1
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Zhang DT, Riccardi E, van Erp TS. Enhanced path sampling using subtrajectory Monte Carlo moves. J Chem Phys 2023; 158:024113. [PMID: 36641412 DOI: 10.1063/5.0127249] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022] Open
Abstract
Path sampling allows the study of rare events, such as chemical reactions, nucleation, and protein folding, via a Monte Carlo (MC) exploration in path space. Instead of configuration points, this method samples short molecular dynamics (MD) trajectories with specific start- and end-conditions. As in configuration MC, its efficiency highly depends on the types of MC moves. Since the last two decades, the central MC move for path sampling has been the so-called shooting move in which a perturbed phase point of the old path is propagated backward and forward in time to generate a new path. Recently, we proposed the subtrajectory moves, stone-skipping (SS) and web-throwing, that are demonstrably more efficient. However, the one-step crossing requirement makes them somewhat more difficult to implement in combination with external MD programs or when the order parameter determination is expensive. In this article, we present strategies to address the issue. The most generic solution is a new member of subtrajectory moves, wire fencing (WF), that is less thrifty than the SS but more versatile. This makes it easier to link path sampling codes with external MD packages and provides a practical solution for cases where the calculation of the order parameter is expensive or not a simple function of geometry. We demonstrate the WF move in a double-well Langevin model, a thin film breaking transition based on classical force fields, and a smaller ruthenium redox reaction at the ab initio level in which the order parameter explicitly depends on the electron density.
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Affiliation(s)
- Daniel T Zhang
- Norwegian University of Science and Technology, Department of Chemistry, NO-7491 Trondheim, Norway
| | - Enrico Riccardi
- Department of Informatics, UiO, Gaustadalléen 23B, 0373 Oslo, Norway
| | - Titus S van Erp
- Norwegian University of Science and Technology, Department of Chemistry, NO-7491 Trondheim, Norway
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2
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Roet S, Zhang DT, van Erp TS. Exchanging Replicas with Unequal Cost, Infinitely and Permanently. J Phys Chem A 2022; 126:8878-8886. [PMID: 36394633 PMCID: PMC9720720 DOI: 10.1021/acs.jpca.2c06004] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/02/2022] [Revised: 10/18/2022] [Indexed: 11/18/2022]
Abstract
We developed a replica exchange method that is effectively parallelizable even if the computational cost of the Monte Carlo moves in the parallel replicas are considerably different, for instance, because the replicas run on different types of processor units or because of the algorithmic complexity. To prove detailed-balance, we make a paradigm shift from the common conceptual viewpoint in which the set of parallel replicas represents a high-dimensional superstate, to an ensemble-based criterion in which the other ensembles represent an environment that might or might not participate in the Monte Carlo move. In addition, based on a recent algorithm for computing permanents, we effectively increase the exchange rate to infinite without the steep factorial scaling as a function of the number of replicas. We illustrate the effectiveness of this replica exchange methodology by combining it with a quantitative path sampling method, replica exchange transition interface sampling (RETIS), in which the costs for a Monte Carlo move can vary enormously as paths in a RETIS algorithm do not have the same length and the average path lengths tend to vary considerably for the different path ensembles that run in parallel. This combination, coined ∞RETIS, was tested on three model systems.
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Affiliation(s)
- Sander Roet
- Department of Chemistry, Norwegian University of Science and Technology (NTNU), N-7491Trondheim, Norway
| | - Daniel T. Zhang
- Department of Chemistry, Norwegian University of Science and Technology (NTNU), N-7491Trondheim, Norway
| | - Titus S. van Erp
- Department of Chemistry, Norwegian University of Science and Technology (NTNU), N-7491Trondheim, Norway
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3
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Hall SW, Díaz Leines G, Sarupria S, Rogal J. Practical guide to replica exchange transition interface sampling and forward flux sampling. J Chem Phys 2022; 156:200901. [DOI: 10.1063/5.0080053] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Path sampling approaches have become invaluable tools to explore the mechanisms and dynamics of the so-called rare events that are characterized by transitions between metastable states separated by sizable free energy barriers. Their practical application, in particular to ever more complex molecular systems, is, however, not entirely trivial. Focusing on replica exchange transition interface sampling (RETIS) and forward flux sampling (FFS), we discuss a range of analysis tools that can be used to assess the quality and convergence of such simulations, which is crucial to obtain reliable results. The basic ideas of a step-wise evaluation are exemplified for the study of nucleation in several systems with different complexities, providing a general guide for the critical assessment of RETIS and FFS simulations.
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Affiliation(s)
- Steven W. Hall
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, USA
| | - Grisell Díaz Leines
- Yusuf Hamied Department of Chemistry, University of Cambridge, Cambridgeshire CB2 1EW, United Kingdom
| | - Sapna Sarupria
- Department of Chemistry, University of Minnesota, Minneapolis, Minnesota 55455, USA
- Department of Chemical and Biomolecular Engineering, Clemson University, Clemson, South Carolina 29634, USA
| | - Jutta Rogal
- Department of Chemistry, New York University, New York, New York 10003, USA
- Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany
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4
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Riccardi E, Krämer A, van Erp TS, Ghysels A. Permeation Rates of Oxygen through a Lipid Bilayer Using Replica Exchange Transition Interface Sampling. J Phys Chem B 2020; 125:193-201. [DOI: 10.1021/acs.jpcb.0c09947] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Enrico Riccardi
- Department of Chemistry, Norwegian University of Science and Technology, Høgskoleringen 5, 7491 Trondheim, Norway
| | - Andreas Krämer
- Laboratory of Computational Biology, National Heart, Lung, and Blood Institute, National Institutes of Health, Bethesda, Maryland 20892, United States
| | - Titus S. van Erp
- Department of Chemistry, Norwegian University of Science and Technology, Høgskoleringen 5, 7491 Trondheim, Norway
- Center for Molecular Modeling (CMM), Ghent University, Technologiepark, Zwijnaarde, Ghent 9000, Belgium
| | - An Ghysels
- IBiTech, Faculty of Engineering and Architecture, Ghent University, Corneel Heymanslaan
10, Block B - entrance 36, 9000 Gent, Belgium
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5
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Yappert R, Kamat K, Peters B. The overdamped transmission coefficient: Recovering the true mean first passage time from an inaccurate reaction coordinate. J Chem Phys 2019; 151:184108. [DOI: 10.1063/1.5117237] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022] Open
Affiliation(s)
- Ryan Yappert
- Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - Kartik Kamat
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106, USA
| | - Baron Peters
- Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
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6
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DeFever RS, Sarupria S. Contour forward flux sampling: Sampling rare events along multiple collective variables. J Chem Phys 2019; 150:024103. [PMID: 30646707 DOI: 10.1063/1.5063358] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/21/2023] Open
Abstract
Many rare event transitions involve multiple collective variables (CVs), and the most appropriate combination of CVs is generally unknown a priori. We thus introduce a new method, contour forward flux sampling (cFFS), to study rare events with multiple CVs simultaneously. cFFS places nonlinear interfaces on-the-fly from the collective progress of the simulations, without any prior knowledge of the energy landscape or appropriate combination of CVs. We demonstrate cFFS on analytical potential energy surfaces and a conformational change in alanine dipeptide.
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Affiliation(s)
- Ryan S DeFever
- Department of Chemical and Biomolecular Engineering, Clemson University, Clemson, South Carolina 29634, USA
| | - Sapna Sarupria
- Department of Chemical and Biomolecular Engineering, Clemson University, Clemson, South Carolina 29634, USA
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7
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Moqadam M, Lervik A, Riccardi E, Venkatraman V, Alsberg BK, van Erp TS. Local initiation conditions for water autoionization. Proc Natl Acad Sci U S A 2018; 115:E4569-E4576. [PMID: 29712836 PMCID: PMC5960278 DOI: 10.1073/pnas.1714070115] [Citation(s) in RCA: 44] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
The pH of liquid water is determined by the infrequent process in which water molecules split into short-lived hydroxide and hydronium ions. This reaction is difficult to probe experimentally and challenging to simulate. One of the open questions is whether the local water structure around a slightly stretched OH bond is actually initiating the eventual breakage of this bond or whether this event is driven by a global ordering that involves many water molecules far away from the reaction center. Here, we investigated the self-ionization of water at room temperature by rare-event ab initio molecular dynamics and obtained autoionization rates and activation energies in good agreement with experiments. Based on the analysis of thousands of molecular trajectories, we identified a couple of local order parameters and show that if a bond stretch occurs when all these parameters are around their ideal range, the chance for the first dissociation step (double-proton jump) increases from [Formula: see text] to 0.4. Understanding these initiation triggers might ultimately allow the steering of chemical reactions.
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Affiliation(s)
- Mahmoud Moqadam
- Department of Chemistry, Norwegian University of Science and Technology, N-7491 Trondheim, Norway
| | - Anders Lervik
- Department of Chemistry, Norwegian University of Science and Technology, N-7491 Trondheim, Norway;
| | - Enrico Riccardi
- Department of Chemistry, Norwegian University of Science and Technology, N-7491 Trondheim, Norway
| | - Vishwesh Venkatraman
- Department of Chemistry, Norwegian University of Science and Technology, N-7491 Trondheim, Norway
| | - Bjørn Kåre Alsberg
- Department of Chemistry, Norwegian University of Science and Technology, N-7491 Trondheim, Norway
| | - Titus S van Erp
- Department of Chemistry, Norwegian University of Science and Technology, N-7491 Trondheim, Norway;
- Center for Molecular Modeling, Ghent University, B9000 Ghent, Belgium
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8
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Cabriolu R, Skjelbred Refsnes KM, Bolhuis PG, van Erp TS. Foundations and latest advances in replica exchange transition interface sampling. J Chem Phys 2017; 147:152722. [DOI: 10.1063/1.4989844] [Citation(s) in RCA: 30] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Raffaela Cabriolu
- Department of Chemistry, Norwegian University of Science and Technology (NTNU), Høgskoleringen 5, 7491 Trondheim, Norway
| | - Kristin M. Skjelbred Refsnes
- Department of Chemistry, Norwegian University of Science and Technology (NTNU), Høgskoleringen 5, 7491 Trondheim, Norway
| | - Peter G. Bolhuis
- Van ’t Hoff Institute for Molecular Sciences, University of Amsterdam, P.O. Box 94157, 1090 GD Amsterdam, The Netherlands
| | - Titus S. van Erp
- Department of Chemistry, Norwegian University of Science and Technology (NTNU), Høgskoleringen 5, 7491 Trondheim, Norway
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9
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Newton AC, Kools R, Swenson DWH, Bolhuis PG. The opposing effects of isotropic and anisotropic attraction on association kinetics of proteins and colloids. J Chem Phys 2017; 147:155101. [DOI: 10.1063/1.5006485] [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)
- Arthur C. Newton
- Van ’t Hoff Institute for Molecular Sciences, Universiteit van Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
| | - Ramses Kools
- Van ’t Hoff Institute for Molecular Sciences, Universiteit van Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
| | - David W. H. Swenson
- Van ’t Hoff Institute for Molecular Sciences, Universiteit van Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
| | - Peter G. Bolhuis
- Van ’t Hoff Institute for Molecular Sciences, Universiteit van Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
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10
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Riccardi E, Dahlen O, van Erp TS. Fast Decorrelating Monte Carlo Moves for Efficient Path Sampling. J Phys Chem Lett 2017; 8:4456-4460. [PMID: 28857565 DOI: 10.1021/acs.jpclett.7b01617] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Many relevant processes in chemistry, physics, and biology are rare events from a computational perspective as they take place beyond the accessible time scale of molecular dynamics (MD). Examples are chemical reactions, nucleation, and conformational changes of biomolecules. Path sampling is an approach to break this time scale limit via a Monte Carlo (MC) sampling of MD trajectories. Still, many trajectories are needed for accurately predicting rate constants. To improve the speed of convergence, we propose two new MC moves, stone skipping and web throwing. In these moves, trajectories are constructed via a sequence of subpaths obeying superdetailed balance. By a reweighting procedure, almost all paths can be accepted. Whereas the generation of a single trajectory becomes more expensive, the reduced correlation results in a significant speedup. For a study on DNA denaturation, the increase was found to be a factor 12.
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Affiliation(s)
- Enrico Riccardi
- Department of Chemistry, Norwegian University of Science and Technology , NO-7491 Trondheim, Norway
| | - Oda Dahlen
- Department of Chemistry, Norwegian University of Science and Technology , NO-7491 Trondheim, Norway
| | - Titus S van Erp
- Department of Chemistry, Norwegian University of Science and Technology , NO-7491 Trondheim, Norway
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11
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Lervik A, Riccardi E, van Erp TS. PyRETIS: A well-done, medium-sized python library for rare events. J Comput Chem 2017; 38:2439-2451. [DOI: 10.1002/jcc.24900] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/10/2017] [Revised: 06/30/2017] [Accepted: 07/13/2017] [Indexed: 01/27/2023]
Affiliation(s)
- Anders Lervik
- Department of Chemistry; Norwegian University of Science and Technology, NO-7491 Trondheim; Norway
| | - Enrico Riccardi
- Department of Chemistry; Norwegian University of Science and Technology, NO-7491 Trondheim; Norway
| | - Titus S. van Erp
- Department of Chemistry; Norwegian University of Science and Technology, NO-7491 Trondheim; Norway
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12
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Zhu F. Calculating transition rates from durations of transition paths. J Chem Phys 2017; 146:124128. [DOI: 10.1063/1.4979058] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023] Open
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13
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van Erp TS, Moqadam M, Riccardi E, Lervik A. Analyzing Complex Reaction Mechanisms Using Path Sampling. J Chem Theory Comput 2016; 12:5398-5410. [DOI: 10.1021/acs.jctc.6b00642] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Titus S. van Erp
- Department of Chemistry,
Faculty of Natural Sciences and Technology, NTNU, Norwegian University of Science and Technology, 7941 Trondheim, Norway
| | - Mahmoud Moqadam
- Department of Chemistry,
Faculty of Natural Sciences and Technology, NTNU, Norwegian University of Science and Technology, 7941 Trondheim, Norway
| | - Enrico Riccardi
- Department of Chemistry,
Faculty of Natural Sciences and Technology, NTNU, Norwegian University of Science and Technology, 7941 Trondheim, Norway
| | - Anders Lervik
- Department of Chemistry,
Faculty of Natural Sciences and Technology, NTNU, Norwegian University of Science and Technology, 7941 Trondheim, Norway
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14
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Affiliation(s)
- Baron Peters
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106;
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15
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Dahlen O, van Erp TS. Mesoscopic modeling of DNA denaturation rates: Sequence dependence and experimental comparison. J Chem Phys 2015; 142:235101. [DOI: 10.1063/1.4922519] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023] Open
Affiliation(s)
- Oda Dahlen
- Department of Chemistry, Norwegian University of Science and Technology (NTNU), Høgskoleringen 5, Realfagbygget D3-117 7491 Trondheim, Norway
| | - Titus S. van Erp
- Department of Chemistry, Norwegian University of Science and Technology (NTNU), Høgskoleringen 5, Realfagbygget D3-117 7491 Trondheim, Norway
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16
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Lervik A, van Erp TS. Gluing Potential Energy Surfaces with Rare Event Simulations. J Chem Theory Comput 2015; 11:2440-50. [DOI: 10.1021/acs.jctc.5b00012] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Anders Lervik
- Department
of Chemistry, Norwegian University of Science and Technology, 7491 Trondheim, Norway
| | - Titus S. van Erp
- Department
of Chemistry, Norwegian University of Science and Technology, 7491 Trondheim, Norway
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17
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Klenin KV. Efficient calculation of rate constants: Downhill versus uphill sampling. J Chem Phys 2014; 141:074103. [DOI: 10.1063/1.4892565] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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18
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Mullen RG, Shea JE, Peters B. Transmission Coefficients, Committors, and Solvent Coordinates in Ion-Pair Dissociation. J Chem Theory Comput 2014; 10:659-67. [DOI: 10.1021/ct4009798] [Citation(s) in RCA: 89] [Impact Index Per Article: 8.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Ryan Gotchy Mullen
- Department of Chemical Engineering, ‡Department of Chemistry & Biochemistry, §Department of Physics, University of California, Santa Barbara, California 93106
| | - Joan-Emma Shea
- Department of Chemical Engineering, ‡Department of Chemistry & Biochemistry, §Department of Physics, University of California, Santa Barbara, California 93106
| | - Baron Peters
- Department of Chemical Engineering, ‡Department of Chemistry & Biochemistry, §Department of Physics, University of California, Santa Barbara, California 93106
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Peters B, Bolhuis PG, Mullen RG, Shea JE. Reaction coordinates, one-dimensional Smoluchowski equations, and a test for dynamical self-consistency. J Chem Phys 2013; 138:054106. [PMID: 23406097 DOI: 10.1063/1.4775807] [Citation(s) in RCA: 65] [Impact Index Per Article: 5.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022] Open
Abstract
We propose a method for identifying accurate reaction coordinates among a set of trial coordinates. The method applies to special cases where motion along the reaction coordinate follows a one-dimensional Smoluchowski equation. In these cases the reaction coordinate can predict its own short-time dynamical evolution, i.e., the dynamics projected from multiple dimensions onto the reaction coordinate depend only on the reaction coordinate itself. To test whether this property holds, we project an ensemble of short trajectory swarms onto trial coordinates and compare projections of individual swarms to projections of the ensemble of swarms. The comparison, quantified by the Kullback-Leibler divergence, is numerically performed for each isosurface of each trial coordinate. The ensemble of short dynamical trajectories is generated only once by sampling along an initial order parameter. The initial order parameter should separate the reactants and products with a free energy barrier, and distributions on isosurfaces of the initial parameter should be unimodal. The method is illustrated for three model free energy landscapes with anisotropic diffusion. Where exact coordinates can be obtained from Kramers-Langer-Berezhkovskii-Szabo theory, results from the new method agree with the exact results. We also examine characteristics of systems where the proposed method fails. We show how dynamical self-consistency is related (through the Chapman-Kolmogorov equation) to the earlier isocommittor criterion, which is based on longer paths.
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Affiliation(s)
- Baron Peters
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106, USA
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20
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Juraszek J, Saladino G, van Erp TS, Gervasio FL. Efficient numerical reconstruction of protein folding kinetics with partial path sampling and pathlike variables. PHYSICAL REVIEW LETTERS 2013; 110:108106. [PMID: 23521305 DOI: 10.1103/physrevlett.110.108106] [Citation(s) in RCA: 36] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/04/2012] [Indexed: 06/01/2023]
Abstract
Numerically predicting rate constants of protein folding and other relevant biological events is still a significant challenge. We show that the combination of partial path transition interface sampling with the optimal interfaces and free-energy profiles provided by path collective variables makes the rate calculation for practical biological applications feasible and efficient. This methodology can reproduce the experimental rate constant of Trp-cage miniprotein folding with the same level of accuracy as transition path sampling at a fraction of the cost.
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Affiliation(s)
- J Juraszek
- Spanish National Cancer Research Centre, CNIO, calle Melchor Fernandez Almagro 3, 28029 Madrid, Spain
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21
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Inertial likelihood maximization for reaction coordinates with high transmission coefficients. Chem Phys Lett 2012. [DOI: 10.1016/j.cplett.2012.10.051] [Citation(s) in RCA: 45] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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22
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Meadley SL, Escobedo FA. Thermodynamics and kinetics of bubble nucleation: Simulation methodology. J Chem Phys 2012; 137:074109. [DOI: 10.1063/1.4745082] [Citation(s) in RCA: 52] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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23
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Johnson ME, Hummer G. Characterization of a dynamic string method for the construction of transition pathways in molecular reactions. J Phys Chem B 2012; 116:8573-83. [PMID: 22616575 PMCID: PMC3406241 DOI: 10.1021/jp212611k] [Citation(s) in RCA: 40] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023]
Abstract
We explore the theoretical foundation of different string methods used to find dominant reaction pathways in high-dimensional configuration spaces. Pathways are assessed by the amount of reactive flux they carry and by their orientation relative to the committor function. By examining the effects of transforming between different collective coordinates that span the same underlying space, we unmask artificial coordinate dependences in strings optimized to follow the free energy gradient. In contrast, strings optimized to follow the drift vector produce reaction pathways that are significantly less sensitive to reparameterizations of the collective coordinates. The differences in these paths arise because the drift vector depends on both the free energy gradient and the diffusion tensor of the coarse collective variables. Anisotropy and position dependence of diffusion tensors arise commonly in spaces of coarse variables, whose generally slow dynamics are obtained by nonlinear projections of the strongly coupled atomic motions. We show here that transition paths constructed to account for dynamics by following the drift vector will (to a close approximation) carry the maximum reactive flux both in systems with isotropic position dependent diffusion and in systems with constant but anisotropic diffusion. We derive a simple method for calculating the committor function along paths that follow the reactive flux. Lastly, we provide guidance for the practical implementation of the dynamic string method.
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Affiliation(s)
- Margaret E. Johnson
- Laboratory of Chemical Physics, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Bethesda, MD 20892-0520, USA
| | - Gerhard Hummer
- Laboratory of Chemical Physics, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Bethesda, MD 20892-0520, USA
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24
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Van Erp TS. Dynamical Rare Event Simulation Techniques for Equilibrium and Nonequilibrium Systems. ADVANCES IN CHEMICAL PHYSICS 2012. [DOI: 10.1002/9781118309513.ch2] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/13/2023]
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25
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Baidakov VG, Bobrov KS, Teterin AS. Cavitation and crystallization in a metastable Lennard-Jones liquid at negative pressures and low temperatures. J Chem Phys 2011; 135:054512. [DOI: 10.1063/1.3623587] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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26
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Peters B. Recent advances in transition path sampling: accurate reaction coordinates, likelihood maximisation and diffusive barrier-crossing dynamics. MOLECULAR SIMULATION 2010. [DOI: 10.1080/08927020903536382] [Citation(s) in RCA: 32] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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27
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Peters B. p(TP|q) peak maximization: Necessary but not sufficient for reaction coordinate accuracy. Chem Phys Lett 2010. [DOI: 10.1016/j.cplett.2010.05.069] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
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28
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Allen RJ, Valeriani C, Rein Ten Wolde P. Forward flux sampling for rare event simulations. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2009; 21:463102. [PMID: 21715864 DOI: 10.1088/0953-8984/21/46/463102] [Citation(s) in RCA: 229] [Impact Index Per Article: 15.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/21/2023]
Abstract
Rare events are ubiquitous in many different fields, yet they are notoriously difficult to simulate because few, if any, events are observed in a conventional simulation run. Over the past several decades, specialized simulation methods have been developed to overcome this problem. We review one recently developed class of such methods, known as forward flux sampling. Forward flux sampling uses a series of interfaces between the initial and final states to calculate rate constants and generate transition paths for rare events in equilibrium or nonequilibrium systems with stochastic dynamics. This review draws together a number of recent advances, summarizes several applications of the method and highlights challenges that remain to be overcome.
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Affiliation(s)
- Rosalind J Allen
- SUPA, School of Physics and Astronomy, University of Edinburgh, Mayfield Road, Edinburgh EH9 3JZ, UK
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Escobedo FA, Borrero EE, Araque JC. Transition path sampling and forward flux sampling. Applications to biological systems. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2009; 21:333101. [PMID: 21828593 DOI: 10.1088/0953-8984/21/33/333101] [Citation(s) in RCA: 48] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/11/2023]
Abstract
The last decade has seen a rapid growth in the number of simulation methods and applications dealing with the sampling of transition pathways of rare nanoscale events. Such studies are crucial, for example, for understanding the mechanism and kinetics of conformational transitions and enzymatic events associated with the function of biomolecules. In this review, a broad account of transition path sampling approaches is provided, starting from the general concepts, progressing to the specific principles that underlie some of the most important methods, and eventually singling out the so-called forward flux sampling method for a more detailed description. This is done because forward flux sampling, despite its appealing simplicity and potential efficiency, has thus far received limited attention from practitioners. While path sampling methods have a widespread application to many types of rare transitional events, here only recent applications involving biomolecules are reviewed, including isomerization, protein folding, and enzyme catalysis.
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Borrero EE, Escobedo FA. Optimizing the sampling and staging for simulations of rare events via forward flux sampling schemes. J Chem Phys 2008; 129:024115. [PMID: 18624524 DOI: 10.1063/1.2953325] [Citation(s) in RCA: 52] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Ernesto E Borrero
- School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, New York 14853, USA
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Borrero EE, Escobedo FA. Reaction coordinates and transition pathways of rare events via forward flux sampling. J Chem Phys 2007; 127:164101. [PMID: 17979313 DOI: 10.1063/1.2776270] [Citation(s) in RCA: 69] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Ernesto E Borrero
- School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, New York 14853, USA
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Peters B, Beckham GT, Trout BL. Extensions to the likelihood maximization approach for finding reaction coordinates. J Chem Phys 2007; 127:034109. [PMID: 17655433 DOI: 10.1063/1.2748396] [Citation(s) in RCA: 137] [Impact Index Per Article: 8.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
This paper extends our previous work on obtaining reaction coordinates from aimless shooting and likelihood maximization. We introduce a simplified version of aimless shooting and a half-trajectory likelihood score based on the committor probability. Additionally, we analyze and compare the absolute log-likelihood score for perfect and approximate reaction coordinates. We also compare the aimless shooting and likelihood maximization approach to the earlier genetic neural network (GNN) approach of Ma and Dinner [J. Phys. Chem. B 109, 6769 (2005)]. For a fixed number of total trajectories in the GNN approach, the accuracy of the transition state ensemble decreases as the number of trajectories per committor probability estimate increases. This quantitatively demonstrates the benefit of individual committor probability realizations over committor probability estimates. Furthermore, when the least squares score of the GNN approach is applied to individual committor probability realizations, the likelihood score still provides a better approximation to the true transition state surface. Finally, the polymorph transition in terephthalic acid demonstrates that the new half-trajectory likelihood scheme estimates the transition state location more accurately than likelihood schemes based on the probability of being on a transition path.
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Affiliation(s)
- Baron Peters
- Centre Européen de Calcul Atomique Moléculaire (CECAM), Ecole Normale Supérieure, 46 Allée d'Italie, 69364 Lyon Cedex 7, France.
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van Erp TS. Reaction rate calculation by parallel path swapping. PHYSICAL REVIEW LETTERS 2007; 98:268301. [PMID: 17678132 DOI: 10.1103/physrevlett.98.268301] [Citation(s) in RCA: 70] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/05/2007] [Indexed: 05/16/2023]
Abstract
The efficiency of path sampling simulations can be improved considerably using the approach of path swapping. For this purpose, we devise a new algorithmic procedure based on the transition interface sampling technique. In the same spirit of parallel tempering, paths between different ensembles are swapped, but the role of temperature is here played by the interface position. We test the method on the denaturation transition of DNA using the Peyrard-Bishop-Dauxois model. We find that the new algorithm gives a reduction of the computational cost by a factor of 20.
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Affiliation(s)
- Titus S van Erp
- Centrum voor Oppervlaktechemie en Katalyse, Katholieke Universiteit Leuven, Kasteelpark Arenberg 23, B-3001 Leuven, Belgium
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Van Erp TS, Caremans TP, Kirschhock CEA, Martens JA. Prospects of transition interface sampling simulations for the theoretical study of zeolite synthesis. Phys Chem Chem Phys 2007; 9:1044-51. [PMID: 17311145 DOI: 10.1039/b614980d] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The transition interface sampling (TIS) technique allows large free energy barriers to be overcome within reasonable simulation time, which is impossible for straightforward molecular dynamics. Still, the method does not impose an artificial driving force, but it surmounts the timescale problem by an importance sampling of true dynamical pathways. Recently, it was shown that the efficiency of TIS when calculating reaction rates is less sensitive to the choice of reaction coordinate than those of the standard free energy based techniques. This could be an important advantage in complex systems for which a good reaction coordinate is usually very difficult to find. We explain the principles of this method and discuss some of the promising applications related to zeolite formation.
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Affiliation(s)
- Titus S Van Erp
- Centre for Surface Chemistry and Catalysis, K.U. Leuven, Kasteelpark Arenberg 23, 3001 Leuven, Belgium.
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