1
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France-Lanord A, Vroylandt H, Salanne M, Rotenberg B, Saitta AM, Pietrucci F. Data-Driven Path Collective Variables. J Chem Theory Comput 2024; 20:3069-3084. [PMID: 38619076 DOI: 10.1021/acs.jctc.4c00123] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/16/2024]
Abstract
Identifying optimal collective variables to model transformations using atomic-scale simulations is a long-standing challenge. We propose a new method for the generation, optimization, and comparison of collective variables that can be thought of as a data-driven generalization of the path collective variable concept. It consists of a kernel ridge regression of the committor probability, which encodes a transformation's progress. The resulting collective variable is one-dimensional, interpretable, and differentiable, making it appropriate for enhanced sampling simulations requiring biasing. We demonstrate the validity of the method on two different applications: a precipitation model and the association of Li+ and F- in water. For the former, we show that global descriptors such as the permutation invariant vector allow reaching an accuracy far from the one achieved via simpler, more intuitive variables. For the latter, we show that information correlated with the transformation mechanism is contained in the first solvation shell only and that inertial effects prevent the derivation of optimal collective variables from the atomic positions only.
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Affiliation(s)
- Arthur France-Lanord
- Institut des Sciences du Calcul et des Données, ISCD, Sorbonne Université, F-75005 Paris, France
- Muséum National d'Histoire Naturelle, UMR CNRS 7590, Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie, IMPMC, Sorbonne Université, F-75005 Paris, France
| | - Hadrien Vroylandt
- Institut des Sciences du Calcul et des Données, ISCD, Sorbonne Université, F-75005 Paris, France
| | - Mathieu Salanne
- Physicochimie des Électrolytes et Nanosystèmes Interfaciaux, Sorbonne Université, CNRS, 4 Place Jussieu, F-75005 Paris, France
- Institut Universitaire de France (IUF), 75231 Paris, France
| | - Benjamin Rotenberg
- Physicochimie des Électrolytes et Nanosystèmes Interfaciaux, Sorbonne Université, CNRS, 4 Place Jussieu, F-75005 Paris, France
| | - A Marco Saitta
- Muséum National d'Histoire Naturelle, UMR CNRS 7590, Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie, IMPMC, Sorbonne Université, F-75005 Paris, France
| | - Fabio Pietrucci
- Muséum National d'Histoire Naturelle, UMR CNRS 7590, Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie, IMPMC, Sorbonne Université, F-75005 Paris, France
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2
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Liu Y, Ghosh TK, Lin G, Chen M. Unbiasing Enhanced Sampling on a High-Dimensional Free Energy Surface with a Deep Generative Model. J Phys Chem Lett 2024; 15:3938-3945. [PMID: 38568182 DOI: 10.1021/acs.jpclett.3c03515] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/12/2024]
Abstract
Biased enhanced sampling methods that utilize collective variables (CVs) are powerful tools for sampling conformational ensembles. Due to their large intrinsic dimensions, efficiently generating conformational ensembles for complex systems requires enhanced sampling on high-dimensional free energy surfaces. While temperature-accelerated molecular dynamics (TAMD) can trivially adopt many CVs in a simulation, unbiasing the simulation to generate unbiased conformational ensembles requires accurate modeling of a high-dimensional CV probability distribution, which is challenging for traditional density estimation techniques. Here we propose an unbiasing method based on the score-based diffusion model, a deep generative learning method that excels in density estimation across complex data landscapes. We demonstrate that this unbiasing approach, tested on multiple TAMD simulations, significantly outperforms traditional unbiasing methods and can generate accurate unbiased conformational ensembles. With the proposed approach, TAMD can adopt CVs that focus on improving sampling efficiency and the proposed unbiasing method enables accurate evaluation of ensemble averages of important chemical features.
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Affiliation(s)
- Yikai Liu
- Department of Mechanical Engineering, Purdue University, West Lafayette, Indiana 47906, United States
| | - Tushar K Ghosh
- Department of Chemistry, Purdue University, West Lafayette, Indiana 47906, United States
| | - Guang Lin
- Department of Mechanical Engineering, Purdue University, West Lafayette, Indiana 47906, United States
| | - Ming Chen
- Department of Chemistry, Purdue University, West Lafayette, Indiana 47906, United States
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3
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Giese TJ, Ekesan Ş, McCarthy E, Tao Y, York DM. Surface-Accelerated String Method for Locating Minimum Free Energy Paths. J Chem Theory Comput 2024; 20:2058-2073. [PMID: 38367218 PMCID: PMC11059188 DOI: 10.1021/acs.jctc.3c01401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/19/2024]
Abstract
We present a surface-accelerated string method (SASM) to efficiently optimize low-dimensional reaction pathways from the sampling performed with expensive quantum mechanical/molecular mechanical (QM/MM) Hamiltonians. The SASM accelerates the convergence of the path using the aggregate sampling obtained from the current and previous string iterations, whereas approaches like the string method in collective variables (SMCV) or the modified string method in collective variables (MSMCV) update the path only from the sampling obtained from the current iteration. Furthermore, the SASM decouples the number of images used to perform sampling from the number of synthetic images used to represent the path. The path is optimized on the current best estimate of the free energy surface obtained from all available sampling, and the proposed set of new simulations is not restricted to being located along the optimized path. Instead, the umbrella potential placement is chosen to extend the range of the free energy surface and improve the quality of the free energy estimates near the path. In this manner, the SASM is shown to improve the exploration for a minimum free energy pathway in regions where the free energy surface is relatively flat. Furthermore, it improves the quality of the free energy profile when the string is discretized with too few images. We compare the SASM, SMCV, and MSMCV using 3 QM/MM applications: a ribozyme methyltransferase reaction using 2 reaction coordinates, the 2'-O-transphosphorylation reaction of Hammerhead ribozyme using 3 reaction coordinates, and a tautomeric reaction in B-DNA using 5 reaction coordinates. We show that SASM converges the paths using roughly 3 times less sampling than the SMCV and MSMCV methods. All three algorithms have been implemented in the FE-ToolKit package made freely available.
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Affiliation(s)
- Timothy J. Giese
- Laboratory for Biomolecular Simulation Research, Institute for Quantitative Biomedicine and Department of Chemistry and Chemical Biology, Rutgers University, Piscataway, NJ 08854, USA
| | - Şölen Ekesan
- Laboratory for Biomolecular Simulation Research, Institute for Quantitative Biomedicine and Department of Chemistry and Chemical Biology, Rutgers University, Piscataway, NJ 08854, USA
| | - Erika McCarthy
- Laboratory for Biomolecular Simulation Research, Institute for Quantitative Biomedicine and Department of Chemistry and Chemical Biology, Rutgers University, Piscataway, NJ 08854, USA
| | - Yujun Tao
- Laboratory for Biomolecular Simulation Research, Institute for Quantitative Biomedicine and Department of Chemistry and Chemical Biology, Rutgers University, Piscataway, NJ 08854, USA
| | - Darrin M. York
- Laboratory for Biomolecular Simulation Research, Institute for Quantitative Biomedicine and Department of Chemistry and Chemical Biology, Rutgers University, Piscataway, NJ 08854, USA
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4
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Rydzewski J, Gökdemir T. Learning Markovian dynamics with spectral maps. J Chem Phys 2024; 160:091102. [PMID: 38436438 DOI: 10.1063/5.0189241] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/27/2023] [Accepted: 02/05/2024] [Indexed: 03/05/2024] Open
Abstract
The long-time behavior of many complex molecular systems can often be described by Markovian dynamics in a slow subspace spanned by a few reaction coordinates referred to as collective variables (CVs). However, determining CVs poses a fundamental challenge in chemical physics. Depending on intuition or trial and error to construct CVs can lead to non-Markovian dynamics with long memory effects, hindering analysis. To address this problem, we continue to develop a recently introduced deep-learning technique called spectral map [J. Rydzewski, J. Phys. Chem. Lett. 14, 5216-5220 (2023)]. Spectral map learns slow CVs by maximizing a spectral gap of a Markov transition matrix describing anisotropic diffusion. Here, to represent heterogeneous and multiscale free-energy landscapes with spectral map, we implement an adaptive algorithm to estimate transition probabilities. Through a Markov state model analysis, we validate that spectral map learns slow CVs related to the dominant relaxation timescales and discerns between long-lived metastable states.
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Affiliation(s)
- Jakub Rydzewski
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, Grudziadzka 5, 87-100 Toruń, Poland
| | - Tuğçe Gökdemir
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, Grudziadzka 5, 87-100 Toruń, Poland
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5
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Lücke M, Winkelmann S, Heitzig J, Molkenthin N, Koltai P. Learning interpretable collective variables for spreading processes on networks. Phys Rev E 2024; 109:L022301. [PMID: 38491651 DOI: 10.1103/physreve.109.l022301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2023] [Accepted: 12/28/2023] [Indexed: 03/18/2024]
Abstract
Collective variables (CVs) are low-dimensional projections of high-dimensional system states. They are used to gain insights into complex emergent dynamical behaviors of processes on networks. The relation between CVs and network measures is not well understood and its derivation typically requires detailed knowledge of both the dynamical system and the network topology. In this Letter, we present a data-driven method for algorithmically learning and understanding CVs for binary-state spreading processes on networks of arbitrary topology. We demonstrate our method using four example networks: the stochastic block model, a ring-shaped graph, a random regular graph, and a scale-free network generated by the Albert-Barabási model. Our results deliver evidence for the existence of low-dimensional CVs even in cases that are not yet understood theoretically.
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Affiliation(s)
- Marvin Lücke
- Modeling and Simulation of Complex Processes, Zuse Institute Berlin, 14195 Berlin, Germany
| | - Stefanie Winkelmann
- Modeling and Simulation of Complex Processes, Zuse Institute Berlin, 14195 Berlin, Germany
| | - Jobst Heitzig
- FutureLab on Game Theory and Networks of Interacting Agents, Potsdam Institute for Climate Impact Research, 14473 Potsdam, Germany and Zuse Institute Berlin, 14195 Berlin, Germany
| | - Nora Molkenthin
- Complexity Science Department, Potsdam Institute for Climate Impact Research, 14473 Potsdam, Germany
| | - Péter Koltai
- Department of Mathematics, University of Bayreuth, 95447 Bayreuth, Germany
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6
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Chen YT, Yang H, Chu JW. Trajectory Statistical Learning of the Potential Mean of Force and Diffusion Coefficient from Molecular Dynamics Simulations. J Phys Chem B 2024; 128:56-66. [PMID: 38165090 DOI: 10.1021/acs.jpcb.3c05245] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2024]
Abstract
Central to studying the conformational changes of a complex protein is understanding the dynamics and energetics involved. Phenomenologically, structural dynamics can be formulated using an overdamped Langevin model along an observable, e.g., the distance between two residues in the protein. The Langevin model is specified by the deterministic force (the potential of mean force, PMF) and stochastic force (characterized by the diffusion coefficient, D). It is therefore of great interest to be able to extract both PMF and D from an observable time series but under the same computational framework. Here, we approach this challenge in molecular dynamics (MD) simulations by treating it as a missing-data Bayesian estimation problem. An important distinction in our methodology is that the entire MD trajectory, as opposed to the individual data elements, is used as the statistical variable in Bayesian imputation. This idea is implemented through an eigen-decomposition procedure for a time-symmetrized Fokker-Planck equation, followed by maximizing the likelihood for parameter estimation. The mathematical expressions for the functional derivatives used in learning PMF and D also provide new physical insights for the manner by which the information on both the deterministic and stochastic forces is encoded in the dynamics data. An all-atom MD simulation of a nontrivial biomolecule case is used to illustrate the application of this approach. We show that, interestingly, the results of trajectory statistical learning can motivate new order parameters for an improved description of the kinetic bottlenecks in conformational changes. Complementing purely data-driven or black-box methods, this work underscores the advantages of physics-based machine learning in gaining chemical insights from quantitative parameter estimation.
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Affiliation(s)
- Yi-Tsao Chen
- Institute of Bioinformatics and Systems Biology, National Yang Ming Chiao Tung University, Hsinchu 30010, Taiwan, Republic of China
| | - Haw Yang
- Department of Chemistry, Princeton University, Princeton, New Jersey 08544, United States
| | - Jhih-Wei Chu
- Institute of Bioinformatics and Systems Biology, Department of Biological Science and Technology, Institute of Molecular Medicine and Bioengineering, and Center for Intelligent Drug Systems and Smart Bio-Devices (IDS2B), National Yang Ming Chiao Tung University, Hsinchu 30010, Taiwan, Republic of China
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7
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Höllring K, Baer A, Vučemilović-Alagić N, Smith DM, Smith AS. Anisotropic molecular diffusion in confinement I: Transport of small particles in potential and density gradients. J Colloid Interface Sci 2023; 650:1930-1940. [PMID: 37517192 DOI: 10.1016/j.jcis.2023.07.088] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/14/2023] [Revised: 07/10/2023] [Accepted: 07/13/2023] [Indexed: 08/01/2023]
Abstract
HYPOTHESIS Diffusion in confinement is an important fundamental problem with significant implications for applications of supported liquid phases. However, resolving the spatially dependent diffusion coefficient, parallel and perpendicular to interfaces, has been a standing issue. In the vicinity of interfaces, density fluctuations as a consequence of layering locally impose statistical drift, which impedes the analysis of spatially dependent diffusion coefficients even further. We hypothesise, that we can derive a model to spatially resolve interface-perpendicular diffusion coefficients based on local lifetime statistics with an extension to explicitly account for the effect of local drift using the Smoluchowski equation, that allows us to resolve anisotropic and spatially dependent diffusivity landscapes at interfaces. METHODS AND SIMULATIONS An analytic relation between local crossing times in system slices and diffusivity as well as an explicit term for calculating drift-induced systematic errors is presented. The method is validated on Molecular Dynamics simulations of bulk water and applied to simulations of water in slit pores. FINDINGS After validation on bulk liquids, we clearly demonstrate the anisotropic nature of diffusion coefficients at interfaces. Significant spatial variations in the diffusivities correlate with interface-induced structuring but cannot be solely attributed to the drift induced by local density fluctuations.
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Affiliation(s)
- Kevin Höllring
- PULS Group, Department of Physics, Friedrich-Alexander Universität Erlangen-Nürnberg, IZNF, Cauerstraße 3, 91058 Erlangen, Germany
| | - Andreas Baer
- PULS Group, Department of Physics, Friedrich-Alexander Universität Erlangen-Nürnberg, IZNF, Cauerstraße 3, 91058 Erlangen, Germany
| | - Nataša Vučemilović-Alagić
- PULS Group, Department of Physics, Friedrich-Alexander Universität Erlangen-Nürnberg, IZNF, Cauerstraße 3, 91058 Erlangen, Germany; Group of Computational Life Sciences, Department of Physical Chemistry, Ruđer Bošković Institute, Bijenička 54, Zagreb, 10000 Croatia
| | - David M Smith
- Group of Computational Life Sciences, Department of Physical Chemistry, Ruđer Bošković Institute, Bijenička 54, Zagreb, 10000 Croatia
| | - Ana-Sunčana Smith
- PULS Group, Department of Physics, Friedrich-Alexander Universität Erlangen-Nürnberg, IZNF, Cauerstraße 3, 91058 Erlangen, Germany; Group of Computational Life Sciences, Department of Physical Chemistry, Ruđer Bošković Institute, Bijenička 54, Zagreb, 10000 Croatia.
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8
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Ko T, Heindel JP, Guan X, Head-Gordon T, Williams-Young DB, Yang C. Using Diffusion Maps to Analyze Reaction Dynamics for a Hydrogen Combustion Benchmark Dataset. J Chem Theory Comput 2023; 19:5872-5885. [PMID: 37585272 PMCID: PMC10500976 DOI: 10.1021/acs.jctc.3c00426] [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: 04/17/2023] [Indexed: 08/18/2023]
Abstract
We use local diffusion maps to assess the quality of two types of collective variables (CVs) for a recently published hydrogen combustion benchmark dataset1 that contains ab initio molecular dynamics (MD) trajectories and normal modes along minimum energy paths. This approach was recently advocated in2 for assessing CVs and analyzing reactions modeled by classical MD simulations. We report the effectiveness of this approach to molecular systems modeled by quantum ab initio MD. In addition to assessing the quality of CVs, we also use global diffusion maps to perform committor analysis as proposed in.2 We show that the committor function obtained from the global diffusion map allows us to identify transition regions of interest in several hydrogen combustion reaction channels.
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Affiliation(s)
- Taehee Ko
- Department
of Mathematics, Penn State University, University Park, Pennsylvania 16802, United States
| | - Joseph P. Heindel
- Kenneth
S. Pitzer Theory Center and Department of Chemistry, University of California, Berkeley, California 94720, United States
- Chemical
Sciences Division, Lawrence Berkeley National
Laboratory, Berkeley, California 94720, United States
| | - Xingyi Guan
- Kenneth
S. Pitzer Theory Center and Department of Chemistry, University of California, Berkeley, California 94720, United States
- Chemical
Sciences Division, Lawrence Berkeley National
Laboratory, Berkeley, California 94720, United States
| | - Teresa Head-Gordon
- Kenneth
S. Pitzer Theory Center and Department of Chemistry, University of California, Berkeley, California 94720, United States
- Departments
of Bioengineering and Chemical and Biomolecular Engineering, University of California, Berkeley, California 94720, United States
- Chemical
Sciences Division, Lawrence Berkeley National
Laboratory, Berkeley, California 94720, United States
| | - David B. Williams-Young
- Applied
Mathematics and Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Chao Yang
- Applied
Mathematics and Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
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9
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Hsu WT, Piomponi V, Merz PT, Bussi G, Shirts MR. Alchemical Metadynamics: Adding Alchemical Variables to Metadynamics to Enhance Sampling in Free Energy Calculations. J Chem Theory Comput 2023; 19:1805-1817. [PMID: 36853624 DOI: 10.1021/acs.jctc.2c01258] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/01/2023]
Abstract
Performing alchemical transformations, in which one molecular system is nonphysically changed to another system, is a popular approach adopted in performing free energy calculations associated with various biophysical processes, such as protein-ligand binding or the transfer of a molecule between environments. While the sampling of alchemical intermediate states in either parallel (e.g., Hamiltonian replica exchange) or serial manner (e.g., expanded ensemble) can bridge the high-probability regions in the configurational space between two end states of interest, alchemical methods can fail in scenarios where the most important slow degrees of freedom in the configurational space are, in large part, orthogonal to the alchemical variable, or if the system gets trapped in a deep basin extending in both the configurational and alchemical space. To alleviate these issues, we propose to use alchemical variables as an additional dimension in metadynamics, making it possible to both sample collective variables and to enhance sampling in free energy calculations simultaneously. In this study, we validate our implementation of "alchemical metadynamics" in PLUMED with test systems and alchemical processes with varying complexities and dimensionalities of collective variable space, including the interconversion between the torsional metastable states of a toy system and the methylation of a nucleoside both in the isolated form and in a duplex. We show that multidimensional alchemical metadynamics can address the challenges mentioned above and further accelerate sampling by introducing configurational collective variables. The method can trivially be combined with other metadynamics-based algorithms implemented in PLUMED. The necessary PLUMED code changes have already been released for general use in PLUMED 2.8.
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Affiliation(s)
- Wei-Tse Hsu
- Department of Chemical and Biological Engineering, University of Colorado at Boulder, Boulder, Colorado 80305, United States
| | - Valerio Piomponi
- Scuola Internazionale Superiore di Studi Avanzati, via Bonomea 265, 34136 Trieste, Italy
| | - Pascal T Merz
- Department of Chemical and Biological Engineering, University of Colorado at Boulder, Boulder, Colorado 80305, United States
| | - Giovanni Bussi
- Scuola Internazionale Superiore di Studi Avanzati, via Bonomea 265, 34136 Trieste, Italy
| | - Michael R Shirts
- Department of Chemical and Biological Engineering, University of Colorado at Boulder, Boulder, Colorado 80305, United States
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10
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She Z, Ge P, Lei H. Data-driven construction of stochastic reduced dynamics encoded with non-Markovian features. J Chem Phys 2023; 158:034102. [PMID: 36681628 DOI: 10.1063/5.0130033] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022] Open
Abstract
One important problem in constructing the reduced dynamics of molecular systems is the accurate modeling of the non-Markovian behavior arising from the dynamics of unresolved variables. The main complication emerges from the lack of scale separations, where the reduced dynamics generally exhibits pronounced memory and non-white noise terms. We propose a data-driven approach to learn the reduced model of multi-dimensional resolved variables that faithfully retains the non-Markovian dynamics. Different from the common approaches based on the direct construction of the memory function, the present approach seeks a set of non-Markovian features that encode the history of the resolved variables and establishes a joint learning of the extended Markovian dynamics in terms of both the resolved variables and these features. The training is based on matching the evolution of the correlation functions of the extended variables that can be directly obtained from the ones of the resolved variables. The constructed model essentially approximates the multi-dimensional generalized Langevin equation and ensures numerical stability without empirical treatment. We demonstrate the effectiveness of the method by constructing the reduced models of molecular systems in terms of both one-dimensional and four-dimensional resolved variables.
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Affiliation(s)
- Zhiyuan She
- Department of Computational Mathematics, Science and Engineering, Michigan State University, East Lansing, Michigan 48824, USA
| | - Pei Ge
- Department of Computational Mathematics, Science and Engineering, Michigan State University, East Lansing, Michigan 48824, USA
| | - Huan Lei
- Department of Computational Mathematics, Science and Engineering and Department of Statistics and Probability, Michigan State University, East Lansing, Michigan 48824, USA
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11
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Evans L, Cameron MK, Tiwary P. Computing committors via Mahalanobis diffusion maps with enhanced sampling data. J Chem Phys 2022; 157:214107. [PMID: 36511548 DOI: 10.1063/5.0122990] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/03/2022] Open
Abstract
The study of phenomena such as protein folding and conformational changes in molecules is a central theme in chemical physics. Molecular dynamics (MD) simulation is the primary tool for the study of transition processes in biomolecules, but it is hampered by a huge timescale gap between the processes of interest and atomic vibrations that dictate the time step size. Therefore, it is imperative to combine MD simulations with other techniques in order to quantify the transition processes taking place on large timescales. In this work, the diffusion map with Mahalanobis kernel, a meshless approach for approximating the Backward Kolmogorov Operator (BKO) in collective variables, is upgraded to incorporate standard enhanced sampling techniques, such as metadynamics. The resulting algorithm, which we call the target measure Mahalanobis diffusion map (tm-mmap), is suitable for a moderate number of collective variables in which one can approximate the diffusion tensor and free energy. Imposing appropriate boundary conditions allows use of the approximated BKO to solve for the committor function and utilization of transition path theory to find the reactive current delineating the transition channels and the transition rate. The proposed algorithm, tm-mmap, is tested on the two-dimensional Moro-Cardin two-well system with position-dependent diffusion coefficient and on alanine dipeptide in two collective variables where the committor, the reactive current, and the transition rate are compared to those computed by the finite element method (FEM). Finally, tm-mmap is applied to alanine dipeptide in four collective variables where the use of finite elements is infeasible.
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Affiliation(s)
- L Evans
- Department of Mathematics, University of Maryland, College Park, Maryland 20742, USA
| | - M K Cameron
- Department of Mathematics, University of Maryland, College Park, Maryland 20742, USA
| | - P Tiwary
- Department of Chemistry and Biochemistry and Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA
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12
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Hassan A, Whitford PC. Identifying Strategies to Experimentally Probe Multidimensional Dynamics in the Ribosome. J Phys Chem B 2022; 126:8460-8471. [PMID: 36256879 DOI: 10.1021/acs.jpcb.2c05706] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2023]
Abstract
The ribosome is a complex biomolecular machine that utilizes large-scale conformational rearrangements to synthesize proteins. For example, during the elongation cycle, the "head" domain of the ribosomal small subunit (SSU) is known to undergo transient rotation events that allow for movement of tRNA molecules (i.e., translocation). While the head may exhibit rigid-body-like properties, the precise relationship between experimentally accessible probes and multidimensional rotations has yet to be established. To address this gap, we perform molecular dynamics simulations of the translocation step of the elongation cycle in the ribosome, where the SSU head spontaneously undergoes rotation and tilt-like motions. With this data set (1250 simulated events), we used statistical and information-theory-based measures to identify possible single-molecule probes that can isolate SSU head rotation and head tilting. This analysis provides a molecular interpretation for previous single-molecule measurements, while establishing a framework for the design of next-generation experiments that may precisely probe the mechanistic and kinetic aspects of the ribosome.
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Affiliation(s)
- Asem Hassan
- Department of Physics, Northeastern University, Dana Research Center 111, 360 Huntington Avenue, Boston, Massachusetts02115, United States.,Center for Theoretical Biological Physics, Northeastern University, 360 Huntington Avenue, Boston, Massachusetts02115, United States
| | - Paul C Whitford
- Department of Physics, Northeastern University, Dana Research Center 111, 360 Huntington Avenue, Boston, Massachusetts02115, United States.,Center for Theoretical Biological Physics, Northeastern University, 360 Huntington Avenue, Boston, Massachusetts02115, United States
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13
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Protein Function Analysis through Machine Learning. Biomolecules 2022; 12:biom12091246. [PMID: 36139085 PMCID: PMC9496392 DOI: 10.3390/biom12091246] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/16/2022] [Revised: 08/22/2022] [Accepted: 08/31/2022] [Indexed: 11/16/2022] Open
Abstract
Machine learning (ML) has been an important arsenal in computational biology used to elucidate protein function for decades. With the recent burgeoning of novel ML methods and applications, new ML approaches have been incorporated into many areas of computational biology dealing with protein function. We examine how ML has been integrated into a wide range of computational models to improve prediction accuracy and gain a better understanding of protein function. The applications discussed are protein structure prediction, protein engineering using sequence modifications to achieve stability and druggability characteristics, molecular docking in terms of protein–ligand binding, including allosteric effects, protein–protein interactions and protein-centric drug discovery. To quantify the mechanisms underlying protein function, a holistic approach that takes structure, flexibility, stability, and dynamics into account is required, as these aspects become inseparable through their interdependence. Another key component of protein function is conformational dynamics, which often manifest as protein kinetics. Computational methods that use ML to generate representative conformational ensembles and quantify differences in conformational ensembles important for function are included in this review. Future opportunities are highlighted for each of these topics.
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14
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Dang NL, Baranger AM, Beveridge DL. High Energy Channeling and Malleable Transition States: Molecular Dynamics Simulations and Free Energy Landscapes for the Thermal Unfolding of Protein U1A and 13 Mutants. Biomolecules 2022; 12:940. [PMID: 35883496 PMCID: PMC9312810 DOI: 10.3390/biom12070940] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/15/2022] [Revised: 06/20/2022] [Accepted: 06/27/2022] [Indexed: 11/20/2022] Open
Abstract
The spliceosome protein U1A is a prototype case of the RNA recognition motif (RRM) ubiquitous in biological systems. The in vitro kinetics of the chemical denaturation of U1A indicate that the unfolding of U1A is a two-state process but takes place via high energy channeling and a malleable transition state, an interesting variation of typical two-state behavior. Molecular dynamics (MD) simulations have been applied extensively to the study of two-state unfolding and folding of proteins and provide an opportunity to obtain a theoretical account of the experimental results and a molecular model for the transition state ensemble. We describe herein all-atom MD studies including explicit solvent of up to 100 ns on the thermal unfolding (UF) of U1A and 13 mutants. Multiple MD UF trajectories are carried out to ensure accuracy and reproducibility. A vector representation of the MD unfolding process in RMSD space is obtained and used to calculate a free energy landscape for U1A unfolding. A corresponding MD simulation and free energy landscape for the protein CI2, well known to follow a simple two state folding/unfolding model, is provided as a control. The results indicate that the unfolding pathway on the MD calculated free energy landscape of U1A shows a markedly extended transition state compared with that of CI2. The MD results support the interpretation of the observed chevron plots for U1A in terms of a high energy, channel-like transition state. Analysis of the MDUF structures shows that the transition state ensemble involves microstates with most of the RRM secondary structure intact but expanded by ~14% with respect to the radius of gyration. Comparison with results on a prototype system indicates that the transition state involves an ensemble of molten globule structures and extends over the region of ~1-35 ns in the trajectories. Additional MDUF simulations were carried out for 13 U1A mutants, and the calculated φ-values show close accord with observed results and serve to validate our methodology.
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Affiliation(s)
| | | | - David L. Beveridge
- Department of Chemistry and Molecular Biophysics Program, Wesleyan University, Middletown, CT 06459, USA; (N.L.D.); (A.M.B.)
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15
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Klimm F. Topological data analysis of truncated contagion maps. CHAOS (WOODBURY, N.Y.) 2022; 32:073108. [PMID: 35907735 DOI: 10.1063/5.0090114] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/03/2022] [Accepted: 06/10/2022] [Indexed: 06/15/2023]
Abstract
The investigation of dynamical processes on networks has been one focus for the study of contagion processes. It has been demonstrated that contagions can be used to obtain information about the embedding of nodes in a Euclidean space. Specifically, one can use the activation times of threshold contagions to construct contagion maps as a manifold-learning approach. One drawback of contagion maps is their high computational cost. Here, we demonstrate that a truncation of the threshold contagions may considerably speed up the construction of contagion maps. Finally, we show that contagion maps may be used to find an insightful low-dimensional embedding for single-cell RNA-sequencing data in the form of cell-similarity networks and so reveal biological manifolds. Overall, our work makes the use of contagion maps as manifold-learning approaches on empirical network data more viable.
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Affiliation(s)
- Florian Klimm
- Department of Computational Molecular Biology, Max Planck Institute for Molecular Genetics, Ihnestraße 63-73, D-14195 Berlin, Germany
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16
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Mehdi S, Wang D, Pant S, Tiwary P. Accelerating All-Atom Simulations and Gaining Mechanistic Understanding of Biophysical Systems through State Predictive Information Bottleneck. J Chem Theory Comput 2022; 18:3231-3238. [PMID: 35384668 DOI: 10.1021/acs.jctc.2c00058] [Citation(s) in RCA: 28] [Impact Index Per Article: 14.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023]
Abstract
An effective implementation of enhanced sampling algorithms for molecular dynamics simulations requires a priori knowledge of the approximate reaction coordinate describing the relevant mechanisms in the system. In this work, we focus on the recently developed artificial intelligence-based State Predictive Information Bottleneck (SPIB) approach and demonstrate how SPIB can learn such a reaction coordinate as a deep neural network even from undersampled trajectories. We exemplify its usefulness by achieving more than 40 times acceleration in simulating two model biophysical systems through well-tempered metadynamics performed by biasing along the SPIB-learned reaction coordinate. These include left- to right-handed chirality transitions in a synthetic helical peptide (Aib)9 and permeation of a small benzoic acid molecule through a synthetic, symmetric phospholipid bilayer. In addition to significantly accelerating the dynamics and achieving back and forth movement between different metastable states, the SPIB-based reaction coordinate gives mechanistic insights into the processes driving these two important problems.
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Affiliation(s)
- Shams Mehdi
- Biophysics Program and Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, United States
| | - Dedi Wang
- Biophysics Program and Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, United States
| | - Shashank Pant
- Center for Biophysics and Quantitative Biology, Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
| | - Pratyush Tiwary
- Department of Chemistry and Biochemistry and Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, United States
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17
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Baltrukevich H, Podlewska S. From Data to Knowledge: Systematic Review of Tools for Automatic Analysis of Molecular Dynamics Output. Front Pharmacol 2022; 13:844293. [PMID: 35359865 PMCID: PMC8960308 DOI: 10.3389/fphar.2022.844293] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/27/2021] [Accepted: 01/26/2022] [Indexed: 12/02/2022] Open
Abstract
An increasing number of crystal structures available on one side, and the boost of computational power available for computer-aided drug design tasks on the other, have caused that the structure-based drug design tools are intensively used in the drug development pipelines. Docking and molecular dynamics simulations, key representatives of the structure-based approaches, provide detailed information about the potential interaction of a ligand with a target receptor. However, at the same time, they require a three-dimensional structure of a protein and a relatively high amount of computational resources. Nowadays, as both docking and molecular dynamics are much more extensively used, the amount of data output from these procedures is also growing. Therefore, there are also more and more approaches that facilitate the analysis and interpretation of the results of structure-based tools. In this review, we will comprehensively summarize approaches for handling molecular dynamics simulations output. It will cover both statistical and machine-learning-based tools, as well as various forms of depiction of molecular dynamics output.
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Affiliation(s)
- Hanna Baltrukevich
- Maj Institute of Pharmacology, Polish Academy of Sciences, Kraków, Poland
- Faculty of Pharmacy, Chair of Technology and Biotechnology of Medical Remedies, Jagiellonian University Medical College in Krakow, Kraków, Poland
| | - Sabina Podlewska
- Maj Institute of Pharmacology, Polish Academy of Sciences, Kraków, Poland
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18
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19
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Badaoui M, Buigues PJ, Berta D, Mandana GM, Gu H, Földes T, Dickson CJ, Hornak V, Kato M, Molteni C, Parsons S, Rosta E. Combined Free-Energy Calculation and Machine Learning Methods for Understanding Ligand Unbinding Kinetics. J Chem Theory Comput 2022; 18:2543-2555. [PMID: 35195418 PMCID: PMC9097281 DOI: 10.1021/acs.jctc.1c00924] [Citation(s) in RCA: 15] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
Abstract
![]()
The
determination of drug residence times, which define the time
an inhibitor is in complex with its target, is a fundamental part
of the drug discovery process. Synthesis and experimental measurements
of kinetic rate constants are, however, expensive and time consuming.
In this work, we aimed to obtain drug residence times computationally.
Furthermore, we propose a novel algorithm to identify molecular design
objectives based on ligand unbinding kinetics. We designed an enhanced
sampling technique to accurately predict the free-energy profiles
of the ligand unbinding process, focusing on the free-energy barrier
for unbinding. Our method first identifies unbinding paths determining
a corresponding set of internal coordinates (ICs) that form contacts
between the protein and the ligand; it then iteratively updates these
interactions during a series of biased molecular dynamics (MD) simulations
to reveal the ICs that are important for the whole of the unbinding
process. Subsequently, we performed finite-temperature string simulations
to obtain the free-energy barrier for unbinding using the set of ICs
as a complex reaction coordinate. Importantly, we also aimed to enable
the further design of drugs focusing on improved residence times.
To this end, we developed a supervised machine learning (ML) approach
with inputs from unbiased “downhill” trajectories initiated
near the transition state (TS) ensemble of the string unbinding path.
We demonstrate that our ML method can identify key ligand–protein
interactions driving the system through the TS. Some of the most important
drugs for cancer treatment are kinase inhibitors. One of these kinase
targets is cyclin-dependent kinase 2 (CDK2), an appealing target for
anticancer drug development. Here, we tested our method using two
different CDK2 inhibitors for the potential further development of
these compounds. We compared the free-energy barriers obtained from
our calculations with those observed in available experimental data.
We highlighted important interactions at the distal ends of the ligands
that can be targeted for improved residence times. Our method provides
a new tool to determine unbinding rates and to identify key structural
features of the inhibitors that can be used as starting points for
novel design strategies in drug discovery.
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Affiliation(s)
- Magd Badaoui
- Department of Chemistry, King's College London, London SE1 1DB, United Kingdom.,Department of Physics and Astronomy, University College London, London WC1E 6BT, United Kingdom
| | - Pedro J Buigues
- Department of Physics and Astronomy, University College London, London WC1E 6BT, United Kingdom
| | - Dénes Berta
- Department of Physics and Astronomy, University College London, London WC1E 6BT, United Kingdom
| | - Gaurav M Mandana
- Department of Chemistry, King's College London, London SE1 1DB, United Kingdom
| | - Hankang Gu
- Department of Physics and Astronomy, University College London, London WC1E 6BT, United Kingdom
| | - Tamás Földes
- Department of Physics and Astronomy, University College London, London WC1E 6BT, United Kingdom
| | - Callum J Dickson
- Computer-Aided Drug Discovery, Global Discovery Chemistry, Novartis Institutes for BioMedical Research, 181 Massachusetts Avenue, Cambridge, Massachusetts 02139, United States
| | - Viktor Hornak
- Computer-Aided Drug Discovery, Global Discovery Chemistry, Novartis Institutes for BioMedical Research, 181 Massachusetts Avenue, Cambridge, Massachusetts 02139, United States
| | - Mitsunori Kato
- Computer-Aided Drug Discovery, Global Discovery Chemistry, Novartis Institutes for BioMedical Research, 181 Massachusetts Avenue, Cambridge, Massachusetts 02139, United States
| | - Carla Molteni
- Department of Physics, King's College London, London WC2R 2LS, United Kingdom
| | - Simon Parsons
- School of Computer Science, University of Lincoln, Lincoln LN6 7TS, United Kingdom
| | - Edina Rosta
- Department of Chemistry, King's College London, London SE1 1DB, United Kingdom.,Department of Physics and Astronomy, University College London, London WC1E 6BT, United Kingdom
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20
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Li W. Optimizing reaction coordinate by flux maximization in the transition path ensemble. J Chem Phys 2022; 156:054117. [DOI: 10.1063/5.0079390] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Wenjin Li
- Institute for Advanced Study, Shenzhen University, Shenzhen, China
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21
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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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22
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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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23
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Musil F, Grisafi A, Bartók AP, Ortner C, Csányi G, Ceriotti M. Physics-Inspired Structural Representations for Molecules and Materials. Chem Rev 2021; 121:9759-9815. [PMID: 34310133 DOI: 10.1021/acs.chemrev.1c00021] [Citation(s) in RCA: 135] [Impact Index Per Article: 45.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022]
Abstract
The first step in the construction of a regression model or a data-driven analysis, aiming to predict or elucidate the relationship between the atomic-scale structure of matter and its properties, involves transforming the Cartesian coordinates of the atoms into a suitable representation. The development of atomic-scale representations has played, and continues to play, a central role in the success of machine-learning methods for chemistry and materials science. This review summarizes the current understanding of the nature and characteristics of the most commonly used structural and chemical descriptions of atomistic structures, highlighting the deep underlying connections between different frameworks and the ideas that lead to computationally efficient and universally applicable models. It emphasizes the link between properties, structures, their physical chemistry, and their mathematical description, provides examples of recent applications to a diverse set of chemical and materials science problems, and outlines the open questions and the most promising research directions in the field.
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Affiliation(s)
- Felix Musil
- Laboratory of Computational Science and Modeling, IMX, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland.,National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - Andrea Grisafi
- Laboratory of Computational Science and Modeling, IMX, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - Albert P Bartók
- Department of Physics and Warwick Centre for Predictive Modelling, School of Engineering, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - Christoph Ortner
- University of British Columbia, Vancouver, British Columbia V6T 1Z2, Canada
| | - Gábor Csányi
- Engineering Laboratory, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, United Kingdom
| | - Michele Ceriotti
- Laboratory of Computational Science and Modeling, IMX, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland.,National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
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24
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Giberti F, Tribello GA, Ceriotti M. Global Free-Energy Landscapes as a Smoothly Joined Collection of Local Maps. J Chem Theory Comput 2021; 17:3292-3308. [PMID: 34003008 DOI: 10.1021/acs.jctc.0c01177] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Enhanced sampling techniques have become an essential tool in computational chemistry and physics, where they are applied to sample activated processes that occur on a time scale that is inaccessible to conventional simulations. Despite their popularity, it is well known that they have constraints that hinder their application to complex problems. The core issue lies in the need to describe the system using a small number of collective variables (CVs). Any slow degree of freedom that is not properly described by the chosen CVs will hinder sampling efficiency. However, the exploration of configuration space is also hampered by including variables that are not relevant for the activated process under study. This paper presents the Adaptive Topography of Landscape for Accelerated Sampling (ATLAS), a new biasing method capable of working with many CVs. The root idea of ATLAS is to apply a divide-and-conquer strategy, where the high-dimensional CVs space is divided into basins, each of which is described by an automatically determined, low-dimensional set of variables. A well-tempered metadynamics-like bias is constructed as a function of these local variables. Indicator functions associated with the basins switch on and off the local biases so that the sampling is performed on a collection of low-dimensional CV spaces that are smoothly combined to generate an effectively high-dimensional bias. The unbiased Boltzmann distribution is recovered through reweighing, making the evaluation of conformational and thermodynamic properties straightforward. The decomposition of the free-energy landscape in local basins can be updated iteratively as the simulation discovers new (meta)stable states.
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Affiliation(s)
- F Giberti
- Laboratory of Computational Science and Modeling, Institute of Materials, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - G A Tribello
- Atomistic Simulation Centre, School of Mathematics and Physics, Queen's University Belfast, Belfast BT14 7EN, United Kingdom
| | - M Ceriotti
- Laboratory of Computational Science and Modeling, Institute of Materials, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
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25
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Abstract
The ability to make sense of the massive amounts of high-dimensional data generated from molecular dynamics simulations is heavily dependent on the knowledge of a low-dimensional manifold (parameterized by a reaction coordinate or RC) that typically distinguishes between relevant metastable states, and which captures the relevant slow dynamics of interest. Methods based on machine learning and artificial intelligence have been proposed over the years to deal with learning such low-dimensional manifolds, but they are often criticized for a disconnect from more traditional and physically interpretable approaches. To deal with such concerns, in this work we propose a deep learning based state predictive information bottleneck approach to learn the RC from high-dimensional molecular simulation trajectories. We demonstrate analytically and numerically how the RC learnt in this approach is connected to the committor in chemical physics and can be used to accurately identify transition states. A crucial hyperparameter in this approach is the time delay or how far into the future the algorithm should make predictions about. Through careful comparisons for benchmark systems, we demonstrate that this hyperparameter choice gives useful control over how coarse-grained we want the metastable state classification of the system to be. We thus believe that this work represents a step forward in systematic application of deep learning based ideas to molecular simulations.
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Affiliation(s)
- Dedi Wang
- Biophysics Program and Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA
| | - Pratyush Tiwary
- Department of Chemistry and Biochemistry and Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA
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26
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Wei J, Zhou T, Zhang X, Tian T. DTFLOW: Inference and Visualization of Single-cell Pseudotime Trajectory Using Diffusion Propagation. GENOMICS, PROTEOMICS & BIOINFORMATICS 2021; 19:306-318. [PMID: 33662626 PMCID: PMC8602766 DOI: 10.1016/j.gpb.2020.08.003] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/13/2019] [Revised: 05/26/2020] [Accepted: 10/29/2020] [Indexed: 12/13/2022]
Abstract
One of the major challenges in single-cell data analysis is the determination of cellular developmental trajectories using single-cell data. Although substantial studies have been conducted in recent years, more effective methods are still strongly needed to infer the developmental processes accurately. This work devises a new method, named DTFLOW, for determining the pseudo-temporal trajectories with multiple branches. DTFLOW consists of two major steps: a new method called Bhattacharyya kernel feature decomposition (BKFD) to reduce the data dimensions, and a novel approach named Reverse Searching on k-nearest neighbor graph (RSKG) to identify the multi-branching processes of cellular differentiation. In BKFD, we first establish a stationary distribution for each cell to represent the transition of cellular developmental states based on the random walk with restart algorithm, and then propose a new distance metric for calculating pseudotime of single cells by introducing the Bhattacharyya kernel matrix. The effectiveness of DTFLOW is rigorously examined by using four single-cell datasets. We compare the efficiency of DTFLOW with the published state-of-the-art methods. Simulation results suggest that DTFLOW has superior accuracy and strong robustness properties for constructing pseudotime trajectories. The Python source code of DTFLOW can be freely accessed at https://github.com/statway/DTFLOW.
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Affiliation(s)
- Jiangyong Wei
- College of Science, Huazhong Agricultural University, Wuhan 430070, China; School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan 430073, China
| | - Tianshou Zhou
- School of Mathematics and Statistics, Sun Yat-sen University, Guangzhou 510275, China
| | - Xinan Zhang
- School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China
| | - Tianhai Tian
- School of Mathematics, Monash University, Melbourne, VIC 3800, Australia.
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27
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Tsai ST, Tiwary P. On the distance between A and B in molecular configuration space. MOLECULAR SIMULATION 2021. [DOI: 10.1080/08927022.2020.1761548] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Affiliation(s)
- Sun-Ting Tsai
- Department of Physics and Institute for Physical Science and Technology, University of Maryland, College Park, MD, USA
| | - Pratyush Tiwary
- Department of Chemistry and Biochemistry and Institute for Physical Science and Technology, University of Maryland, College Park, MD, USA
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28
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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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29
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Spectral Properties of Effective Dynamics from Conditional Expectations. ENTROPY 2021; 23:e23020134. [PMID: 33494443 PMCID: PMC7912208 DOI: 10.3390/e23020134] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/15/2020] [Accepted: 01/18/2021] [Indexed: 01/03/2023]
Abstract
The reduction of high-dimensional systems to effective models on a smaller set of variables is an essential task in many areas of science. For stochastic dynamics governed by diffusion processes, a general procedure to find effective equations is the conditioning approach. In this paper, we are interested in the spectrum of the generator of the resulting effective dynamics, and how it compares to the spectrum of the full generator. We prove a new relative error bound in terms of the eigenfunction approximation error for reversible systems. We also present numerical examples indicating that, if Kramers–Moyal (KM) type approximations are used to compute the spectrum of the reduced generator, it seems largely insensitive to the time window used for the KM estimators. We analyze the implications of these observations for systems driven by underdamped Langevin dynamics, and show how meaningful effective dynamics can be defined in this setting.
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30
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Löffler M, Picard A. Spectral thresholding for the estimation of Markov chain transition operators. Electron J Stat 2021. [DOI: 10.1214/21-ejs1935] [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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31
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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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32
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Pant S, Smith Z, Wang Y, Tajkhorshid E, Tiwary P. Confronting pitfalls of AI-augmented molecular dynamics using statistical physics. J Chem Phys 2020; 153:234118. [PMID: 33353347 PMCID: PMC7863682 DOI: 10.1063/5.0030931] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/25/2020] [Accepted: 11/29/2020] [Indexed: 12/31/2022] Open
Abstract
Artificial intelligence (AI)-based approaches have had indubitable impact across the sciences through the ability to extract relevant information from raw data. Recently, AI has also found use in enhancing the efficiency of molecular simulations, wherein AI derived slow modes are used to accelerate the simulation in targeted ways. However, while typical fields where AI is used are characterized by a plethora of data, molecular simulations, per construction, suffer from limited sampling and thus limited data. As such, the use of AI in molecular simulations can suffer from a dangerous situation where the AI-optimization could get stuck in spurious regimes, leading to incorrect characterization of the reaction coordinate (RC) for the problem at hand. When such an incorrect RC is then used to perform additional simulations, one could start to deviate progressively from the ground truth. To deal with this problem of spurious AI-solutions, here, we report a novel and automated algorithm using ideas from statistical mechanics. It is based on the notion that a more reliable AI-solution will be one that maximizes the timescale separation between slow and fast processes. To learn this timescale separation even from limited data, we use a maximum caliber-based framework. We show the applicability of this automatic protocol for three classic benchmark problems, namely, the conformational dynamics of a model peptide, ligand-unbinding from a protein, and folding/unfolding energy landscape of the C-terminal domain of protein G. We believe that our work will lead to increased and robust use of trustworthy AI in molecular simulations of complex systems.
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Affiliation(s)
- Shashank Pant
- NIH Center for Macromolecular Modeling and Bioinformatics, Beckman Institute for Advanced Science and Technology, Department of Biochemistry, Center for Biophysics and Quantitative Biology, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | | | | | - Emad Tajkhorshid
- NIH Center for Macromolecular Modeling and Bioinformatics, Beckman Institute for Advanced Science and Technology, Department of Biochemistry, Center for Biophysics and Quantitative Biology, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
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33
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Hruska E, Balasubramanian V, Lee H, Jha S, Clementi C. Extensible and Scalable Adaptive Sampling on Supercomputers. J Chem Theory Comput 2020; 16:7915-7925. [PMID: 33170696 DOI: 10.1021/acs.jctc.0c00991] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022]
Abstract
The accurate sampling of protein dynamics is an ongoing challenge despite the utilization of high-performance computer (HPC) systems. Utilizing only "brute force" molecular dynamics (MD) simulations requires an unacceptably long time to solution. Adaptive sampling methods allow a more effective sampling of protein dynamics than standard MD simulations. Depending on the restarting strategy, the speed up can be more than 1 order of magnitude. One challenge limiting the utilization of adaptive sampling by domain experts is the relatively high complexity of efficiently running adaptive sampling on HPC systems. We discuss how the ExTASY framework can set up new adaptive sampling strategies and reliably execute resulting workflows at scale on HPC platforms. Here, the folding dynamics of four proteins are predicted with no a priori information.
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Affiliation(s)
- Eugen Hruska
- Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, United States.,Department of Physics & Astronomy, Rice University, Houston, Texas 77005, United States
| | - Vivekanandan Balasubramanian
- Department of Electrical and Computer Engineering, Rutgers University, Piscataway, New Jersey 08854, United States
| | - Hyungro Lee
- Department of Electrical and Computer Engineering, Rutgers University, Piscataway, New Jersey 08854, United States
| | - Shantenu Jha
- Department of Electrical and Computer Engineering, Rutgers University, Piscataway, New Jersey 08854, United States
| | - Cecilia Clementi
- Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, United States.,Department of Physics & Astronomy, Rice University, Houston, Texas 77005, United States.,Department of Physics, Freie Universität, 14195 Berlin, Germany.,Department of Chemistry, Rice University, Houston, Texas 77005, United States
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34
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Ford DM, Dendukuri A, Kalyoncu G, Luu K, Patitz MJ. Machine learning to identify variables in thermodynamically small systems. Comput Chem Eng 2020. [DOI: 10.1016/j.compchemeng.2020.106989] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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35
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Functional plasticity and evolutionary adaptation of allosteric regulation. Proc Natl Acad Sci U S A 2020; 117:25445-25454. [PMID: 32999067 DOI: 10.1073/pnas.2002613117] [Citation(s) in RCA: 56] [Impact Index Per Article: 14.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022] Open
Abstract
Allostery is a fundamental regulatory mechanism of protein function. Despite notable advances, understanding the molecular determinants of allostery remains an elusive goal. Our current knowledge of allostery is principally shaped by a structure-centric view, which makes it difficult to understand the decentralized character of allostery. We present a function-centric approach using deep mutational scanning to elucidate the molecular basis and underlying functional landscape of allostery. We show that allosteric signaling exhibits a high degree of functional plasticity and redundancy through myriad mutational pathways. Residues critical for allosteric signaling are surprisingly poorly conserved while those required for structural integrity are highly conserved, suggesting evolutionary pressure to preserve fold over function. Our results suggest multiple solutions to the thermodynamic conditions of cooperativity, in contrast to the common view of a finely tuned allosteric residue network maintained under selection.
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36
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Bernetti M, Bertazzo M, Masetti M. Data-Driven Molecular Dynamics: A Multifaceted Challenge. Pharmaceuticals (Basel) 2020; 13:E253. [PMID: 32961909 PMCID: PMC7557855 DOI: 10.3390/ph13090253] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/25/2020] [Revised: 09/14/2020] [Accepted: 09/16/2020] [Indexed: 12/18/2022] Open
Abstract
The big data concept is currently revolutionizing several fields of science including drug discovery and development. While opening up new perspectives for better drug design and related strategies, big data analysis strongly challenges our current ability to manage and exploit an extraordinarily large and possibly diverse amount of information. The recent renewal of machine learning (ML)-based algorithms is key in providing the proper framework for addressing this issue. In this respect, the impact on the exploitation of molecular dynamics (MD) simulations, which have recently reached mainstream status in computational drug discovery, can be remarkable. Here, we review the recent progress in the use of ML methods coupled to biomolecular simulations with potentially relevant implications for drug design. Specifically, we show how different ML-based strategies can be applied to the outcome of MD simulations for gaining knowledge and enhancing sampling. Finally, we discuss how intrinsic limitations of MD in accurately modeling biomolecular systems can be alleviated by including information coming from experimental data.
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Affiliation(s)
- Mattia Bernetti
- Scuola Internazionale Superiore di Studi Avanzati (SISSA), via Bonomea 265, I-34136 Trieste, Italy;
| | - Martina Bertazzo
- Computational Sciences, Istituto Italiano di Tecnologia, via Morego 30, I-16163 Genova, Italy;
| | - Matteo Masetti
- Department of Pharmacy and Biotechnology, Alma Mater Studiorum—Università di Bologna, via Belmeloro 6, I-40126 Bologna, Italy
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37
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Gkeka P, Stoltz G, Barati Farimani A, Belkacemi Z, Ceriotti M, Chodera JD, Dinner AR, Ferguson AL, Maillet JB, Minoux H, Peter C, Pietrucci F, Silveira A, Tkatchenko A, Trstanova Z, Wiewiora R, Lelièvre T. Machine Learning Force Fields and Coarse-Grained Variables in Molecular Dynamics: Application to Materials and Biological Systems. J Chem Theory Comput 2020; 16:4757-4775. [PMID: 32559068 PMCID: PMC8312194 DOI: 10.1021/acs.jctc.0c00355] [Citation(s) in RCA: 82] [Impact Index Per Article: 20.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Abstract
Machine learning encompasses tools and algorithms that are now becoming popular in almost all scientific and technological fields. This is true for molecular dynamics as well, where machine learning offers promises of extracting valuable information from the enormous amounts of data generated by simulation of complex systems. We provide here a review of our current understanding of goals, benefits, and limitations of machine learning techniques for computational studies on atomistic systems, focusing on the construction of empirical force fields from ab initio databases and the determination of reaction coordinates for free energy computation and enhanced sampling.
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Affiliation(s)
- Paraskevi Gkeka
- Integrated Drug Discovery, Sanofi R&D, 91385 Chilly-Mazarin, France
| | - Gabriel Stoltz
- CERMICS, Ecole des Ponts, Marne-la-Vallée, France
- Matherials Project-Team, Inria Paris, 75012 Paris, France
| | | | - Zineb Belkacemi
- Integrated Drug Discovery, Sanofi R&D, 91385 Chilly-Mazarin, France
- CERMICS, Ecole des Ponts, Marne-la-Vallée, France
| | - Michele Ceriotti
- Laboratory of Computational Science and Modelling, Institute of Materials, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
| | - John D Chodera
- Computational and Systems Biology Program, Sloan Kettering Institute, Memorial Sloan Kettering Cancer Center, New York, New York 10065, United States
| | - Aaron R Dinner
- Department of Chemistry, The University of Chicago, Chicago, Illinois 60637, United States
| | - Andrew L Ferguson
- Pritzker School of Molecular Engineering, University of Chicago, 5640 South Ellis Avenue, Chicago, Illinois 60637, United States
| | | | - Hervé Minoux
- Integrated Drug Discovery, Sanofi R&D, 94403 Vitry-sur-Seine, France
| | | | - Fabio Pietrucci
- UMR CNRS 7590, MNHN, Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie, Sorbonne Université, 75005 Paris, France
| | - Ana Silveira
- Computational and Systems Biology Program, Sloan Kettering Institute, Memorial Sloan Kettering Cancer Center, New York, New York 10065, United States
| | - Alexandre Tkatchenko
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg City, Luxembourg
| | - Zofia Trstanova
- School of Mathematics, The University of Edinburgh, Edinburgh EH9 3FD, U.K
| | - Rafal Wiewiora
- Computational and Systems Biology Program, Sloan Kettering Institute, Memorial Sloan Kettering Cancer Center, New York, New York 10065, United States
| | - Tony Lelièvre
- CERMICS, Ecole des Ponts, Marne-la-Vallée, France
- Matherials Project-Team, Inria Paris, 75012 Paris, France
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38
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Wang J, Chmiela S, Müller KR, Noé F, Clementi C. Ensemble learning of coarse-grained molecular dynamics force fields with a kernel approach. J Chem Phys 2020; 152:194106. [DOI: 10.1063/5.0007276] [Citation(s) in RCA: 27] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023] Open
Affiliation(s)
- Jiang Wang
- Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, USA
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
| | - Stefan Chmiela
- Machine Learning Group, Technische Universität Berlin, 10587 Berlin, Germany
| | - Klaus-Robert Müller
- Machine Learning Group, Technische Universität Berlin, 10587 Berlin, Germany
- Department of Brain and Cognitive Engineering, Korea University, Seoul 02841, South Korea
- Max Planck Institute for Informatics, Saarbrücken 66123, Germany
| | - Frank Noé
- Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, USA
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
- Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
- Department of Physics, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany
| | - Cecilia Clementi
- Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, USA
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
- Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
- Department of Physics, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany
- Department of Physics, Rice University, Houston, Texas 77005, USA
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39
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Bozkurt Varolgüneş Y, Bereau T, Rudzinski JF. Interpretable embeddings from molecular simulations using Gaussian mixture variational autoencoders. MACHINE LEARNING-SCIENCE AND TECHNOLOGY 2020. [DOI: 10.1088/2632-2153/ab80b7] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/08/2023]
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40
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Sidky H, Chen W, Ferguson AL. Machine learning for collective variable discovery and enhanced sampling in biomolecular simulation. Mol Phys 2020. [DOI: 10.1080/00268976.2020.1737742] [Citation(s) in RCA: 26] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Affiliation(s)
- Hythem Sidky
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, IL, USA
| | - Wei Chen
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL, USA
| | - Andrew L. Ferguson
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, IL, USA
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41
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Alam FF, Rahman T, Shehu A. Evaluating Autoencoder-Based Featurization and Supervised Learning for Protein Decoy Selection. Molecules 2020; 25:E1146. [PMID: 32143444 PMCID: PMC7179114 DOI: 10.3390/molecules25051146] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/15/2020] [Revised: 02/18/2020] [Accepted: 02/25/2020] [Indexed: 11/24/2022] Open
Abstract
Rapid growth in molecular structure data is renewing interest in featurizing structure. Featurizations that retain information on biological activity are particularly sought for protein molecules, where decades of research have shown that indeed structure encodes function. Research on featurization of protein structure is active, but here we assess the promise of autoencoders. Motivated by rapid progress in neural network research, we investigate and evaluate autoencoders on yielding linear and nonlinear featurizations of protein tertiary structures. An additional reason we focus on autoencoders as the engine to obtain featurizations is the versatility of their architectures and the ease with which changes to architecture yield linear versus nonlinear features. While open-source neural network libraries, such as Keras, which we employ here, greatly facilitate constructing, training, and evaluating autoencoder architectures and conducting model search, autoencoders have not yet gained popularity in the structure biology community. Here we demonstrate their utility in a practical context. Employing autoencoder-based featurizations, we address the classic problem of decoy selection in protein structure prediction. Utilizing off-the-shelf supervised learning methods, we demonstrate that the featurizations are indeed meaningful and allow detecting active tertiary structures, thus opening the way for further avenues of research.
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Affiliation(s)
- Fardina Fathmiul Alam
- Department of Computer Science, George Mason University, Fairfax, VA 22030, USA; (F.F.A.); (T.R.)
| | - Taseef Rahman
- Department of Computer Science, George Mason University, Fairfax, VA 22030, USA; (F.F.A.); (T.R.)
| | - Amarda Shehu
- Department of Computer Science, George Mason University, Fairfax, VA 22030, USA; (F.F.A.); (T.R.)
- Center for Advancing Human-Machine Partnerships, George Mason University, Fairfax, VA 22030, USA
- Department of Bioengineering, George Mason University, Fairfax, VA 22030, USA
- School of Systems Biology, George Mason University, Fairfax, VA 22030, USA
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42
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Meyer H, Pelagejcev P, Schilling T. Non-Markovian out-of-equilibrium dynamics: A general numerical procedure to construct time-dependent memory kernels for coarse-grained observables. ACTA ACUST UNITED AC 2020. [DOI: 10.1209/0295-5075/128/40001] [Citation(s) in RCA: 22] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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43
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Trstanova Z, Leimkuhler B, Lelièvre T. Local and global perspectives on diffusion maps in the analysis of molecular systems. Proc Math Phys Eng Sci 2020; 476:20190036. [PMID: 32082050 PMCID: PMC7016551 DOI: 10.1098/rspa.2019.0036] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/30/2019] [Accepted: 11/04/2019] [Indexed: 01/10/2023] Open
Abstract
Diffusion maps approximate the generator of Langevin dynamics from simulation data. They afford a means of identifying the slowly evolving principal modes of high-dimensional molecular systems. When combined with a biasing mechanism, diffusion maps can accelerate the sampling of the stationary Boltzmann-Gibbs distribution. In this work, we contrast the local and global perspectives on diffusion maps, based on whether or not the data distribution has been fully explored. In the global setting, we use diffusion maps to identify metastable sets and to approximate the corresponding committor functions of transitions between them. We also discuss the use of diffusion maps within the metastable sets, formalizing the locality via the concept of the quasi-stationary distribution and justifying the convergence of diffusion maps within a local equilibrium. This perspective allows us to propose an enhanced sampling algorithm. We demonstrate the practical relevance of these approaches both for simple models and for molecular dynamics problems (alanine dipeptide and deca-alanine).
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Affiliation(s)
- Z. Trstanova
- School of Mathematics, University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh EH9 3FD, UK
| | - B. Leimkuhler
- School of Mathematics, University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh EH9 3FD, UK
| | - T. Lelièvre
- CERMICS (ENPC), INRIA, Marne-la-Vallée 77455, France
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44
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Shi W, Jia T, Li A. Quasi-classical trajectory analysis with isometric feature mapping and locally linear embedding: deep insights into the multichannel reaction on an NH3+(4A) potential energy surface. Phys Chem Chem Phys 2020; 22:17460-17471. [DOI: 10.1039/d0cp01941k] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Abstract
Two manifold learning methods, isometric feature mapping and locally linear embedding, are applied to the analysis of quasi-classical trajectories for multi-channel reaction NH+ + H2 → N + H3+/NH2+ + H.
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Affiliation(s)
- Weiliang Shi
- Key Laboratory of Synthetic and Natural Functional Molecule of the Ministry of Education
- College of Chemistry and Materials Science
- Northwest University
- Xi’an
- P. R. China
| | - Tian Jia
- Key Laboratory of Synthetic and Natural Functional Molecule of the Ministry of Education
- College of Chemistry and Materials Science
- Northwest University
- Xi’an
- P. R. China
| | - Anyang Li
- Key Laboratory of Synthetic and Natural Functional Molecule of the Ministry of Education
- College of Chemistry and Materials Science
- Northwest University
- Xi’an
- P. R. China
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45
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Noé F. Machine Learning for Molecular Dynamics on Long Timescales. MACHINE LEARNING MEETS QUANTUM PHYSICS 2020. [DOI: 10.1007/978-3-030-40245-7_16] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
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46
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Ma Y, Ferguson AL. Inverse design of self-assembling colloidal crystals with omnidirectional photonic bandgaps. SOFT MATTER 2019; 15:8808-8826. [PMID: 31603182 DOI: 10.1039/c9sm01500k] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Open colloidal lattices possessing omnidirectional photonic bandgaps in the visible or near-visible regime are attractive optical materials the realization of which has remained elusive. We report the use of an inverse design strategy termed landscape engineering that rationally sculpts the free energy self-assembly landscape using evolutionary algorithms to discover anisotropic patchy colloids capable of spontaneously assembling pyrochlore and cubic diamond lattices possessing complete photonic bandgaps. We validate the designs in computer simulations to demonstrate the defect-free formation of these lattices via a two-stage hierarchical assembly mechanism. Our approach demonstrates a principled strategy for the inverse design of self-assembling colloids for the bottom-up fabrication of desired crystal lattices.
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Affiliation(s)
- Yutao Ma
- Pritzker School of Molecular Engineering, University of Chicago, 5640 South Ellis Avenue, Chicago, IL 60637, USA.
| | - Andrew L Ferguson
- Pritzker School of Molecular Engineering, University of Chicago, 5640 South Ellis Avenue, Chicago, IL 60637, USA.
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47
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Affiliation(s)
- Frank Noé
- Department of Mathematics and Computer Science, Freie Universität Berlin, Berlin, Germany
- Department of Physics, Freie Universität Berlin, Berlin, Germany
| | - Edina Rosta
- Department of Chemistry, Kings College London, London, England
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48
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Yang H, Bandarkar P, Horne R, Leite VBP, Chahine J, Whitford PC. Diffusion of tRNA inside the ribosome is position-dependent. J Chem Phys 2019; 151:085102. [PMID: 31470725 DOI: 10.1063/1.5113814] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In recent years, there has been a growing interest to quantify the energy landscape that governs ribosome dynamics. However, in order to quantitatively integrate theoretical predictions and experimental measurements, it is essential that one has a detailed understanding of the associated diffusive properties. Here, all-atom explicit-solvent simulations (50 μs of aggregate sampling) predict that the diffusion coefficient of a tRNA molecule will depend on its position within the ribosome. Specifically, during aa-tRNA accommodation (i.e., the process by which tRNA enters the ribosome), the apparent diffusion coefficient decreases by approximately an order of magnitude. By comparing these to values obtained with an energetically "smooth" model, we show that the observed nonuniform behavior likely arises from electrostatic and solvation interactions between the tRNA and ribosome. These calculations also reveal the hierarchical character of ribosomal energetics, where steric interactions induce a large-scale free-energy barrier, and short-scale roughness determines the rate of diffusive movement across the landscape.
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Affiliation(s)
- Huan Yang
- Department of Physics, Northeastern University, Dana Research Center 111, 360 Huntington Ave., Boston, Massachusetts 02115, USA
| | - Prasad Bandarkar
- Department of Physics, Northeastern University, Dana Research Center 111, 360 Huntington Ave., Boston, Massachusetts 02115, USA
| | - Ransom Horne
- Department of Physics, Northeastern University, Dana Research Center 111, 360 Huntington Ave., Boston, Massachusetts 02115, USA
| | - Vitor B P Leite
- São Paulo State University (UNESP), IBILCE, São José do Rio Preto, Brazil
| | - Jorge Chahine
- São Paulo State University (UNESP), IBILCE, São José do Rio Preto, Brazil
| | - Paul C Whitford
- Department of Physics, Northeastern University, Dana Research Center 111, 360 Huntington Ave., Boston, Massachusetts 02115, USA
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49
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Tan Q, Duan M, Li M, Han L, Huo S. Approximating dynamic proximity with a hybrid geometry energy-based kernel for diffusion maps. J Chem Phys 2019; 151:105101. [PMID: 31521094 DOI: 10.1063/1.5100968] [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
The diffusion map is a dimensionality reduction method. The reduction coordinates are associated with the leading eigenfunctions of the backward Fokker-Planck operator, providing a dynamic meaning for these coordinates. One of the key factors that affect the accuracy of diffusion map embedding is the dynamic measure implemented in the Gaussian kernel. A common practice in diffusion map study of molecular systems is to approximate dynamic proximity with RMSD (root-mean-square deviation). In this paper, we present a hybrid geometry-energy based kernel. Since high energy-barriers may exist between geometrically similar conformations, taking both RMSD and energy difference into account in the kernel can better describe conformational transitions between neighboring conformations and lead to accurate embedding. We applied our diffusion map method to the β-hairpin of the B1 domain of streptococcal protein G and to Trp-cage. Our results in β-hairpin show that the diffusion map embedding achieves better results with the hybrid kernel than that with the RMSD-based kernel in terms of free energy landscape characterization and a new correlation measure between the cluster center Euclidean distances in the reduced-dimension space and the reciprocals of the total net flow between these clusters. In addition, our diffusion map analysis of the ultralong molecular dynamics trajectory of Trp-cage has provided a unified view of its folding mechanism. These promising results demonstrate the effectiveness of our diffusion map approach in the analysis of the dynamics and thermodynamics of molecular systems. The hybrid geometry-energy criterion could be also useful as a general dynamic measure for other purposes.
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Affiliation(s)
- Qingzhe Tan
- Gustaf H. Carlson School of Chemistry and Biochemistry, Clark University, 950 Main Street, Worcester, Massachusetts 01610, USA
| | - Mojie Duan
- Gustaf H. Carlson School of Chemistry and Biochemistry, Clark University, 950 Main Street, Worcester, Massachusetts 01610, USA
| | - Minghai Li
- Gustaf H. Carlson School of Chemistry and Biochemistry, Clark University, 950 Main Street, Worcester, Massachusetts 01610, USA
| | - Li Han
- Department of Math and Computer Science, Clark University, Worcester, Massachusetts 01610, USA
| | - Shuanghong Huo
- Gustaf H. Carlson School of Chemistry and Biochemistry, Clark University, 950 Main Street, Worcester, Massachusetts 01610, USA
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50
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Nüske F, Boninsegna L, Clementi C. Coarse-graining molecular systems by spectral matching. J Chem Phys 2019; 151:044116. [DOI: 10.1063/1.5100131] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023] Open
Affiliation(s)
- Feliks Nüske
- Center for Theoretical Biological Physics and Department of Chemistry, Rice University, Houston, Texas 77005-1892, USA
| | - Lorenzo Boninsegna
- Center for Theoretical Biological Physics and Department of Chemistry, Rice University, Houston, Texas 77005-1892, USA
| | - Cecilia Clementi
- Center for Theoretical Biological Physics and Department of Chemistry, Rice University, Houston, Texas 77005-1892, USA
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