51
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Porter JR, Zimmerman MI, Bowman GR. Enspara: Modeling molecular ensembles with scalable data structures and parallel computing. J Chem Phys 2019; 150:044108. [PMID: 30709308 DOI: 10.1063/1.5063794] [Citation(s) in RCA: 31] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Markov state models (MSMs) are quantitative models of protein dynamics that are useful for uncovering the structural fluctuations that proteins undergo, as well as the mechanisms of these conformational changes. Given the enormity of conformational space, there has been ongoing interest in identifying a small number of states that capture the essential features of a protein. Generally, this is achieved by making assumptions about the properties of relevant features-for example, that the most important features are those that change slowly. An alternative strategy is to keep as many degrees of freedom as possible and subsequently learn from the model which of the features are most important. In these larger models, however, traditional approaches quickly become computationally intractable. In this paper, we present enspara, a library for working with MSMs that provides several novel algorithms and specialized data structures that dramatically improve the scalability of traditional MSM methods. This includes ragged arrays for minimizing memory requirements, message passing interface-parallelized implementations of compute-intensive operations, and a flexible framework for model construction and analysis.
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Affiliation(s)
- J R Porter
- Department of Biochemistry and Molecular Biophysics, Washington University School of Medicine, 660 South Euclid Avenue, St. Louis, Missouri 63110, USA
| | - M I Zimmerman
- Department of Biochemistry and Molecular Biophysics, Washington University School of Medicine, 660 South Euclid Avenue, St. Louis, Missouri 63110, USA
| | - G R Bowman
- Department of Biochemistry and Molecular Biophysics, Washington University School of Medicine, 660 South Euclid Avenue, St. Louis, Missouri 63110, USA
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52
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Rudzinski JF, Radu M, Bereau T. Automated detection of many-particle solvation states for accurate characterizations of diffusion kinetics. J Chem Phys 2019; 150:024102. [PMID: 30646696 DOI: 10.1063/1.5064808] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/17/2023] Open
Abstract
Discrete-space kinetic models, i.e., Markov state models, have emerged as powerful tools for reducing the complexity of trajectories generated from molecular dynamics simulations. These models require configuration-space representations that accurately characterize the relevant dynamics. Well-established, low-dimensional order parameters for constructing this representation have led to widespread application of Markov state models to study conformational dynamics in biomolecular systems. On the contrary, applications to characterize single-molecule diffusion processes have been scarce and typically employ system-specific, higher-dimensional order parameters to characterize the local solvation state of the molecule. In this work, we propose an automated method for generating a coarse configuration-space representation, using generic features of the solvation structure-the coordination numbers about each particle. To overcome the inherent noisy behavior of these low-dimensional observables, we treat the features as indicators of an underlying, latent Markov process. The resulting hidden Markov models filter the trajectories of each feature into the most likely latent solvation state at each time step. The filtered trajectories are then used to construct a configuration-space discretization, which accurately describes the diffusion kinetics. The method is validated on a standard model for glassy liquids, where particle jumps between local cages determine the diffusion properties of the system. Not only do the resulting models provide quantitatively accurate characterizations of the diffusion constant, but they also reveal a mechanistic description of diffusive jumps, quantifying the heterogeneity of local diffusion.
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Affiliation(s)
| | - Marc Radu
- Max Planck Institute for Polymer Research, Mainz 55128, Germany
| | - Tristan Bereau
- Max Planck Institute for Polymer Research, Mainz 55128, Germany
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53
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Klus S, Bittracher A, Schuster I, Schütte C. A kernel-based approach to molecular conformation analysis. J Chem Phys 2018; 149:244109. [DOI: 10.1063/1.5063533] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022] Open
Affiliation(s)
- Stefan Klus
- Department of Mathematics and Computer Science, Freie Universität Berlin, 14195 Berlin, Germany
| | - Andreas Bittracher
- Department of Mathematics and Computer Science, Freie Universität Berlin, 14195 Berlin, Germany
| | | | - Christof Schütte
- Department of Mathematics and Computer Science, Freie Universität Berlin, 14195 Berlin, Germany
- Zuse Institute Berlin, 14195 Berlin, Germany
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54
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Zhou H, Wang F, Tao P. t-Distributed Stochastic Neighbor Embedding Method with the Least Information Loss for Macromolecular Simulations. J Chem Theory Comput 2018; 14:5499-5510. [PMID: 30252473 PMCID: PMC6679899 DOI: 10.1021/acs.jctc.8b00652] [Citation(s) in RCA: 50] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/08/2023]
Abstract
Dimensionality reduction methods are usually applied on molecular dynamics simulations of macromolecules for analysis and visualization purposes. It is normally desired that suitable dimensionality reduction methods could clearly distinguish functionally important states with different conformations for the systems of interest. However, common dimensionality reduction methods for macromolecules simulations, including predefined order parameters and collective variables (CVs), principal component analysis (PCA), and time-structure based independent component analysis (t-ICA), only have limited success due to significant key structural information loss. Here, we introduced the t-distributed stochastic neighbor embedding (t-SNE) method as a dimensionality reduction method with minimum structural information loss widely used in bioinformatics for analyses of macromolecules, especially biomacromolecules simulations. It is demonstrated that both one-dimensional (1D) and two-dimensional (2D) models of the t-SNE method are superior to distinguish important functional states of a model allosteric protein system for free energy and mechanistic analysis. Projections of the model protein simulations onto 1D and 2D t-SNE surfaces provide both clear visual cues and quantitative information, which is not readily available using other methods, regarding the transition mechanism between two important functional states of this protein.
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Affiliation(s)
- Hongyu Zhou
- Department of Chemistry, Center for Scientific Computation, Center for Drug Discovery, Design, and Delivery (CD4), Southern Methodist University, Dallas, Texas 75275, United States of America
| | - Feng Wang
- Department of Chemistry, Center for Scientific Computation, Center for Drug Discovery, Design, and Delivery (CD4), Southern Methodist University, Dallas, Texas 75275, United States of America
| | - Peng Tao
- Department of Chemistry, Center for Scientific Computation, Center for Drug Discovery, Design, and Delivery (CD4), Southern Methodist University, Dallas, Texas 75275, United States of America
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55
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Chen W, Tan AR, Ferguson AL. Collective variable discovery and enhanced sampling using autoencoders: Innovations in network architecture and error function design. J Chem Phys 2018; 149:072312. [PMID: 30134681 DOI: 10.1063/1.5023804] [Citation(s) in RCA: 80] [Impact Index Per Article: 13.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023] Open
Abstract
Auto-associative neural networks ("autoencoders") present a powerful nonlinear dimensionality reduction technique to mine data-driven collective variables from molecular simulation trajectories. This technique furnishes explicit and differentiable expressions for the nonlinear collective variables, making it ideally suited for integration with enhanced sampling techniques for accelerated exploration of configurational space. In this work, we describe a number of sophistications of the neural network architectures to improve and generalize the process of interleaved collective variable discovery and enhanced sampling. We employ circular network nodes to accommodate periodicities in the collective variables, hierarchical network architectures to rank-order the collective variables, and generalized encoder-decoder architectures to support bespoke error functions for network training to incorporate prior knowledge. We demonstrate our approach in blind collective variable discovery and enhanced sampling of the configurational free energy landscapes of alanine dipeptide and Trp-cage using an open-source plugin developed for the OpenMM molecular simulation package.
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Affiliation(s)
- Wei Chen
- Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois 61801, USA
| | - Aik Rui Tan
- Department of Materials Science and Engineering, University of Illinois at Urbana-Champaign, 1304 West Green Street, Urbana, Illinois 61801, USA
| | - Andrew L Ferguson
- Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois 61801, USA
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56
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Hernández CX, Wayment-Steele HK, Sultan MM, Husic BE, Pande VS. Variational encoding of complex dynamics. Phys Rev E 2018; 97:062412. [PMID: 30011547 DOI: 10.1103/physreve.97.062412] [Citation(s) in RCA: 89] [Impact Index Per Article: 14.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/01/2017] [Indexed: 11/07/2022]
Abstract
Often the analysis of time-dependent chemical and biophysical systems produces high-dimensional time-series data for which it can be difficult to interpret which individual features are most salient. While recent work from our group and others has demonstrated the utility of time-lagged covariate models to study such systems, linearity assumptions can limit the compression of inherently nonlinear dynamics into just a few characteristic components. Recent work in the field of deep learning has led to the development of the variational autoencoder (VAE), which is able to compress complex datasets into simpler manifolds. We present the use of a time-lagged VAE, or variational dynamics encoder (VDE), to reduce complex, nonlinear processes to a single embedding with high fidelity to the underlying dynamics. We demonstrate how the VDE is able to capture nontrivial dynamics in a variety of examples, including Brownian dynamics and atomistic protein folding. Additionally, we demonstrate a method for analyzing the VDE model, inspired by saliency mapping, to determine what features are selected by the VDE model to describe dynamics. The VDE presents an important step in applying techniques from deep learning to more accurately model and interpret complex biophysics.
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Affiliation(s)
| | | | - Mohammad M Sultan
- Chemistry Department, Stanford University, Stanford, California, USA
| | - Brooke E Husic
- Chemistry Department, Stanford University, Stanford, California, USA
| | - Vijay S Pande
- Biophysics Program, Stanford University, Stanford, California, USA.,Chemistry Department, Stanford University, Stanford, California, USA
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57
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Wehmeyer C, Noé F. Time-lagged autoencoders: Deep learning of slow collective variables for molecular kinetics. J Chem Phys 2018; 148:241703. [PMID: 29960344 DOI: 10.1063/1.5011399] [Citation(s) in RCA: 167] [Impact Index Per Article: 27.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Inspired by the success of deep learning techniques in the physical and chemical sciences, we apply a modification of an autoencoder type deep neural network to the task of dimension reduction of molecular dynamics data. We can show that our time-lagged autoencoder reliably finds low-dimensional embeddings for high-dimensional feature spaces which capture the slow dynamics of the underlying stochastic processes-beyond the capabilities of linear dimension reduction techniques.
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Affiliation(s)
- Christoph Wehmeyer
- Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
| | - Frank Noé
- Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
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58
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Husic BE, Pande VS. Note: MSM lag time cannot be used for variational model selection. J Chem Phys 2018; 147:176101. [PMID: 29117698 DOI: 10.1063/1.5002086] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The variational principle for conformational dynamics has enabled the systematic construction of Markov state models through the optimization of hyperparameters by approximating the transfer operator. In this note, we discuss why the lag time of the operator being approximated must be held constant in the variational approach.
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Affiliation(s)
- Brooke E Husic
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
| | - Vijay S Pande
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
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59
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Krivov SV. Protein Folding Free Energy Landscape along the Committor - the Optimal Folding Coordinate. J Chem Theory Comput 2018; 14:3418-3427. [PMID: 29791148 DOI: 10.1021/acs.jctc.8b00101] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Recent advances in simulation and experiment have led to dramatic increases in the quantity and complexity of produced data, which makes the development of automated analysis tools very important. A powerful approach to analyze dynamics contained in such data sets is to describe/approximate it by diffusion on a free energy landscape - free energy as a function of reaction coordinates (RC). For the description to be quantitatively accurate, RCs should be chosen in an optimal way. Recent theoretical results show that such an optimal RC exists; however, determining it for practical systems is a very difficult unsolved problem. Here we describe a solution to this problem. We describe an adaptive nonparametric approach to accurately determine the optimal RC (the committor) for an equilibrium trajectory of a realistic system. In contrast to alternative approaches, which require a functional form with many parameters to approximate an RC and thus extensive expertise with the system, the suggested approach is nonparametric and can approximate any RC with high accuracy without system specific information. To avoid overfitting for a realistically sampled system, the approach performs RC optimization in an adaptive manner by focusing optimization on less optimized spatiotemporal regions of the RC. The power of the approach is illustrated on a long equilibrium atomistic folding simulation of HP35 protein. We have determined the optimal folding RC - the committor, which was confirmed by passing a stringent committor validation test. It allowed us to determine a first quantitatively accurate protein folding free energy landscape. We have confirmed the recent theoretical results that diffusion on such a free energy profile can be used to compute exactly the equilibrium flux, the mean first passage times, and the mean transition path times between any two points on the profile. We have shown that the mean squared displacement along the optimal RC grows linear with time as for simple diffusion. The free energy profile allowed us to obtain a direct rigorous estimate of the pre-exponential factor for the folding dynamics.
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Affiliation(s)
- Sergei V Krivov
- Astbury Center for Structural Molecular Biology , University of Leeds , Leeds LS2 9JT , United Kingdom
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60
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Litzinger F, Boninsegna L, Wu H, Nüske F, Patel R, Baraniuk R, Noé F, Clementi C. Rapid Calculation of Molecular Kinetics Using Compressed Sensing. J Chem Theory Comput 2018; 14:2771-2783. [DOI: 10.1021/acs.jctc.8b00089] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Florian Litzinger
- Freie Universität Berlin, Department of Mathematics and Computer Science, Arnimallee 6, 14195 Berlin, Germany
| | - Lorenzo Boninsegna
- Rice University, Center for Theoretical Biological Physics and Department of Chemistry, Houston, Texas 77005, United States
| | - Hao Wu
- Freie Universität Berlin, Department of Mathematics and Computer Science, Arnimallee 6, 14195 Berlin, Germany
| | - Feliks Nüske
- Rice University, Center for Theoretical Biological Physics and Department of Chemistry, Houston, Texas 77005, United States
| | - Raajen Patel
- Rice University, Department of Electrical and Computer Engineering, Houston, Texas 77005, United States
| | - Richard Baraniuk
- Rice University, Department of Electrical and Computer Engineering, Houston, Texas 77005, United States
| | - Frank Noé
- Freie Universität Berlin, Department of Mathematics and Computer Science, Arnimallee 6, 14195 Berlin, Germany
- Rice University, Center for Theoretical Biological Physics and Department of Chemistry, Houston, Texas 77005, United States
| | - Cecilia Clementi
- Rice University, Center for Theoretical Biological Physics and Department of Chemistry, Houston, Texas 77005, United States
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61
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Mittal S, Shukla D. Recruiting machine learning methods for molecular simulations of proteins. MOLECULAR SIMULATION 2018. [DOI: 10.1080/08927022.2018.1448976] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/12/2023]
Affiliation(s)
- Shriyaa Mittal
- Center for Biophysics and Quantitative Biology, University of Illinois at Urbana-Champaign , Urbana, IL, USA
| | - Diwakar Shukla
- Center for Biophysics and Quantitative Biology, University of Illinois at Urbana-Champaign , Urbana, IL, USA
- Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign , Urbana, IL, USA
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62
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Sultan MM, Wayment-Steele HK, Pande VS. Transferable Neural Networks for Enhanced Sampling of Protein Dynamics. J Chem Theory Comput 2018. [DOI: 10.1021/acs.jctc.8b00025] [Citation(s) in RCA: 60] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
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63
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64
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Affiliation(s)
- Brooke E. Husic
- Department of Chemistry, Stanford University, Stanford, California 94305, United States
| | - Vijay S. Pande
- Department of Chemistry, Stanford University, Stanford, California 94305, United States
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65
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Miranda WE, Ngo VA, Perissinotti LL, Noskov SY. Computational membrane biophysics: From ion channel interactions with drugs to cellular function. BIOCHIMICA ET BIOPHYSICA ACTA. PROTEINS AND PROTEOMICS 2017; 1865:1643-1653. [PMID: 28847523 PMCID: PMC5764198 DOI: 10.1016/j.bbapap.2017.08.008] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/07/2017] [Revised: 08/16/2017] [Accepted: 08/16/2017] [Indexed: 12/16/2022]
Abstract
The rapid development of experimental and computational techniques has changed fundamentally our understanding of cellular-membrane transport. The advent of powerful computers and refined force-fields for proteins, ions, and lipids has expanded the applicability of Molecular Dynamics (MD) simulations. A myriad of cellular responses is modulated through the binding of endogenous and exogenous ligands (e.g. neurotransmitters and drugs, respectively) to ion channels. Deciphering the thermodynamics and kinetics of the ligand binding processes to these membrane proteins is at the heart of modern drug development. The ever-increasing computational power has already provided insightful data on the thermodynamics and kinetics of drug-target interactions, free energies of solvation, and partitioning into lipid bilayers for drugs. This review aims to provide a brief summary about modeling approaches to map out crucial binding pathways with intermediate conformations and free-energy surfaces for drug-ion channel binding mechanisms that are responsible for multiple effects on cellular functions. We will discuss post-processing analysis of simulation-generated data, which are then transformed to kinetic models to better understand the molecular underpinning of the experimental observables under the influence of drugs or mutations in ion channels. This review highlights crucial mathematical frameworks and perspectives on bridging different well-established computational techniques to connect the dynamics and timescales from all-atom MD and free energy simulations of ion channels to the physiology of action potentials in cellular models. This article is part of a Special Issue entitled: Biophysics in Canada, edited by Lewis Kay, John Baenziger, Albert Berghuis and Peter Tieleman.
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Affiliation(s)
- Williams E Miranda
- Centre for Molecular Simulations, Department of Biological Sciences, University of Calgary, Calgary, AB, Canada
| | - Van A Ngo
- Centre for Molecular Simulations, Department of Biological Sciences, University of Calgary, Calgary, AB, Canada
| | - Laura L Perissinotti
- Centre for Molecular Simulations, Department of Biological Sciences, University of Calgary, Calgary, AB, Canada
| | - Sergei Yu Noskov
- Centre for Molecular Simulations, Department of Biological Sciences, University of Calgary, Calgary, AB, Canada.
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66
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Wang W, Cao S, Zhu L, Huang X. Constructing Markov State Models to elucidate the functional conformational changes of complex biomolecules. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2017. [DOI: 10.1002/wcms.1343] [Citation(s) in RCA: 52] [Impact Index Per Article: 7.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
Affiliation(s)
- Wei Wang
- Department of ChemistryThe Hong Kong University of Science and Technology Kowloon Hong Kong
- Center of Systems Biology and Human HealthThe Hong Kong University of Science and Technology Kowloon Hong Kong
| | - Siqin Cao
- Department of ChemistryThe Hong Kong University of Science and Technology Kowloon Hong Kong
| | - Lizhe Zhu
- Department of ChemistryThe Hong Kong University of Science and Technology Kowloon Hong Kong
- Center of Systems Biology and Human HealthThe Hong Kong University of Science and Technology Kowloon Hong Kong
| | - Xuhui Huang
- Department of ChemistryThe Hong Kong University of Science and Technology Kowloon Hong Kong
- Center of Systems Biology and Human HealthThe Hong Kong University of Science and Technology Kowloon Hong Kong
- Hong Kong Branch of Chinese National Engineering Research Center for Tissue Restoration & ReconstructionThe Hong Kong University of Science and Technology Kowloon Hong Kong
- HKUST‐Shenzhen Research Institute Shenzhen China
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67
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Sultan MM, Pande VS. Transfer Learning from Markov Models Leads to Efficient Sampling of Related Systems. J Phys Chem B 2017; 122:5291-5299. [DOI: 10.1021/acs.jpcb.7b06896] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022]
Affiliation(s)
- Mohammad M. Sultan
- Department of Chemistry, Stanford University, 318 Campus Drive, Stanford, California 94305, United States
| | - Vijay S. Pande
- Department of Chemistry, Stanford University, 318 Campus Drive, Stanford, California 94305, United States
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68
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M. Sultan M, Pande VS. tICA-Metadynamics: Accelerating Metadynamics by Using Kinetically Selected Collective Variables. J Chem Theory Comput 2017; 13:2440-2447. [DOI: 10.1021/acs.jctc.7b00182] [Citation(s) in RCA: 97] [Impact Index Per Article: 13.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Affiliation(s)
- Mohammad M. Sultan
- Department of Chemistry, Stanford University, 318 Campus Drive, Stanford, California 94305, United States
| | - Vijay S. Pande
- Department of Chemistry, Stanford University, 318 Campus Drive, Stanford, California 94305, United States
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69
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Wu H, Nüske F, Paul F, Klus S, Koltai P, Noé F. Variational Koopman models: Slow collective variables and molecular kinetics from short off-equilibrium simulations. J Chem Phys 2017; 146:154104. [DOI: 10.1063/1.4979344] [Citation(s) in RCA: 69] [Impact Index Per Article: 9.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022] Open
Affiliation(s)
- Hao Wu
- Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
| | - Feliks Nüske
- Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
| | - Fabian Paul
- Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
| | - Stefan Klus
- Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
| | - Péter Koltai
- Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
| | - Frank Noé
- Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
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70
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Gao K, Zhao Y. A Network of Conformational Transitions in the Apo Form of NDM-1 Enzyme Revealed by MD Simulation and a Markov State Model. J Phys Chem B 2017; 121:2952-2960. [PMID: 28319394 DOI: 10.1021/acs.jpcb.7b00062] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/21/2023]
Abstract
New Delhi metallo-β-lactamase-1 (NDM-1) is a novel β-lactamase enzyme that confers enteric bacteria with nearly complete resistance to all β-lactam antibiotics, so it raises a formidable and global threat to human health. However, the binding mechanism between apo-NDM-1 and antibiotics as well as related conformational changes remains poorly understood, which largely hinders the overcoming of its antibiotic resistance. In our study, long-time conventional molecular dynamics simulation and Markov state models were applied to reveal both the dynamical and conformational landscape of apo-NDM-1: the MD simulation demonstrates that loop L3, which is responsible for antibiotic binding, is the most flexible and undergoes dramatic conformational changes; moreover, the Markov state model built from the simulation maps four metastable states including open, semiopen, and closed conformations of loop L3 as well as frequent transitions between the states. Our findings propose a possible conformational selection model for the binding mechanism between apo-NDM-1 and antibiotics, which facilitates the design of novel inhibitors and antibiotics.
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Affiliation(s)
- Kaifu Gao
- Institute of Biophysics and Department of Physics, Central China Normal University , Wuhan 430079, P. R. China
| | - Yunjie Zhao
- Institute of Biophysics and Department of Physics, Central China Normal University , Wuhan 430079, P. R. China
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71
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Noé F, Clementi C. Collective variables for the study of long-time kinetics from molecular trajectories: theory and methods. Curr Opin Struct Biol 2017; 43:141-147. [PMID: 28327454 DOI: 10.1016/j.sbi.2017.02.006] [Citation(s) in RCA: 98] [Impact Index Per Article: 14.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/12/2016] [Accepted: 02/20/2017] [Indexed: 12/23/2022]
Abstract
Collective variables are an important concept to study high-dimensional dynamical systems, such as molecular dynamics of macromolecules, liquids, or polymers, in particular to define relevant metastable states and state-transition or phase-transition. Over the past decade, a rigorous mathematical theory has been formulated to define optimal collective variables to characterize slow dynamical processes. Here we review recent developments, including a variational principle to find optimal approximations to slow collective variables from simulation data, and algorithms such as the time-lagged independent component analysis. Using these concepts, a distance metric can be defined that quantifies how slowly molecular conformations interconvert. Extensions and open questions are discussed.
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Affiliation(s)
- Frank Noé
- Department of Mathematics and Computer Science, FU Berlin, Arnimallee 6, 14195 Berlin, Germany.
| | - Cecilia Clementi
- Center for Theoretical Biological Physics, and Department of Chemistry, Rice University, 6100 Main Street, Houston, TX 77005, United States.
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72
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McGibbon RT, Husic BE, Pande VS. Identification of simple reaction coordinates from complex dynamics. J Chem Phys 2017; 146:044109. [PMID: 28147508 PMCID: PMC5272828 DOI: 10.1063/1.4974306] [Citation(s) in RCA: 55] [Impact Index Per Article: 7.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/18/2016] [Accepted: 01/05/2017] [Indexed: 11/14/2022] Open
Abstract
Reaction coordinates are widely used throughout chemical physics to model and understand complex chemical transformations. We introduce a definition of the natural reaction coordinate, suitable for condensed phase and biomolecular systems, as a maximally predictive one-dimensional projection. We then show that this criterion is uniquely satisfied by a dominant eigenfunction of an integral operator associated with the ensemble dynamics. We present a new sparse estimator for these eigenfunctions which can search through a large candidate pool of structural order parameters and build simple, interpretable approximations that employ only a small number of these order parameters. Example applications with a small molecule's rotational dynamics and simulations of protein conformational change and folding show that this approach can filter through statistical noise to identify simple reaction coordinates from complex dynamics.
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Affiliation(s)
- Robert T McGibbon
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
| | - Brooke E Husic
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
| | - Vijay S Pande
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
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73
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Wan H, Zhou G, Voelz VA. A Maximum-Caliber Approach to Predicting Perturbed Folding Kinetics Due to Mutations. J Chem Theory Comput 2016; 12:5768-5776. [PMID: 27951664 DOI: 10.1021/acs.jctc.6b00938] [Citation(s) in RCA: 39] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We present a maximum-caliber method for inferring transition rates of a Markov state model (MSM) with perturbed equilibrium populations given estimates of state populations and rates for an unperturbed MSM. It is similar in spirit to previous approaches, but given the inclusion of prior information, it is more robust and simple to implement. We examine its performance in simple biased diffusion models of kinetics and then apply the method to predicting changes in folding rates for several highly nontrivial protein folding systems for which non-native interactions play a significant role, including (1) tryptophan variants of the GB1 hairpin, (2) salt-bridge mutations of the Fs peptide helix, and (3) MSMs built from ultralong folding trajectories of FiP35 and GTT variants of the WW domain. In all cases, the method correctly predicts changes in folding rates, suggesting the wide applicability of maximum-caliber approaches to efficiently predict how mutations perturb protein conformational dynamics.
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Affiliation(s)
- Hongbin Wan
- Department of Chemistry, Temple University , Philadelphia, Pennsylvania 19122, United States
| | - Guangfeng Zhou
- Department of Chemistry, Temple University , Philadelphia, Pennsylvania 19122, United States
| | - Vincent A Voelz
- Department of Chemistry, Temple University , Philadelphia, Pennsylvania 19122, United States
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74
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Noé F, Banisch R, Clementi C. Commute Maps: Separating Slowly Mixing Molecular Configurations for Kinetic Modeling. J Chem Theory Comput 2016; 12:5620-5630. [DOI: 10.1021/acs.jctc.6b00762] [Citation(s) in RCA: 43] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Frank Noé
- Department
of Mathematics, Computer Science and Bioinformatics, FU Berlin, Arnimallee
6, 14195 Berlin, Germany
| | - Ralf Banisch
- Department
of Mathematics, Computer Science and Bioinformatics, FU Berlin, Arnimallee
6, 14195 Berlin, Germany
| | - Cecilia Clementi
- Center
for Theoretical Biological Physics, and Department of Chemistry, Rice University, 6100 Main Street, Houston, Texas 77005, United States
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75
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Banushkina PV, Krivov SV. Optimal reaction coordinates. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2016. [DOI: 10.1002/wcms.1276] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Affiliation(s)
- Polina V. Banushkina
- Astbury Center for Structural Molecular Biology; Faculty of Biological Sciences, University of Leeds; Leeds UK
| | - Sergei V. Krivov
- Astbury Center for Structural Molecular Biology; Faculty of Biological Sciences, University of Leeds; Leeds UK
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76
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Matsunaga Y, Komuro Y, Kobayashi C, Jung J, Mori T, Sugita Y. Dimensionality of Collective Variables for Describing Conformational Changes of a Multi-Domain Protein. J Phys Chem Lett 2016; 7:1446-51. [PMID: 27049936 DOI: 10.1021/acs.jpclett.6b00317] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
Collective variables (CVs) are often used in molecular dynamics simulations based on enhanced sampling algorithms to investigate large conformational changes of a protein. The choice of CVs in these simulations is essential because it affects simulation results and impacts the free-energy profile, the minimum free-energy pathway (MFEP), and the transition-state structure. Here we examine how many CVs are required to capture the correct transition-state structure during the open-to-close motion of adenylate kinase using a coarse-grained model in the mean forces string method to search the MFEP. Various numbers of large amplitude principal components are tested as CVs in the simulations. The incorporation of local coordinates into CVs, which is possible in higher dimensional CV spaces, is important for capturing a reliable MFEP. The Bayesian measure proposed by Best and Hummer is sensitive to the choice of CVs, showing sharp peaks when the transition-state structure is captured. We thus evaluate the required number of CVs needed in enhanced sampling simulations for describing protein conformational changes.
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Affiliation(s)
- Yasuhiro Matsunaga
- RIKEN Advanced Institute for Computational Science , 7-1-26 minatojima-minamimachi, Chuo-ku, Kobe, Hyogo 650-0047, Japan
| | - Yasuaki Komuro
- RIKEN, Theoretical Molecular Science Laboratory , 2-1 Hirosawa, Wako-shi, Saitama 351-0198, Japan
| | - Chigusa Kobayashi
- RIKEN Advanced Institute for Computational Science , 7-1-26 minatojima-minamimachi, Chuo-ku, Kobe, Hyogo 650-0047, Japan
| | - Jaewoon Jung
- RIKEN Advanced Institute for Computational Science , 7-1-26 minatojima-minamimachi, Chuo-ku, Kobe, Hyogo 650-0047, Japan
- RIKEN, iTHES , 2-1 Hirosawa, Wako-shi, Saitama 351-0198, Japan
| | - Takaharu Mori
- RIKEN, Theoretical Molecular Science Laboratory , 2-1 Hirosawa, Wako-shi, Saitama 351-0198, Japan
- RIKEN, iTHES , 2-1 Hirosawa, Wako-shi, Saitama 351-0198, Japan
| | - Yuji Sugita
- RIKEN Advanced Institute for Computational Science , 7-1-26 minatojima-minamimachi, Chuo-ku, Kobe, Hyogo 650-0047, Japan
- RIKEN, Theoretical Molecular Science Laboratory , 2-1 Hirosawa, Wako-shi, Saitama 351-0198, Japan
- RIKEN, iTHES , 2-1 Hirosawa, Wako-shi, Saitama 351-0198, Japan
- RIKEN Quantitative Biology Center , Integrated Innovation Building 7F, 6-7-1 minatojima-minamimachi, Chuo-ku, Kobe, Hyogo 650-0047, Japan
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77
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Zhou G, Voelz VA. Using Kinetic Network Models To Probe Non-Native Salt-Bridge Effects on α-Helix Folding. J Phys Chem B 2016; 120:926-35. [PMID: 26769494 DOI: 10.1021/acs.jpcb.5b11767] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023]
Abstract
Salt-bridge interactions play an important role in stabilizing many protein structures, and have been shown to be designable features for protein design. In this work, we study the effects of non-native salt bridges on the folding of a soluble alanine-based peptide (Fs peptide) using extensive all-atom molecular dynamics simulations performed on the Folding@home distributed computing platform. Using Markov State Models, we show how non-native salt-bridges affect the folding kinetics of Fs peptide by perturbing specific conformational states. Furthermore, we present methods for the automatic detection and analysis of such states. These results provide insight into helix folding mechanisms and useful information to guide simulation-based computational protein design.
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Affiliation(s)
- Guangfeng Zhou
- Department of Chemistry, Temple University , 1901 North 13th Street, Beury Hall, Philadelphia, Pennsylvania 19122, United States
| | - Vincent A Voelz
- Department of Chemistry, Temple University , 1901 North 13th Street, Beury Hall, Philadelphia, Pennsylvania 19122, United States
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78
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Banushkina PV, Krivov SV. Nonparametric variational optimization of reaction coordinates. J Chem Phys 2015; 143:184108. [DOI: 10.1063/1.4935180] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Polina V. Banushkina
- Astbury Center for Structural Molecular Biology, Faculty of Biological Sciences, University of Leeds, Leeds LS2 9JT, United Kingdom
| | - Sergei V. Krivov
- Astbury Center for Structural Molecular Biology, Faculty of Biological Sciences, University of Leeds, Leeds LS2 9JT, United Kingdom
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79
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Blöchliger N, Caflisch A, Vitalis A. Weighted Distance Functions Improve Analysis of High-Dimensional Data: Application to Molecular Dynamics Simulations. J Chem Theory Comput 2015; 11:5481-92. [DOI: 10.1021/acs.jctc.5b00618] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Nicolas Blöchliger
- Department of Biochemistry, University of Zurich, Winterthurerstrasse
190, CH-8057 Zurich, Zurich, Switzerland
| | - Amedeo Caflisch
- Department of Biochemistry, University of Zurich, Winterthurerstrasse
190, CH-8057 Zurich, Zurich, Switzerland
| | - Andreas Vitalis
- Department of Biochemistry, University of Zurich, Winterthurerstrasse
190, CH-8057 Zurich, Zurich, Switzerland
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80
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Scherer MK, Trendelkamp-Schroer B, Paul F, Pérez-Hernández G, Hoffmann M, Plattner N, Wehmeyer C, Prinz JH, Noé F. PyEMMA 2: A Software Package for Estimation, Validation, and Analysis of Markov Models. J Chem Theory Comput 2015; 11:5525-42. [PMID: 26574340 DOI: 10.1021/acs.jctc.5b00743] [Citation(s) in RCA: 684] [Impact Index Per Article: 76.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Abstract
Markov (state) models (MSMs) and related models of molecular kinetics have recently received a surge of interest as they can systematically reconcile simulation data from either a few long or many short simulations and allow us to analyze the essential metastable structures, thermodynamics, and kinetics of the molecular system under investigation. However, the estimation, validation, and analysis of such models is far from trivial and involves sophisticated and often numerically sensitive methods. In this work we present the open-source Python package PyEMMA ( http://pyemma.org ) that provides accurate and efficient algorithms for kinetic model construction. PyEMMA can read all common molecular dynamics data formats, helps in the selection of input features, provides easy access to dimension reduction algorithms such as principal component analysis (PCA) and time-lagged independent component analysis (TICA) and clustering algorithms such as k-means, and contains estimators for MSMs, hidden Markov models, and several other models. Systematic model validation and error calculation methods are provided. PyEMMA offers a wealth of analysis functions such that the user can conveniently compute molecular observables of interest. We have derived a systematic and accurate way to coarse-grain MSMs to few states and to illustrate the structures of the metastable states of the system. Plotting functions to produce a manuscript-ready presentation of the results are available. In this work, we demonstrate the features of the software and show new methodological concepts and results produced by PyEMMA.
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Affiliation(s)
- Martin K Scherer
- Department for Mathematics and Computer Science, Freie Universität , Arnimallee 6, Berlin 14195, Germany
| | | | - Fabian Paul
- Department for Mathematics and Computer Science, Freie Universität , Arnimallee 6, Berlin 14195, Germany
| | - Guillermo Pérez-Hernández
- Department for Mathematics and Computer Science, Freie Universität , Arnimallee 6, Berlin 14195, Germany
| | - Moritz Hoffmann
- Department for Mathematics and Computer Science, Freie Universität , Arnimallee 6, Berlin 14195, Germany
| | - Nuria Plattner
- Department for Mathematics and Computer Science, Freie Universität , Arnimallee 6, Berlin 14195, Germany
| | - Christoph Wehmeyer
- Department for Mathematics and Computer Science, Freie Universität , Arnimallee 6, Berlin 14195, Germany
| | - Jan-Hendrik Prinz
- Department for Mathematics and Computer Science, Freie Universität , Arnimallee 6, Berlin 14195, Germany
| | - Frank Noé
- Department for Mathematics and Computer Science, Freie Universität , Arnimallee 6, Berlin 14195, Germany
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81
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Noé F, Clementi C. Kinetic distance and kinetic maps from molecular dynamics simulation. J Chem Theory Comput 2015; 11:5002-11. [PMID: 26574285 DOI: 10.1021/acs.jctc.5b00553] [Citation(s) in RCA: 121] [Impact Index Per Article: 13.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023]
Abstract
Characterizing macromolecular kinetics from molecular dynamics (MD) simulations requires a distance metric that can distinguish slowly interconverting states. Here, we build upon diffusion map theory and define a kinetic distance metric for irreducible Markov processes that quantifies how slowly molecular conformations interconvert. The kinetic distance can be computed given a model that approximates the eigenvalues and eigenvectors (reaction coordinates) of the MD Markov operator. Here, we employ the time-lagged independent component analysis (TICA). The TICA components can be scaled to provide a kinetic map in which the Euclidean distance corresponds to the kinetic distance. As a result, the question of how many TICA dimensions should be kept in a dimensionality reduction approach becomes obsolete, and one parameter less needs to be specified in the kinetic model construction. We demonstrate the approach using TICA and Markov state model (MSM) analyses for illustrative models, protein conformation dynamics in bovine pancreatic trypsin inhibitor and protein-inhibitor association in trypsin and benzamidine. We find that the total kinetic variance (TKV) is an excellent indicator of model quality and can be used to rank different input feature sets.
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Affiliation(s)
- Frank Noé
- FU Berlin , Department of Mathematics, Computer Science and Bioinformatics, Arnimallee 6, 14195 Berlin, Germany
| | - Cecilia Clementi
- Center for Theoretical Biological Physics, and Department of Chemistry, Rice University , Houston, Texas 77005, United States
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82
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Vitalini F, Noé F, Keller BG. A Basis Set for Peptides for the Variational Approach to Conformational Kinetics. J Chem Theory Comput 2015; 11:3992-4004. [DOI: 10.1021/acs.jctc.5b00498] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/22/2023]
Affiliation(s)
- F. Vitalini
- Department
of Biology, Chemistry, Pharmacy, Freie Universität Berlin, Takustraße
3, D-14195 Berlin, Germany
| | - F. Noé
- Department
of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, D-14195 Berlin, Germany
| | - B. G. Keller
- Department
of Biology, Chemistry, Pharmacy, Freie Universität Berlin, Takustraße
3, D-14195 Berlin, Germany
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