity. J Chem Phys 2015; 143:134111. [DOI: 10.1063/1.4931596] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023] Open
Affiliation(s)
- Kirill Zinovjev
- Departament de Química Física, Universitat de València, 46100 Burjassot, Spain
| | - Iñaki Tuñón
- Departament de Química Física, Universitat de València, 46100 Burjassot, Spain
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12
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Chung LW, Sameera WMC, Ramozzi R, Page AJ, Hatanaka M, Petrova GP, Harris TV, Li X, Ke Z, Liu F, Li HB, Ding L, Morokuma K. The ONIOM Method and Its Applications. Chem Rev 2015; 115:5678-796. [PMID: 25853797 DOI: 10.1021/cr5004419] [Citation(s) in RCA: 758] [Impact Index Per Article: 84.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Affiliation(s)
- Lung Wa Chung
- †Department of Chemistry, South University of Science and Technology of China, Shenzhen 518055, China
| | - W M C Sameera
- ‡Fukui Institute for Fundamental Chemistry, Kyoto University, 34-4 Takano Nishihiraki-cho, Sakyo, Kyoto 606-8103, Japan
| | - Romain Ramozzi
- ‡Fukui Institute for Fundamental Chemistry, Kyoto University, 34-4 Takano Nishihiraki-cho, Sakyo, Kyoto 606-8103, Japan
| | - Alister J Page
- §Newcastle Institute for Energy and Resources, The University of Newcastle, Callaghan 2308, Australia
| | - Miho Hatanaka
- ‡Fukui Institute for Fundamental Chemistry, Kyoto University, 34-4 Takano Nishihiraki-cho, Sakyo, Kyoto 606-8103, Japan
| | - Galina P Petrova
- ∥Faculty of Chemistry and Pharmacy, University of Sofia, Bulgaria Boulevard James Bourchier 1, 1164 Sofia, Bulgaria
| | - Travis V Harris
- ‡Fukui Institute for Fundamental Chemistry, Kyoto University, 34-4 Takano Nishihiraki-cho, Sakyo, Kyoto 606-8103, Japan.,⊥Department of Chemistry, State University of New York at Oswego, Oswego, New York 13126, United States
| | - Xin Li
- #State Key Laboratory of Molecular Reaction Dynamics, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, China
| | - Zhuofeng Ke
- ∇School of Chemistry and Chemical Engineering, Sun Yat-sen University, Guangzhou 510275, China
| | - Fengyi Liu
- ○Key Laboratory of Macromolecular Science of Shaanxi Province, School of Chemistry and Chemical Engineering, Shaanxi Normal University, Xi'an, Shaanxi 710119, China
| | - Hai-Bei Li
- ■School of Ocean, Shandong University, Weihai 264209, China
| | - Lina Ding
- ▲School of Pharmaceutical Sciences, Zhengzhou University, 100 Kexue Avenue, Zhengzhou, Henan 450001, China
| | - Keiji Morokuma
- ‡Fukui Institute for Fundamental Chemistry, Kyoto University, 34-4 Takano Nishihiraki-cho, Sakyo, Kyoto 606-8103, Japan
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13
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Affiliation(s)
- Xiaofei Xu
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125;
| | | | - Isamu Kusaka
- William G. Lowrie Department of Chemical and Biomolecular Engineering, The Koffolt Laboratories, The Ohio State University, Columbus, Ohio 43210
| | - Zhen-Gang Wang
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125;
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14
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Bohner MU, Zeman J, Smiatek J, Arnold A, Kästner J. Nudged-elastic band used to find reaction coordinates based on the free energy. J Chem Phys 2014; 140:074109. [DOI: 10.1063/1.4865220] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
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15
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Zinovjev K, Ruiz-Pernía JJ, Tuñón I. Toward an Automatic Determination of Enzymatic Reaction Mechanisms and Their Activation Free Energies. J Chem Theory Comput 2013; 9:3740-9. [PMID: 26584125 DOI: 10.1021/ct400153r] [Citation(s) in RCA: 30] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Abstract
We present a combination of the string method and a path collective variable for the exploration of the free energy surface associated to a chemical reaction in condensed environments. The on-the-fly string method is employed to find the minimum free energy paths on a multidimensional free energy surface defined in terms of interatomic distances, which is a convenient selection to study bond forming/breaking processes. Once the paths have been determined, a reaction coordinate is defined as a measure of the advance of the system along these paths. This reaction coordinate can be then used to trace the reaction Potential of Mean Force from which the activation free energy can be obtained. This combination of methodologies has been here applied to the study, by means of Quantum Mechanics/Molecular Mechanics simulations, of the reaction catalyzed by guanidinoacetate methyltransferase. This enzyme catalyzes the methylation of guanidinoacetate by S-adenosyl-l-methionine, a reaction that involves a methyl transfer and a proton transfer and for which different reaction mechanisms have been proposed.
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Affiliation(s)
- Kirill Zinovjev
- Departament de Química Física, Universitat de València , 46100 Burjassot, Spain.,Departament de Química Física i Analítica, Universitat Jaume I , 12071 Castellón, Spain
| | - J Javier Ruiz-Pernía
- Departament de Química Física i Analítica, Universitat Jaume I , 12071 Castellón, Spain
| | - Iñaki Tuñón
- Departament de Química Física, Universitat de València , 46100 Burjassot, Spain
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16
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Lee TS, Radak BK, Pabis A, York DM. A New Maximum Likelihood Approach for Free Energy Profile Construction from Molecular Simulations. J Chem Theory Comput 2012; 9:153-164. [PMID: 23457427 DOI: 10.1021/ct300703z] [Citation(s) in RCA: 68] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Abstract
A novel variational method for construction of free energy profiles from molecular simulation data is presented. The variational free energy profile (VFEP) method uses the maximum likelihood principle applied to the global free energy profile based on the entire set of simulation data (e.g from multiple biased simulations) that spans the free energy surface. The new method addresses common obstacles in two major problems usually observed in traditional methods for estimating free energy surfaces: the need for overlap in the re-weighting procedure and the problem of data representation. Test cases demonstrate that VFEP outperforms other methods in terms of the amount and sparsity of the data needed to construct the overall free energy profiles. For typical chemical reactions, only ~5 windows and ~20-35 independent data points per window are sufficient to obtain an overall qualitatively correct free energy profile with sampling errors an order of magnitude smaller than the free energy barrier. The proposed approach thus provides a feasible mechanism to quickly construct the global free energy profile and identify free energy barriers and basins in free energy simulations via a robust, variational procedure that determines an analytic representation of the free energy profile without the requirement of numerically unstable histograms or binning procedures. It can serve as a new framework for biased simulations and is suitable to be used together with other methods to tackle with the free energy estimation problem.
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Affiliation(s)
- Tai-Sung Lee
- BioMaPS Institute for Quantitative Biology and Department of Chemistry and Chemical Biology, Rutgers University, Piscataway, NJ 08854, USA
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