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Ehrlacher V, Lelièvre T, Monmarché P. Adaptive force biasing algorithms: New convergence results and tensor approximations of the bias. ANN APPL PROBAB 2022. [DOI: 10.1214/21-aap1775] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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2
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Appeldorn JH, Lemcke S, Speck T, Nikoubashman A. Employing Artificial Neural Networks to Identify Reaction Coordinates and Pathways for Self-Assembly. J Phys Chem B 2022; 126:5007-5016. [DOI: 10.1021/acs.jpcb.2c02232] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
Affiliation(s)
- Jörn H. Appeldorn
- Institute of Physics, Johannes Gutenberg-University Mainz, Staudingerweg 7-9, 55128 Mainz, Germany
| | - Simon Lemcke
- Institute of Physics, Johannes Gutenberg-University Mainz, Staudingerweg 7-9, 55128 Mainz, Germany
| | - Thomas Speck
- Institute of Physics, Johannes Gutenberg-University Mainz, Staudingerweg 7-9, 55128 Mainz, Germany
| | - Arash Nikoubashman
- Institute of Physics, Johannes Gutenberg-University Mainz, Staudingerweg 7-9, 55128 Mainz, Germany
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3
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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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4
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Paul TK, Taraphder S. Nonlinear Reaction Coordinate of an Enzyme Catalyzed Proton Transfer Reaction. J Phys Chem B 2022; 126:1413-1425. [PMID: 35138854 DOI: 10.1021/acs.jpcb.1c08760] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Abstract
We present an in-depth study on the theoretical calculation of an optimum reaction coordinate as a linear or nonlinear combination of important collective variables (CVs) sampled from an ensemble of reactive transition paths for an intramolecular proton transfer reaction catalyzed by the enzyme human carbonic anhydrase (HCA) II. The linear models are optimized by likelihood maximization for a given number of CVs. The nonlinear models are based on an artificial neural network with the same number of CVs and optimized by minimizing the root-mean-square error in comparison to a training set of committor estimators generated for the given transition. The nonlinear reaction coordinate thus obtained yields the free energy of activation and rate constant as 9.46 kcal mol-1 and 1.25 × 106 s-1, respectively. These estimates are found to be in quantitative agreement with the known experimental results. We have also used an extended autoencoder model to show that a similar analysis can be carried out using a single CV only. The resultant free energies and kinetics of the reaction slightly overestimate the experimental data. The implications of these results are discussed using a detailed microkinetic scheme of the proton transfer reaction catalyzed by HCA II.
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Affiliation(s)
- Tanmoy Kumar Paul
- Department of Chemistry, Indian Institute of Technology Kharagpur, Kharagpur 721302, India
| | - Srabani Taraphder
- Department of Chemistry, Indian Institute of Technology Kharagpur, Kharagpur 721302, India
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5
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González-Fernández C, Bringas E, Oostenbrink C, Ortiz I. In silico investigation and surmounting of Lipopolysaccharide barrier in Gram-Negative Bacteria: How far has molecular dynamics Come? Comput Struct Biotechnol J 2022; 20:5886-5901. [PMID: 36382192 PMCID: PMC9636410 DOI: 10.1016/j.csbj.2022.10.039] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/26/2022] [Revised: 10/24/2022] [Accepted: 10/24/2022] [Indexed: 11/29/2022] Open
Abstract
Lipopolysaccharide (LPS), a main component of the outer membrane of Gram-negative bacteria, has crucial implications on both antibiotic resistance and the overstimulation of the host innate immune system. Fighting against these global concerns calls for the molecular understanding of the barrier function and immunostimulatory ability of LPS. Molecular dynamics (MD) simulations have become an invaluable tool for uncovering important findings in LPS research. While the reach of MD simulations for investigating the immunostimulatory ability of LPS has been already outlined, little attention has been paid to the role of MD simulations for exploring its barrier function and synthesis. Herein, we give an overview about the impact of MD simulations on gaining insight into the shield role and synthesis pathway of LPS, which have attracted considerable attention to discover molecules able to surmount antibiotic resistance, either circumventing LPS defenses or disrupting its synthesis. We specifically focus on the enhanced sampling and free energy calculation methods that have been combined with MD simulations to address such research. We also highlight the use of special-purpose MD supercomputers, the importance of appropriate LPS and ions parameterization to obtain reliable results, and the complementary views that MD and wet-lab experiments provide. Thereby, this work, which covers the last five years of research, apart from outlining the phenomena and strategies that are being explored, evidences the valuable insights that are gained by MD, which may be useful to advance antibiotic design, and what the prospects of this in silico method could be in LPS research.
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Affiliation(s)
- Cristina González-Fernández
- Department of Chemical and Biomolecular Engineering, ETSIIT, University of Cantabria, Avda. Los Castros s/n, 39005 Santander, Spain
| | - Eugenio Bringas
- Department of Chemical and Biomolecular Engineering, ETSIIT, University of Cantabria, Avda. Los Castros s/n, 39005 Santander, Spain
| | - Chris Oostenbrink
- Institute for Molecular Modeling and Simulation, BOKU – University of Natural Resources and Life Sciences, Muthgasse 18, 1190 Vienna, Austria
| | - Inmaculada Ortiz
- Department of Chemical and Biomolecular Engineering, ETSIIT, University of Cantabria, Avda. Los Castros s/n, 39005 Santander, Spain
- Corresponding author.
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6
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Vlachas PR, Zavadlav J, Praprotnik M, Koumoutsakos P. Accelerated Simulations of Molecular Systems through Learning of Effective Dynamics. J Chem Theory Comput 2021; 18:538-549. [PMID: 34890204 DOI: 10.1021/acs.jctc.1c00809] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Abstract
Simulations are vital for understanding and predicting the evolution of complex molecular systems. However, despite advances in algorithms and special purpose hardware, accessing the time scales necessary to capture the structural evolution of biomolecules remains a daunting task. In this work, we present a novel framework to advance simulation time scales by up to 3 orders of magnitude by learning the effective dynamics (LED) of molecular systems. LED augments the equation-free methodology by employing a probabilistic mapping between coarse and fine scales using mixture density network (MDN) autoencoders and evolves the non-Markovian latent dynamics using long short-term memory MDNs. We demonstrate the effectiveness of LED in the Müller-Brown potential, the Trp cage protein, and the alanine dipeptide. LED identifies explainable reduced-order representations, i.e., collective variables, and can generate, at any instant, all-atom molecular trajectories consistent with the collective variables. We believe that the proposed framework provides a dramatic increase to simulation capabilities and opens new horizons for the effective modeling of complex molecular systems.
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Affiliation(s)
- Pantelis R Vlachas
- Computational Science and Engineering Laboratory, ETH Zurich, CH-8092, Switzerland
| | - Julija Zavadlav
- Professorship of Multiscale Modeling of Fluid Materials, TUM School of Engineering and Design, Technical University of Munich, 85748 Garching bei München, Germany.,Munich Data Science Institute, Technical University of Munich, 85748 Munich, Germany
| | - Matej Praprotnik
- Laboratory for Molecular Modeling, National Institute of Chemistry, SI-1001 Ljubljana, Slovenia.,Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, SI-1000 Ljubljana, Slovenia
| | - Petros Koumoutsakos
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, United States
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7
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Tsai ST, Smith Z, Tiwary P. SGOOP-d: Estimating Kinetic Distances and Reaction Coordinate Dimensionality for Rare Event Systems from Biased/Unbiased Simulations. J Chem Theory Comput 2021; 17:6757-6765. [PMID: 34662516 DOI: 10.1021/acs.jctc.1c00431] [Citation(s) in RCA: 17] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022]
Abstract
Understanding kinetics including reaction pathways and associated transition rates is an important yet difficult problem in numerous chemical and biological systems, especially in situations with multiple competing pathways. When these high-dimensional systems are projected on low-dimensional coordinates, which are often needed for enhanced sampling or for interpretation of simulations and experiments, one can end up losing the kinetic connectivity of the underlying high-dimensional landscape. Thus, in the low-dimensional projection, metastable states might appear closer or further than they actually are. To deal with this issue, in this work, we develop a formalism that learns a multidimensional yet minimally complex reaction coordinate (RC) for generic high-dimensional systems. When projected along this RC, all possible kinetically relevant pathways can be demarcated and the true high-dimensional connectivity is maintained. One of the defining attributes of our method lies in that it can work on long unbiased simulations as well as biased simulations often needed for rare event systems. We demonstrate the utility of the method by studying a range of model systems including conformational transitions in a small peptide Ace-Ala3-Nme, where we show how two-dimensional and three-dimensional RCs found by our previously published spectral gap optimization method "SGOOP" [Tiwary, P. and Berne, B. J. Proc. Natl. Acad. Sci. 2016, 113, 2839] can capture the kinetics for 23 and all 28 out of the 28 dominant state-to-state transitions, respectively.
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Affiliation(s)
- Sun-Ting Tsai
- Department of Physics and Institute for Physical Science and Technology, University of Maryland, College Park 20742, Maryland, United States
| | - Zachary Smith
- Biophysics Program and Institute for Physical Science and Technology, University of Maryland, College Park 20742, Maryland, United States
| | - Pratyush Tiwary
- Department of Chemistry and Biochemistry and Institute for Physical Science and Technology, University of Maryland, College Park 20742, Maryland, United States
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Thomas T, Roux B. TYROSINE KINASES: COMPLEX MOLECULAR SYSTEMS CHALLENGING COMPUTATIONAL METHODOLOGIES. THE EUROPEAN PHYSICAL JOURNAL. B 2021; 94:203. [PMID: 36524055 PMCID: PMC9749240 DOI: 10.1140/epjb/s10051-021-00207-7] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/22/2021] [Accepted: 09/14/2021] [Indexed: 05/28/2023]
Abstract
Classical molecular dynamics (MD) simulations based on atomic models play an increasingly important role in a wide range of applications in physics, biology, and chemistry. Nonetheless, generating genuine knowledge about biological systems using MD simulations remains challenging. Protein tyrosine kinases are important cellular signaling enzymes that regulate cell growth, proliferation, metabolism, differentiation, and migration. Due to the large conformational changes and long timescales involved in their function, these kinases present particularly challenging problems to modern computational and theoretical frameworks aimed at elucidating the dynamics of complex biomolecular systems. Markov state models have achieved limited success in tackling the broader conformational ensemble and biased methods are often employed to examine specific long timescale events. Recent advances in machine learning continue to push the limitations of current methodologies and provide notable improvements when integrated with the existing frameworks. A broad perspective is drawn from a critical review of recent studies.
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Glielmo A, Husic BE, Rodriguez A, Clementi C, Noé F, Laio A. Unsupervised Learning Methods for Molecular Simulation Data. Chem Rev 2021; 121:9722-9758. [PMID: 33945269 PMCID: PMC8391792 DOI: 10.1021/acs.chemrev.0c01195] [Citation(s) in RCA: 116] [Impact Index Per Article: 38.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/05/2020] [Indexed: 12/21/2022]
Abstract
Unsupervised learning is becoming an essential tool to analyze the increasingly large amounts of data produced by atomistic and molecular simulations, in material science, solid state physics, biophysics, and biochemistry. In this Review, we provide a comprehensive overview of the methods of unsupervised learning that have been most commonly used to investigate simulation data and indicate likely directions for further developments in the field. In particular, we discuss feature representation of molecular systems and present state-of-the-art algorithms of dimensionality reduction, density estimation, and clustering, and kinetic models. We divide our discussion into self-contained sections, each discussing a specific method. In each section, we briefly touch upon the mathematical and algorithmic foundations of the method, highlight its strengths and limitations, and describe the specific ways in which it has been used-or can be used-to analyze molecular simulation data.
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Affiliation(s)
- Aldo Glielmo
- International
School for Advanced Studies (SISSA) 34014 Trieste, Italy
| | - Brooke E. Husic
- Freie
Universität Berlin, Department of Mathematics
and Computer Science, 14195 Berlin, Germany
| | - Alex Rodriguez
- International Centre for Theoretical
Physics (ICTP), Condensed Matter and Statistical
Physics Section, 34100 Trieste, Italy
| | - Cecilia Clementi
- Freie
Universität Berlin, Department for
Physics, 14195 Berlin, Germany
- Rice
University Houston, Department of Chemistry, Houston, Texas 77005, United States
| | - Frank Noé
- Freie
Universität Berlin, Department of Mathematics
and Computer Science, 14195 Berlin, Germany
- Freie
Universität Berlin, Department for
Physics, 14195 Berlin, Germany
- Rice
University Houston, Department of Chemistry, Houston, Texas 77005, United States
| | - Alessandro Laio
- International
School for Advanced Studies (SISSA) 34014 Trieste, Italy
- International Centre for Theoretical
Physics (ICTP), Condensed Matter and Statistical
Physics Section, 34100 Trieste, Italy
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10
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Klus S, Bittracher A, Schuster I, Schütte C. A kernel-based approach to molecular conformation analysis. J Chem Phys 2018; 149:244109. [DOI: 10.1063/1.5063533] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022] Open
Affiliation(s)
- Stefan Klus
- Department of Mathematics and Computer Science, Freie Universität Berlin, 14195 Berlin, Germany
| | - Andreas Bittracher
- Department of Mathematics and Computer Science, Freie Universität Berlin, 14195 Berlin, Germany
| | | | - Christof Schütte
- Department of Mathematics and Computer Science, Freie Universität Berlin, 14195 Berlin, Germany
- Zuse Institute Berlin, 14195 Berlin, Germany
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