1
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Hulm A, Ochsenfeld C. Improved Sampling of Adaptive Path Collective Variables by Stabilized Extended-System Dynamics. J Chem Theory Comput 2023; 19:9202-9210. [PMID: 38078670 PMCID: PMC10753802 DOI: 10.1021/acs.jctc.3c00938] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/25/2023] [Revised: 11/08/2023] [Accepted: 11/08/2023] [Indexed: 12/27/2023]
Abstract
Because of the complicated multistep nature of many biocatalytic reactions, an a priori definition of reaction coordinates is difficult. Therefore, we apply enhanced sampling algorithms along with adaptive path collective variables (PCVs), which converge to the minimum free energy path (MFEP) during the simulation. We show how PCVs can be combined with the highly efficient well-tempered metadynamics extended-system adaptive biasing force (WTM-eABF) hybrid sampling algorithm, offering dramatically increased sampling efficiency due to its fast adaptation to path updates. For this purpose, we address discontinuities of PCVs that can arise due to path shortcutting or path updates with a novel stabilization algorithm for extended-system methods. In addition, we show how the convergence of simulations can be further accelerated by utilizing the multistate Bennett's acceptance ratio (MBAR) estimator. These methods are applied to the first step of the enzymatic reaction mechanism of pseudouridine synthases, where the ability of path WTM-eABF to efficiently explore intricate molecular transitions is demonstrated.
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Affiliation(s)
- Andreas Hulm
- Chair
of Theoretical Chemistry, Department of Chemistry, LMU Munich, Butenandtstr. 5, München D-81377, Germany
| | - Christian Ochsenfeld
- Chair
of Theoretical Chemistry, Department of Chemistry, LMU Munich, Butenandtstr. 5, München D-81377, Germany
- Max
Planck Institute for Solid State Research, Heisenbergstr. 1, Stuttgart D-70569, Germany
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2
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Zhao X, Jin G, Guo D, Xiao X, Nan J, Wu C. Dissolution mechanism of Fe 3O 4 scale by 1-hydroxyethane-1,1-diphosphonic acid: an ab initio molecular metadynamics study. Phys Chem Chem Phys 2023; 25:23901-23908. [PMID: 37642508 DOI: 10.1039/d3cp01736b] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/31/2023]
Abstract
Using the ab initio molecular metadynamics method, the adsorption of the structure of 1-hydroxyethane-1,1-diphosphonic acid (HEDP) on the Fe3O4 surface and subsequent detachment of Fe atoms from the surface were simulated, and the dissolution mechanism by which HEDP dissolves Fe3O4 scale at room temperature while other organic acids cannot was elucidated. The adsorbed hydroxyl groups, water and HEDP on the Fe3O4 surface play a synergistic role in detaching the Fe ions, which increases the coordination number of the Fe atoms and weakens the original Fe-O bond strength. In addition, the strong coordination ability and flexible molecular structure of HEDP also facilitate dissolution of Fe3O4 scale by breaking down the chemical bonds and forming Fe-HEDP complexes. The free energy surface for the dissolution reaction shows a low barrier, and the descaling reaction is easily accomplished.
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Affiliation(s)
- Xiaoyang Zhao
- School of Geomatic and Environmental Engineering, Henan Polytechnic Institute, Nanyang 473000, P. R. China
| | - Guo Jin
- School of Automation Engineering, Henan Polytechnic Institute, Nanyang 473000, P. R. China
| | - Ding Guo
- School of Geomatic and Environmental Engineering, Henan Polytechnic Institute, Nanyang 473000, P. R. China
| | - Xin Xiao
- School of Chemistry, South China Normal University, Guangzhou 510006, P. R. China.
| | - Junmin Nan
- School of Chemistry, South China Normal University, Guangzhou 510006, P. R. China.
| | - Chen Wu
- Department of Physics, School of Science, Harbin University of Science and Technology, Harbin 150080, P. R. China.
- College of Material Science and Engineering, Key Laboratory of Advanced Structural Materials, Ministry of Education, Changchun University of Technology, Changchun 130012, P. R. China
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3
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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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4
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Lazzeri G, Micheletti C, Pasquali S, Faccioli P. RNA folding pathways from all-atom simulations with a variationally improved history-dependent bias. Biophys J 2023; 122:3089-3098. [PMID: 37355771 PMCID: PMC10432211 DOI: 10.1016/j.bpj.2023.06.012] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/07/2023] [Revised: 05/03/2023] [Accepted: 06/15/2023] [Indexed: 06/26/2023] Open
Abstract
Atomically detailed simulations of RNA folding have proven very challenging in view of the difficulties of developing realistic force fields and the intrinsic computational complexity of sampling rare conformational transitions. As a step forward in tackling these issues, we extend to RNA an enhanced path-sampling method previously successfully applied to proteins. In this scheme, the information about the RNA's native structure is harnessed by a soft history-dependent biasing force promoting the generation of productive folding trajectories in an all-atom force field with explicit solvent. A rigorous variational principle is then applied to minimize the effect of the bias. Here, we report on an application of this method to RNA molecules from 20 to 47 nucleotides long and increasing topological complexity. By comparison with analog simulations performed on small proteins with similar size and architecture, we show that the RNA folding landscape is significantly more frustrated, even for relatively small chains with a simple topology. The predicted RNA folding mechanisms are found to be consistent with the available experiments and some of the existing coarse-grained models. Due to its computational performance, this scheme provides a promising platform to efficiently gather atomistic RNA folding trajectories, thus retain the information about the chemical composition of the sequence.
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Affiliation(s)
- Gianmarco Lazzeri
- Frankfurt Institute for Advanced Studies, Frankfurt am Main, Germany; Physics Department of Trento University, Povo (Trento), Italy
| | | | - Samuela Pasquali
- Laboratoire Cibles Thérapeutiques et Conception de Médicaments, Université Paris Cité, Paris, France; Laboratoire Biologie Fonctionnelle et Adaptative, Université Paris Cité, Paris, France.
| | - Pietro Faccioli
- Physics Department of Trento University, Povo (Trento), Italy; INFN-TIFPA, Povo (Trento), Italy.
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5
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Dominic AJ, Cao S, Montoya-Castillo A, Huang X. Memory Unlocks the Future of Biomolecular Dynamics: Transformative Tools to Uncover Physical Insights Accurately and Efficiently. J Am Chem Soc 2023; 145:9916-9927. [PMID: 37104720 DOI: 10.1021/jacs.3c01095] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/29/2023]
Abstract
Conformational changes underpin function and encode complex biomolecular mechanisms. Gaining atomic-level detail of how such changes occur has the potential to reveal these mechanisms and is of critical importance in identifying drug targets, facilitating rational drug design, and enabling bioengineering applications. While the past two decades have brought Markov state model techniques to the point where practitioners can regularly use them to glimpse the long-time dynamics of slow conformations in complex systems, many systems are still beyond their reach. In this Perspective, we discuss how including memory (i.e., non-Markovian effects) can reduce the computational cost to predict the long-time dynamics in these complex systems by orders of magnitude and with greater accuracy and resolution than state-of-the-art Markov state models. We illustrate how memory lies at the heart of successful and promising techniques, ranging from the Fokker-Planck and generalized Langevin equations to deep-learning recurrent neural networks and generalized master equations. We delineate how these techniques work, identify insights that they can offer in biomolecular systems, and discuss their advantages and disadvantages in practical settings. We show how generalized master equations can enable the investigation of, for example, the gate-opening process in RNA polymerase II and demonstrate how our recent advances tame the deleterious influence of statistical underconvergence of the molecular dynamics simulations used to parameterize these techniques. This represents a significant leap forward that will enable our memory-based techniques to interrogate systems that are currently beyond the reach of even the best Markov state models. We conclude by discussing some current challenges and future prospects for how exploiting memory will open the door to many exciting opportunities.
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Affiliation(s)
- Anthony J Dominic
- Department of Chemistry, University of Colorado Boulder, Boulder, Colorado 80309, USA
| | - Siqin Cao
- Department of Chemistry, Theoretical Chemistry Institute, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA
| | | | - Xuhui Huang
- Department of Chemistry, Theoretical Chemistry Institute, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA
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6
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Jung H, Covino R, Arjun A, Leitold C, Dellago C, Bolhuis PG, Hummer G. Machine-guided path sampling to discover mechanisms of molecular self-organization. NATURE COMPUTATIONAL SCIENCE 2023; 3:334-345. [PMID: 38177937 PMCID: PMC10766509 DOI: 10.1038/s43588-023-00428-z] [Citation(s) in RCA: 24] [Impact Index Per Article: 24.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/15/2023] [Accepted: 03/10/2023] [Indexed: 01/06/2024]
Abstract
Molecular self-organization driven by concerted many-body interactions produces the ordered structures that define both inanimate and living matter. Here we present an autonomous path sampling algorithm that integrates deep learning and transition path theory to discover the mechanism of molecular self-organization phenomena. The algorithm uses the outcome of newly initiated trajectories to construct, validate and-if needed-update quantitative mechanistic models. Closing the learning cycle, the models guide the sampling to enhance the sampling of rare assembly events. Symbolic regression condenses the learned mechanism into a human-interpretable form in terms of relevant physical observables. Applied to ion association in solution, gas-hydrate crystal formation, polymer folding and membrane-protein assembly, we capture the many-body solvent motions governing the assembly process, identify the variables of classical nucleation theory, uncover the folding mechanism at different levels of resolution and reveal competing assembly pathways. The mechanistic descriptions are transferable across thermodynamic states and chemical space.
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Affiliation(s)
- Hendrik Jung
- Department of Theoretical Biophysics, Max Planck Institute of Biophysics, Frankfurt am Main, Germany
| | - Roberto Covino
- Frankfurt Institute for Advanced Studies, Frankfurt am Main, Germany
| | - A Arjun
- van 't Hoff Institute for Molecular Sciences, University of Amsterdam, Amsterdam, The Netherlands
| | | | | | - Peter G Bolhuis
- van 't Hoff Institute for Molecular Sciences, University of Amsterdam, Amsterdam, The Netherlands
| | - Gerhard Hummer
- Department of Theoretical Biophysics, Max Planck Institute of Biophysics, Frankfurt am Main, Germany.
- Institute of Biophysics, Goethe University Frankfurt, Frankfurt am Main, Germany.
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7
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Tom R, Gao S, Yang Y, Zhao K, Bier I, Buchanan EA, Zaykov A, Havlas Z, Michl J, Marom N. Inverse Design of Tetracene Polymorphs with Enhanced Singlet Fission Performance by Property-Based Genetic Algorithm Optimization. CHEMISTRY OF MATERIALS : A PUBLICATION OF THE AMERICAN CHEMICAL SOCIETY 2023; 35:1373-1386. [PMID: 36999121 PMCID: PMC10042130 DOI: 10.1021/acs.chemmater.2c03444] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/17/2022] [Revised: 01/06/2023] [Indexed: 06/19/2023]
Abstract
The efficiency of solar cells may be improved by using singlet fission (SF), in which one singlet exciton splits into two triplet excitons. SF occurs in molecular crystals. A molecule may crystallize in more than one form, a phenomenon known as polymorphism. Crystal structure may affect SF performance. In the common form of tetracene, SF is experimentally known to be slightly endoergic. A second, metastable polymorph of tetracene has been found to exhibit better SF performance. Here, we conduct inverse design of the crystal packing of tetracene using a genetic algorithm (GA) with a fitness function tailored to simultaneously optimize the SF rate and the lattice energy. The property-based GA successfully generates more structures predicted to have higher SF rates and provides insight into packing motifs associated with improved SF performance. We find a putative polymorph predicted to have superior SF performance to the two forms of tetracene, whose structures have been determined experimentally. The putative structure has a lattice energy within 1.5 kJ/mol of the most stable common form of tetracene.
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Affiliation(s)
- Rithwik Tom
- Department
of Physics, Carnegie Mellon University, Pittsburgh, Pennsylvania15213, United States
| | - Siyu Gao
- Department
of Materials Science and Engineering, Carnegie
Mellon University, Pittsburgh, Pennsylvania15213, United States
| | - Yi Yang
- Department
of Materials Science and Engineering, Carnegie
Mellon University, Pittsburgh, Pennsylvania15213, United States
| | - Kaiji Zhao
- Department
of Materials Science and Engineering, Carnegie
Mellon University, Pittsburgh, Pennsylvania15213, United States
| | - Imanuel Bier
- Department
of Materials Science and Engineering, Carnegie
Mellon University, Pittsburgh, Pennsylvania15213, United States
| | - Eric A. Buchanan
- Department
of Chemistry, University of Colorado, Boulder, Colorado80309, United States
| | - Alexandr Zaykov
- Institute
of Organic Chemistry and Biochemistry, Czech
Academy of Sciences, 16610Prague 6, Czech
Republic
- Department
of Physical Chemistry, University of Chemistry
and Technology, 166 28Prague 6, Czech Republic
| | - Zdeněk Havlas
- Institute
of Organic Chemistry and Biochemistry, Czech
Academy of Sciences, 16610Prague 6, Czech
Republic
| | - Josef Michl
- Department
of Chemistry, University of Colorado, Boulder, Colorado80309, United States
- Institute
of Organic Chemistry and Biochemistry, Czech
Academy of Sciences, 16610Prague 6, Czech
Republic
| | - Noa Marom
- Department
of Physics, Carnegie Mellon University, Pittsburgh, Pennsylvania15213, United States
- Department
of Materials Science and Engineering, Carnegie
Mellon University, Pittsburgh, Pennsylvania15213, United States
- Department
of Chemistry, Carnegie Mellon University, Pittsburgh, Pennsylvania15213, United States
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8
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Exploring catalytic reaction networks with machine learning. Nat Catal 2023. [DOI: 10.1038/s41929-022-00896-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2023]
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9
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Neha, Tiwari V, Mondal S, Kumari N, Karmakar T. Collective Variables for Crystallization Simulations-from Early Developments to Recent Advances. ACS OMEGA 2023; 8:127-146. [PMID: 36643553 PMCID: PMC9835087 DOI: 10.1021/acsomega.2c06310] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/30/2022] [Accepted: 12/08/2022] [Indexed: 03/11/2024]
Abstract
Crystallization is an important physicochemical process which has relevance in material science, biology, and the environment. Decades of experimental and theoretical efforts have been made to understand this fundamental symmetry-breaking transition. While experiments provide equilibrium structures and shapes of crystals, they are limited to unraveling how molecules aggregate to form crystal nuclei that subsequently transform into bulk crystals. Computer simulations, mainly molecular dynamics (MD), can provide such microscopic details during the early stage of a crystallization event. Crystallization is a rare event that takes place in time scales much longer than a typical equilibrium MD simulation can sample. This inadequate sampling of the MD method can be easily circumvented by the use of enhanced sampling (ES) simulations. In most of the ES methods, the fluctuations of a system's slow degrees of freedom, called collective variables (CVs), are enhanced by applying a bias potential. This transforms the system from one state to the other within a short time scale. The most crucial part of such CV-based ES methods is to find suitable CVs, which often needs intuition and several trial-and-error optimization steps. Over the years, a plethora of CVs has been developed and applied in the study of crystallization. In this review, we provide a brief overview of CVs that have been developed and used in ES simulations to study crystallization from melt or solution. These CVs can be categorized mainly into four types: (i) spherical particle-based, (ii) molecular template-based, (iii) physical property-based, and (iv) CVs obtained from dimensionality reduction techniques. We present the context-based evolution of CVs, discuss the current challenges, and propose future directions to further develop effective CVs for the study of crystallization of complex systems.
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Affiliation(s)
| | | | | | | | - Tarak Karmakar
- Department of Chemistry, Indian Institute of Technology, Delhi, Hauz Khas, New Delhi110016, India
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10
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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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11
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Tsai ST, Fields E, Xu Y, Kuo EJ, Tiwary P. Path sampling of recurrent neural networks by incorporating known physics. Nat Commun 2022; 13:7231. [PMID: 36433982 PMCID: PMC9700810 DOI: 10.1038/s41467-022-34780-x] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/29/2022] [Accepted: 11/07/2022] [Indexed: 11/27/2022] Open
Abstract
Recurrent neural networks have seen widespread use in modeling dynamical systems in varied domains such as weather prediction, text prediction and several others. Often one wishes to supplement the experimentally observed dynamics with prior knowledge or intuition about the system. While the recurrent nature of these networks allows them to model arbitrarily long memories in the time series used in training, it makes it harder to impose prior knowledge or intuition through generic constraints. In this work, we present a path sampling approach based on principle of Maximum Caliber that allows us to include generic thermodynamic or kinetic constraints into recurrent neural networks. We show the method here for a widely used type of recurrent neural network known as long short-term memory network in the context of supplementing time series collected from different application domains. These include classical Molecular Dynamics of a protein and Monte Carlo simulations of an open quantum system continuously losing photons to the environment and displaying Rabi oscillations. Our method can be easily generalized to other generative artificial intelligence models and to generic time series in different areas of physical and social sciences, where one wishes to supplement limited data with intuition or theory based corrections.
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Affiliation(s)
- Sun-Ting Tsai
- grid.164295.d0000 0001 0941 7177Department of Physics, University of Maryland, College Park, MD 20742 USA ,grid.164295.d0000 0001 0941 7177Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742 USA
| | - Eric Fields
- grid.164295.d0000 0001 0941 7177Department of Chemistry and Biochemistry, University of Maryland, College Park, MD 20742 USA ,grid.164295.d0000 0001 0941 7177Department of Computer Science, University of Maryland, College Park, MD 20742 USA
| | - Yijia Xu
- grid.164295.d0000 0001 0941 7177Department of Physics, University of Maryland, College Park, MD 20742 USA ,grid.164295.d0000 0001 0941 7177Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742 USA ,grid.94225.38000000012158463XJoint Quantum Institute and Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, MD 20742 USA
| | - En-Jui Kuo
- grid.164295.d0000 0001 0941 7177Department of Physics, University of Maryland, College Park, MD 20742 USA ,grid.94225.38000000012158463XJoint Quantum Institute and Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, MD 20742 USA
| | - Pratyush Tiwary
- grid.164295.d0000 0001 0941 7177Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742 USA ,grid.164295.d0000 0001 0941 7177Department of Chemistry and Biochemistry, University of Maryland, College Park, MD 20742 USA
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12
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Salahub DR. Multiscale molecular modelling: from electronic structure to dynamics of nanosystems and beyond. Phys Chem Chem Phys 2022; 24:9051-9081. [PMID: 35389399 DOI: 10.1039/d1cp05928a] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
Abstract
Important contemporary biological and materials problems often depend on interactions that span orders of magnitude differences in spatial and temporal dimensions. This Tutorial Review attempts to provide an introduction to such fascinating problems through a series of case studies, aimed at beginning researchers, graduate students, postdocs and more senior colleagues who are changing direction to focus on multiscale aspects of their research. The choice of specific examples is highly personal, with examples either chosen from our own work or outstanding multiscale efforts from the literature. I start with various embedding schemes, as exemplified by polarizable continuum models, 3-D RISM, molecular DFT and frozen-density embedding. Next, QM/MM (quantum mechanical/molecular mechanical) techniques are the workhorse of pm-to-nm/ps-to-ns simulations; examples are drawn from enzymes and from nanocatalysis for oil-sands upgrading. Using polarizable force-fields in the QM/MM framework represents a burgeoning subfield; with examples from ion channels and electron dynamics in molecules subject to strong external fields, probing the atto-second dynamics of the electrons with RT-TDDFT (real-time - time-dependent density functional theory) eventually coupled with nuclear motion through the Ehrenfest approximation. This is followed by a section on coarse graining, bridging dimensions from atoms to cells. The penultimate chapter gives a quick overview of multiscale approaches that extend into the meso- and macro-scales, building on atomistic and coarse-grained techniques to enter the world of materials engineering, on the one hand, and cell biology, on the other. A final chapter gives just a glimpse of the burgeoning impact of machine learning on the structure-dynamics front. I aim to capture the excitement of contemporary leading-edge breakthroughs in the description of physico-chemical systems and processes in complex environments, with only enough historical content to provide context and aid the next generation of methodological development. While I aim also for a clear description of the essence of methodological breakthroughs, equations are kept to a minimum and detailed formalism and implementation details are left to the references. My approach is very selective (case studies) rather than exhaustive. I think that these case studies should provide fodder to build as complete a reference tree on multiscale modelling as the reader may wish, through forward and backward citation analysis. I hope that my choices of cases will excite interest in newcomers and help to fuel the growth of multiscale modelling in general.
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Affiliation(s)
- Dennis R Salahub
- Department of Chemistry, Department of Physics and Astronomy, CMS-Centre for Molecular Simulation, IQST-Institute for Quantum Science and Technology, Quantum Alberta, University of Calgary, Calgary, Alberta, T2N 1N4, Canada.
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13
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Kikutsuji T, Mori Y, Okazaki KI, Mori T, Kim K, Matubayasi N. Explaining reaction coordinates of alanine dipeptide isomerization obtained from deep neural networks using Explainable Artificial Intelligence (XAI). J Chem Phys 2022; 156:154108. [DOI: 10.1063/5.0087310] [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
A method for obtaining appropriate reaction coordinates is required to identify transition states distinguishing product and reactant in complex molecular systems. Recently, abundant research has been devoted to obtaining reaction coordinates using artificial neural networks from deep learning literature, where many collective variables are typically utilized in the input layer. However, it is difficult to explain the details of which collective variables contribute to the predicted reaction coordinates owing to the complexity of the nonlinear functions in deep neural networks. To overcome this limitation, we used Explainable Artificial Intelligence (XAI) methods of the Local Interpretable Model-agnostic Explanation (LIME) and the game theory-based framework known as Shapley Additive exPlanations (SHAP). We demonstrated that XAI enables us to obtain the degree of contribution of each collective variable to reaction coordinates that is determined by nonlinear regressions with deep learning for the committor of the alanine dipeptide isomerization in vacuum. In particular, both LIME and SHAP provide important features to the predicted reaction coordinates, which are characterized by appropriate dihedral angles consistent with those previously reported from the committor test analysis. The present study offers an AI-aided framework to explain the appropriate reaction coordinates, which acquires considerable significance when the number of degrees of freedom increases.
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Affiliation(s)
| | | | - Kei-ichi Okazaki
- Department of Theoretical and Computational Molecular Science, Institute for Molecular Science, Japan
| | - Toshifumi Mori
- Kyushu University Institute for Materials Chemistry and Engineering, Japan
| | - Kang Kim
- Graduate School of Engineering Science, Osaka University - Toyonaka Campus, Japan
| | - Nobuyuki Matubayasi
- Division of Chemical Engineering, Graduate School of Engineering Science, Osaka University, Japan
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14
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Ketkaew R, Creazzo F, Luber S. Machine Learning-Assisted Discovery of Hidden States in Expanded Free Energy Space. J Phys Chem Lett 2022; 13:1797-1805. [PMID: 35171614 DOI: 10.1021/acs.jpclett.1c04004] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
Collective variables (CVs) are crucial parameters in enhanced sampling calculations and strongly impact the quality of the obtained free energy surface. However, many existing CVs are unique to and dependent on the system they are constructed with, making the developed CV non-transferable to other systems. Herein, we develop a non-instructor-led deep autoencoder neural network (DAENN) for discovering general-purpose CVs. The DAENN is used to train a model by learning molecular representations upon unbiased trajectories that contain only the reactant conformers. The prior knowledge of nonconstraint reactants coupled with the here-introduced topology variable and loss-like penalty function are only required to make the biasing method able to expand its configurational (phase) space to unexplored energy basins. Our developed autoencoder is efficient and relatively inexpensive to use in terms of a priori knowledge, enabling one to automatically search for hidden CVs of the reaction of interest.
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Affiliation(s)
- Rangsiman Ketkaew
- Department of Chemistry, University of Zurich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
| | - Fabrizio Creazzo
- Department of Chemistry, University of Zurich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
| | - Sandra Luber
- Department of Chemistry, University of Zurich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
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15
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Raucci U, Rizzi V, Parrinello M. Discover, Sample, and Refine: Exploring Chemistry with Enhanced Sampling Techniques. J Phys Chem Lett 2022; 13:1424-1430. [PMID: 35119863 DOI: 10.1021/acs.jpclett.1c03993] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
Over the last few decades, enhanced sampling methods have been continuously improved. Here, we exploit this progress and propose a modular workflow for blind reaction discovery and determination of reaction paths. In a three-step strategy, at first we use a collective variable derived from spectral graph theory in conjunction with the explore variant of the on-the-fly probability enhanced sampling method to drive reaction discovery runs. Once different chemical products are determined, we construct an ad-hoc neural network-based collective variable to improve sampling, and finally we refine the results using the free energy perturbation theory and a more accurate Hamiltonian. We apply this strategy to both intramolecular and intermolecular reactions. Our workflow requires minimal user input and extends the power of ab initio molecular dynamics to explore and characterize the reaction space.
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Affiliation(s)
- Umberto Raucci
- Italian Institute of Technology, Via E. Melen 83, 16152, Genova, Italy
| | - Valerio Rizzi
- Italian Institute of Technology, Via E. Melen 83, 16152, Genova, Italy
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16
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Belkacemi Z, Gkeka P, Lelièvre T, Stoltz G. Chasing Collective Variables Using Autoencoders and Biased Trajectories. J Chem Theory Comput 2021; 18:59-78. [PMID: 34965117 DOI: 10.1021/acs.jctc.1c00415] [Citation(s) in RCA: 22] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Abstract
Free energy biasing methods have proven to be powerful tools to accelerate the simulation of important conformational changes of molecules by modifying the sampling measure. However, most of these methods rely on the prior knowledge of low-dimensional slow degrees of freedom, i.e., collective variables (CVs). Alternatively, such CVs can be identified using machine learning (ML) and dimensionality reduction algorithms. In this context, approaches where the CVs are learned in an iterative way using adaptive biasing have been proposed: at each iteration, the learned CV is used to perform free energy adaptive biasing to generate new data and learn a new CV. In this paper, we introduce a new iterative method involving CV learning with autoencoders: Free Energy Biasing and Iterative Learning with AutoEncoders (FEBILAE). Our method includes a reweighting scheme to ensure that the learning model optimizes the same loss at each iteration and achieves CV convergence. Using the alanine dipeptide system and the solvated chignolin mini-protein system as examples, we present results of our algorithm using the extended adaptive biasing force as the free energy adaptive biasing method.
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Affiliation(s)
- Zineb Belkacemi
- CERMICS, Ecole des Ponts ParisTech, 77455 Marne-la-Vallée, France.,Structure Design and Informatics, Sanofi 1371 R&D, 91385 Chilly-Mazarin, France
| | - Paraskevi Gkeka
- Structure Design and Informatics, Sanofi 1371 R&D, 91385 Chilly-Mazarin, France
| | - Tony Lelièvre
- CERMICS, Ecole des Ponts ParisTech, 77455 Marne-la-Vallée, France.,MATHERIALS Team-Project, Inria, 75589 Paris, France
| | - Gabriel Stoltz
- CERMICS, Ecole des Ponts ParisTech, 77455 Marne-la-Vallée, France.,MATHERIALS Team-Project, Inria, 75589 Paris, France
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17
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Bal KM. Nucleation rates from small scale atomistic simulations and transition state theory. J Chem Phys 2021; 155:144111. [PMID: 34654300 DOI: 10.1063/5.0063398] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023] Open
Abstract
The evaluation of nucleation rates from molecular dynamics trajectories is hampered by the slow nucleation time scale and impact of finite size effects. Here, we show that accurate nucleation rates can be obtained in a very general fashion relying only on the free energy barrier, transition state theory, and a simple dynamical correction for diffusive recrossing. In this setup, the time scale problem is overcome by using enhanced sampling methods, in casu metadynamics, whereas the impact of finite size effects can be naturally circumvented by reconstructing the free energy surface from an appropriate ensemble. Approximations from classical nucleation theory are avoided. We demonstrate the accuracy of the approach by calculating macroscopic rates of droplet nucleation from argon vapor, spanning 16 orders of magnitude and in excellent agreement with literature results, all from simulations of very small (512 atom) systems.
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Affiliation(s)
- Kristof M Bal
- Department of Chemistry and NANOlab Center of Excellence, University of Antwerp, Universiteitsplein 1, 2610 Antwerp, Belgium
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18
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Badin M, Martoňák R. Nucleating a Different Coordination in a Crystal under Pressure: A Study of the B1-B2 Transition in NaCl by Metadynamics. PHYSICAL REVIEW LETTERS 2021; 127:105701. [PMID: 34533357 DOI: 10.1103/physrevlett.127.105701] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/05/2021] [Accepted: 07/21/2021] [Indexed: 06/13/2023]
Abstract
Here we propose an NPT metadynamics simulation scheme for pressure-induced structural phase transitions, using coordination number and volume as collective variables, and apply it to the reconstructive structural transformation B1-B2 in NaCl. By studying systems with size up to 64 000 atoms we reach a regime beyond collective mechanism and observe transformations proceeding via nucleation and growth. We also reveal the crossover of the transition mechanism from Buerger-like for smaller systems to Watanabe-Tolédano for larger ones. The scheme is likely to be applicable to a broader class of pressure-induced structural transitions, allowing study of complex nucleation effects and bringing simulations closer to realistic conditions.
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Affiliation(s)
- Matej Badin
- SISSA - Scuola Internazionale Superiore di Studi Avanzati, Via Bonomea 265, 34136 Trieste, Italy
- Department of Experimental Physics, Faculty of Mathematics, Physics and Informatics, Comenius University in Bratislava, Mlynská Dolina F2, 842 48 Bratislava, Slovakia
| | - Roman Martoňák
- Department of Experimental Physics, Faculty of Mathematics, Physics and Informatics, Comenius University in Bratislava, Mlynská Dolina F2, 842 48 Bratislava, Slovakia
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19
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Keith JA, Vassilev-Galindo V, Cheng B, Chmiela S, Gastegger M, Müller KR, Tkatchenko A. Combining Machine Learning and Computational Chemistry for Predictive Insights Into Chemical Systems. Chem Rev 2021; 121:9816-9872. [PMID: 34232033 PMCID: PMC8391798 DOI: 10.1021/acs.chemrev.1c00107] [Citation(s) in RCA: 190] [Impact Index Per Article: 63.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/04/2021] [Indexed: 12/23/2022]
Abstract
Machine learning models are poised to make a transformative impact on chemical sciences by dramatically accelerating computational algorithms and amplifying insights available from computational chemistry methods. However, achieving this requires a confluence and coaction of expertise in computer science and physical sciences. This Review is written for new and experienced researchers working at the intersection of both fields. We first provide concise tutorials of computational chemistry and machine learning methods, showing how insights involving both can be achieved. We follow with a critical review of noteworthy applications that demonstrate how computational chemistry and machine learning can be used together to provide insightful (and useful) predictions in molecular and materials modeling, retrosyntheses, catalysis, and drug design.
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Affiliation(s)
- John A. Keith
- Department
of Chemical and Petroleum Engineering Swanson School of Engineering, University of Pittsburgh, Pittsburgh, Pennsylvania 15261, United States
| | - Valentin Vassilev-Galindo
- Department
of Physics and Materials Science, University
of Luxembourg, L-1511 Luxembourg City, Luxembourg
| | - Bingqing Cheng
- Accelerate
Programme for Scientific Discovery, Department
of Computer Science and Technology, 15 J. J. Thomson Avenue, Cambridge CB3 0FD, United Kingdom
| | - Stefan Chmiela
- Department
of Software Engineering and Theoretical Computer Science, Technische Universität Berlin, 10587, Berlin, Germany
| | - Michael Gastegger
- Department
of Software Engineering and Theoretical Computer Science, Technische Universität Berlin, 10587, Berlin, Germany
| | - Klaus-Robert Müller
- Machine
Learning Group, Technische Universität
Berlin, 10587, Berlin, Germany
- Department
of Artificial Intelligence, Korea University, Anam-dong, Seongbuk-gu, Seoul, 02841, Korea
- Max-Planck-Institut für Informatik, 66123 Saarbrücken, Germany
- Google Research, Brain Team, 10117 Berlin, Germany
| | - Alexandre Tkatchenko
- Department
of Physics and Materials Science, University
of Luxembourg, L-1511 Luxembourg City, Luxembourg
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20
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Rydzewski J, Valsson O. Multiscale Reweighted Stochastic Embedding: Deep Learning of Collective Variables for Enhanced Sampling. J Phys Chem A 2021; 125:6286-6302. [PMID: 34213915 PMCID: PMC8389995 DOI: 10.1021/acs.jpca.1c02869] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/30/2021] [Revised: 06/17/2021] [Indexed: 12/29/2022]
Abstract
Machine learning methods provide a general framework for automatically finding and representing the essential characteristics of simulation data. This task is particularly crucial in enhanced sampling simulations. There we seek a few generalized degrees of freedom, referred to as collective variables (CVs), to represent and drive the sampling of the free energy landscape. In theory, these CVs should separate different metastable states and correspond to the slow degrees of freedom of the studied physical process. To this aim, we propose a new method that we call multiscale reweighted stochastic embedding (MRSE). Our work builds upon a parametric version of stochastic neighbor embedding. The technique automatically learns CVs that map a high-dimensional feature space to a low-dimensional latent space via a deep neural network. We introduce several new advancements to stochastic neighbor embedding methods that make MRSE especially suitable for enhanced sampling simulations: (1) weight-tempered random sampling as a landmark selection scheme to obtain training data sets that strike a balance between equilibrium representation and capturing important metastable states lying higher in free energy; (2) a multiscale representation of the high-dimensional feature space via a Gaussian mixture probability model; and (3) a reweighting procedure to account for training data from a biased probability distribution. We show that MRSE constructs low-dimensional CVs that can correctly characterize the different metastable states in three model systems: the Müller-Brown potential, alanine dipeptide, and alanine tetrapeptide.
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Affiliation(s)
- Jakub Rydzewski
- Institute
of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, Grudziadzka 5, 87-100 Torun, Poland
| | - Omar Valsson
- Max
Planck Institute for Polymer Research, Ackermannweg 10, Mainz D-55128, Germany
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21
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Giraldo-Barreto J, Ortiz S, Thiede EH, Palacio-Rodriguez K, Carpenter B, Barnett AH, Cossio P. A Bayesian approach to extracting free-energy profiles from cryo-electron microscopy experiments. Sci Rep 2021; 11:13657. [PMID: 34211017 PMCID: PMC8249403 DOI: 10.1038/s41598-021-92621-1] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/04/2021] [Accepted: 06/01/2021] [Indexed: 11/08/2022] Open
Abstract
Cryo-electron microscopy (cryo-EM) extracts single-particle density projections of individual biomolecules. Although cryo-EM is widely used for 3D reconstruction, due to its single-particle nature it has the potential to provide information about a biomolecule's conformational variability and underlying free-energy landscape. However, treating cryo-EM as a single-molecule technique is challenging because of the low signal-to-noise ratio (SNR) in individual particles. In this work, we propose the cryo-BIFE method (cryo-EM Bayesian Inference of Free-Energy profiles), which uses a path collective variable to extract free-energy profiles and their uncertainties from cryo-EM images. We test the framework on several synthetic systems where the imaging parameters and conditions were controlled. We found that for realistic cryo-EM environments and relevant biomolecular systems, it is possible to recover the underlying free energy, with the pose accuracy and SNR as crucial determinants. We then use the method to study the conformational transitions of a calcium-activated channel with real cryo-EM particles. Interestingly, we recover not only the most probable conformation (used to generate a high-resolution reconstruction of the calcium-bound state) but also a metastable state that corresponds to the calcium-unbound conformation. As expected for turnover transitions within the same sample, the activation barriers are on the order of [Formula: see text]. We expect our tool for extracting free-energy profiles from cryo-EM images to enable more complete characterization of the thermodynamic ensemble of biomolecules.
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Affiliation(s)
- Julian Giraldo-Barreto
- Biophysics of Tropical Diseases Max Planck Tandem Group, University of Antioquia UdeA, Calle 70 No. 52-21, Medellín, Colombia
- Magnetism and Simulation Group, University of Antioquia UdeA, Calle 70 No. 52-21, Medellín, Colombia
| | - Sebastian Ortiz
- Biophysics of Tropical Diseases Max Planck Tandem Group, University of Antioquia UdeA, Calle 70 No. 52-21, Medellín, Colombia
| | - Erik H Thiede
- Center for Computational Mathematics, Flatiron Institute, New York City, USA
| | - Karen Palacio-Rodriguez
- Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie, Sorbonne Université, Paris, France
| | - Bob Carpenter
- Center for Computational Mathematics, Flatiron Institute, New York City, USA
| | - Alex H Barnett
- Center for Computational Mathematics, Flatiron Institute, New York City, USA
| | - Pilar Cossio
- Biophysics of Tropical Diseases Max Planck Tandem Group, University of Antioquia UdeA, Calle 70 No. 52-21, Medellín, Colombia.
- Department of Theoretical Biophysics, Max Planck Institute of Biophysics, 60438, Frankfurt am Main, Germany.
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22
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Hooft F, Pérez de Alba Ortíz A, Ensing B. Discovering Collective Variables of Molecular Transitions via Genetic Algorithms and Neural Networks. J Chem Theory Comput 2021; 17:2294-2306. [PMID: 33662202 PMCID: PMC8047796 DOI: 10.1021/acs.jctc.0c00981] [Citation(s) in RCA: 20] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/23/2020] [Indexed: 01/13/2023]
Abstract
With the continual improvement of computing hardware and algorithms, simulations have become a powerful tool for understanding all sorts of (bio)molecular processes. To handle the large simulation data sets and to accelerate slow, activated transitions, a condensed set of descriptors, or collective variables (CVs), is needed to discern the relevant dynamics that describes the molecular process of interest. However, proposing an adequate set of CVs that can capture the intrinsic reaction coordinate of the molecular transition is often extremely difficult. Here, we present a framework to find an optimal set of CVs from a pool of candidates using a combination of artificial neural networks and genetic algorithms. The approach effectively replaces the encoder of an autoencoder network with genes to represent the latent space, i.e., the CVs. Given a selection of CVs as input, the network is trained to recover the atom coordinates underlying the CV values at points along the transition. The network performance is used as an estimator of the fitness of the input CVs. Two genetic algorithms optimize the CV selection and the neural network architecture. The successful retrieval of optimal CVs by this framework is illustrated at the hand of two case studies: the well-known conformational change in the alanine dipeptide molecule and the more intricate transition of a base pair in B-DNA from the classic Watson-Crick pairing to the alternative Hoogsteen pairing. Key advantages of our framework include the following: optimal interpretable CVs, avoiding costly calculation of committor or time-correlation functions, and automatic hyperparameter optimization. In addition, we show that applying a time-delay between the network input and output allows for enhanced selection of slow variables. Moreover, the network can also be used to generate molecular configurations of unexplored microstates, for example, for augmentation of the simulation data.
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Affiliation(s)
- Ferry Hooft
- Van ’t Hoff Institute
for Molecular Sciences, AI4Science Laboratory, and Amsterdam Center
for Multiscale Modeling, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
| | - Alberto Pérez de Alba Ortíz
- Van ’t Hoff Institute
for Molecular Sciences, AI4Science Laboratory, and Amsterdam Center
for Multiscale Modeling, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
| | - Bernd Ensing
- Van ’t Hoff Institute
for Molecular Sciences, AI4Science Laboratory, and Amsterdam Center
for Multiscale Modeling, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
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23
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Musil F, Veit M, Goscinski A, Fraux G, Willatt MJ, Stricker M, Junge T, Ceriotti M. Efficient implementation of atom-density representations. J Chem Phys 2021; 154:114109. [DOI: 10.1063/5.0044689] [Citation(s) in RCA: 23] [Impact Index Per Article: 7.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Félix Musil
- Laboratory of Computational Science and Modeling, Institute of Materials, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
- National Center for Computational Design and Discovery of Novel Materials (MARVEL), Lausanne, Switzerland
| | - Max Veit
- Laboratory of Computational Science and Modeling, Institute of Materials, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
- National Center for Computational Design and Discovery of Novel Materials (MARVEL), Lausanne, Switzerland
| | - Alexander Goscinski
- Laboratory of Computational Science and Modeling, Institute of Materials, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - Guillaume Fraux
- Laboratory of Computational Science and Modeling, Institute of Materials, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - Michael J. Willatt
- Laboratory of Computational Science and Modeling, Institute of Materials, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - Markus Stricker
- Laboratory for Multiscale Mechanics Modeling, Institute of Mechanical Engineering, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
- Interdisciplinary Centre for Advanced Materials Simulation, Ruhr-University Bochum, Universitätsstraße 150, 44801 Bochum, Germany
| | - Till Junge
- Laboratory for Multiscale Mechanics Modeling, Institute of Mechanical Engineering, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - Michele Ceriotti
- Laboratory of Computational Science and Modeling, Institute of Materials, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
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24
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Radhakrishnan R. A survey of multiscale modeling: Foundations, historical milestones, current status, and future prospects. AIChE J 2021; 67:e17026. [PMID: 33790479 PMCID: PMC7988612 DOI: 10.1002/aic.17026] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/08/2020] [Revised: 08/09/2020] [Accepted: 08/13/2020] [Indexed: 01/14/2023]
Abstract
Research problems in the domains of physical, engineering, biological sciences often span multiple time and length scales, owing to the complexity of information transfer underlying mechanisms. Multiscale modeling (MSM) and high-performance computing (HPC) have emerged as indispensable tools for tackling such complex problems. We review the foundations, historical developments, and current paradigms in MSM. A paradigm shift in MSM implementations is being fueled by the rapid advances and emerging paradigms in HPC at the dawn of exascale computing. Moreover, amidst the explosion of data science, engineering, and medicine, machine learning (ML) integrated with MSM is poised to enhance the capabilities of standard MSM approaches significantly, particularly in the face of increasing problem complexity. The potential to blend MSM, HPC, and ML presents opportunities for unbound innovation and promises to represent the future of MSM and explainable ML that will likely define the fields in the 21st century.
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Affiliation(s)
- Ravi Radhakrishnan
- Department of Chemical and Biomolecular EngineeringPenn Institute for Computational Science, University of PennsylvaniaPhiladelphiaPhiladelphiaUSA
- Department of BioengineeringPenn Institute for Computational Science, University of PennsylvaniaPhiladelphiaPhiladelphiaUSA
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25
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Karmakar T, Invernizzi M, Rizzi V, Parrinello M. Collective variables for the study of crystallisation. Mol Phys 2021. [DOI: 10.1080/00268976.2021.1893848] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/30/2023]
Affiliation(s)
- Tarak Karmakar
- Institute of Computational Sciences, Faculty of Informatics, Universit della Svizzera italiana, Lugano, Switzerland
- Department of Chemistry and Applied Biosciences, ETH Zurich, Zurich, Switzerland
- Italian Institute of Technology, Genova, Italy
| | - Michele Invernizzi
- Institute of Computational Sciences, Faculty of Informatics, Universit della Svizzera italiana, Lugano, Switzerland
- Italian Institute of Technology, Genova, Italy
- Department of Physics, ETH Zurich, Zurich, Switzerland
| | - Valerio Rizzi
- Institute of Computational Sciences, Faculty of Informatics, Universit della Svizzera italiana, Lugano, Switzerland
- Department of Chemistry and Applied Biosciences, ETH Zurich, Zurich, Switzerland
- Italian Institute of Technology, Genova, Italy
| | - Michele Parrinello
- Institute of Computational Sciences, Faculty of Informatics, Universit della Svizzera italiana, Lugano, Switzerland
- Department of Chemistry and Applied Biosciences, ETH Zurich, Zurich, Switzerland
- Italian Institute of Technology, Genova, Italy
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26
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Chen M. Collective variable-based enhanced sampling and machine learning. THE EUROPEAN PHYSICAL JOURNAL. B 2021; 94:211. [PMID: 34697536 PMCID: PMC8527828 DOI: 10.1140/epjb/s10051-021-00220-w] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/02/2021] [Accepted: 10/03/2021] [Indexed: 05/14/2023]
Abstract
ABSTRACT Collective variable-based enhanced sampling methods have been widely used to study thermodynamic properties of complex systems. Efficiency and accuracy of these enhanced sampling methods are affected by two factors: constructing appropriate collective variables for enhanced sampling and generating accurate free energy surfaces. Recently, many machine learning techniques have been developed to improve the quality of collective variables and the accuracy of free energy surfaces. Although machine learning has achieved great successes in improving enhanced sampling methods, there are still many challenges and open questions. In this perspective, we shall review recent developments on integrating machine learning techniques and collective variable-based enhanced sampling approaches. We also discuss challenges and future research directions including generating kinetic information, exploring high-dimensional free energy surfaces, and efficiently sampling all-atom configurations.
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Affiliation(s)
- Ming Chen
- Department of Chemistry, Purdue University, West Lafayette, IN 47907 USA
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27
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Song H, Vogt-Maranto L, Wiscons R, Matzger AJ, Tuckerman ME. Generating Cocrystal Polymorphs with Information Entropy Driven by Molecular Dynamics-Based Enhanced Sampling. J Phys Chem Lett 2020; 11:9751-9758. [PMID: 33141590 DOI: 10.1021/acs.jpclett.0c02647] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Predicting structures of organic molecular cocrystals is a challenging task when considering the immense number of possible intermolecular orientations. Use of the Shannon information entropy, constructed from an intermolecular orientational spatial distribution function, to drive a search for crystal structures via enhanced molecular dynamics can be an efficient way to map out a landscape of putative polymorphs. Here, the Shannon entropy is used to generate a set of collective variables for differentiating polymorphs of a 1:1 cocrystal of resorcinol and urea. We show that driven adiabatic free energy dynamics, a particular enhanced-sampling approach, combined with these entropy variables, can transform the stable phase into alternate polymorphs. Density functional theory calculations confirm that a structure obtained from the enhanced molecular dynamics is stable at pressures above 1 GPa. We thus show that enhanced sampling should be considered an integral component of crystal structure searching protocols for systems with multiple independent molecules.
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Affiliation(s)
- Hongxing Song
- Department of Chemistry, New York University, New York, New York 10003, United States
| | - Leslie Vogt-Maranto
- Department of Chemistry, New York University, New York, New York 10003, United States
| | - Ren Wiscons
- Department of Chemistry and Macromolecular Science and Engineering Program, University of Michigan, 930 North University Avenue, Ann Arbor, Michigan 48109-1055, United States
| | - Adam J Matzger
- Department of Chemistry and Macromolecular Science and Engineering Program, University of Michigan, 930 North University Avenue, Ann Arbor, Michigan 48109-1055, United States
| | - Mark E Tuckerman
- Department of Chemistry, New York University, New York, New York 10003, United States
- Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, United States
- NYU-ECNU Center for Computational Chemistry at NYU Shanghai, 3663 Zhongshan Road North, Shanghai 200062, China
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28
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Bogojeski M, Vogt-Maranto L, Tuckerman ME, Müller KR, Burke K. Quantum chemical accuracy from density functional approximations via machine learning. Nat Commun 2020; 11:5223. [PMID: 33067479 PMCID: PMC7567867 DOI: 10.1038/s41467-020-19093-1] [Citation(s) in RCA: 121] [Impact Index Per Article: 30.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2020] [Accepted: 09/24/2020] [Indexed: 12/21/2022] Open
Abstract
Kohn-Sham density functional theory (DFT) is a standard tool in most branches of chemistry, but accuracies for many molecules are limited to 2-3 kcal ⋅ mol-1 with presently-available functionals. Ab initio methods, such as coupled-cluster, routinely produce much higher accuracy, but computational costs limit their application to small molecules. In this paper, we leverage machine learning to calculate coupled-cluster energies from DFT densities, reaching quantum chemical accuracy (errors below 1 kcal ⋅ mol-1) on test data. Moreover, density-based Δ-learning (learning only the correction to a standard DFT calculation, termed Δ-DFT ) significantly reduces the amount of training data required, particularly when molecular symmetries are included. The robustness of Δ-DFT is highlighted by correcting "on the fly" DFT-based molecular dynamics (MD) simulations of resorcinol (C6H4(OH)2) to obtain MD trajectories with coupled-cluster accuracy. We conclude, therefore, that Δ-DFT facilitates running gas-phase MD simulations with quantum chemical accuracy, even for strained geometries and conformer changes where standard DFT fails.
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Affiliation(s)
- Mihail Bogojeski
- Machine Learning Group, Technische Universität Berlin, Marchstr. 23, 10587, Berlin, Germany
| | | | - Mark E Tuckerman
- Department of Chemistry, New York University, New York, NY, 10003, USA.
- Courant Institute of Mathematical Science, New York University, New York, NY, 10012, USA.
- NYU-ECNU Center for Computational Chemistry at NYU Shanghai, 3663 Zhongshan Road North, Shanghai, 200062, China.
| | - Klaus-Robert Müller
- Machine Learning Group, Technische Universität Berlin, Marchstr. 23, 10587, Berlin, Germany.
- Department of Artificial Intelligence, Korea University, Anam-dong, Seongbuk-gu, Seoul, 02841, Korea.
- Max-Planck-Institut für Informatik, Stuhlsatzenhausweg, 66123, Saarbrücken, Germany.
| | - Kieron Burke
- Department of Physics and Astronomy, University of California, Irvine, CA, 92697, USA.
- Department of Chemistry, University of California, Irvine, CA, 92697, USA.
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29
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Kamrava S, Tahmasebi P, Sahimi M, Arbabi S. Phase transitions, percolation, fracture of materials, and deep learning. Phys Rev E 2020; 102:011001. [PMID: 32794896 DOI: 10.1103/physreve.102.011001] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/05/2020] [Accepted: 06/24/2020] [Indexed: 11/07/2022]
Abstract
Percolation and fracture propagation in disordered solids represent two important problems in science and engineering that are characterized by phase transitions: loss of macroscopic connectivity at the percolation threshold p_{c} and formation of a macroscopic fracture network at the incipient fracture point (IFP). Percolation also represents the fracture problem in the limit of very strong disorder. An important unsolved problem is accurate prediction of physical properties of systems undergoing such transitions, given limited data far from the transition point. There is currently no theoretical method that can use limited data for a region far from a transition point p_{c} or the IFP and predict the physical properties all the way to that point, including their location. We present a deep neural network (DNN) for predicting such properties of two- and three-dimensional systems and in particular their percolation probability, the threshold p_{c}, the elastic moduli, and the universal Poisson ratio at p_{c}. All the predictions are in excellent agreement with the data. In particular, the DNN predicts correctly p_{c}, even though the training data were for the state of the systems far from p_{c}. This opens up the possibility of using the DNN for predicting physical properties of many types of disordered materials that undergo phase transformation, for which limited data are available for only far from the transition point.
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Affiliation(s)
- Serveh Kamrava
- Mork Family Department of Chemical Engineering and Materials Science, University of Southern California, Los Angeles, California 90089-1211, USA
| | - Pejman Tahmasebi
- Department of Petroleum Engineering, University of Wyoming, Laramie, Wyoming 82071, USA
| | - Muhammad Sahimi
- Mork Family Department of Chemical Engineering and Materials Science, University of Southern California, Los Angeles, California 90089-1211, USA
| | - Sepehr Arbabi
- Department of Chemical Engineering, University of Texas of the Permian Basin, Odessa, Texas 79762, USA
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Zhang J, Lei YK, Zhang Z, Chang J, Li M, Han X, Yang L, Yang YI, Gao YQ. A Perspective on Deep Learning for Molecular Modeling and Simulations. J Phys Chem B 2020. [DOI: 10.1021/acs.jpcb.0c04473] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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31
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Zhang J, Lei YK, Zhang Z, Chang J, Li M, Han X, Yang L, Yang YI, Gao YQ. A Perspective on Deep Learning for Molecular Modeling and Simulations. J Phys Chem A 2020; 124:6745-6763. [PMID: 32786668 DOI: 10.1021/acs.jpca.0c04473] [Citation(s) in RCA: 24] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
Abstract
Deep learning is transforming many areas in science, and it has great potential in modeling molecular systems. However, unlike the mature deployment of deep learning in computer vision and natural language processing, its development in molecular modeling and simulations is still at an early stage, largely because the inductive biases of molecules are completely different from those of images or texts. Footed on these differences, we first reviewed the limitations of traditional deep learning models from the perspective of molecular physics and wrapped up some relevant technical advancement at the interface between molecular modeling and deep learning. We do not focus merely on the ever more complex neural network models; instead, we introduce various useful concepts and ideas brought by modern deep learning. We hope that transacting these ideas into molecular modeling will create new opportunities. For this purpose, we summarized several representative applications, ranging from supervised to unsupervised and reinforcement learning, and discussed their connections with the emerging trends in deep learning. Finally, we give an outlook for promising directions which may help address the existing issues in the current framework of deep molecular modeling.
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Affiliation(s)
- Jun Zhang
- Institute of Systems and Physical Biology, Shenzhen Bay Laboratory, 518055 Shenzhen, China
- Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
| | - Yao-Kun Lei
- Beijing National Laboratory for Molecular Sciences, College of Chemistry and Molecular Engineering, Peking University, 100871 Beijing, China
| | - Zhen Zhang
- Department of Physics, Tangshan Normal University, 063000 Tangshan, China
| | - Junhan Chang
- Beijing National Laboratory for Molecular Sciences, College of Chemistry and Molecular Engineering, Peking University, 100871 Beijing, China
| | - Maodong Li
- Institute of Systems and Physical Biology, Shenzhen Bay Laboratory, 518055 Shenzhen, China
| | - Xu Han
- Beijing National Laboratory for Molecular Sciences, College of Chemistry and Molecular Engineering, Peking University, 100871 Beijing, China
| | - Lijiang Yang
- Beijing National Laboratory for Molecular Sciences, College of Chemistry and Molecular Engineering, Peking University, 100871 Beijing, China
| | - Yi Isaac Yang
- Institute of Systems and Physical Biology, Shenzhen Bay Laboratory, 518055 Shenzhen, China
| | - Yi Qin Gao
- Institute of Systems and Physical Biology, Shenzhen Bay Laboratory, 518055 Shenzhen, China
- Beijing National Laboratory for Molecular Sciences, College of Chemistry and Molecular Engineering, Peking University, 100871 Beijing, China
- Beijing Advanced Innovation Center for Genomics, Peking University, 100871 Beijing, China
- Biomedical Pioneering Innovation Center, Peking University, 100871 Beijing, China
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32
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Bonati L, Rizzi V, Parrinello M. Data-Driven Collective Variables for Enhanced Sampling. J Phys Chem Lett 2020; 11:2998-3004. [PMID: 32239945 DOI: 10.1021/acs.jpclett.0c00535] [Citation(s) in RCA: 74] [Impact Index Per Article: 18.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Designing an appropriate set of collective variables is crucial to the success of several enhanced sampling methods. Here we focus on how to obtain such variables from information limited to the metastable states. We characterize these states by a large set of descriptors and employ neural networks to compress this information in a lower-dimensional space, using Fisher's linear discriminant as an objective function to maximize the discriminative power of the network. We test this method on alanine dipeptide, using the nonlinearly separable data set composed by atomic distances. We then study an intermolecular aldol reaction characterized by a concerted mechanism. The resulting variables are able to promote sampling by drawing nonlinear paths in the physical space connecting the fluctuations between metastable basins. Lastly, we interpret the behavior of the neural network by studying its relation to the physical variables. Through the identification of its most relevant features, we are able to gain chemical insight into the process.
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Affiliation(s)
- Luigi Bonati
- Department of Physics, ETH Zurich, 8092 Zurich, Switzerland
- Institute of Computational Sciences, Università della Svizzera italiana, via Buffi 13, 6900 Lugano, Switzerland
| | - Valerio Rizzi
- Institute of Computational Sciences, Università della Svizzera italiana, via Buffi 13, 6900 Lugano, Switzerland
- Department of Chemistry and Applied Biosciences, ETH Zurich, 8092 Zurich, Switzerland
| | - Michele Parrinello
- Institute of Computational Sciences, Università della Svizzera italiana, via Buffi 13, 6900 Lugano, Switzerland
- Department of Chemistry and Applied Biosciences, ETH Zurich, 8092 Zurich, Switzerland
- Italian Institute of Technology, Via Morego 30, 16163 Genova, Italy
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