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Blumer O, Reuveni S, Hirshberg B. Short-Time Infrequent Metadynamics for Improved Kinetics Inference. J Chem Theory Comput 2024; 20:3484-3491. [PMID: 38668722 PMCID: PMC11099961 DOI: 10.1021/acs.jctc.4c00170] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/09/2024] [Revised: 04/02/2024] [Accepted: 04/02/2024] [Indexed: 05/15/2024]
Abstract
Infrequent Metadynamics is a popular method to obtain the rates of long time-scale processes from accelerated simulations. The inference procedure is based on rescaling the first-passage times of the Metadynamics trajectories using a bias-dependent acceleration factor. While useful in many cases, it is limited to Poisson kinetics, and a reliable estimation of the unbiased rate requires slow bias deposition and prior knowledge of efficient collective variables. Here, we propose an improved inference scheme, which is based on two key observations: (1) the time-independent rate of Poisson processes can be estimated using short trajectories only. (2) Short trajectories experience minimal bias, and their rescaled first-passage times follow the unbiased distribution even for relatively high deposition rates and suboptimal collective variables. Therefore, by basing the inference procedure on short time scales, we obtain an improved trade-off between speedup and accuracy at no additional computational cost, especially when employing suboptimal collective variables. We demonstrate the improved inference scheme for a model system and two molecular systems.
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Affiliation(s)
- Ofir Blumer
- School
of Chemistry, Tel Aviv University, Tel Aviv 6997801, Israel
| | - Shlomi Reuveni
- School
of Chemistry, Tel Aviv University, Tel Aviv 6997801, Israel
- The
Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv 6997801, Israel
- The
Center for Physics and Chemistry of Living Systems, Tel Aviv University, Tel Aviv 6997801, Israel
| | - Barak Hirshberg
- School
of Chemistry, Tel Aviv University, Tel Aviv 6997801, Israel
- The
Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv 6997801, Israel
- The
Center for Physics and Chemistry of Living Systems, Tel Aviv University, Tel Aviv 6997801, Israel
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Ray D, Parrinello M. Kinetics from Metadynamics: Principles, Applications, and Outlook. J Chem Theory Comput 2023; 19:5649-5670. [PMID: 37585703 DOI: 10.1021/acs.jctc.3c00660] [Citation(s) in RCA: 17] [Impact Index Per Article: 17.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/18/2023]
Abstract
Metadynamics is a popular enhanced sampling algorithm for computing the free energy landscape of rare events by using molecular dynamics simulation. Ten years ago, Tiwary and Parrinello introduced the infrequent metadynamics approach for calculating the kinetics of transitions across free energy barriers. Since then, metadynamics-based methods for obtaining rate constants have attracted significant attention in computational molecular science. Such methods have been applied to study a wide range of problems, including protein-ligand binding, protein folding, conformational transitions, chemical reactions, catalysis, and nucleation. Here, we review the principles of elucidating kinetics from metadynamics-like approaches, subsequent methodological developments in this area, and successful applications on chemical, biological, and material systems. We also highlight the challenges of reconstructing accurate kinetics from enhanced sampling simulations and the scope of future developments.
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Affiliation(s)
- Dhiman Ray
- Atomistic Simulations, Italian Institute of Technology, Via Enrico Melen 83, 16152 Genova, Italy
| | - Michele Parrinello
- Atomistic Simulations, Italian Institute of Technology, Via Enrico Melen 83, 16152 Genova, Italy
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3
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Ray D, Ansari N, Rizzi V, Invernizzi M, Parrinello M. Rare Event Kinetics from Adaptive Bias Enhanced Sampling. J Chem Theory Comput 2022; 18:6500-6509. [PMID: 36194840 DOI: 10.1021/acs.jctc.2c00806] [Citation(s) in RCA: 15] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023]
Abstract
We introduce a novel enhanced sampling approach named on-the-fly probability enhanced sampling (OPES) flooding for calculating the kinetics of rare events from atomistic molecular dynamics simulation. This method is derived from the OPES approach [Invernizzi and Parrinello, J. Phys. Chem. Lett. 2020, 11, 7, 2731-2736], which has been recently developed for calculating converged free energy surfaces for complex systems. In this paper, we describe the theoretical details of the OPES flooding technique and demonstrate the application on three systems of increasing complexity: barrier crossing in a two-dimensional double-well potential, conformational transition in the alanine dipeptide in the gas phase, and the folding and unfolding of the chignolin polypeptide in an aqueous environment. From extensive tests, we show that the calculation of accurate kinetics not only requires the transition state to be bias-free, but the amount of bias deposited should also not exceed the effective barrier height measured along the chosen collective variables. In this vein, the possibility of computing rates from biasing suboptimal order parameters has also been explored. Furthermore, we describe the choice of optimum parameter combinations for obtaining accurate results from limited computational effort.
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Affiliation(s)
- Dhiman Ray
- Atomistic Simulations, Italian Institute of Technology, Via Enrico Melen 83, 16152 Genova, Italy
| | - Narjes Ansari
- Atomistic Simulations, Italian Institute of Technology, Via Enrico Melen 83, 16152 Genova, Italy
| | - Valerio Rizzi
- Atomistic Simulations, Italian Institute of Technology, Via Enrico Melen 83, 16152 Genova, Italy.,School of Pharmaceutical Sciences and Institute of Pharmaceutical Sciences of Western Switzerland (ISPSO), University of Geneva, Rue Michel Servet 1, 1211 Genève 4, Switzerland
| | | | - Michele Parrinello
- Atomistic Simulations, Italian Institute of Technology, Via Enrico Melen 83, 16152 Genova, Italy
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4
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Palacio-Rodriguez K, Vroylandt H, Stelzl LS, Pietrucci F, Hummer G, Cossio P. Transition Rates and Efficiency of Collective Variables from Time-Dependent Biased Simulations. J Phys Chem Lett 2022; 13:7490-7496. [PMID: 35939819 DOI: 10.1021/acs.jpclett.2c01807] [Citation(s) in RCA: 11] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
Simulations with adaptive time-dependent bias enable an efficient exploration of the conformational space of a system. However, the dynamic information is altered by the bias. Infrequent metadynamics recovers the transition rate of crossing a barrier, if the collective variables are ideal and there is no bias deposition near the transition state. Unfortunately, these conditions are not always fulfilled. To overcome these limitations, and inspired by single-molecule force spectroscopy, we use Kramers' theory for calculating the barrier-crossing rate when a time-dependent bias is added to the system. We assess the efficiency of collective variables parameter by measuring how efficiently the bias accelerates the transitions. We present approximate analytical expressions of the survival probability, reproducing the barrier-crossing time statistics and enabling the extraction of the unbiased transition rate even for challenging cases. We explore the limits of our method and provide convergence criteria to assess its validity.
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Affiliation(s)
- Karen Palacio-Rodriguez
- Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie, Sorbonne Université, Muséum National d'Histoire Naturelle, CNRS UMR 7590, 75005 Paris, France
- Biophysics of Tropical Diseases Max Planck Tandem Group, University of Antioquia, 050010 Medellín, Colombia
| | - Hadrien Vroylandt
- Institut des sciences du calcul et des données, Sorbonne Université, 75005 Paris, France
| | - Lukas S Stelzl
- Faculty of Biology, Johannes Gutenberg University Mainz, 55128 Mainz, Germany
- KOMET 1, Institute of Physics, Johannes Gutenberg University Mainz, 55099 Mainz, Germany
- Institute of Molecular Biology, 55128 Mainz, Germany
- Department of Theoretical Biophysics, Max Planck Institute of Biophysics, 60438 Frankfurt am Main, Germany
| | - Fabio Pietrucci
- Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie, Sorbonne Université, Muséum National d'Histoire Naturelle, CNRS UMR 7590, 75005 Paris, France
| | - Gerhard Hummer
- Department of Theoretical Biophysics, Max Planck Institute of Biophysics, 60438 Frankfurt am Main, Germany
- Institute for Biophysics, Goethe University Frankfurt, 60438 Frankfurt am Main, Germany
| | - Pilar Cossio
- Biophysics of Tropical Diseases Max Planck Tandem Group, University of Antioquia, 050010 Medellín, Colombia
- Department of Theoretical Biophysics, Max Planck Institute of Biophysics, 60438 Frankfurt am Main, Germany
- Center for Computational Mathematics, Flatiron Institute, 10010 New York, United States
- Center for Computational Biology, Flatiron Institute, 10010 New York, United States
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Khan SA, Dickson BM, Peters B. How fluxional reactants limit the accuracy/efficiency of infrequent metadynamics. J Chem Phys 2020; 153:054125. [DOI: 10.1063/5.0006980] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
Affiliation(s)
- Salman A. Khan
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106-5080, USA
| | | | - Baron Peters
- Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
- Department of Chemistry and Biochemistry, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
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Krep L, Kopp WA, Kröger LC, Döntgen M, Leonhard K. Exploring the Chemistry of Low‐Temperature Ignition by Pressure‐Accelerated Dynamics. CHEMSYSTEMSCHEM 2020. [DOI: 10.1002/syst.201900043] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023]
Affiliation(s)
- Lukas Krep
- Institute of Technical Thermodynamics RWTH Aachen University Aachen 52062 Germany
| | | | | | - Malte Döntgen
- Institute of Technical Thermodynamics RWTH Aachen University Aachen 52062 Germany
- School of Engineering Brown University Providence RI 02912 USA
| | - Kai Leonhard
- Institute of Technical Thermodynamics RWTH Aachen University Aachen 52062 Germany
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