1
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Aristoff D, Johnson M, Simpson G, Webber RJ. The fast committor machine: Interpretable prediction with kernels. J Chem Phys 2024; 161:084113. [PMID: 39193940 DOI: 10.1063/5.0222798] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/10/2024] [Accepted: 08/07/2024] [Indexed: 08/29/2024] Open
Abstract
In the study of stochastic systems, the committor function describes the probability that a system starting from an initial configuration x will reach a set B before a set A. This paper introduces an efficient and interpretable algorithm for approximating the committor, called the "fast committor machine" (FCM). The FCM uses simulated trajectory data to build a kernel-based model of the committor. The kernel function is constructed to emphasize low-dimensional subspaces that optimally describe the A to B transitions. The coefficients in the kernel model are determined using randomized linear algebra, leading to a runtime that scales linearly with the number of data points. In numerical experiments involving a triple-well potential and alanine dipeptide, the FCM yields higher accuracy and trains more quickly than a neural network with the same number of parameters. The FCM is also more interpretable than the neural net.
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Affiliation(s)
- David Aristoff
- Mathematics, Colorado State University, Fort Collins, Colorado 80523, USA
| | - Mats Johnson
- Mathematics, Colorado State University, Fort Collins, Colorado 80523, USA
| | - Gideon Simpson
- Mathematics, Drexel University, Philadelphia, Pennsylvania 19104, USA
| | - Robert J Webber
- Mathematics, University of California San Diego, La Jolla, California 92093, USA
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2
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Singh AN, Limmer DT. Splitting probabilities as optimal controllers of rare reactive events. J Chem Phys 2024; 161:054113. [PMID: 39101534 DOI: 10.1063/5.0203840] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2024] [Accepted: 07/10/2024] [Indexed: 08/06/2024] Open
Abstract
The committor constitutes the primary quantity of interest within chemical kinetics as it is understood to encode the ideal reaction coordinate for a rare reactive event. We show the generative utility of the committor in that it can be used explicitly to produce a reactive trajectory ensemble that exhibits numerically exact statistics as that of the original transition path ensemble. This is done by relating a time-dependent analog of the committor that solves a generalized bridge problem to the splitting probability that solves a boundary value problem under a bistable assumption. By invoking stochastic optimal control and spectral theory, we derive a general form for the optimal controller of a bridge process that connects two metastable states expressed in terms of the splitting probability. This formalism offers an alternative perspective into the role of the committor and its gradients in that they encode force fields that guarantee reactivity, generating trajectories that are statistically identical to the way that a system would react autonomously.
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Affiliation(s)
- Aditya N Singh
- Department of Chemistry, University of California, Berkeley, California 94720, USA
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - David T Limmer
- Department of Chemistry, University of California, Berkeley, California 94720, USA
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
- Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
- Kavli Energy Nanoscience Institute at Berkeley, Berkeley, California 94720, USA
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3
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Fu H, Bian H, Shao X, Cai W. Collective Variable-Based Enhanced Sampling: From Human Learning to Machine Learning. J Phys Chem Lett 2024; 15:1774-1783. [PMID: 38329095 DOI: 10.1021/acs.jpclett.3c03542] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/09/2024]
Abstract
Enhanced-sampling algorithms relying on collective variables (CVs) are extensively employed to study complex (bio)chemical processes that are not amenable to brute-force molecular simulations. The selection of appropriate CVs characterizing the slow movement modes is of paramount importance for reliable and efficient enhanced-sampling simulations. In this Perspective, we first review the application and limitations of CVs obtained from chemical and geometrical intuition. We also introduce path-sampling algorithms, which can identify path-like CVs in a high-dimensional free-energy space. Machine-learning algorithms offer a viable approach to finding suitable CVs by analyzing trajectories from preliminary simulations. We discuss both the performance of machine-learning-derived CVs in enhanced-sampling simulations of experimental models and the challenges involved in applying these CVs to realistic, complex molecular assemblies. Moreover, we provide a prospective view of the potential advancements of machine-learning algorithms for the development of CVs in the field of enhanced-sampling simulations.
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Affiliation(s)
- Haohao Fu
- Research Center for Analytical Sciences, Frontiers Science Center for New Organic Matter, College of Chemistry, Nankai University, Tianjin Key Laboratory of Biosensing and Molecular Recognition, State Key Laboratory of Medicinal Chemical Biology, Tianjin 300071, China
- Haihe Laboratory of Sustainable Chemical Transformations, Tianjin 300192, China
| | - Hengwei Bian
- Research Center for Analytical Sciences, Frontiers Science Center for New Organic Matter, College of Chemistry, Nankai University, Tianjin Key Laboratory of Biosensing and Molecular Recognition, State Key Laboratory of Medicinal Chemical Biology, Tianjin 300071, China
- Haihe Laboratory of Sustainable Chemical Transformations, Tianjin 300192, China
| | - Xueguang Shao
- Research Center for Analytical Sciences, Frontiers Science Center for New Organic Matter, College of Chemistry, Nankai University, Tianjin Key Laboratory of Biosensing and Molecular Recognition, State Key Laboratory of Medicinal Chemical Biology, Tianjin 300071, China
- Haihe Laboratory of Sustainable Chemical Transformations, Tianjin 300192, China
| | - Wensheng Cai
- Research Center for Analytical Sciences, Frontiers Science Center for New Organic Matter, College of Chemistry, Nankai University, Tianjin Key Laboratory of Biosensing and Molecular Recognition, State Key Laboratory of Medicinal Chemical Biology, Tianjin 300071, China
- Haihe Laboratory of Sustainable Chemical Transformations, Tianjin 300192, China
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4
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Lazzeri G, Jung H, Bolhuis PG, Covino R. Molecular Free Energies, Rates, and Mechanisms from Data-Efficient Path Sampling Simulations. J Chem Theory Comput 2023; 19:9060-9076. [PMID: 37988412 PMCID: PMC10753783 DOI: 10.1021/acs.jctc.3c00821] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/28/2023] [Revised: 10/24/2023] [Accepted: 10/24/2023] [Indexed: 11/23/2023]
Abstract
Molecular dynamics is a powerful tool for studying the thermodynamics and kinetics of complex molecular events. However, these simulations can rarely sample the required time scales in practice. Transition path sampling overcomes this limitation by collecting unbiased trajectories and capturing the relevant events. Moreover, the integration of machine learning can boost the sampling while simultaneously learning a quantitative representation of the mechanism. Still, the resulting trajectories are by construction non-Boltzmann-distributed, preventing the calculation of free energies and rates. We developed an algorithm to approximate the equilibrium path ensemble from machine-learning-guided path sampling data. At the same time, our algorithm provides efficient sampling, mechanism, free energy, and rates of rare molecular events at a very moderate computational cost. We tested the method on the folding of the mini-protein chignolin. Our algorithm is straightforward and data-efficient, opening the door to applications in many challenging molecular systems.
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Affiliation(s)
- Gianmarco Lazzeri
- Frankfurt
Institute for Advanced Studies, Frankfurt am Main, 60438, Germany
- Goethe
University Frankfurt, Frankfurt
am Main, 60438, Germany
| | - Hendrik Jung
- Goethe
University Frankfurt, Frankfurt
am Main, 60438, Germany
- Department
of Theoretical Biophysics, Max Planck Institute
of Biophysics, Frankfurt
am Main, 60438, Germany
| | - Peter G. Bolhuis
- Van’t
Hoff Institute for Molecular Sciences, University
of Amsterdam, Amsterdam, 1090GD, The Netherlands
| | - Roberto Covino
- Frankfurt
Institute for Advanced Studies, Frankfurt am Main, 60438, Germany
- Goethe
University Frankfurt, Frankfurt
am Main, 60438, Germany
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5
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Antoniou D, Zoi I, Schwartz SD. Atomistic description of the relationship between protein dynamics and catalysis with transition path sampling. Methods Enzymol 2023; 685:319-340. [PMID: 37245906 PMCID: PMC10228753 DOI: 10.1016/bs.mie.2023.03.005] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
Despite initial resistance, it has been increasingly accepted that protein dynamics plays a role in enzymatic catalysis. There have been two lines of research. Some works study slow conformational motions that are not coupled to the reaction coordinate, but guide the system towards catalytically competent conformations. Understanding at the atomistic level how this is accomplished has remained elusive except for a few systems. In this review we focus on fast sub-picosecond motions that are coupled to the reaction coordinate. The use of Transition Path Sampling has allowed us an atomistic description of how these rate-promoting vibrational motions are incorporated in the reaction mechanism. We will also show how we used insights from rate-promoting motions in protein design.
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Affiliation(s)
- Dimitri Antoniou
- Department of Biochemistry, University of Arizona, Tucson, AZ, United States
| | - Ioanna Zoi
- Department of Biochemistry, University of Arizona, Tucson, AZ, United States
| | - Steven D Schwartz
- Department of Biochemistry, University of Arizona, Tucson, AZ, United States.
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6
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Reiner M, Bachmair B, Tiefenbacher MX, Mai S, González L, Marquetand P, Dellago C. Nonadiabatic Forward Flux Sampling for Excited-State Rare Events. J Chem Theory Comput 2023; 19:1657-1671. [PMID: 36856706 PMCID: PMC10061683 DOI: 10.1021/acs.jctc.2c01088] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/01/2022] [Indexed: 03/02/2023]
Abstract
We present a rare event sampling scheme applicable to coupled electronic excited states. In particular, we extend the forward flux sampling (FFS) method for rare event sampling to a nonadiabatic version (NAFFS) that uses the trajectory surface hopping (TSH) method for nonadiabatic dynamics. NAFFS is applied to two dynamically relevant excited-state models that feature an avoided crossing and a conical intersection with tunable parameters. We investigate how nonadiabatic couplings, temperature, and reaction barriers affect transition rate constants in regimes that cannot be otherwise obtained with plain, traditional TSH. The comparison with reference brute-force TSH simulations for limiting cases of rareness shows that NAFFS can be several orders of magnitude cheaper than conventional TSH and thus represents a conceptually novel tool to extend excited-state dynamics to time scales that are able to capture rare nonadiabatic events.
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Affiliation(s)
- Madlen
Maria Reiner
- Research
Platform on Accelerating Photoreaction Discovery (ViRAPID), University of Vienna, Währinger Strasse 17, 1090 Vienna, Austria
- Vienna
Doctoral School in Physics, University of
Vienna, Boltzmanngasse
5, 1090 Vienna, Austria
| | - Brigitta Bachmair
- Research
Platform on Accelerating Photoreaction Discovery (ViRAPID), University of Vienna, Währinger Strasse 17, 1090 Vienna, Austria
- Vienna
Doctoral School in Chemistry, University
of Vienna, Währinger
Strasse 42, 1090 Vienna, Austria
| | - Maximilian Xaver Tiefenbacher
- Research
Platform on Accelerating Photoreaction Discovery (ViRAPID), University of Vienna, Währinger Strasse 17, 1090 Vienna, Austria
- Vienna
Doctoral School in Chemistry, University
of Vienna, Währinger
Strasse 42, 1090 Vienna, Austria
| | - Sebastian Mai
- Institute
of Theoretical Chemistry, Faculty of Chemistry, University of Vienna, Währinger Strasse 17, 1090 Vienna, Austria
| | - Leticia González
- Research
Platform on Accelerating Photoreaction Discovery (ViRAPID), University of Vienna, Währinger Strasse 17, 1090 Vienna, Austria
- Institute
of Theoretical Chemistry, Faculty of Chemistry, University of Vienna, Währinger Strasse 17, 1090 Vienna, Austria
| | - Philipp Marquetand
- Research
Platform on Accelerating Photoreaction Discovery (ViRAPID), University of Vienna, Währinger Strasse 17, 1090 Vienna, Austria
- Institute
of Theoretical Chemistry, Faculty of Chemistry, University of Vienna, Währinger Strasse 17, 1090 Vienna, Austria
| | - Christoph Dellago
- Research
Platform on Accelerating Photoreaction Discovery (ViRAPID), University of Vienna, Währinger Strasse 17, 1090 Vienna, Austria
- Faculty
of Physics, University of Vienna, Kolingasse 14-16, 1090 Vienna, Austria
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7
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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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8
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Lam J, Pietrucci F. Critical comparison of general-purpose collective variables for crystal nucleation. Phys Rev E 2023; 107:L012601. [PMID: 36797915 DOI: 10.1103/physreve.107.l012601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/25/2022] [Accepted: 01/06/2023] [Indexed: 06/18/2023]
Abstract
The nucleation of crystals is a prominent phenomenon in science and technology that still lacks a full atomic-scale understanding. Much work has been devoted to identifying order parameters able to track the process, from the inception of early nuclei to their maturing to critical size until growth of an extended crystal. We critically assess and compare two powerful distance-based collective variables, an effective entropy derived from liquid state theory and the path variable based on permutation invariant vectors using the Kob-Andersen binary mixture and a combination of enhanced-sampling techniques. Our findings reveal a comparable ability to drive nucleation when a bias potential is applied, and comparable free-energy barriers and structural features. Yet, we also found an imperfect correlation with the committor probability on the barrier top which was bypassed by changing the order parameter definition.
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Affiliation(s)
- Julien Lam
- CEMES, Centre National de la Recherche Scientifique and Université de Toulouse, 29 rue Jeanne Marvig, 31055 Toulouse Cedex, France
- Université Lille, Centre National de la Recherche Scientifique, INRA, ENSCL, UMR 8207, UMET, Unité Matériaux et Transformations, F 59000 Lille, France
| | - Fabio Pietrucci
- Sorbonne Université, Centre National de la Recherche Scientifique, UMR 7590, IMPMC, 75005 Paris, France
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9
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Abstract
This Perspective reviews the use of Transition Path Sampling methods to study enzymatically catalyzed chemical reactions. First applied by our group to an enzymatic reaction over 15 years ago, the method has uncovered basic principles in enzymatic catalysis such as the protein promoting vibration, and it has also helped harmonize such ideas as electrostatic preorganization with dynamic views of enzyme function. It is now being used to help uncover principles of protein design necessary to artificial enzyme creation.
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Affiliation(s)
- Steven D Schwartz
- Department of Chemistry and Biochemistry University of Arizona Tucson, Arizona 85721, United States
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10
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Sanchez-Burgos I, Tejedor AR, Vega C, Conde MM, Sanz E, Ramirez J, Espinosa JR. Homogeneous ice nucleation rates for mW and TIP4P/ICE models through Lattice Mold calculations. J Chem Phys 2022; 157:094503. [DOI: 10.1063/5.0101383] [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
Water freezing is the most common liquid-to-crystal phase transition on Earth, however, despite its critical implications on climate change and cryopreservation among other disciplines, its characterization through experimental and computational techniques remains elusive. In this work, we make use of computer simulations to measure the nucleation rate (J) of water at normal pressure under different supercooling conditions, ranging from 215 to 240K. We employ two different water models, mW, a coarse-grained potential for water, and TIP4P/ICE, an atomistic non-polarizable water model that provides one of the most accurate representations of the different ice phases. To evaluate J, we apply the Lattice Mold technique, a computational method based on the use of molds to induce the nucleus formation from the metastable liquid under conditions at which observing spontaneous nucleation would be unfeasible. With this method, we obtain estimates of the nucleation rate for ice Ih, Ic and a stacking mixture of ice Ih/Ic; reaching consensus with most of the previously reported rates, although differing with some others. Furthermore, we confirm that the predicted nucleation rates by the TIP4P/ICE model are in better agreement with experimental data than those obtained through the mW potential. Taken together, our study provides a reliable methodology to measure nucleation rates in a simple and computationally efficient manner which contributes to benchmarking the freezing behaviour of two popular water models.
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Affiliation(s)
| | | | - Carlos Vega
- Departamento de Quimica Fisica, Universidad Complutense de Madrid Facultad de Ciencias Químicas, Spain
| | - Maria M. Conde
- Universidad Politécnica de Madrid Escuela Técnica Superior de Ingenieros Industriales, Spain
| | | | - Jorge Ramirez
- Chemical Engineering, Universidad Politécnica de Madrid Escuela Técnica Superior de Ingenieros Industriales, Spain
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11
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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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12
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Antoniou D, Schwartz SD. Method for Identifying Common Features in Reactive Trajectories of a Transition Path Sampling Ensemble. J Chem Theory Comput 2022; 18:3997-4004. [PMID: 35536190 DOI: 10.1021/acs.jctc.2c00186] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Simulation methods like transition path sampling (TPS) generate an abundance of information buried in the collection of reactive trajectories that they generate. However, only limited use has been made of this information, mainly for the identification of the reaction coordinate. The standard TPS tools have been designed for monitoring the progress of the system from reactants to products. However, the reaction coordinate does not contain all the information regarding the mechanism. In our earlier work, we have used TPS on enzymatic systems and have identified important motions in the reactant well that prepares the system for the reaction. Since these events take place in the reactant well, they are beyond the reach of standard TPS postprocessing methods. We present a simple scheme for identifying the common trends in enzymatic trajectories. This scheme was designed for a specific class of enzymatic reactions: it can be used for identifying motions that guide the system to reaction-ready conformations. We have applied it to two enzymatic systems that we have studied in the past, formate dehydrogenase and purine nucleoside phosphorylase, and we were able to identify interactions, far from the transition state, that are important for preparing the system for the reaction but that had been overlooked in earlier work.
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Affiliation(s)
- Dimitri Antoniou
- Department of Chemistry and Biochemistry, University of Arizona, 1306 East University Blvd., Tucson, Arizona 85721, United States
| | - Steven D Schwartz
- Department of Chemistry and Biochemistry, University of Arizona, 1306 East University Blvd., Tucson, Arizona 85721, United States
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13
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Chen S, Peterson CW, Parker JA, Rice SA, Ferguson AL, Scherer NF. Data-driven reaction coordinate discovery in overdamped and non-conservative systems: application to optical matter structural isomerization. Nat Commun 2021; 12:2548. [PMID: 33953159 PMCID: PMC8099877 DOI: 10.1038/s41467-021-22794-w] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/21/2020] [Accepted: 03/22/2021] [Indexed: 11/09/2022] Open
Abstract
Optical matter (OM) systems consist of (nano-)particle constituents in solution that can self-organize into ordered arrays that are bound by electrodynamic interactions. They also manifest non-conservative forces, and the motions of the nano-particles are overdamped; i.e., they exhibit diffusive trajectories. We propose a data-driven approach based on principal components analysis (PCA) to determine the collective modes of non-conservative overdamped systems, such as OM structures, and harmonic linear discriminant analysis (HLDA) of time trajectories to estimate the reaction coordinate for structural transitions. We demonstrate the approach via electrodynamics-Langevin dynamics simulations of six electrodynamically-bound nanoparticles in an incident laser beam. The reaction coordinate we discover is in excellent accord with a rigorous committor analysis, and the identified mechanism for structural isomerization is in very good agreement with the experimental observations. The PCA-HLDA approach to data-driven discovery of reaction coordinates can aid in understanding and eventually controlling non-conservative and overdamped systems including optical and active matter systems.
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Affiliation(s)
- Shiqi Chen
- Department of Chemistry, University of Chicago, Chicago, IL, USA
- James Franck Institute, University of Chicago, Chicago, IL, USA
| | - Curtis W Peterson
- Department of Chemistry, University of Chicago, Chicago, IL, USA
- James Franck Institute, University of Chicago, Chicago, IL, USA
| | - John A Parker
- James Franck Institute, University of Chicago, Chicago, IL, USA
- Department of Physics, University of Chicago, Chicago, IL, USA
| | - Stuart A Rice
- Department of Chemistry, University of Chicago, Chicago, IL, USA
- James Franck Institute, University of Chicago, Chicago, IL, USA
| | - Andrew L Ferguson
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, IL, USA.
| | - Norbert F Scherer
- Department of Chemistry, University of Chicago, Chicago, IL, USA.
- James Franck Institute, University of Chicago, Chicago, IL, USA.
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14
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Bolhuis PG, Swenson DWH. Transition Path Sampling as Markov Chain Monte Carlo of Trajectories: Recent Algorithms, Software, Applications, and Future Outlook. ADVANCED THEORY AND SIMULATIONS 2021. [DOI: 10.1002/adts.202000237] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
Affiliation(s)
- Peter G. Bolhuis
- Amsterdam Center for Multiscale Modeling van 't Hoff Institute for Molecular Sciences University of Amsterdam PO Box 94157 1090 GD Amsterdam The Netherlands
| | - David W. H. Swenson
- Centre Blaise Pascal Ecole Normale Superieure 46, allée d'Italie 69364 Lyon Cedex 07 France
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15
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Peters BL, Deng J, Ferguson AL. Free energy calculations of the functional selectivity of 5-HT2B G protein-coupled receptor. PLoS One 2020; 15:e0243313. [PMID: 33296400 PMCID: PMC7725398 DOI: 10.1371/journal.pone.0243313] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/21/2020] [Accepted: 11/18/2020] [Indexed: 12/16/2022] Open
Abstract
G Protein-Coupled Receptors (GPCRs) mediate intracellular signaling in response to extracellular ligand binding and are the target of one-third of approved drugs. Ligand binding modulates the GPCR molecular free energy landscape by preferentially stabilizing active or inactive conformations that dictate intracellular protein recruitment and downstream signaling. We perform enhanced sampling molecular dynamics simulations to recover the free energy surfaces of a thermostable mutant of the GPCR serotonin receptor 5-HT2B in the unliganded form and bound to a lysergic acid diethylamide (LSD) agonist and lisuride antagonist. LSD binding imparts a ∼110 kJ/mol driving force for conformational rearrangement into an active state. The lisuride-bound form is structurally similar to the apo form and only ∼24 kJ/mol more stable. This work quantifies ligand-induced conformational specificity and functional selectivity of 5-HT2B and presents a platform for high-throughput virtual screening of ligands and rational engineering of the ligand-bound molecular free energy landscape.
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Affiliation(s)
- Brandon L. Peters
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois, United States of America
| | - Jinxia Deng
- Zoetis Inc, Kalamazoo, Michigan, United States of America
| | - Andrew L. Ferguson
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois, United States of America
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16
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Decherchi S, Cavalli A. Thermodynamics and Kinetics of Drug-Target Binding by Molecular Simulation. Chem Rev 2020; 120:12788-12833. [PMID: 33006893 PMCID: PMC8011912 DOI: 10.1021/acs.chemrev.0c00534] [Citation(s) in RCA: 127] [Impact Index Per Article: 31.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/28/2020] [Indexed: 12/19/2022]
Abstract
Computational studies play an increasingly important role in chemistry and biophysics, mainly thanks to improvements in hardware and algorithms. In drug discovery and development, computational studies can reduce the costs and risks of bringing a new medicine to market. Computational simulations are mainly used to optimize promising new compounds by estimating their binding affinity to proteins. This is challenging due to the complexity of the simulated system. To assess the present and future value of simulation for drug discovery, we review key applications of advanced methods for sampling complex free-energy landscapes at near nonergodicity conditions and for estimating the rate coefficients of very slow processes of pharmacological interest. We outline the statistical mechanics and computational background behind this research, including methods such as steered molecular dynamics and metadynamics. We review recent applications to pharmacology and drug discovery and discuss possible guidelines for the practitioner. Recent trends in machine learning are also briefly discussed. Thanks to the rapid development of methods for characterizing and quantifying rare events, simulation's role in drug discovery is likely to expand, making it a valuable complement to experimental and clinical approaches.
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Affiliation(s)
- Sergio Decherchi
- Computational
and Chemical Biology, Fondazione Istituto
Italiano di Tecnologia, 16163 Genoa, Italy
| | - Andrea Cavalli
- Computational
and Chemical Biology, Fondazione Istituto
Italiano di Tecnologia, 16163 Genoa, Italy
- Department
of Pharmacy and Biotechnology, University
of Bologna, 40126 Bologna, Italy
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17
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Sawato T, Yamaguchi M. Synthetic Chemical Systems Involving Self‐Catalytic Reactions of Helicene Oligomer Foldamers. Chempluschem 2020; 85:2017-2038. [DOI: 10.1002/cplu.202000489] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/24/2020] [Revised: 08/18/2020] [Indexed: 12/15/2022]
Affiliation(s)
- Tsukasa Sawato
- Department of Organic Chemistry Graduate School of Pharmaceutical Sciences Tohoku University Aoba Sendai 980-8578 Japan
| | - Masahiko Yamaguchi
- State Key Laboratory of Fine Chemicals Dalian University of Technology Dalian 116024 China
- Department of Organic Chemistry Graduate School of Pharmaceutical Sciences Tohoku University Aoba Sendai 980-8578 Japan
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18
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Hussain S, Haji-Akbari A. Studying rare events using forward-flux sampling: Recent breakthroughs and future outlook. J Chem Phys 2020; 152:060901. [DOI: 10.1063/1.5127780] [Citation(s) in RCA: 27] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Sarwar Hussain
- Department of Chemical and Environmental Engineering, Yale University, New Haven, Connecticut 06520, USA
| | - Amir Haji-Akbari
- Department of Chemical and Environmental Engineering, Yale University, New Haven, Connecticut 06520, USA
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19
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Klein MC, Roberts E. Automatic error control during forward flux sampling of rare events in master equation models. J Chem Phys 2020; 152:035102. [PMID: 31968949 DOI: 10.1063/1.5129461] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Enhanced sampling methods, such as forward flux sampling (FFS), have great capacity for accelerating stochastic simulations of nonequilibrium biochemical systems involving rare events. However, the description of the tradeoffs between simulation efficiency and error in FFS remains incomplete. We present a novel and mathematically rigorous analysis of the errors in FFS that, for the first time, covers the contribution of every phase of the simulation. We derive a closed form expression for the optimally efficient count of samples to take in each FFS phase in terms of a fixed constraint on sampling error. We introduce a new method, forward flux pilot sampling (FFPilot), that is designed to take full advantage of our optimizing equation without prior information or assumptions about the phase weights and costs along the transition path. In simulations of both single and multidimensional gene regulatory networks, FFPilot is able to completely control sampling error. We then discuss how memory effects can introduce additional error when relaxation along the transition path is slow. This extra error can be traced to correlations between the FFS phases and can be controlled by monitoring the covariance between them. Finally, we show that, in sets of simulations with matched error, FFPilot is on the order of tens-to-hundreds of times faster than direct sampling and noticeably more efficient than previous FFS methods.
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Affiliation(s)
- Max C Klein
- Department of Biophysics, Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Elijah Roberts
- Department of Biophysics, Johns Hopkins University, Baltimore, Maryland 21218, USA
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20
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Nowak C, Misra M, Escobedo FA. Framework for Inverse Mapping Chemistry-Agnostic Coarse-Grained Simulation Models into Chemistry-Specific Models. J Chem Inf Model 2019; 59:5045-5056. [DOI: 10.1021/acs.jcim.9b00232] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
Affiliation(s)
- Christian Nowak
- School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, New York 14853, United States
| | - Mayank Misra
- School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, New York 14853, United States
| | - Fernando A. Escobedo
- School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, New York 14853, United States
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21
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Abstract
The kinetics of drug binding and unbinding is assuming an increasingly crucial role in the long, costly process of bringing a new medicine to patients. For example, the time a drug spends in contact with its biological target is known as residence time (the inverse of the kinetic constant of the drug-target unbinding, 1/ koff). Recent reports suggest that residence time could predict drug efficacy in vivo, perhaps even more effectively than conventional thermodynamic parameters (free energy, enthalpy, entropy). There are many experimental and computational methods for predicting drug-target residence time at an early stage of drug discovery programs. Here, we review and discuss the methodological approaches to estimating drug binding kinetics and residence time. We first introduce the theoretical background of drug binding kinetics from a physicochemical standpoint. We then analyze the recent literature in the field, starting from the experimental methodologies and applications thereof and moving to theoretical and computational approaches to the kinetics of drug binding and unbinding. We acknowledge the central role of molecular dynamics and related methods, which comprise a great number of the computational methods and applications reviewed here. However, we also consider kinetic Monte Carlo. We conclude with the outlook that drug (un)binding kinetics may soon become a go/no go step in the discovery and development of new medicines.
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Affiliation(s)
- Mattia Bernetti
- Department of Pharmacy and Biotechnology, University of Bologna, I-40126 Bologna, Italy
| | - Matteo Masetti
- Department of Pharmacy and Biotechnology, University of Bologna, I-40126 Bologna, Italy
| | - Walter Rocchia
- CONCEPT Laboratory, Istituto Italiano di Tecnologia, I-16163 Genova, Italy
| | - Andrea Cavalli
- Department of Pharmacy and Biotechnology, University of Bologna, I-40126 Bologna, Italy
- Computational Sciences Domain, Istituto Italiano di Tecnologia, I-16163 Genova, Italy
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22
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Wang F, Orioli S, Ianeselli A, Spagnolli G, A Beccara S, Gershenson A, Faccioli P, Wintrode PL. All-Atom Simulations Reveal How Single-Point Mutations Promote Serpin Misfolding. Biophys J 2019; 114:2083-2094. [PMID: 29742402 DOI: 10.1016/j.bpj.2018.03.027] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/21/2017] [Revised: 03/09/2018] [Accepted: 03/13/2018] [Indexed: 10/17/2022] Open
Abstract
Protein misfolding is implicated in many diseases, including serpinopathies. For the canonical inhibitory serpin α1-antitrypsin, mutations can result in protein deficiencies leading to lung disease, and misfolded mutants can accumulate in hepatocytes, leading to liver disease. Using all-atom simulations based on the recently developed bias functional algorithm, we elucidate how wild-type α1-antitrypsin folds and how the disease-associated S (Glu264Val) and Z (Glu342Lys) mutations lead to misfolding. The deleterious Z mutation disrupts folding at an early stage, whereas the relatively benign S mutant shows late-stage minor misfolding. A number of suppressor mutations ameliorate the effects of the Z mutation, and simulations on these mutants help to elucidate the relative roles of steric clashes and electrostatic interactions in Z misfolding. These results demonstrate a striking correlation between atomistic events and disease severity and shine light on the mechanisms driving chains away from their correct folding routes.
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Affiliation(s)
- Fang Wang
- Department of Pharmaceutical Sciences, University of Maryland School of Pharmacy, Baltimore, Maryland
| | - Simone Orioli
- Dipartimento di Fisica, Università degli Studi di Trento, Povo (Trento), Italy; Trento Institute for Fundamental Physics and Applications, Povo (Trento), Italy
| | - Alan Ianeselli
- Dipartimento di Fisica, Università degli Studi di Trento, Povo (Trento), Italy; Trento Institute for Fundamental Physics and Applications, Povo (Trento), Italy
| | - Giovanni Spagnolli
- Dipartimento di Fisica, Università degli Studi di Trento, Povo (Trento), Italy; Trento Institute for Fundamental Physics and Applications, Povo (Trento), Italy
| | - Silvio A Beccara
- Dipartimento di Fisica, Università degli Studi di Trento, Povo (Trento), Italy; Trento Institute for Fundamental Physics and Applications, Povo (Trento), Italy
| | - Anne Gershenson
- Department of Biochemistry and Molecular Biology, University of Massachusetts Amherst, Amherst, Massachusetts.
| | - Pietro Faccioli
- Dipartimento di Fisica, Università degli Studi di Trento, Povo (Trento), Italy; Trento Institute for Fundamental Physics and Applications, Povo (Trento), Italy.
| | - Patrick L Wintrode
- Department of Pharmaceutical Sciences, University of Maryland School of Pharmacy, Baltimore, Maryland.
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23
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Dämgen MA, Biggin PC. Computational methods to examine conformational changes and ligand-binding properties: Examples in neurobiology. Neurosci Lett 2019. [DOI: 10.1016/j.neulet.2018.03.004] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
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24
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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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25
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Ribeiro JML, Tsai ST, Pramanik D, Wang Y, Tiwary P. Kinetics of Ligand-Protein Dissociation from All-Atom Simulations: Are We There Yet? Biochemistry 2018; 58:156-165. [PMID: 30547565 DOI: 10.1021/acs.biochem.8b00977] [Citation(s) in RCA: 32] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
Abstract
Large parallel gains in the development of both computational resources and sampling methods have now made it possible to simulate dissociation events in ligand-protein complexes with all-atom resolution. Such encouraging progress, together with the inherent spatiotemporal resolution associated with molecular simulations, has left their use for investigating dissociation processes brimming with potential, both in rational drug design, where it can be an invaluable tool for determining the mechanistic driving forces behind dissociation rate constants, and in force-field development, where it can provide a catalog of transient molecular structures with which to refine force fields. Although much progress has been made in making force fields more accurate, reducing their error for transient structures along a transition path could yet prove to be a critical development helping to make kinetic predictions much more accurate. In what follows, we will provide a state-of-the-art compilation of the enhanced sampling methods based on molecular dynamics (MD) simulations used to investigate the kinetics and mechanisms of ligand-protein dissociation processes. Due to the time scales of such processes being slower than what is accessible using straightforward MD simulations, several ingenious schemes are being devised at a rapid rate to overcome this obstacle. Here we provide an up-to-date compendium of such methods and their achievements and shortcomings in extracting mechanistic insight into ligand-protein dissociation. We conclude with a critical and provocative appraisal attempting to answer the title of this Perspective.
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Affiliation(s)
- João Marcelo Lamim Ribeiro
- Department of Chemistry and Biochemistry , University of Maryland , College Park , Maryland 20742 , United States.,Institute for Physical Science and Technology , University of Maryland , College Park , Maryland 20742 , United States
| | - Sun-Ting Tsai
- Institute for Physical Science and Technology , University of Maryland , College Park , Maryland 20742 , United States.,Department of Physics , University of Maryland , College Park , Maryland 20742 , United States
| | - Debabrata Pramanik
- Department of Chemistry and Biochemistry , University of Maryland , College Park , Maryland 20742 , United States.,Institute for Physical Science and Technology , University of Maryland , College Park , Maryland 20742 , United States
| | - Yihang Wang
- Institute for Physical Science and Technology , University of Maryland , College Park , Maryland 20742 , United States.,Biophysics Program , University of Maryland , College Park , Maryland 20742 , United States
| | - Pratyush Tiwary
- Department of Chemistry and Biochemistry , University of Maryland , College Park , Maryland 20742 , United States.,Institute for Physical Science and Technology , University of Maryland , College Park , Maryland 20742 , United States
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26
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Bacci M, Langini C, Vymětal J, Caflisch A, Vitalis A. Focused conformational sampling in proteins. J Chem Phys 2018; 147:195102. [PMID: 29166086 DOI: 10.1063/1.4996879] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2023] Open
Abstract
A detailed understanding of the conformational dynamics of biological molecules is difficult to obtain by experimental techniques due to resolution limitations in both time and space. Computer simulations avoid these in theory but are often too short to sample rare events reliably. Here we show that the progress index-guided sampling (PIGS) protocol can be used to enhance the sampling of rare events in selected parts of biomolecules without perturbing the remainder of the system. The method is very easy to use as it only requires as essential input a set of several features representing the parts of interest sufficiently. In this feature space, new states are discovered by spontaneous fluctuations alone and in unsupervised fashion. Because there are no energetic biases acting on phase space variables or projections thereof, the trajectories PIGS generates can be analyzed directly in the framework of transition networks. We demonstrate the possibility and usefulness of such focused explorations of biomolecules with two loops that are part of the binding sites of bromodomains, a family of epigenetic "reader" modules. This real-life application uncovers states that are structurally and kinetically far away from the initial crystallographic structures and are also metastable. Representative conformations are intended to be used in future high-throughput virtual screening campaigns.
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Affiliation(s)
- Marco Bacci
- Department of Biochemistry, University of Zurich, Winterthurerstrasse 190, CH-8057 Zurich, Switzerland
| | - Cassiano Langini
- Department of Biochemistry, University of Zurich, Winterthurerstrasse 190, CH-8057 Zurich, Switzerland
| | - Jiří Vymětal
- Department of Biochemistry, University of Zurich, Winterthurerstrasse 190, CH-8057 Zurich, Switzerland
| | - Amedeo Caflisch
- Department of Biochemistry, University of Zurich, Winterthurerstrasse 190, CH-8057 Zurich, Switzerland
| | - Andreas Vitalis
- Department of Biochemistry, University of Zurich, Winterthurerstrasse 190, CH-8057 Zurich, Switzerland
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27
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Bhattacharya S, Xu L, Thompson D. Revisiting the earliest signatures of amyloidogenesis: Roadmaps emerging from computational modeling and experiment. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2018. [DOI: 10.1002/wcms.1359] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/31/2023]
Affiliation(s)
- Shayon Bhattacharya
- Department of Physics, Bernal InstituteUniversity of LimerickLimerickIreland
| | - Liang Xu
- Department of Physics, Bernal InstituteUniversity of LimerickLimerickIreland
| | - Damien Thompson
- Department of Physics, Bernal InstituteUniversity of LimerickLimerickIreland
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28
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Sidky H, Colón YJ, Helfferich J, Sikora BJ, Bezik C, Chu W, Giberti F, Guo AZ, Jiang X, Lequieu J, Li J, Moller J, Quevillon MJ, Rahimi M, Ramezani-Dakhel H, Rathee VS, Reid DR, Sevgen E, Thapar V, Webb MA, Whitmer JK, de Pablo JJ. SSAGES: Software Suite for Advanced General Ensemble Simulations. J Chem Phys 2018; 148:044104. [DOI: 10.1063/1.5008853] [Citation(s) in RCA: 65] [Impact Index Per Article: 10.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2023] Open
Affiliation(s)
- Hythem Sidky
- Department of Chemical and Biomolecular Engineering, University of Notre Dame, Notre Dame, Indiana 46556, USA
| | - Yamil J. Colón
- Institute for Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA
- Institute for Molecular Engineering and Materials Science Division, Argonne National Laboratory, Lemont, Illinois 60439, USA
| | - Julian Helfferich
- Institute for Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA
- Steinbuch Center for Computing, Karlsruhe Institute of Technology, Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Germany
| | - Benjamin J. Sikora
- Department of Chemical and Biomolecular Engineering, University of Notre Dame, Notre Dame, Indiana 46556, USA
| | - Cody Bezik
- Institute for Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA
| | - Weiwei Chu
- Institute for Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA
| | - Federico Giberti
- Institute for Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA
| | - Ashley Z. Guo
- Institute for Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA
| | - Xikai Jiang
- Institute for Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA
| | - Joshua Lequieu
- Institute for Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA
| | - Jiyuan Li
- Institute for Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA
| | - Joshua Moller
- Institute for Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA
| | - Michael J. Quevillon
- Department of Chemical and Biomolecular Engineering, University of Notre Dame, Notre Dame, Indiana 46556, USA
| | - Mohammad Rahimi
- Institute for Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA
| | - Hadi Ramezani-Dakhel
- Institute for Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA
- Department of Biochemistry and Molecular Biology, University of Chicago, Chicago, Illinois 60637, USA
| | - Vikramjit S. Rathee
- Department of Chemical and Biomolecular Engineering, University of Notre Dame, Notre Dame, Indiana 46556, USA
| | - Daniel R. Reid
- Institute for Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA
| | - Emre Sevgen
- Institute for Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA
| | - Vikram Thapar
- Institute for Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA
| | - Michael A. Webb
- Institute for Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA
- Institute for Molecular Engineering and Materials Science Division, Argonne National Laboratory, Lemont, Illinois 60439, USA
| | - Jonathan K. Whitmer
- Department of Chemical and Biomolecular Engineering, University of Notre Dame, Notre Dame, Indiana 46556, USA
| | - Juan J. de Pablo
- Institute for Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA
- Institute for Molecular Engineering and Materials Science Division, Argonne National Laboratory, Lemont, Illinois 60439, USA
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29
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Gooneie A, Schuschnigg S, Holzer C. A Review of Multiscale Computational Methods in Polymeric Materials. Polymers (Basel) 2017; 9:E16. [PMID: 30970697 PMCID: PMC6432151 DOI: 10.3390/polym9010016] [Citation(s) in RCA: 86] [Impact Index Per Article: 12.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/20/2016] [Revised: 12/07/2016] [Accepted: 12/22/2016] [Indexed: 11/17/2022] Open
Abstract
Polymeric materials display distinguished characteristics which stem from the interplay of phenomena at various length and time scales. Further development of polymer systems critically relies on a comprehensive understanding of the fundamentals of their hierarchical structure and behaviors. As such, the inherent multiscale nature of polymer systems is only reflected by a multiscale analysis which accounts for all important mechanisms. Since multiscale modelling is a rapidly growing multidisciplinary field, the emerging possibilities and challenges can be of a truly diverse nature. The present review attempts to provide a rather comprehensive overview of the recent developments in the field of multiscale modelling and simulation of polymeric materials. In order to understand the characteristics of the building blocks of multiscale methods, first a brief review of some significant computational methods at individual length and time scales is provided. These methods cover quantum mechanical scale, atomistic domain (Monte Carlo and molecular dynamics), mesoscopic scale (Brownian dynamics, dissipative particle dynamics, and lattice Boltzmann method), and finally macroscopic realm (finite element and volume methods). Afterwards, different prescriptions to envelope these methods in a multiscale strategy are discussed in details. Sequential, concurrent, and adaptive resolution schemes are presented along with the latest updates and ongoing challenges in research. In sequential methods, various systematic coarse-graining and backmapping approaches are addressed. For the concurrent strategy, we aimed to introduce the fundamentals and significant methods including the handshaking concept, energy-based, and force-based coupling approaches. Although such methods are very popular in metals and carbon nanomaterials, their use in polymeric materials is still limited. We have illustrated their applications in polymer science by several examples hoping for raising attention towards the existing possibilities. The relatively new adaptive resolution schemes are then covered including their advantages and shortcomings. Finally, some novel ideas in order to extend the reaches of atomistic techniques are reviewed. We conclude the review by outlining the existing challenges and possibilities for future research.
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Affiliation(s)
- Ali Gooneie
- Chair of Polymer Processing, Montanuniversitaet Leoben, Otto Gloeckel-Strasse 2, 8700 Leoben, Austria.
| | - Stephan Schuschnigg
- Chair of Polymer Processing, Montanuniversitaet Leoben, Otto Gloeckel-Strasse 2, 8700 Leoben, Austria.
| | - Clemens Holzer
- Chair of Polymer Processing, Montanuniversitaet Leoben, Otto Gloeckel-Strasse 2, 8700 Leoben, Austria.
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30
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Affiliation(s)
- Baron Peters
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106;
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31
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Hinckley DM, Lequieu JP, de Pablo JJ. Coarse-grained modeling of DNA oligomer hybridization: length, sequence, and salt effects. J Chem Phys 2015; 141:035102. [PMID: 25053341 DOI: 10.1063/1.4886336] [Citation(s) in RCA: 44] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
Abstract
A recently published coarse-grained DNA model [D. M. Hinckley, G. S. Freeman, J. K. Whitmer, and J. J. de Pablo, J. Chem. Phys. 139, 144903 (2013)] is used to study the hybridization mechanism of DNA oligomers. Forward flux sampling is used to construct ensembles of reactive trajectories from which the effects of sequence, length, and ionic strength are revealed. Heterogeneous sequences are observed to hybridize via the canonical zippering mechanism. In contrast, homogeneous sequences hybridize through a slithering mechanism, while more complex base pair displacement processes are observed for repetitive sequences. In all cases, the formation of non-native base pairs leads to an increase in the observed hybridization rate constants beyond those observed in sequences where only native base pairs are permitted. The scaling of rate constants with length is captured by extending existing hybridization theories to account for the formation of non-native base pairs. Furthermore, that scaling is found to be similar for oligomeric and polymeric systems, suggesting that similar physics is involved.
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Affiliation(s)
- Daniel M Hinckley
- Department of Chemical and Biological Engineering, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA
| | - Joshua P Lequieu
- Institute for Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA
| | - Juan J de Pablo
- Institute for Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA
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32
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Paul S, Taraphder S. Determination of the Reaction Coordinate for a Key Conformational Fluctuation in Human Carbonic Anhydrase II. J Phys Chem B 2015; 119:11403-15. [DOI: 10.1021/acs.jpcb.5b03655] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022]
Affiliation(s)
- Sanjib Paul
- Department of Chemistry, Indian Institute of Technology, Kharagpur 721302, India
| | - Srabani Taraphder
- Department of Chemistry, Indian Institute of Technology, Kharagpur 721302, India
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33
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Palmer JC, Debenedetti PG. Recent advances in molecular simulation: A chemical engineering perspective. AIChE J 2015. [DOI: 10.1002/aic.14706] [Citation(s) in RCA: 45] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Affiliation(s)
- Jeremy C. Palmer
- Dept. of Chemical and Biomolecular Engineering; University of Houston; Houston TX 77204
| | - Pablo G. Debenedetti
- Dept. of Chemical and Biological Engineering; Princeton University; Princeton NJ 08544
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34
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Affiliation(s)
- Xiaofei Xu
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125;
| | | | - Isamu Kusaka
- William G. Lowrie Department of Chemical and Biomolecular Engineering, The Koffolt Laboratories, The Ohio State University, Columbus, Ohio 43210
| | - Zhen-Gang Wang
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125;
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35
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Kratzer K, Arnold A, Allen RJ. Automatic, optimized interface placement in forward flux sampling simulations. J Chem Phys 2013; 138:164112. [DOI: 10.1063/1.4801866] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023] Open
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36
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Ferguson AL, Giovambattista N, Rossky PJ, Panagiotopoulos AZ, Debenedetti PG. A computational investigation of the phase behavior and capillary sublimation of water confined between nanoscale hydrophobic plates. J Chem Phys 2012; 137:144501. [DOI: 10.1063/1.4755750] [Citation(s) in RCA: 38] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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37
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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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38
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Lewis JI, Moss DJ, Knotts TA. Multiple molecule effects on the cooperativity of protein folding transitions in simulations. J Chem Phys 2012; 136:245101. [DOI: 10.1063/1.4729604] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023] Open
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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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Everaers R, Rosa A. Multi-scale modeling of diffusion-controlled reactions in polymers: Renormalisation of reactivity parameters. J Chem Phys 2012; 136:014902. [DOI: 10.1063/1.3673444] [Citation(s) in RCA: 11] [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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Jacobson LC, Matsumoto M, Molinero V. Order parameters for the multistep crystallization of clathrate hydrates. J Chem Phys 2011; 135:074501. [PMID: 21861570 DOI: 10.1063/1.3613667] [Citation(s) in RCA: 54] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Recent reports indicate that the crystallization of clathrate hydrates occurs in multiple steps that involve amorphous intermediates and metastable clathrate crystals. The elucidation of the reaction coordinate for clathrate crystallization requires the use of order parameters able to identify the reactants, products, and intermediates in the crystallization pathway. Nevertheless, existing order parameters cannot distinguish between amorphous and crystalline clathrates or between different clathrate crystals. In this work, we present the first set of order parameters that discern between the sI and sII clathrate crystals, the amorphous clathrates, the blob of solvent-separated guests and the liquid solution. These order parameters can be used to monitor the advance of the crystallization and for the efficient implementation of methods to sample the rare clathrate nucleation events in molecular simulations. We illustrate the use of these order parameters in the analysis of the growth and the dissolution of clathrate crystals and the spontaneous nucleation and growth of clathrates under conditions of high supercooling.
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Affiliation(s)
- Liam C Jacobson
- Department of Chemistry, University of Utah, 315 South 1400 East, Salt Lake City, Utah 84112-0850, USA
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Borrero EE, Weinwurm M, Dellago C. Optimizing transition interface sampling simulations. J Chem Phys 2011; 134:244118. [DOI: 10.1063/1.3601919] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Borrero EE, Dellago C. Overcoming barriers in trajectory space: mechanism and kinetics of rare events via Wang-Landau enhanced transition path sampling. J Chem Phys 2011; 133:134112. [PMID: 20942528 DOI: 10.1063/1.3496376] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Within the framework of transition path sampling (TPS), activation energies can be computed as path ensemble averages without a priori information about the reaction mechanism [C. Dellago and P. G. Bolhuis, Mol. Simul. 30, 795 (2004)]. Activation energies computed for different conditions can then be used to determine by numerical integration the rate constant for a system of interest from the rate constant known for a reference system. However, in systems with complex potential energy surfaces, multiple reaction pathways may exist making ergodic sampling of trajectory space difficult. Here, we present a combination of TPS with the Wang-Landau (WL) flat-histogram algorithm for an efficient sampling of the transition path ensemble. This method, denoted by WL-TPS, has the advantage that from one single simulation, activation energies at different temperatures can be determined even for systems with multiple reaction mechanisms. The proposed methodology for rate constant calculations does not require the knowledge of the reaction coordinate and is generally applicable to Arrhenius and non-Arrhenius processes. We illustrate the applicability of this technique by studying a two-dimensional toy system consisting of a triatomic molecule immersed in a fluid of repulsive soft disks. We also provide an expression for the calculation of activation volumes from path averages such that the pressure dependence of the rate constant can be obtained by numerical integration.
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Affiliation(s)
- Ernesto E Borrero
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
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Velez-Vega C, Borrero EE, Escobedo FA. Kinetics and mechanism of the unfolding native-to-loop transition of Trp-cage in explicit solvent via optimized forward flux sampling simulations. J Chem Phys 2011; 133:105103. [PMID: 20849192 DOI: 10.1063/1.3474803] [Citation(s) in RCA: 30] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The native-to-loop (N-L) unfolding transition of Trp-cage protein was studied via optimized forward flux sampling (FFS) methods with trajectories evolved using molecular dynamics. The rate constant calculated from our simulations is in good agreement with the experimental value for the native-to-unfolded transition of this protein; furthermore, the trajectories sampled a phase region consistent with that reported in previous studies for the N-L transition using transition path sampling and transition interface sampling. A new variant of FFS is proposed and implemented that allows a better control of a constant flux of partial paths. A reaction coordinate model was obtained, at no extra cost, from the transition path ensemble generated by FFS, through iterative use of the FFS-least-square estimation method [E. E. Borrero and F. A. Escobedo, J. Chem. Phys. 127, 164101 (2007)] and an adaptive staging optimization algorithm [E. E. Borrero and F. A. Escobedo, J. Chem. Phys. 129, 024115 (2008)]. Finally, we further elucidate the unfolding mechanism by correlating the unfolding progress with changes in the root mean square deviation from the α carbons of the native state, the root mean square deviation from an ideal α-helix, and other structural properties of the protein.
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Affiliation(s)
- Camilo Velez-Vega
- School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, New York 14853, USA
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Filion L, Hermes M, Ni R, Dijkstra M. Crystal nucleation of hard spheres using molecular dynamics, umbrella sampling, and forward flux sampling: A comparison of simulation techniques. J Chem Phys 2010; 133:244115. [DOI: 10.1063/1.3506838] [Citation(s) in RCA: 150] [Impact Index Per Article: 10.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Applications of computational science for understanding enzymatic deconstruction of cellulose. Curr Opin Biotechnol 2010; 22:231-8. [PMID: 21168322 DOI: 10.1016/j.copbio.2010.11.005] [Citation(s) in RCA: 80] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/19/2010] [Accepted: 11/07/2010] [Indexed: 10/18/2022]
Abstract
Understanding the molecular-level mechanisms that enzymes employ to deconstruct plant cell walls is a fundamental scientific challenge with significant ramifications for renewable fuel production from biomass. In nature, bacteria and fungi use enzyme cocktails that include processive and non-processive cellulases and hemicellulases to convert cellulose and hemicellulose to soluble sugars. Catalyzed by an accelerated biofuels R&D portfolio, there is now a wealth of new structural and experimental insights related to cellulases and the structure of plant cell walls. From this background, computational approaches commonly used in other fields are now poised to offer insights complementary to experiments designed to probe mechanisms of plant cell wall deconstruction. Here we outline the current status of computational approaches for a collection of critical problems in cellulose deconstruction. We discuss path sampling methods to measure rates of elementary steps of enzyme action, coarse-grained modeling for understanding macromolecular, cellulosomal complexes, methods to screen for enzyme improvements, and studies of cellulose at the molecular level. Overall, simulation is a complementary tool to understand carbohydrate-active enzymes and plant cell walls, which will enable industrial processes for the production of advanced, renewable fuels.
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Adams DA, Ziff RM, Sander LM. Computation of nucleation at a nonequilibrium first-order phase transition using a rare-event algorithm. J Chem Phys 2010; 133:174107. [DOI: 10.1063/1.3499321] [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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Schmitt Y, Hähl H, Gilow C, Mantz H, Jacobs K, Leidinger O, Bellion M, Santen L. Structural evolution of protein-biofilms: Simulations and experiments. BIOMICROFLUIDICS 2010; 4:32201. [PMID: 21045923 PMCID: PMC2967234 DOI: 10.1063/1.3488672] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/21/2010] [Accepted: 08/23/2010] [Indexed: 05/15/2023]
Abstract
The control of biofilm formation is a challenging goal that has not been reached yet in many aspects. One unsolved question is the role of van der Waals forces and another is the importance of mutual interactions between the adsorbing and the adsorbed biomolecules ("critical crowding"). In this study, a combined experimental and theoretical approach is presented, which fundamentally probes both aspects. On three model proteins-lysozyme, α-amylase, and bovine serum albumin-the adsorption kinetics is studied experimentally. Composite substrates are used enabling a separation of the short- and the long-range forces. Although usually neglected, experimental evidence is given for the influence of van der Waals forces on the protein adsorption as revealed by in situ ellipsometry. The three proteins were chosen for their different conformational stabilities in order to investigate the influence of conformational changes on the adsorption kinetics. Monte Carlo simulations are used to develop a model for these experimental results by assuming an internal degree of freedom to represent conformational changes. The simulations also provide data on the distribution of adsorption sites. By in situ atomic force microscopy we can also test this distribution experimentally, which opens the possibility to, e.g., investigate the interactions between adsorbed proteins.
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Zhang BW, Jasnow D, Zuckerman DM. The "weighted ensemble" path sampling method is statistically exact for a broad class of stochastic processes and binning procedures. J Chem Phys 2010; 132:054107. [PMID: 20136305 PMCID: PMC2830257 DOI: 10.1063/1.3306345] [Citation(s) in RCA: 133] [Impact Index Per Article: 9.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/17/2009] [Accepted: 01/12/2010] [Indexed: 11/14/2022] Open
Abstract
The "weighted ensemble" method, introduced by Huber and Kim [Biophys. J. 70, 97 (1996)], is one of a handful of rigorous approaches to path sampling of rare events. Expanding earlier discussions, we show that the technique is statistically exact for a wide class of Markovian and non-Markovian dynamics. The derivation is based on standard path-integral (path probability) ideas, but recasts the weighted-ensemble approach as simple "resampling" in path space. Similar reasoning indicates that arbitrary nonstatic binning procedures, which merely guide the resampling process, are also valid. Numerical examples confirm the claims, including the use of bins which can adaptively find the target state in a simple model.
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Affiliation(s)
- Bin W Zhang
- Department of Computational Biology, School of Medicine, University of Pittsburgh, Pennsylvania 15260, USA
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50
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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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