1
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Rydzewski J. Spectral Map for Slow Collective Variables, Markovian Dynamics, and Transition State Ensembles. J Chem Theory Comput 2024. [PMID: 39265157 DOI: 10.1021/acs.jctc.4c00428] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/14/2024]
Abstract
Understanding the behavior of complex molecular systems is a fundamental problem in physical chemistry. To describe the long-time dynamics of such systems, which is responsible for their most informative characteristics, we can identify a few slow collective variables (CVs) while treating the remaining fast variables as thermal noise. This enables us to simplify the dynamics and treat it as diffusion in a free-energy landscape spanned by slow CVs, effectively rendering the dynamics Markovian. Our recent statistical learning technique, spectral map [Rydzewski, J. J. Phys. Chem. Lett. 2023, 14(22), 5216-5220], explores this strategy to learn slow CVs by maximizing a spectral gap of a transition matrix. In this work, we introduce several advancements into our framework, using a high-dimensional reversible folding process of a protein as an example. We implement an algorithm for coarse-graining Markov transition matrices to partition the reduced space of slow CVs kinetically and use it to define a transition state ensemble. We show that slow CVs learned by spectral map closely approach the Markovian limit for an overdamped diffusion. We demonstrate that coordinate-dependent diffusion coefficients only slightly affect the constructed free-energy landscapes. Finally, we present how spectral maps can be used to quantify the importance of features and compare slow CVs with structural descriptors commonly used in protein folding. Overall, we demonstrate that a single slow CV learned by spectral map can be used as a physical reaction coordinate to capture essential characteristics of protein folding.
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Affiliation(s)
- Jakub Rydzewski
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, Grudziadzka 5, 87-100 Toruń, Poland
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2
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Schäfer JL, Keller BG. Implementation of Girsanov Reweighting in OpenMM and Deeptime. J Phys Chem B 2024; 128:6014-6027. [PMID: 38865491 PMCID: PMC11215775 DOI: 10.1021/acs.jpcb.4c01702] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/14/2024] [Revised: 05/22/2024] [Accepted: 05/22/2024] [Indexed: 06/14/2024]
Abstract
Classical molecular dynamics (MD) simulations provide invaluable insights into complex molecular systems but face limitations in capturing phenomena occurring on time scales beyond their reach. To bridge this gap, various enhanced sampling techniques have been developed, which are complemented by reweighting techniques to recover the unbiased dynamics. Girsanov reweighting is a reweighting technique that reweights simulation paths, generated by a stochastic MD integrator, without evoking an effective model of the dynamics. Instead, it calculates the relative path probability density at the time resolution of the MD integrator. Efficient implementation of Girsanov reweighting requires that the reweighting factors are calculated on-the-fly during the simulations and thus needs to be implemented within the MD integrator. Here, we present a comprehensive guide for implementing Girsanov reweighting into MD simulations. We demonstrate the implementation in the MD simulation package OpenMM by extending the library openmmtools. Additionally, we implemented a reweighted Markov state model estimator within the time series analysis package Deeptime.
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Affiliation(s)
- Joana-Lysiane Schäfer
- Department of Biology, Chemistry, and
Pharmacy, Freie Universität Berlin, Berlin 14195, Germany
| | - Bettina G. Keller
- Department of Biology, Chemistry, and
Pharmacy, Freie Universität Berlin, Berlin 14195, Germany
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3
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Keller BG, Bolhuis PG. Dynamical Reweighting for Biased Rare Event Simulations. Annu Rev Phys Chem 2024; 75:137-162. [PMID: 38941527 DOI: 10.1146/annurev-physchem-083122-124538] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/30/2024]
Abstract
Dynamical reweighting techniques aim to recover the correct molecular dynamics from a simulation at a modified potential energy surface. They are important for unbiasing enhanced sampling simulations of molecular rare events. Here, we review the theoretical frameworks of dynamical reweighting for modified potentials. Based on an overview of kinetic models with increasing level of detail, we discuss techniques to reweight two-state dynamics, multistate dynamics, and path integrals. We explore the natural link to transition path sampling and how the effect of nonequilibrium forces can be reweighted. We end by providing an outlook on how dynamical reweighting integrates with techniques for optimizing collective variables and with modern potential energy surfaces.
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Affiliation(s)
- Bettina G Keller
- Department of Biology, Chemistry and Pharmacy, Freie Universität Berlin, Berlin, Germany;
| | - Peter G Bolhuis
- Van 't Hoff Institute for Molecular Sciences, University of Amsterdam, Amsterdam, The Netherlands
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4
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Kleiman DE, Nadeem H, Shukla D. Adaptive Sampling Methods for Molecular Dynamics in the Era of Machine Learning. J Phys Chem B 2023; 127:10669-10681. [PMID: 38081185 DOI: 10.1021/acs.jpcb.3c04843] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2023]
Abstract
Molecular dynamics (MD) simulations are fundamental computational tools for the study of proteins and their free energy landscapes. However, sampling protein conformational changes through MD simulations is challenging due to the relatively long time scales of these processes. Many enhanced sampling approaches have emerged to tackle this problem, including biased sampling and path-sampling methods. In this Perspective, we focus on adaptive sampling algorithms. These techniques differ from other approaches because the thermodynamic ensemble is preserved and the sampling is enhanced solely by restarting MD trajectories at particularly chosen seeds rather than introducing biasing forces. We begin our treatment with an overview of theoretically transparent methods, where we discuss principles and guidelines for adaptive sampling. Then, we present a brief summary of select methods that have been applied to realistic systems in the past. Finally, we discuss recent advances in adaptive sampling methodology powered by deep learning techniques, as well as their shortcomings.
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Affiliation(s)
- Diego E Kleiman
- Center for Biophysics and Quantitative Biology, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
| | - Hassan Nadeem
- Department of Bioengineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
| | - Diwakar Shukla
- Center for Biophysics and Quantitative Biology, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
- Department of Bioengineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
- Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
- Department of Plant Biology, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
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5
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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: 21] [Impact Index Per Article: 21.0] [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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6
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Bolhuis PG, Brotzakis ZF, Keller BG. Optimizing molecular potential models by imposing kinetic constraints with path reweighting. J Chem Phys 2023; 159:074102. [PMID: 37581416 DOI: 10.1063/5.0151166] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/19/2023] [Accepted: 06/19/2023] [Indexed: 08/16/2023] Open
Abstract
Empirical force fields employed in molecular dynamics simulations of complex systems are often optimized to reproduce experimentally determined structural and thermodynamic properties. In contrast, experimental knowledge about the interconversion rates between metastable states in such systems is hardly ever incorporated in a force field due to a lack of an efficient approach. Here, we introduce such a framework based on the relationship between dynamical observables, such as rate constants, and the underlying molecular model parameters using the statistical mechanics of trajectories. Given a prior ensemble of molecular dynamics trajectories produced with imperfect force field parameters, the approach allows for the optimal adaption of these parameters such that the imposed constraint of equally predicted and experimental rate constant is obeyed. To do so, the method combines the continuum path ensemble maximum caliber approach with path reweighting methods for stochastic dynamics. When multiple solutions are found, the method selects automatically the combination that corresponds to the smallest perturbation of the entire path ensemble, as required by the maximum entropy principle. To show the validity of the approach, we illustrate the method on simple test systems undergoing rare event dynamics. Next to simple 2D potentials, we explore particle models representing molecular isomerization reactions and protein-ligand unbinding. Besides optimal interaction parameters, the methodology gives physical insights into what parts of the model are most sensitive to the kinetics. We discuss the generality and broad implications of the methodology.
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Affiliation(s)
- Peter G Bolhuis
- van 't Hoff Institute for Molecular Sciences, University of Amsterdam, P.O. Box 94157, 1090 GD Amsterdam, The Netherlands
| | - Z Faidon Brotzakis
- Department of Chemistry, University of Cambridge, Cambridge CB2 1EW, United Kingdom
| | - Bettina G Keller
- Department of Biology, Chemistry, Pharmacy, Freie Universität Berlin, Arnimallee 22, D-14195 Berlin, Germany
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7
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Chen H, Roux B, Chipot C. Discovering Reaction Pathways, Slow Variables, and Committor Probabilities with Machine Learning. J Chem Theory Comput 2023; 19:4414-4426. [PMID: 37224455 PMCID: PMC11372462 DOI: 10.1021/acs.jctc.3c00028] [Citation(s) in RCA: 10] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/26/2023]
Abstract
A significant challenge faced by atomistic simulations is the difficulty, and often impossibility, to sample the transitions between metastable states of the free-energy landscape associated with slow molecular processes. Importance-sampling schemes represent an appealing option to accelerate the underlying dynamics by smoothing out the relevant free-energy barriers, but require the definition of suitable reaction-coordinate (RC) models expressed in terms of compact low-dimensional sets of collective variables (CVs). While most computational studies of slow molecular processes have traditionally relied on educated guesses based on human intuition to reduce the dimensionality of the problem at hand, a variety of machine-learning (ML) algorithms have recently emerged as powerful alternatives to discover meaningful CVs capable of capturing the dynamics of the slowest degrees of freedom. Considering a simple paradigmatic situation in which the long-time dynamics is dominated by the transition between two known metastable states, we compare two variational data-driven ML methods based on Siamese neural networks aimed at discovering a meaningful RC model─the slowest decorrelating CV of the molecular process, and the committor probability to first reach one of the two metastable states. One method is the state-free reversible variational approach for Markov processes networks (VAMPnets), or SRVs─the other, inspired by the transition path theory framework, is the variational committor-based neural networks, or VCNs. The relationship and the ability of these methodologies to discover the relevant descriptors of the slow molecular process of interest are illustrated with a series of simple model systems. We also show that both strategies are amenable to importance-sampling schemes through an appropriate reweighting algorithm that approximates the kinetic properties of the transition.
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Affiliation(s)
- Haochuan Chen
- Laboratoire International Associé Centre National de la Recherche Scientifique et University of Illinois at Urbana-Champaign, Unité Mixte de Recherche n°7019, Université de Lorraine, B.P. 70239, 54506 Vandœuvre-lès-Nancy cedex, France
| | - Benoît Roux
- Department of Biochemistry and Molecular Biology, University of Chicago, Chicago, 60637, United States
| | - Christophe Chipot
- Laboratoire International Associé Centre National de la Recherche Scientifique et University of Illinois at Urbana-Champaign, Unité Mixte de Recherche n°7019, Université de Lorraine, B.P. 70239, 54506 Vandœuvre-lès-Nancy cedex, France
- Department of Biochemistry and Molecular Biology, University of Chicago, Chicago, 60637, United States
- NIH Center for Macromolecular Modeling and Bioinformatics, Beckman Institute for Advanced Science and Technology, and Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
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8
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Shmilovich K, Ferguson AL. Girsanov Reweighting Enhanced Sampling Technique (GREST): On-the-Fly Data-Driven Discovery of and Enhanced Sampling in Slow Collective Variables. J Phys Chem A 2023; 127:3497-3517. [PMID: 37036804 DOI: 10.1021/acs.jpca.3c00505] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/11/2023]
Abstract
Molecular dynamics simulations of microscopic phenomena are limited by the short integration time steps which are required for numerical stability but which limit the practically achievable simulation time scales. Collective variable (CV) enhanced sampling techniques apply biases to predefined collective coordinates to promote barrier crossing, phase space exploration, and sampling of rare events. The efficacy of these techniques is contingent on the selection of good CVs correlated with the molecular motions governing the long-time dynamical evolution of the system. In this work, we introduce Girsanov Reweighting Enhanced Sampling Technique (GREST) as an adaptive sampling scheme that interleaves rounds of data-driven slow CV discovery and enhanced sampling along these coordinates. Since slow CVs are inherently dynamical quantities, a key ingredient in our approach is the use of both thermodynamic and dynamical Girsanov reweighting corrections for rigorous estimation of slow CVs from biased simulation data. We demonstrate our approach on a toy 1D 4-well potential, a simple biomolecular system alanine dipeptide, and the Trp-Leu-Ala-Leu-Leu (WLALL) pentapeptide. In each case GREST learns appropriate slow CVs and drives sampling of all thermally accessible metastable states starting from zero prior knowledge of the system. We make GREST accessible to the community via a publicly available open source Python package.
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Affiliation(s)
- Kirill Shmilovich
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States
| | - Andrew L Ferguson
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States
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9
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Shao L, Ma J, Prelesnik JL, Zhou Y, Nguyen M, Zhao M, Jenekhe SA, Kalinin SV, Ferguson AL, Pfaendtner J, Mundy CJ, De Yoreo JJ, Baneyx F, Chen CL. Hierarchical Materials from High Information Content Macromolecular Building Blocks: Construction, Dynamic Interventions, and Prediction. Chem Rev 2022; 122:17397-17478. [PMID: 36260695 DOI: 10.1021/acs.chemrev.2c00220] [Citation(s) in RCA: 17] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023]
Abstract
Hierarchical materials that exhibit order over multiple length scales are ubiquitous in nature. Because hierarchy gives rise to unique properties and functions, many have sought inspiration from nature when designing and fabricating hierarchical matter. More and more, however, nature's own high-information content building blocks, proteins, peptides, and peptidomimetics, are being coopted to build hierarchy because the information that determines structure, function, and interfacial interactions can be readily encoded in these versatile macromolecules. Here, we take stock of recent progress in the rational design and characterization of hierarchical materials produced from high-information content blocks with a focus on stimuli-responsive and "smart" architectures. We also review advances in the use of computational simulations and data-driven predictions to shed light on how the side chain chemistry and conformational flexibility of macromolecular blocks drive the emergence of order and the acquisition of hierarchy and also on how ionic, solvent, and surface effects influence the outcomes of assembly. Continued progress in the above areas will ultimately usher in an era where an understanding of designed interactions, surface effects, and solution conditions can be harnessed to achieve predictive materials synthesis across scale and drive emergent phenomena in the self-assembly and reconfiguration of high-information content building blocks.
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Affiliation(s)
- Li Shao
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99354, United States
| | - Jinrong Ma
- Molecular Engineering and Sciences Institute, University of Washington, Seattle, Washington 98195, United States
| | - Jesse L Prelesnik
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Yicheng Zhou
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99354, United States
| | - Mary Nguyen
- Department of Chemical Engineering, University of Washington, Seattle, Washington 98195, United States.,Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Mingfei Zhao
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States
| | - Samson A Jenekhe
- Department of Chemical Engineering, University of Washington, Seattle, Washington 98195, United States.,Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Sergei V Kalinin
- Department of Materials Science and Engineering, University of Tennessee, Knoxville, Tennessee 37996, United States
| | - Andrew L Ferguson
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States
| | - Jim Pfaendtner
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99354, United States.,Materials Science and Engineering, University of Washington, Seattle, Washington 98195, United States
| | - Christopher J Mundy
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99354, United States.,Department of Chemical Engineering, University of Washington, Seattle, Washington 98195, United States
| | - James J De Yoreo
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99354, United States.,Materials Science and Engineering, University of Washington, Seattle, Washington 98195, United States
| | - François Baneyx
- Molecular Engineering and Sciences Institute, University of Washington, Seattle, Washington 98195, United States.,Department of Chemical Engineering, University of Washington, Seattle, Washington 98195, United States
| | - Chun-Long Chen
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99354, United States.,Department of Chemical Engineering, University of Washington, Seattle, Washington 98195, United States
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10
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Kieninger S, Keller BG. GROMACS Stochastic Dynamics and BAOAB Are Equivalent Configurational Sampling Algorithms. J Chem Theory Comput 2022; 18:5792-5798. [DOI: 10.1021/acs.jctc.2c00585] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Stefanie Kieninger
- Department of Biology, Chemistry, Pharmacy, Freie Universität Berlin, Arnimallee 22, D-14195 Berlin, Germany
| | - Bettina G. Keller
- Department of Biology, Chemistry, Pharmacy, Freie Universität Berlin, Arnimallee 22, D-14195 Berlin, Germany
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11
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Ahmad K, Rizzi A, Capelli R, Mandelli D, Lyu W, Carloni P. Enhanced-Sampling Simulations for the Estimation of Ligand Binding Kinetics: Current Status and Perspective. Front Mol Biosci 2022; 9:899805. [PMID: 35755817 PMCID: PMC9216551 DOI: 10.3389/fmolb.2022.899805] [Citation(s) in RCA: 30] [Impact Index Per Article: 15.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/19/2022] [Accepted: 05/09/2022] [Indexed: 12/12/2022] Open
Abstract
The dissociation rate (k off) associated with ligand unbinding events from proteins is a parameter of fundamental importance in drug design. Here we review recent major advancements in molecular simulation methodologies for the prediction of k off. Next, we discuss the impact of the potential energy function models on the accuracy of calculated k off values. Finally, we provide a perspective from high-performance computing and machine learning which might help improve such predictions.
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Affiliation(s)
- Katya Ahmad
- Computational Biomedicine (IAS-5/INM-9), Forschungszentrum Jülich, Jülich, Germany
| | - Andrea Rizzi
- Computational Biomedicine (IAS-5/INM-9), Forschungszentrum Jülich, Jülich, Germany
- Atomistic Simulations, Istituto Italiano di Tecnologia, Genova, Italy
| | - Riccardo Capelli
- Department of Applied Science and Technology (DISAT), Politecnico di Torino, Torino, Italy
| | - Davide Mandelli
- Computational Biomedicine (IAS-5/INM-9), Forschungszentrum Jülich, Jülich, Germany
| | - Wenping Lyu
- Warshel Institute for Computational Biology, School of Life and Health Sciences, The Chinese University of Hong Kong (Shenzhen), Shenzhen, China
- School of Chemistry and Materials Science, University of Science and Technology of China, Hefei, China
| | - Paolo Carloni
- Computational Biomedicine (IAS-5/INM-9), Forschungszentrum Jülich, Jülich, Germany
- Molecular Neuroscience and Neuroimaging (INM-11), Forschungszentrum Jülich, Jülich, Germany
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12
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Motta S, Callea L, Bonati L, Pandini A. PathDetect-SOM: A Neural Network Approach for the Identification of Pathways in Ligand Binding Simulations. J Chem Theory Comput 2022; 18:1957-1968. [PMID: 35213804 PMCID: PMC8908765 DOI: 10.1021/acs.jctc.1c01163] [Citation(s) in RCA: 15] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
![]()
Understanding the
process of ligand–protein recognition
is important to unveil biological mechanisms and to guide drug discovery
and design. Enhanced-sampling molecular dynamics is now routinely
used to simulate the ligand binding process, resulting in the need
for suitable tools for the analysis of large data sets of binding
events. Here, we designed, implemented, and tested PathDetect-SOM,
a tool based on self-organizing maps to build concise visual models
of the ligand binding pathways sampled along single simulations or
replicas. The tool performs a geometric clustering of the trajectories
and traces the pathways over an easily interpretable 2D map and, using
an approximate transition matrix, it can build a graph model of concurrent
pathways. The tool was tested on three study cases representing different
types of problems and simulation techniques. A clear reconstruction
of the sampled pathways was derived in all cases, and useful information
on the energetic features of the processes was recovered. The tool
is available at https://github.com/MottaStefano/PathDetect-SOM.
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Affiliation(s)
- Stefano Motta
- Department of Earth and Environmental Sciences, University of Milano-Bicocca, Milan 20126, Italy
| | - Lara Callea
- Department of Earth and Environmental Sciences, University of Milano-Bicocca, Milan 20126, Italy
| | - Laura Bonati
- Department of Earth and Environmental Sciences, University of Milano-Bicocca, Milan 20126, Italy
| | - Alessandro Pandini
- Department of Computer Science, Brunel University London, Uxbridge UB8 3PH, U.K.,The Thomas Young Centre for Theory and Simulation of Materials, London SW7 2AZ, U.K
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13
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Kamenik AS, Linker SM, Riniker S. Enhanced sampling without borders: on global biasing functions and how to reweight them. Phys Chem Chem Phys 2022; 24:1225-1236. [PMID: 34935813 PMCID: PMC8768491 DOI: 10.1039/d1cp04809k] [Citation(s) in RCA: 18] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/20/2021] [Accepted: 12/14/2021] [Indexed: 12/17/2022]
Abstract
Molecular dynamics (MD) simulations are a powerful tool to follow the time evolution of biomolecular motions in atomistic resolution. However, the high computational demand of these simulations limits the timescales of motions that can be observed. To resolve this issue, so called enhanced sampling techniques are developed, which extend conventional MD algorithms to speed up the simulation process. Here, we focus on techniques that apply global biasing functions. We provide a broad overview of established enhanced sampling methods and promising new advances. As the ultimate goal is to retrieve unbiased information from biased ensembles, we also discuss benefits and limitations of common reweighting schemes. In addition to concisely summarizing critical assumptions and implications, we highlight the general application opportunities as well as uncertainties of global enhanced sampling.
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Affiliation(s)
- Anna S Kamenik
- Laboratory of Physical Chemistry, ETH Zurich, Vladimir-Prelog-Weg 2, 8093 Zurich, Switzerland.
| | - Stephanie M Linker
- Laboratory of Physical Chemistry, ETH Zurich, Vladimir-Prelog-Weg 2, 8093 Zurich, Switzerland.
| | - Sereina Riniker
- Laboratory of Physical Chemistry, ETH Zurich, Vladimir-Prelog-Weg 2, 8093 Zurich, Switzerland.
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14
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Jones M, Ashwood B, Tokmakoff A, Ferguson AL. Determining Sequence-Dependent DNA Oligonucleotide Hybridization and Dehybridization Mechanisms Using Coarse-Grained Molecular Simulation, Markov State Models, and Infrared Spectroscopy. J Am Chem Soc 2021; 143:17395-17411. [PMID: 34644072 PMCID: PMC8554761 DOI: 10.1021/jacs.1c05219] [Citation(s) in RCA: 21] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/20/2021] [Indexed: 11/29/2022]
Abstract
A robust understanding of the sequence-dependent thermodynamics of DNA hybridization has enabled rapid advances in DNA nanotechnology. A fundamental understanding of the sequence-dependent kinetics and mechanisms of hybridization and dehybridization remains comparatively underdeveloped. In this work, we establish new understanding of the sequence-dependent hybridization/dehybridization kinetics and mechanism within a family of self-complementary pairs of 10-mer DNA oligomers by integrating coarse-grained molecular simulation, machine learning of the slow dynamical modes, data-driven inference of long-time kinetic models, and experimental temperature-jump infrared spectroscopy. For a repetitive ATATATATAT sequence, we resolve a rugged dynamical landscape comprising multiple metastable states, numerous competing hybridization/dehybridization pathways, and a spectrum of dynamical relaxations. Introduction of a G:C pair at the terminus (GATATATATC) or center (ATATGCATAT) of the sequence reduces the ruggedness of the dynamics landscape by eliminating a number of metastable states and reducing the number of competing dynamical pathways. Only by introducing a G:C pair midway between the terminus and the center to maximally disrupt the repetitive nature of the sequence (ATGATATCAT) do we recover a canonical "all-or-nothing" two-state model of hybridization/dehybridization with no intermediate metastable states. Our results establish new understanding of the dynamical richness of sequence-dependent kinetics and mechanisms of DNA hybridization/dehybridization by furnishing quantitative and predictive kinetic models of the dynamical transition network between metastable states, present a molecular basis with which to understand experimental temperature jump data, and furnish foundational design rules by which to rationally engineer the kinetics and pathways of DNA association and dissociation for DNA nanotechnology applications.
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Affiliation(s)
- Michael
S. Jones
- Pritzker
School of Molecular Engineering, The University
of Chicago, 5640 South Ellis Avenue, Chicago, Illinois 60637, United
States
| | - Brennan Ashwood
- Department
of Chemistry, Institute for Biophysical Dynamics, and James Franck
Institute, The University of Chicago, 929 East 57th Street, Chicago, Illinois 60637, United States
| | - Andrei Tokmakoff
- Department
of Chemistry, Institute for Biophysical Dynamics, and James Franck
Institute, The University of Chicago, 929 East 57th Street, Chicago, Illinois 60637, United States
| | - Andrew L. Ferguson
- Pritzker
School of Molecular Engineering, The University
of Chicago, 5640 South Ellis Avenue, Chicago, Illinois 60637, United
States
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15
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Bause M, Bereau T. Reweighting non-equilibrium steady-state dynamics along collective variables. J Chem Phys 2021; 154:134105. [PMID: 33832234 DOI: 10.1063/5.0042972] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022] Open
Abstract
Computer simulations generate microscopic trajectories of complex systems at a single thermodynamic state point. We recently introduced a Maximum Caliber (MaxCal) approach for dynamical reweighting. Our approach mapped these trajectories to a Markovian description on the configurational coordinates and reweighted path probabilities as a function of external forces. Trajectory probabilities can be dynamically reweighted both from and to equilibrium or non-equilibrium steady states. As the system's dimensionality increases, an exhaustive description of the microtrajectories becomes prohibitive-even with a Markovian assumption. Instead, we reduce the dimensionality of the configurational space to collective variables (CVs). Going from configurational to CV space, we define local entropy productions derived from configurationally averaged mean forces. The entropy production is shown to be a suitable constraint on MaxCal for non-equilibrium steady states expressed as a function of CVs. We test the reweighting procedure on two systems: a particle subject to a two-dimensional potential and a coarse-grained peptide. Our CV-based MaxCal approach expands dynamical reweighting to larger systems, for both static and dynamical properties, and across a large range of driving forces.
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Affiliation(s)
- Marius Bause
- Max Planck Institute for Polymer Research, 55128 Mainz, Germany
| | - Tristan Bereau
- Max Planck Institute for Polymer Research, 55128 Mainz, Germany
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16
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Sicard F, Koskin V, Annibale A, Rosta E. Position-Dependent Diffusion from Biased Simulations and Markov State Model Analysis. J Chem Theory Comput 2021; 17:2022-2033. [DOI: 10.1021/acs.jctc.0c01151] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
Affiliation(s)
- François Sicard
- Department of Chemistry, King’s College London, SE1 1DB London, U.K
- Department of Physics and Astronomy, University College London, WC1E 6BT London, U.K
| | - Vladimir Koskin
- Department of Chemistry, King’s College London, SE1 1DB London, U.K
- Department of Physics and Astronomy, University College London, WC1E 6BT London, U.K
| | - Alessia Annibale
- Department of Mathematics, King’s College London, SE11 6NJ London, U.K
| | - Edina Rosta
- Department of Chemistry, King’s College London, SE1 1DB London, U.K
- Department of Physics and Astronomy, University College London, WC1E 6BT London, U.K
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17
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Kieninger S, Keller BG. Path probability ratios for Langevin dynamics-Exact and approximate. J Chem Phys 2021; 154:094102. [PMID: 33685138 DOI: 10.1063/5.0038408] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022] Open
Abstract
Path reweighting is a principally exact method to estimate dynamic properties from biased simulations-provided that the path probability ratio matches the stochastic integrator used in the simulation. Previously reported path probability ratios match the Euler-Maruyama scheme for overdamped Langevin dynamics. Since molecular dynamics simulations use Langevin dynamics rather than overdamped Langevin dynamics, this severely impedes the application of path reweighting methods. Here, we derive the path probability ratio ML for Langevin dynamics propagated by a variant of the Langevin Leapfrog integrator. This new path probability ratio allows for exact reweighting of Langevin dynamics propagated by this integrator. We also show that a previously derived approximate path probability ratio Mapprox differs from the exact ML only by O(ξ4Δt4) and thus yields highly accurate dynamic reweighting results. (Δt is the integration time step, and ξ is the collision rate.) The results are tested, and the efficiency of path reweighting is explored using butane as an example.
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Affiliation(s)
- S Kieninger
- Department of Biology, Chemistry, Pharmacy, Freie Universität Berlin, Arnimallee 22, D-14195 Berlin, Germany
| | - B G Keller
- Department of Biology, Chemistry, Pharmacy, Freie Universität Berlin, Arnimallee 22, D-14195 Berlin, Germany
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18
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Linker SM, Weiß RG, Riniker S. Connecting dynamic reweighting Algorithms: Derivation of the dynamic reweighting family tree. J Chem Phys 2020; 153:234106. [PMID: 33353335 DOI: 10.1063/5.0019687] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Thermally driven processes of molecular systems include transitions of energy barriers on the microsecond timescales and higher. Sufficient sampling of such processes with molecular dynamics simulations is challenging and often requires accelerating slow transitions using external biasing potentials. Different dynamic reweighting algorithms have been proposed in the past few years to recover the unbiased kinetics from biased systems. However, it remains an open question if and how these dynamic reweighting approaches are connected. In this work, we establish the link between the two main reweighting types, i.e., path-based and energy-based reweighting. We derive a path-based correction factor for the energy-based dynamic histogram analysis method, thus connecting the previously separate reweighting types. We show that the correction factor can be used to combine the advantages of path-based and energy-based reweighting algorithms: it is integrator independent, more robust, and at the same time able to reweight time-dependent biases. We can furthermore demonstrate the relationship between two independently derived path-based reweighting algorithms. Our theoretical findings are verified on a one-dimensional four-well system. By connecting different dynamic reweighting algorithms, this work helps to clarify the strengths and limitations of the different methods and enables a more robust usage of the combined types.
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Affiliation(s)
- Stephanie M Linker
- Laboratory of Physical Chemistry, ETH Zurich, Vladimir-Prelog-Weg 2, 8093 Zurich, Switzerland
| | - R Gregor Weiß
- Laboratory of Physical Chemistry, ETH Zurich, Vladimir-Prelog-Weg 2, 8093 Zurich, Switzerland
| | - Sereina Riniker
- Laboratory of Physical Chemistry, ETH Zurich, Vladimir-Prelog-Weg 2, 8093 Zurich, Switzerland
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19
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Gkeka P, Stoltz G, Barati Farimani A, Belkacemi Z, Ceriotti M, Chodera JD, Dinner AR, Ferguson AL, Maillet JB, Minoux H, Peter C, Pietrucci F, Silveira A, Tkatchenko A, Trstanova Z, Wiewiora R, Lelièvre T. Machine Learning Force Fields and Coarse-Grained Variables in Molecular Dynamics: Application to Materials and Biological Systems. J Chem Theory Comput 2020; 16:4757-4775. [PMID: 32559068 PMCID: PMC8312194 DOI: 10.1021/acs.jctc.0c00355] [Citation(s) in RCA: 82] [Impact Index Per Article: 20.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Abstract
Machine learning encompasses tools and algorithms that are now becoming popular in almost all scientific and technological fields. This is true for molecular dynamics as well, where machine learning offers promises of extracting valuable information from the enormous amounts of data generated by simulation of complex systems. We provide here a review of our current understanding of goals, benefits, and limitations of machine learning techniques for computational studies on atomistic systems, focusing on the construction of empirical force fields from ab initio databases and the determination of reaction coordinates for free energy computation and enhanced sampling.
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Affiliation(s)
- Paraskevi Gkeka
- Integrated Drug Discovery, Sanofi R&D, 91385 Chilly-Mazarin, France
| | - Gabriel Stoltz
- CERMICS, Ecole des Ponts, Marne-la-Vallée, France
- Matherials Project-Team, Inria Paris, 75012 Paris, France
| | | | - Zineb Belkacemi
- Integrated Drug Discovery, Sanofi R&D, 91385 Chilly-Mazarin, France
- CERMICS, Ecole des Ponts, Marne-la-Vallée, France
| | - Michele Ceriotti
- Laboratory of Computational Science and Modelling, Institute of Materials, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
| | - John D Chodera
- Computational and Systems Biology Program, Sloan Kettering Institute, Memorial Sloan Kettering Cancer Center, New York, New York 10065, United States
| | - Aaron R Dinner
- Department of Chemistry, The University of Chicago, Chicago, Illinois 60637, United States
| | - Andrew L Ferguson
- Pritzker School of Molecular Engineering, University of Chicago, 5640 South Ellis Avenue, Chicago, Illinois 60637, United States
| | | | - Hervé Minoux
- Integrated Drug Discovery, Sanofi R&D, 94403 Vitry-sur-Seine, France
| | | | - Fabio Pietrucci
- UMR CNRS 7590, MNHN, Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie, Sorbonne Université, 75005 Paris, France
| | - Ana Silveira
- Computational and Systems Biology Program, Sloan Kettering Institute, Memorial Sloan Kettering Cancer Center, New York, New York 10065, United States
| | - Alexandre Tkatchenko
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg City, Luxembourg
| | - Zofia Trstanova
- School of Mathematics, The University of Edinburgh, Edinburgh EH9 3FD, U.K
| | - Rafal Wiewiora
- Computational and Systems Biology Program, Sloan Kettering Institute, Memorial Sloan Kettering Cancer Center, New York, New York 10065, United States
| | - Tony Lelièvre
- CERMICS, Ecole des Ponts, Marne-la-Vallée, France
- Matherials Project-Team, Inria Paris, 75012 Paris, France
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20
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Mandelli D, Hirshberg B, Parrinello M. Metadynamics of Paths. PHYSICAL REVIEW LETTERS 2020; 125:026001. [PMID: 32701329 DOI: 10.1103/physrevlett.125.026001] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/17/2020] [Revised: 05/09/2020] [Accepted: 06/12/2020] [Indexed: 05/27/2023]
Abstract
We present a method to sample reactive pathways via biased molecular dynamics simulations in trajectory space. We show that the use of enhanced sampling techniques enables unconstrained exploration of multiple reaction routes. Time correlation functions are conveniently computed via reweighted averages along a single trajectory and kinetic rates are accessed at no additional cost. These abilities are illustrated analyzing a model potential and the umbrella inversion of NH_{3} in water. The algorithm allows a parallel implementation and promises to be a powerful tool for the study of rare events.
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Affiliation(s)
- Davide Mandelli
- Atomistic Simulations, Italian Institute of Technology, via Morego 30, 16163 Genova, Italy
| | - Barak Hirshberg
- Department of Chemistry and Applied Biosciences, ETH Zurich, 8092 Zurich, Switzerland
- Institute of Computational Sciences, Università della Svizzera Italiana, 6900 Lugano, Switzerland
| | - Michele Parrinello
- Atomistic Simulations, Italian Institute of Technology, via Morego 30, 16163 Genova, Italy
- Department of Chemistry and Applied Biosciences, ETH Zurich, 8092 Zurich, Switzerland
- Institute of Computational Sciences, Università della Svizzera Italiana, 6900 Lugano, Switzerland
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21
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Sidky H, Chen W, Ferguson AL. Machine learning for collective variable discovery and enhanced sampling in biomolecular simulation. Mol Phys 2020. [DOI: 10.1080/00268976.2020.1737742] [Citation(s) in RCA: 26] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Affiliation(s)
- Hythem Sidky
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, IL, USA
| | - Wei Chen
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL, USA
| | - Andrew L. Ferguson
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, IL, USA
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22
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Kieninger S, Donati L, Keller BG. Dynamical reweighting methods for Markov models. Curr Opin Struct Biol 2020; 61:124-131. [PMID: 31958761 DOI: 10.1016/j.sbi.2019.12.018] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/17/2019] [Revised: 12/13/2019] [Accepted: 12/26/2019] [Indexed: 12/21/2022]
Abstract
Conformational dynamics is essential to biomolecular processes. Markov State Models (MSMs) are widely used to elucidate dynamic properties of molecular systems from unbiased Molecular Dynamics (MD). However, the implementation of reweighting schemes for MSMs to analyze biased simulations is still at an early stage of development. Several dynamical reweighing approaches have been proposed, which can be classified as approaches based on (i) Kramers rate theory, (ii) rescaling of the probability density flux, (iii) reweighting by formulating a likelihood function, (iv) path reweighting. We present the state-of-the-art and discuss the methodological differences of these methods, their limitations and recent applications.
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Affiliation(s)
- Stefanie Kieninger
- Freie Universität Berlin, Department of Biology, Chemistry, Pharmacy, Arnimallee 22, D-14194 Berlin, Germany
| | - Luca Donati
- Freie Universität Berlin, Department of Biology, Chemistry, Pharmacy, Arnimallee 22, D-14194 Berlin, Germany
| | - Bettina G Keller
- Freie Universität Berlin, Department of Biology, Chemistry, Pharmacy, Arnimallee 22, D-14194 Berlin, Germany.
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23
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Bause M, Wittenstein T, Kremer K, Bereau T. Microscopic reweighting for nonequilibrium steady-state dynamics. Phys Rev E 2019; 100:060103. [PMID: 31962494 DOI: 10.1103/physreve.100.060103] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2019] [Indexed: 06/10/2023]
Abstract
Computer simulations generate trajectories at a single, well-defined thermodynamic state point. Statistical reweighting offers the means to reweight static and dynamical properties to different equilibrium state points by means of analytic relations. We extend these ideas to nonequilibrium steady states by relying on a maximum path entropy formalism subject to physical constraints. Stochastic thermodynamics analytically relates the forward and backward probabilities of any pathway through the external nonconservative force, enabling reweighting both in and out of equilibrium. We avoid the combinatorial explosion of microtrajectories by systematically constructing pathways through Markovian transitions. We further identify a quantity that is invariant to dynamical reweighting, analogous to the density of states in equilibrium reweighting.
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Affiliation(s)
- Marius Bause
- Max Planck Institute for Polymer Research, 55128 Mainz, Germany
| | | | - Kurt Kremer
- Max Planck Institute for Polymer Research, 55128 Mainz, Germany
| | - Tristan Bereau
- Max Planck Institute for Polymer Research, 55128 Mainz, Germany
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24
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Provasi D. Ligand-Binding Calculations with Metadynamics. METHODS IN MOLECULAR BIOLOGY (CLIFTON, N.J.) 2019; 2022:233-253. [PMID: 31396906 DOI: 10.1007/978-1-4939-9608-7_10] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
Abstract
All-atom molecular dynamics simulations can capture the dynamic degrees of freedom that characterize molecular recognition, the knowledge of which constitutes the cornerstone of rational approaches to drug design and optimization. In particular, enhanced sampling algorithms, such as metadynamics, are powerful tools to dramatically reduce the computational cost required for a mechanistic description of the binding process. Here, we describe the essential details characterizing these simulation strategies, focusing on the critical step of identifying suitable reaction coordinates, as well as on the different analysis algorithms to estimate binding affinity and residence times. We conclude with a survey of published applications that provides explicit examples of successful simulations for several targets.
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Affiliation(s)
- Davide Provasi
- Department of Pharmacological Sciences, Icahn School of Medicine at Mount Sinai, New York, NY, USA.
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25
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Ernst N, Fackeldey K, Volkamer A, Opatz O, Weber M. Computation of temperature-dependent dissociation rates of metastable protein–ligand complexes. MOLECULAR SIMULATION 2019. [DOI: 10.1080/08927022.2019.1610949] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
Affiliation(s)
- Natalia Ernst
- Numerical Analysis and Modelling, Zuse Institute Berlin (ZIB), Berlin, Germany
| | - Konstantin Fackeldey
- Numerical Analysis and Modelling, Zuse Institute Berlin (ZIB), Berlin, Germany
- Institute for Mathematics, Technical University Berlin (TUB), Berlin, Germany
| | - Andrea Volkamer
- In silico Toxicology Group, Institute of Physiology, Charité Universittsmedizin Berlin, Berlin, Germany
| | - Oliver Opatz
- Center for Space Medicine Berlin, Institute of Physiology, Charité Universittsmedizin Berlin, Berlin, Germany
| | - Marcus Weber
- Numerical Analysis and Modelling, Zuse Institute Berlin (ZIB), Berlin, Germany
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26
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Hruska E, Abella JR, Nüske F, Kavraki LE, Clementi C. Quantitative comparison of adaptive sampling methods for protein dynamics. J Chem Phys 2019; 149:244119. [PMID: 30599712 DOI: 10.1063/1.5053582] [Citation(s) in RCA: 33] [Impact Index Per Article: 6.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
Abstract
Adaptive sampling methods, often used in combination with Markov state models, are becoming increasingly popular for speeding up rare events in simulation such as molecular dynamics (MD) without biasing the system dynamics. Several adaptive sampling strategies have been proposed, but it is not clear which methods perform better for different physical systems. In this work, we present a systematic evaluation of selected adaptive sampling strategies on a wide selection of fast folding proteins. The adaptive sampling strategies were emulated using models constructed on already existing MD trajectories. We provide theoretical limits for the sampling speed-up and compare the performance of different strategies with and without using some a priori knowledge of the system. The results show that for different goals, different adaptive sampling strategies are optimal. In order to sample slow dynamical processes such as protein folding without a priori knowledge of the system, a strategy based on the identification of a set of metastable regions is consistently the most efficient, while a strategy based on the identification of microstates performs better if the goal is to explore newer regions of the conformational space. Interestingly, the maximum speed-up achievable for the adaptive sampling of slow processes increases for proteins with longer folding times, encouraging the application of these methods for the characterization of slower processes, beyond the fast-folding proteins considered here.
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Affiliation(s)
- Eugen Hruska
- Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, USA
| | - Jayvee R Abella
- Department of Computer Science, Rice University, Houston, Texas 77005, USA
| | - Feliks Nüske
- Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, USA
| | - Lydia E Kavraki
- Department of Computer Science, Rice University, Houston, Texas 77005, USA
| | - Cecilia Clementi
- Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, USA
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27
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Donati L, Heida M, Keller BG, Weber M. Estimation of the infinitesimal generator by square-root approximation. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:425201. [PMID: 30192232 DOI: 10.1088/1361-648x/aadfc8] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
In recent years, for the analysis of molecular processes, the estimation of time-scales and transition rates has become fundamental. Estimating the transition rates between molecular conformations is-from a mathematical point of view-an invariant subspace projection problem. We present a method to project the infinitesimal generator acting on function space to a low-dimensional rate matrix. This projection can be performed in two steps. First, we discretize the conformational space in a Voronoi tessellation, then the transition rates between adjacent cells is approximated by the geometric average of the Boltzmann weights of the Voronoi cells. This method demonstrates that there is a direct relation between the potential energy surface of molecular structures and the transition rates of conformational changes. We will show also that this approximation is correct and converges to the generator of the Smoluchowski equation in the limit of infinitely small Voronoi cells. We present results for a two dimensional diffusion process and alanine dipeptide as a high-dimensional system.
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Affiliation(s)
- Luca Donati
- Department of Biology, Chemistry, Pharmacy, Freie Universität Berlin, Takustraße 3, 14195 Berlin, Germany
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28
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Fujisaki H, Moritsugu K, Matsunaga Y. Exploring Configuration Space and Path Space of Biomolecules Using Enhanced Sampling Techniques-Searching for Mechanism and Kinetics of Biomolecular Functions. Int J Mol Sci 2018; 19:E3177. [PMID: 30326661 PMCID: PMC6213965 DOI: 10.3390/ijms19103177] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/13/2018] [Revised: 10/10/2018] [Accepted: 10/11/2018] [Indexed: 01/07/2023] Open
Abstract
To understand functions of biomolecules such as proteins, not only structures but their conformational change and kinetics need to be characterized, but its atomistic details are hard to obtain both experimentally and computationally. Here, we review our recent computational studies using novel enhanced sampling techniques for conformational sampling of biomolecules and calculations of their kinetics. For efficiently characterizing the free energy landscape of a biomolecule, we introduce the multiscale enhanced sampling method, which uses a combined system of atomistic and coarse-grained models. Based on the idea of Hamiltonian replica exchange, we can recover the statistical properties of the atomistic model without any biases. We next introduce the string method as a path search method to calculate the minimum free energy pathways along a multidimensional curve in high dimensional space. Finally we introduce novel methods to calculate kinetics of biomolecules based on the ideas of path sampling: one is the Onsager⁻Machlup action method, and the other is the weighted ensemble method. Some applications of the above methods to biomolecular systems are also discussed and illustrated.
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Grants
- JPMJPR1679 Japan Science and Technology Agency
- 16K00059 Ministry of Education, Culture, Sports, Science and Technology
- 17KT0101 Ministry of Education, Culture, Sports, Science and Technology
- 25840060 Ministry of Education, Culture, Sports, Science and Technology
- 15K18520 Ministry of Education, Culture, Sports, Science and Technology
- JP18am0101109 Japan Agency for Medical Research and Development
- 17gm0810012h0001 Japan Agency for Medical Research and Development
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Affiliation(s)
- Hiroshi Fujisaki
- Department of Physics, Nippon Medical School, 1-7-1 Kyonan-cho, Musashino, Tokyo 180-0023, Japan.
- AMED-CREST, Japan Agency for Medical Research and Development, 1-1-5 Sendagi, Bunkyo-ku, Tokyo 113-8603, Japan.
| | - Kei Moritsugu
- Graduate School of Medical Life Science, Yokohama City University, 1-7-29 Suehiro-cho, Tsurumi-ku, Yokohama 230-0045, Japan.
| | - Yasuhiro Matsunaga
- RIKEN Center for Computational Science, 7-1-26 Minatojima-minamimachi, Chuo-ku, Kobe, Hyogo 650-0047, Japan.
- JST PRESTO, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan.
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29
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Kells A, Annibale A, Rosta E. Limiting relaxation times from Markov state models. J Chem Phys 2018; 149:072324. [DOI: 10.1063/1.5027203] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
Affiliation(s)
- Adam Kells
- Department of Chemistry, King’s College London, SE1 1DB London, United Kingdom
| | - Alessia Annibale
- Department of Mathematics, King’s College London, WC2R 2LS London, United Kingdom
| | - Edina Rosta
- Department of Chemistry, King’s College London, SE1 1DB London, United Kingdom
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30
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Donati L, Keller BG. Girsanov reweighting for metadynamics simulations. J Chem Phys 2018; 149:072335. [DOI: 10.1063/1.5027728] [Citation(s) in RCA: 34] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023] Open
Affiliation(s)
- Luca Donati
- Department of Biology, Chemistry, Pharmacy, Freie Universität Berlin, Takustraße 3, D-14195 Berlin, Germany
| | - Bettina G. Keller
- Department of Biology, Chemistry, Pharmacy, Freie Universität Berlin, Takustraße 3, D-14195 Berlin, Germany
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31
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Sadeghi M, Weikl TR, Noé F. Particle-based membrane model for mesoscopic simulation of cellular dynamics. J Chem Phys 2018; 148:044901. [PMID: 29390800 DOI: 10.1063/1.5009107] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022] Open
Abstract
We present a simple and computationally efficient coarse-grained and solvent-free model for simulating lipid bilayer membranes. In order to be used in concert with particle-based reaction-diffusion simulations, the model is purely based on interacting and reacting particles, each representing a coarse patch of a lipid monolayer. Particle interactions include nearest-neighbor bond-stretching and angle-bending and are parameterized so as to reproduce the local membrane mechanics given by the Helfrich energy density over a range of relevant curvatures. In-plane fluidity is implemented with Monte Carlo bond-flipping moves. The physical accuracy of the model is verified by five tests: (i) Power spectrum analysis of equilibrium thermal undulations is used to verify that the particle-based representation correctly captures the dynamics predicted by the continuum model of fluid membranes. (ii) It is verified that the input bending stiffness, against which the potential parameters are optimized, is accurately recovered. (iii) Isothermal area compressibility modulus of the membrane is calculated and is shown to be tunable to reproduce available values for different lipid bilayers, independent of the bending rigidity. (iv) Simulation of two-dimensional shear flow under a gravity force is employed to measure the effective in-plane viscosity of the membrane model and show the possibility of modeling membranes with specified viscosities. (v) Interaction of the bilayer membrane with a spherical nanoparticle is modeled as a test case for large membrane deformations and budding involved in cellular processes such as endocytosis. The results are shown to coincide well with the predicted behavior of continuum models, and the membrane model successfully mimics the expected budding behavior. We expect our model to be of high practical usability for ultra coarse-grained molecular dynamics or particle-based reaction-diffusion simulations of biological systems.
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Affiliation(s)
- Mohsen Sadeghi
- Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
| | - Thomas R Weikl
- Department of Theory and Bio-Systems, Max Planck Institute of Colloids and Interfaces, Science Park Golm, 14424 Potsdam, Germany
| | - Frank Noé
- Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
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32
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Affiliation(s)
- Brooke E. Husic
- Department of Chemistry, Stanford University, Stanford, California 94305, United States
| | - Vijay S. Pande
- Department of Chemistry, Stanford University, Stanford, California 94305, United States
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33
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Lie HC, Quer J. Some connections between importance sampling and enhanced sampling methods in molecular dynamics. J Chem Phys 2017; 147:194107. [DOI: 10.1063/1.4989495] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022] Open
Affiliation(s)
- H. C. Lie
- Zuse Institut Berlin, Takustrasse 7, 14195 Berlin, Germany
- Institut für Mathematik, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
| | - J. Quer
- Zuse Institut Berlin, Takustrasse 7, 14195 Berlin, Germany
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