1
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Ono J, Matsumura Y, Mori T, Saito S. Conformational Dynamics in Proteins: Entangled Slow Fluctuations and Nonequilibrium Reaction Events. J Phys Chem B 2024; 128:20-32. [PMID: 38133567 DOI: 10.1021/acs.jpcb.3c05307] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2023]
Abstract
Proteins exhibit conformational fluctuations and changes over various time scales, ranging from rapid picosecond-scale local atomic motions to slower microsecond-scale global conformational transformations. In the presence of these intricate fluctuations, chemical reactions occur and functions emerge. These conformational fluctuations of proteins are not merely stochastic random motions but possess distinct spatiotemporal characteristics. Moreover, chemical reactions do not always proceed along a single reaction coordinate in a quasi-equilibrium manner. Therefore, it is essential to understand spatiotemporal conformational fluctuations of proteins and the conformational change processes associated with reactions. In this Perspective, we shed light on the complex dynamics of proteins and their role in enzyme catalysis by presenting recent results regarding dynamic couplings and disorder in the conformational dynamics of proteins and rare but rapid enzymatic reaction events obtained from molecular dynamics simulations.
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Affiliation(s)
- Junichi Ono
- Waseda Research Institute for Science and Engineering (WISE), Waseda University, 3-4-1 Okubo, Shinjuku, Tokyo 169-8555, Japan
| | - Yoshihiro Matsumura
- Institute for Chemical Reaction Design and Discovery (WPI-ICReDD), Hokkaido University, Sapporo, Hokkaido 001-0021, Japan
| | - Toshifumi Mori
- Institute for Materials Chemistry and Engineering, Kyushu University, Kasuga, Fukuoka 816-8580, Japan
- Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Kasuga, Fukuoka 816-8580, Japan
| | - Shinji Saito
- Institute for Molecular Science, Okazaki, Aichi 444-8585, Japan
- The Graduate University for Advanced Studies (SOKENDAI), Okazaki, Aichi 444-8585, Japan
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2
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Yeh CY, Izaguirre JA, Greisman JB, Willmore L, Maragakis P, Shaw DE. A Conserved Local Structural Motif Controls the Kinetics of PTP1B Catalysis. J Chem Inf Model 2023. [PMID: 37378552 DOI: 10.1021/acs.jcim.3c00286] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/29/2023]
Abstract
Protein tyrosine phosphatase 1B (PTP1B) is a negative regulator of the insulin and leptin signaling pathways, making it a highly attractive target for the treatment of type II diabetes. For PTP1B to perform its enzymatic function, a loop referred to as the "WPD loop" must transition between open (catalytically incompetent) and closed (catalytically competent) conformations, which have both been resolved by X-ray crystallography. Although prior studies have established this transition as the rate-limiting step for catalysis, the transition mechanism for PTP1B and other PTPs has been unclear. Here we present an atomically detailed model of WPD loop transitions in PTP1B based on unbiased, long-timescale molecular dynamics simulations and weighted ensemble simulations. We found that a specific WPD loop region─the PDFG motif─acted as the key conformational switch, with structural changes to the motif being necessary and sufficient for transitions between long-lived open and closed states of the loop. Simulations starting from the closed state repeatedly visited open states of the loop that quickly closed again unless the infrequent conformational switching of the motif stabilized the open state. The functional importance of the PDFG motif is supported by the fact that it is well conserved across PTPs. Bioinformatic analysis shows that the PDFG motif is also conserved, and adopts two distinct conformations, in deiminases, and the related DFG motif is known to function as a conformational switch in many kinases, suggesting that PDFG-like motifs may control transitions between structurally distinct, long-lived conformational states in multiple protein families.
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Affiliation(s)
- Christine Y Yeh
- D. E. Shaw Research, New York, New York 10036, United States
| | | | - Jack B Greisman
- D. E. Shaw Research, New York, New York 10036, United States
| | | | - Paul Maragakis
- D. E. Shaw Research, New York, New York 10036, United States
| | - David E Shaw
- D. E. Shaw Research, New York, New York 10036, United States
- Department of Biochemistry and Molecular Biophysics, Columbia University, New York, New York 10032, United States
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3
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Spiriti J, Noé F, Wong CF. Simulation of ligand dissociation kinetics from the protein kinase PYK2. J Comput Chem 2022; 43:1911-1922. [PMID: 36073605 PMCID: PMC9976590 DOI: 10.1002/jcc.26991] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/19/2022] [Revised: 06/11/2022] [Accepted: 08/03/2022] [Indexed: 11/09/2022]
Abstract
Early-stage drug discovery projects often focus on equilibrium binding affinity to the target alongside selectivity and other pharmaceutical properties. The kinetics of drug binding are ignored but can have significant influence on drug efficacy. Therefore, increasing attention has been paid on evaluating drug-binding kinetics early in a drug discovery process. Simulating drug-binding kinetics at the atomic level is challenging for the long time scale involved. Here, we used the transition-based reweighting analysis method (TRAM) with the Markov state model to study the dissociation of a ligand from the protein kinase PYK2. TRAM combines biased and unbiased simulations to reduce computational costs. This work used the umbrella sampling technique for the biased simulations. Although using the potential of mean force from umbrella sampling simulations with the transition-state theory over-estimated the dissociation rate by three orders of magnitude, TRAM gave a dissociation rate within an order of magnitude of the experimental value.
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Affiliation(s)
- Justin Spiriti
- Department of Chemistry and Biochemistry, University of Missouri-St. Louis, St. Louis, Missouri, USA
| | - Frank Noé
- Department of Mathematics and Computer Science, Freie Universität Berlin, Berlin, Germany
- Department of Physics, Freie Universität Berlin, Berlin, Germany
| | - Chung F. Wong
- Department of Chemistry and Biochemistry, University of Missouri-St. Louis, St. Louis, Missouri, USA
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4
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Russo JD, Zhang S, Leung JMG, Bogetti AT, Thompson JP, DeGrave AJ, Torrillo PA, Pratt AJ, Wong KF, Xia J, Copperman J, Adelman JL, Zwier MC, LeBard DN, Zuckerman DM, Chong LT. WESTPA 2.0: High-Performance Upgrades for Weighted Ensemble Simulations and Analysis of Longer-Timescale Applications. J Chem Theory Comput 2022; 18:638-649. [PMID: 35043623 PMCID: PMC8825686 DOI: 10.1021/acs.jctc.1c01154] [Citation(s) in RCA: 15] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/13/2023]
Abstract
The weighted ensemble (WE) family of methods is one of several statistical mechanics-based path sampling strategies that can provide estimates of key observables (rate constants and pathways) using a fraction of the time required by direct simulation methods such as molecular dynamics or discrete-state stochastic algorithms. WE methods oversee numerous parallel trajectories using intermittent overhead operations at fixed time intervals, enabling facile interoperability with any dynamics engine. Here, we report on the major upgrades to the WESTPA software package, an open-source, high-performance framework that implements both basic and recently developed WE methods. These upgrades offer substantial improvements over traditional WE methods. The key features of the new WESTPA 2.0 software enhance the efficiency and ease of use: an adaptive binning scheme for more efficient surmounting of large free energy barriers, streamlined handling of large simulation data sets, exponentially improved analysis of kinetics, and developer-friendly tools for creating new WE methods, including a Python API and resampler module for implementing both binned and "binless" WE strategies.
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Affiliation(s)
- John D Russo
- Department of Biomedical Engineering, Oregon Health and Science University, Portland, Oregon 97239-3098, United States
| | - She Zhang
- OpenEye Scientific, Santa Fe, New Mexico 87508, United States
| | - Jeremy M G Leung
- Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, United States
| | - Anthony T Bogetti
- Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, United States
| | - Jeff P Thompson
- OpenEye Scientific, Santa Fe, New Mexico 87508, United States
| | - Alex J DeGrave
- Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, United States
| | - Paul A Torrillo
- Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, United States
| | - A J Pratt
- Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, United States
| | - Kim F Wong
- Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, United States
| | - Junchao Xia
- OpenEye Scientific, Santa Fe, New Mexico 87508, United States
| | - Jeremy Copperman
- Department of Biomedical Engineering, Oregon Health and Science University, Portland, Oregon 97239-3098, United States
| | - Joshua L Adelman
- Department of Biological Sciences, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, United States
| | - Matthew C Zwier
- Department of Chemistry, Drake University, Des Moines, Iowa 50311-4505, United States
| | - David N LeBard
- OpenEye Scientific, Santa Fe, New Mexico 87508, United States
| | - Daniel M Zuckerman
- Department of Biomedical Engineering, Oregon Health and Science University, Portland, Oregon 97239-3098, United States
| | - Lillian T Chong
- Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, United States
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5
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Matsumura Y, Saito S. Microscopic insights into dynamic disorder in the isomerization dynamics of the protein BPTI. J Chem Phys 2021; 154:224113. [PMID: 34241205 DOI: 10.1063/5.0055152] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Understanding the dynamic disorder behind a process, i.e., the dynamic effect of fluctuations that occur on a timescale slower or comparable with the timescale of the process, is essential for elucidating the dynamics and kinetics of complicated molecular processes in biomolecules and liquids. Despite numerous theoretical studies of single-molecule kinetics, our microscopic understanding of dynamic disorder remains limited. In the present study, we investigate the microscopic aspects of dynamic disorder in the isomerization dynamics of the Cys14-Cys38 disulfide bond in the protein bovine pancreatic trypsin inhibitor, which has been observed by nuclear magnetic resonance. We use a theoretical model with a stochastic transition rate coefficient, which is calculated from the 1-ms-long time molecular dynamics trajectory obtained by Shaw et al. [Science 330, 341-346 (2010)]. The isomerization dynamics are expressed by the transitions between coarse-grained states consisting of internal states, i.e., conformational sub-states. In this description, the rate for the transition from the coarse-grained states is stochastically modulated due to fluctuations between internal states. We examine the survival probability for the conformational transitions from a coarse-grained state using a theoretical model, which is a good approximation to the directly calculated survival probability. The dynamic disorder changes from a slow modulation limit to a fast modulation limit depending on the aspects of the coarse-grained states. Our analysis of the rate modulations behind the survival probability, in relation to the fluctuations between internal states, reveals the microscopic origin of dynamic disorder.
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Affiliation(s)
| | - Shinji Saito
- Institute for Molecular Science, Myodaiji, Okazaki, Aichi 444-8585, Japan
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6
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Suárez E, Wiewiora RP, Wehmeyer C, Noé F, Chodera JD, Zuckerman DM. What Markov State Models Can and Cannot Do: Correlation versus Path-Based Observables in Protein-Folding Models. J Chem Theory Comput 2021; 17:3119-3133. [PMID: 33904312 PMCID: PMC8127341 DOI: 10.1021/acs.jctc.0c01154] [Citation(s) in RCA: 30] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Markov state models (MSMs) have been widely applied to study the kinetics and pathways of protein conformational dynamics based on statistical analysis of molecular dynamics (MD) simulations. These MSMs coarse-grain both configuration space and time in ways that limit what kinds of observables they can reproduce with high fidelity over different spatial and temporal resolutions. Despite their popularity, there is still limited understanding of which biophysical observables can be computed from these MSMs in a robust and unbiased manner, and which suffer from the space-time coarse-graining intrinsic in the MSM model. Most theoretical arguments and practical validity tests for MSMs rely on long-time equilibrium kinetics, such as the slowest relaxation time scales and experimentally observable time-correlation functions. Here, we perform an extensive assessment of the ability of well-validated protein folding MSMs to accurately reproduce path-based observable such as mean first-passage times (MFPTs) and transition path mechanisms compared to a direct trajectory analysis. We also assess a recently proposed class of history-augmented MSMs (haMSMs) that exploit additional information not accounted for in standard MSMs. We conclude with some practical guidance on the use of MSMs to study various problems in conformational dynamics of biomolecules. In brief, MSMs can accurately reproduce correlation functions slower than the lag time, but path-based observables can only be reliably reproduced if the lifetimes of states exceed the lag time, which is a much stricter requirement. Even in the presence of short-lived states, we find that haMSMs reproduce path-based observables more reliably.
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Affiliation(s)
- Ernesto Suárez
- Advanced Biomedical Computational Science, Frederick National Laboratory for Cancer Research, Frederick, MD 21702
| | - Rafal P. Wiewiora
- Computational and Systems Biology Program, Sloan Kettering Institute, Memorial Sloan Kettering Cancer Center, New York, NY 10065
| | | | | | - John D. Chodera
- Computational and Systems Biology Program, Sloan Kettering Institute, Memorial Sloan Kettering Cancer Center, New York, NY 10065
| | - Daniel M. Zuckerman
- Department of Biomedical Engineering, Oregon Health and Science University, Portland, OR 97239
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7
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Bause M, Bereau T. Reweighting non-equilibrium steady-state dynamics along collective variables. J Chem Phys 2021; 154:134105. [PMID: 33832234 DOI: 10.1063/5.0042972] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022] Open
Abstract
Computer simulations generate microscopic trajectories of complex systems at a single thermodynamic state point. We recently introduced a Maximum Caliber (MaxCal) approach for dynamical reweighting. Our approach mapped these trajectories to a Markovian description on the configurational coordinates and reweighted path probabilities as a function of external forces. Trajectory probabilities can be dynamically reweighted both from and to equilibrium or non-equilibrium steady states. As the system's dimensionality increases, an exhaustive description of the microtrajectories becomes prohibitive-even with a Markovian assumption. Instead, we reduce the dimensionality of the configurational space to collective variables (CVs). Going from configurational to CV space, we define local entropy productions derived from configurationally averaged mean forces. The entropy production is shown to be a suitable constraint on MaxCal for non-equilibrium steady states expressed as a function of CVs. We test the reweighting procedure on two systems: a particle subject to a two-dimensional potential and a coarse-grained peptide. Our CV-based MaxCal approach expands dynamical reweighting to larger systems, for both static and dynamical properties, and across a large range of driving forces.
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Affiliation(s)
- Marius Bause
- Max Planck Institute for Polymer Research, 55128 Mainz, Germany
| | - Tristan Bereau
- Max Planck Institute for Polymer Research, 55128 Mainz, Germany
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8
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Copperman J, Zuckerman DM. Accelerated Estimation of Long-Timescale Kinetics from Weighted Ensemble Simulation via Non-Markovian "Microbin" Analysis. J Chem Theory Comput 2020; 16:6763-6775. [PMID: 32990438 PMCID: PMC8045600 DOI: 10.1021/acs.jctc.0c00273] [Citation(s) in RCA: 19] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023]
Abstract
The weighted ensemble (WE) simulation strategy provides unbiased sampling of nonequilibrium processes, such as molecular folding or binding, but the extraction of rate constants relies on characterizing steady-state behavior. Unfortunately, WE simulations of sufficiently complex systems will not relax to steady state on observed simulation times. Here, we show that a postsimulation clustering of molecular configurations into "microbins" using methods developed in the Markov State Model (MSM) community can yield unbiased kinetics from WE data before steady-state convergence of the WE simulation itself. Because WE trajectories are directional and not equilibrium distributed, the history-augmented MSM (haMSM) formulation can be used, which yields the mean first-passage time (MFPT) without bias for arbitrarily small lag times. Accurate kinetics can be obtained while bypassing the often prohibitive convergence requirements of the nonequilibrium weighted ensemble. We validate the method in a simple diffusive process on a two-dimensional (2D) random energy landscape and then analyze atomistic protein folding simulations using WE molecular dynamics. We report significant progress toward the unbiased estimation of protein folding times and pathways, though key challenges remain.
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Affiliation(s)
- Jeremy Copperman
- Department of Biomedical Engineering, Oregon Health and Science University, Portland, Oregon 97239, United States
| | - Daniel M Zuckerman
- Department of Biomedical Engineering, Oregon Health and Science University, Portland, Oregon 97239, United States
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9
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Sharpe DJ, Wales DJ. Efficient and exact sampling of transition path ensembles on Markovian networks. J Chem Phys 2020; 153:024121. [DOI: 10.1063/5.0012128] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
Affiliation(s)
- Daniel J. Sharpe
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - David J. Wales
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
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10
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Braka A, Garnier N, Bonnet P, Aci-Sèche S. Residence Time Prediction of Type 1 and 2 Kinase Inhibitors from Unbinding Simulations. J Chem Inf Model 2019; 60:342-348. [DOI: 10.1021/acs.jcim.9b00497] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/13/2023]
Affiliation(s)
- Abdennour Braka
- Institut de Chimie Organique et Analytique (ICOA), UMR7311 Université d’Orléans-CNRS, Rue de Chartres—BP 6759, 45067 Orléans Cedex 2, France
- Centre de Biophysique Moléculaire (CBM) UPR 4301, CNRS, Rue Charles Sadron, 45071 Orléans Cedex 2, France
| | - Norbert Garnier
- Centre de Biophysique Moléculaire (CBM) UPR 4301, CNRS, Rue Charles Sadron, 45071 Orléans Cedex 2, France
| | - Pascal Bonnet
- Institut de Chimie Organique et Analytique (ICOA), UMR7311 Université d’Orléans-CNRS, Rue de Chartres—BP 6759, 45067 Orléans Cedex 2, France
| | - Samia Aci-Sèche
- Institut de Chimie Organique et Analytique (ICOA), UMR7311 Université d’Orléans-CNRS, Rue de Chartres—BP 6759, 45067 Orléans Cedex 2, France
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11
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Agarwal A, Hengartner NW, Gnanakaran S, Voter AF. Computing long time scale biomolecular dynamics using quasi-stationary distribution kinetic Monte Carlo (QSD-KMC). J Chem Phys 2019; 151:074109. [PMID: 31438708 DOI: 10.1063/1.5094457] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023] Open
Abstract
It is a challenge to obtain an accurate model of the state-to-state dynamics of a complex biological system from molecular dynamics (MD) simulations. In recent years, Markov state models have gained immense popularity for computing state-to-state dynamics from a pool of short MD simulations. However, the assumption that the underlying dynamics on the reduced space is Markovian induces a systematic bias in the model, especially in biomolecular systems with complicated energy landscapes. To address this problem, we have devised a new approach we call quasistationary distribution kinetic Monte Carlo (QSD-KMC) that gives accurate long time state-to-state evolution while retaining the entire time resolution even when the dynamics is highly non-Markovian. The proposed method is a kinetic Monte Carlo approach that takes advantage of two concepts: (i) the quasistationary distribution, the distribution that results when a trajectory remains in one state for a long time (the dephasing time), such that the next escape is Markovian, and (ii) dynamical corrections theory, which properly accounts for the correlated events that occur as a trajectory passes from state to state before it settles again. In practice, this is achieved by specifying, for each escape, the intermediate states and the final state that has resulted from the escape. Implementation of QSD-KMC imposes stricter requirements on the lengths of the trajectories than in a Markov state model approach as the trajectories must be long enough to dephase. However, the QSD-KMC model produces state-to-state trajectories that are statistically indistinguishable from an MD trajectory mapped onto the discrete set of states for an arbitrary choice of state decomposition. Furthermore, the aforementioned concepts can be used to construct a Monte Carlo approach to optimize the state boundaries regardless of the initial choice of states. We demonstrate the QSD-KMC method on two one-dimensional model systems, one of which is a driven nonequilibrium system, and on two well-characterized biomolecular systems.
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Affiliation(s)
- Animesh Agarwal
- Theoretical Biology and Biophysics Group, Los Alamos National Laboratory, Los Alamos, New Mexico 87544, USA
| | - Nicolas W Hengartner
- Theoretical Biology and Biophysics Group, Los Alamos National Laboratory, Los Alamos, New Mexico 87544, USA
| | - S Gnanakaran
- Theoretical Biology and Biophysics Group, Los Alamos National Laboratory, Los Alamos, New Mexico 87544, USA
| | - Arthur F Voter
- Theoretical Division T-1, Los Alamos National Laboratory, Los Alamos, New Mexico 87544, USA
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12
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Mostofian B, Zuckerman DM. Statistical Uncertainty Analysis for Small-Sample, High Log-Variance Data: Cautions for Bootstrapping and Bayesian Bootstrapping. J Chem Theory Comput 2019; 15:3499-3509. [PMID: 31002504 PMCID: PMC6754704 DOI: 10.1021/acs.jctc.9b00015] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Recent advances in molecular simulations allow the evaluation of previously unattainable observables, such as rate constants for protein folding. However, these calculations are usually computationally expensive, and even significant computing resources may result in a small number of independent estimates spread over many orders of magnitude. Such small-sample, high "log-variance" data are not readily amenable to analysis using the standard uncertainty (i.e., "standard error of the mean") because unphysical negative limits of confidence intervals result. Bootstrapping, a natural alternative guaranteed to yield a confidence interval within the minimum and maximum values, also exhibits a striking systematic bias of the lower confidence limit in log space. As we show, bootstrapping artifactually assigns high probability to improbably low mean values. A second alternative, the Bayesian bootstrap strategy, does not suffer from the same deficit and is more logically consistent with the type of confidence interval desired. The Bayesian bootstrap provides uncertainty intervals that are more reliable than those from the standard bootstrap method but must be used with caution nevertheless. Neither standard nor Bayesian bootstrapping can overcome the intrinsic challenge of underestimating the mean from small-size, high log-variance samples. Our conclusions are based on extensive analysis of model distributions and reanalysis of multiple independent atomistic simulations. Although we only analyze rate constants, similar considerations will apply to related calculations, potentially including highly nonlinear averages like the Jarzynski relation.
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Affiliation(s)
- Barmak Mostofian
- Department of Biomedical Engineering, School of Medicine, Oregon Health & Science University, Portland, Oregon
| | - Daniel M. Zuckerman
- Department of Biomedical Engineering, School of Medicine, Oregon Health & Science University, Portland, Oregon
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13
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Lee HS, Ahn SH, Darve EF. The multi-dimensional generalized Langevin equation for conformational motion of proteins. J Chem Phys 2019; 150:174113. [PMID: 31067888 DOI: 10.1063/1.5055573] [Citation(s) in RCA: 23] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022] Open
Abstract
Using the generalized Langevin equation (GLE) is a promising approach to build coarse-grained (CG) models of molecular systems since the GLE model often leads to more accurate thermodynamic and kinetic predictions than Brownian dynamics or Langevin models by including a more sophisticated friction with memory. The GLE approach has been used for CG coordinates such as the center of mass of a group of atoms with pairwise decomposition and for a single CG coordinate. We present a GLE approach when CG coordinates are multiple generalized coordinates, defined, in general, as nonlinear functions of microscopic atomic coordinates. The CG model for multiple generalized coordinates is described by the multidimensional GLE from the Mori-Zwanzig formalism, which includes an exact memory matrix. We first present a method to compute the memory matrix in a multidimensional GLE using trajectories of a full system. Then, in order to reduce the computational cost of computing the multidimensional friction with memory, we introduce a method that maps the GLE to an extended Markovian system. In addition, we study the effect of using a nonconstant mass matrix in the CG model. In particular, we include mass-dependent terms in the mean force. We used the proposed CG model to describe the conformational motion of a solvated alanine dipeptide system, with two dihedral angles as the CG coordinates. We showed that the CG model can accurately reproduce two important kinetic quantities: the velocity autocorrelation function and the distribution of first passage times.
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Affiliation(s)
- Hee Sun Lee
- Mechanical Engineering Department, Stanford University, Stanford, California 94305, USA
| | - Surl-Hee Ahn
- Chemistry Department, Stanford University, Stanford, California 94305, USA
| | - Eric F Darve
- Mechanical Engineering Department, Stanford University, Stanford, California 94305, USA
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14
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Adhikari U, Mostofian B, Copperman J, Subramanian SR, Petersen AA, Zuckerman DM. Computational Estimation of Microsecond to Second Atomistic Folding Times. J Am Chem Soc 2019; 141:6519-6526. [PMID: 30892023 PMCID: PMC6660137 DOI: 10.1021/jacs.8b10735] [Citation(s) in RCA: 34] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Despite the development of massively parallel computing hardware including inexpensive graphics processing units (GPUs), it has remained infeasible to simulate the folding of atomistic proteins at room temperature using conventional molecular dynamics (MD) beyond the microsecond scale. Here, we report the folding of atomistic, implicitly solvated protein systems with folding times τ ranging from ∼10 μs to ∼100 ms using the weighted ensemble (WE) strategy in combination with GPU computing. Starting from an initial structure or set of structures, WE organizes an ensemble of GPU-accelerated MD trajectory segments via intermittent pruning and replication events to generate statistically unbiased estimates of rate constants for rare events such as folding; no biasing forces are used. Although the variance among atomistic WE folding runs is significant, multiple independent runs are used to reduce and quantify statistical uncertainty. Folding times are estimated directly from WE probability flux and from history-augmented Markov analysis of the WE data. Three systems were examined: NTL9 at low solvent viscosity (yielding τf = 0.8-9 μs), NTL9 at water-like viscosity (τf = 0.2-2 ms), and Protein G at low viscosity (τf = 3-200 ms). In all cases, the folding time, uncertainty, and ensemble properties could be estimated from WE simulation; for Protein G, this characterization required significantly less overall computing than would be required to observe a single folding event with conventional MD simulations. Our results suggest that the use and calibration of force fields and solvent models for precise estimation of kinetic quantities is becoming feasible.
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Affiliation(s)
- Upendra Adhikari
- Department of Biomedical Engineering, School of Medicine, Oregon Health & Science University, Portland, OR 97239
| | - Barmak Mostofian
- Department of Biomedical Engineering, School of Medicine, Oregon Health & Science University, Portland, OR 97239
| | - Jeremy Copperman
- Department of Biomedical Engineering, School of Medicine, Oregon Health & Science University, Portland, OR 97239
| | | | - Andrew A. Petersen
- NCSU Data Science Resources, North Carolina State University, Raleigh, NC 27695
| | - Daniel M. Zuckerman
- Department of Biomedical Engineering, School of Medicine, Oregon Health & Science University, Portland, OR 97239
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15
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Saglam AS, Chong LT. Protein-protein binding pathways and calculations of rate constants using fully-continuous, explicit-solvent simulations. Chem Sci 2019; 10:2360-2372. [PMID: 30881664 PMCID: PMC6385678 DOI: 10.1039/c8sc04811h] [Citation(s) in RCA: 58] [Impact Index Per Article: 11.6] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/28/2018] [Accepted: 12/26/2018] [Indexed: 11/21/2022] Open
Abstract
A grand challenge in the field of biophysics has been the complete characterization of protein-protein binding processes at atomic resolution. This characterization requires the direct simulation of binding pathways starting from the initial, unbound state and proceeding through states that are too transient to be captured by experiment. Here, we applied the weighted ensemble path sampling strategy to orchestrate atomistic simulation of protein-protein binding pathways. Our simulation generated 203 fully-continuous and independent pathways along with rate constants for the binding process involving the barnase and barstar proteins. Results reveal multiple binding pathways along a "funnel-like" free energy landscape in which the formation of the "encounter complex" intermediate is rate-limiting followed by a relatively rapid rearrangement of the encounter complex to the bound state. Among all diffusional collisions, only ∼11% were productive. In the most probable binding pathways, the proteins rotated to a large extent (likely via electrostatic steering) in order to collide productively followed by "rolling" of the proteins along each other's binding interfaces to reach the bound state. Consistent with experiment, R59 was identified as the most kinetically important barnase residue for the binding process. Furthermore, protein desolvation occurs late in the binding process during the rearrangement of the encounter complex to the bound state. Notably, the positions of crystallographic water molecules that bridge hydrogen bonds between barnase and barstar are occupied in the bound-state ensemble. Our simulation was completed in a month using 1600 CPU cores at a time, demonstrating that it is now practical to carry out atomistic simulations of protein-protein binding.
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Affiliation(s)
- Ali S Saglam
- University of Pittsburgh , Department of Chemistry , 219 Parkman Avenue , Pittsburgh , PA 15260 , USA . ; Tel: +1-412-624-6026
| | - Lillian T Chong
- University of Pittsburgh , Department of Chemistry , 219 Parkman Avenue , Pittsburgh , PA 15260 , USA . ; Tel: +1-412-624-6026
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Xiao J, Salsbury FR. Na +-binding modes involved in thrombin's allosteric response as revealed by molecular dynamics simulations, correlation networks and Markov modeling. Phys Chem Chem Phys 2019; 21:4320-4330. [PMID: 30724273 PMCID: PMC6993936 DOI: 10.1039/c8cp07293k] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Abstract
The monovalent sodium ion (Na+) is a critical modulator of thrombin. However, the mechanism of thrombin's activation by Na+ has been widely debated for more than twenty years. Details of the linkage between thrombin and Na+ remain vague due to limited temporal and spatial resolution in experiments. In this work, we combine microsecond scale atomic-detailed molecular dynamics simulations with correlation network analyses and hidden Markov modeling to probe the detailed thermodynamic and kinetic picture of Na+-binding events and their resulting allosteric responses in thrombin. We reveal that ASP189 and ALA190 comprise a stable Na+-binding site (referred as "inner" Na+-binding site) along with the previously known one (referred as "outer" Na+-binding site). The corresponding newly identified Na+-binding mode introduces significant allosteric responses in thrombin's regulatory regions by stabilizing selected torsion angles of residues responsive to Na+-binding. Our Markov model indicates that the bound Na+ prefers to transfer between the two Na+-binding sites when an unbinding event takes place. These results suggest a testable hypothesis of a substrate-driven Na+ migration (ΔG ∼ 1.7 kcal mol-1) from the "inner" Na+-binding site to the "outer" one during thrombin's catalytic activities. The binding of a Na+ ion at the "inner" Na+-binding site should be inferred as a prerequisite for thrombin's efficient recognition to the substrate, which opens a new angle for our understanding of Na+-binding's allosteric activation on thrombin and sheds light on detailed processes in thrombin's activation.
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Affiliation(s)
- Jiajie Xiao
- Department of Physics, Wake Forest University, Winston Salem, NC, USA.
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Fujisaki H, Moritsugu K, Mitsutake A, Suetani H. Conformational change of a biomolecule studied by the weighted ensemble method: Use of the diffusion map method to extract reaction coordinates. J Chem Phys 2018; 149:134112. [PMID: 30292230 DOI: 10.1063/1.5049420] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We simulate the nonequilibrium ensemble dynamics of a biomolecule using the weighted ensemble method, which was introduced in molecular dynamics simulations by Huber and Kim and further developed by Zuckerman and co-workers. As the order parameters to characterize its conformational change, we here use the coordinates derived from the diffusion map (DM) method, one of the manifold learning techniques. As a concrete example, we study the kinetic properties of a small peptide, chignolin in explicit water, and calculate the conformational change between the folded and misfolded states in a nonequilibrium way. We find that the transition time scales thus obtained are comparable to those using previously employed hydrogen-bond distances as the order parameters. Since the DM method only uses the 3D Cartesian coordinates of a peptide, this shows that the DM method can extract the important distance information of the peptide without relying on chemical intuition. The time scales are compared well with the previous results using different techniques, non-Markovian analysis and core-set milestoning for a single long trajectory. We also find that the most significant DM coordinate turns out to extract a dihedral angle of glycine, and the previously studied relaxation modes are well correlated with the most significant DM coordinates.
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Affiliation(s)
- Hiroshi Fujisaki
- Department of Physics, Nippon Medical School, 1-7-1 Kyonan-cho, Musashino, Tokyo 180-0023, Japan
| | - Kei Moritsugu
- Graduate School of Medical Life Science, Yokohama City University, 1-7-29 Suehirocho, Tsurumi, Yokohama 230-0045, Japan
| | - Ayori Mitsutake
- Department of Physics, School of Science and Technology, Meiji University, 1-1-1 Higashi-Mita, Tama-ku, Kawasaki, Kanagawa 214-8571, Japan
| | - Hiromichi Suetani
- Faculty of Science and Technology, Oita University, 700 Dannoharu, Oita 870-1192, Japan
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Abstract
The weighted ensemble (WE) methodology orchestrates quasi-independent parallel simulations run with intermittent communication that can enhance sampling of rare events such as protein conformational changes, folding, and binding. The WE strategy can achieve superlinear scaling-the unbiased estimation of key observables such as rate constants and equilibrium state populations to greater precision than would be possible with ordinary parallel simulation. WE software can be used to control any dynamics engine, such as standard molecular dynamics and cell-modeling packages. This article reviews the theoretical basis of WE and goes on to describe successful applications to a number of complex biological processes-protein conformational transitions, (un)binding, and assembly processes, as well as cell-scale processes in systems biology. We furthermore discuss the challenges that need to be overcome in the next phase of WE methodological development. Overall, the combined advances in WE methodology and software have enabled the simulation of long-timescale processes that would otherwise not be practical on typical computing resources using standard simulation.
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Affiliation(s)
- Daniel M Zuckerman
- Department of Biomedical Engineering, Oregon Health and Science University, Portland, Oregon 97239;
| | - Lillian T Chong
- Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260;
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Suárez E, Adelman JL, Zuckerman DM. Accurate Estimation of Protein Folding and Unfolding Times: Beyond Markov State Models. J Chem Theory Comput 2016; 12:3473-81. [PMID: 27340835 PMCID: PMC5022777 DOI: 10.1021/acs.jctc.6b00339] [Citation(s) in RCA: 52] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022]
Abstract
Because standard molecular dynamics (MD) simulations are unable to access time scales of interest in complex biomolecular systems, it is common to "stitch together" information from multiple shorter trajectories using approximate Markov state model (MSM) analysis. However, MSMs may require significant tuning and can yield biased results. Here, by analyzing some of the longest protein MD data sets available (>100 μs per protein), we show that estimators constructed based on exact non-Markovian (NM) principles can yield significantly improved mean first-passage times (MFPTs) for protein folding and unfolding. In some cases, MSM bias of more than an order of magnitude can be corrected when identical trajectory data are reanalyzed by non-Markovian approaches. The NM analysis includes "history" information, higher order time correlations compared to MSMs, that is available in every MD trajectory. The NM strategy is insensitive to fine details of the states used and works well when a fine time-discretization (i.e., small "lag time") is used.
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Affiliation(s)
- Ernesto Suárez
- Department of Computational and Systems Biology, University of Pittsburgh , Pittsburgh, Pennsylvania 15260, United States
| | - Joshua L Adelman
- Department of Biological Sciences, University of Pittsburgh , Pittsburgh, Pennsylvania 15260, United States
| | - Daniel M Zuckerman
- Department of Computational and Systems Biology, University of Pittsburgh , Pittsburgh, Pennsylvania 15260, United States
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