1
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Keller BG, Bolhuis PG. Dynamical Reweighting for Biased Rare Event Simulations. Annu Rev Phys Chem 2024; 75:137-162. [PMID: 38941527 DOI: 10.1146/annurev-physchem-083122-124538] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/30/2024]
Abstract
Dynamical reweighting techniques aim to recover the correct molecular dynamics from a simulation at a modified potential energy surface. They are important for unbiasing enhanced sampling simulations of molecular rare events. Here, we review the theoretical frameworks of dynamical reweighting for modified potentials. Based on an overview of kinetic models with increasing level of detail, we discuss techniques to reweight two-state dynamics, multistate dynamics, and path integrals. We explore the natural link to transition path sampling and how the effect of nonequilibrium forces can be reweighted. We end by providing an outlook on how dynamical reweighting integrates with techniques for optimizing collective variables and with modern potential energy surfaces.
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Affiliation(s)
- Bettina G Keller
- Department of Biology, Chemistry and Pharmacy, Freie Universität Berlin, Berlin, Germany;
| | - Peter G Bolhuis
- Van 't Hoff Institute for Molecular Sciences, University of Amsterdam, Amsterdam, The Netherlands
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2
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Voelz VA, Pande VS, Bowman GR. Folding@home: Achievements from over 20 years of citizen science herald the exascale era. Biophys J 2023; 122:2852-2863. [PMID: 36945779 PMCID: PMC10398258 DOI: 10.1016/j.bpj.2023.03.028] [Citation(s) in RCA: 15] [Impact Index Per Article: 15.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/02/2022] [Revised: 01/26/2023] [Accepted: 03/16/2023] [Indexed: 03/23/2023] Open
Abstract
Simulations of biomolecules have enormous potential to inform our understanding of biology but require extremely demanding calculations. For over 20 years, the Folding@home distributed computing project has pioneered a massively parallel approach to biomolecular simulation, harnessing the resources of citizen scientists across the globe. Here, we summarize the scientific and technical advances this perspective has enabled. As the project's name implies, the early years of Folding@home focused on driving advances in our understanding of protein folding by developing statistical methods for capturing long-timescale processes and facilitating insight into complex dynamical processes. Success laid a foundation for broadening the scope of Folding@home to address other functionally relevant conformational changes, such as receptor signaling, enzyme dynamics, and ligand binding. Continued algorithmic advances, hardware developments such as graphics processing unit (GPU)-based computing, and the growing scale of Folding@home have enabled the project to focus on new areas where massively parallel sampling can be impactful. While previous work sought to expand toward larger proteins with slower conformational changes, new work focuses on large-scale comparative studies of different protein sequences and chemical compounds to better understand biology and inform the development of small-molecule drugs. Progress on these fronts enabled the community to pivot quickly in response to the COVID-19 pandemic, expanding to become the world's first exascale computer and deploying this massive resource to provide insight into the inner workings of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) virus and aid the development of new antivirals. This success provides a glimpse of what is to come as exascale supercomputers come online and as Folding@home continues its work.
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Affiliation(s)
- Vincent A Voelz
- Department of Chemistry, Temple University, Philadelphia, Pennsylvania
| | | | - Gregory R Bowman
- Departments of Biochemistry & Biophysics and of Bioengineering, University of Pennsylvania, Philadelphia, Pennsylvania.
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3
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Ge Y, Voelz VA. Estimation of binding rates and affinities from multiensemble Markov models and ligand decoupling. J Chem Phys 2022; 156:134115. [PMID: 35395889 PMCID: PMC8993428 DOI: 10.1063/5.0088024] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Accurate and efficient simulation of the thermodynamics and kinetics of protein-ligand interactions is crucial for computational drug discovery. Multiensemble Markov Model (MEMM) estimators can provide estimates of both binding rates and affinities from collections of short trajectories but have not been systematically explored for situations when a ligand is decoupled through scaling of non-bonded interactions. In this work, we compare the performance of two MEMM approaches for estimating ligand binding affinities and rates: (1) the transition-based reweighting analysis method (TRAM) and (2) a Maximum Caliber (MaxCal) based method. As a test system, we construct a small host-guest system where the ligand is a single uncharged Lennard-Jones (LJ) particle, and the receptor is an 11-particle icosahedral pocket made from the same atom type. To realistically mimic a protein-ligand binding system, the LJ ϵ parameter was tuned, and the system was placed in a periodic box with 860 TIP3P water molecules. A benchmark was performed using over 80 µs of unbiased simulation, and an 18-state Markov state model was used to estimate reference binding affinities and rates. We then tested the performance of TRAM and MaxCal when challenged with limited data. Both TRAM and MaxCal approaches perform better than conventional Markov state models, with TRAM showing better convergence and accuracy. We find that subsampling of trajectories to remove time correlation improves the accuracy of both TRAM and MaxCal and that in most cases, only a single biased ensemble to enhance sampled transitions is required to make accurate estimates.
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Affiliation(s)
- Yunhui Ge
- Department of Pharmaceutical Sciences, University of California, Irvine, California 92697, USA
| | - Vincent A Voelz
- Department of Chemistry, Temple University, Philadelphia, Pennsylvania 19122, USA
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4
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Voelz VA, Ge Y, Raddi RM. Reconciling Simulations and Experiments With BICePs: A Review. Front Mol Biosci 2021; 8:661520. [PMID: 34046431 PMCID: PMC8144449 DOI: 10.3389/fmolb.2021.661520] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/30/2021] [Accepted: 04/12/2021] [Indexed: 02/04/2023] Open
Abstract
Bayesian Inference of Conformational Populations (BICePs) is an algorithm developed to reconcile simulated ensembles with sparse experimental measurements. The Bayesian framework of BICePs enables population reweighting as a post-simulation processing step, with several advantages over existing methods, including the proper use of reference potentials, and the estimation of a Bayes factor-like quantity called the BICePs score for model selection. Here, we summarize the theory underlying this method in context with related algorithms, review the history of BICePs applications to date, and discuss current shortcomings along with future plans for improvement.
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Affiliation(s)
- Vincent A. Voelz
- Department of Chemistry, Temple University, Philadelphia, PA, United States
| | - Yunhui Ge
- Department of Pharmaceutical Sciences, University of California, Irvine, Irvine, CA, United States
| | - Robert M. Raddi
- Department of Chemistry, Temple University, Philadelphia, PA, United States
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5
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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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6
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Donati L, Weber M, Keller BG. Markov models from the square root approximation of the Fokker-Planck equation: calculating the grid-dependent flux. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:115902. [PMID: 33352543 DOI: 10.1088/1361-648x/abd5f7] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Molecular dynamics (MD) are extremely complex, yet understanding the slow components of their dynamics is essential to understanding their macroscopic properties. To achieve this, one models the MD as a stochastic process and analyses the dominant eigenfunctions of the associated Fokker-Planck operator, or of closely related transfer operators. So far, the calculation of the discretized operators requires extensive MD simulations. The square-root approximation of the Fokker-Planck equation is a method to calculate transition rates as a ratio of the Boltzmann densities of neighboring grid cells times a flux, and can in principle be calculated without a simulation. In a previous work we still used MD simulations to determine the flux. Here, we propose several methods to calculate the exact or approximate flux for various grid types, and thus estimate the rate matrix without a simulation. Using model potentials we test computational efficiency of the methods, and the accuracy with which they reproduce the dominant eigenfunctions and eigenvalues. For these model potentials, rate matrices with up to [Formula: see text] states can be obtained within seconds on a single high-performance compute server if regular grids are used.
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Affiliation(s)
- Luca Donati
- Department of Biology, Chemistry, Pharmacy, Freie Universität Berlin, Takustraße 3, D-14195 Berlin, Germany
| | - Marcus Weber
- Zuse Institute Berlin, Takustr. 7, 14195 Berlin, Germany
| | - Bettina G Keller
- Department of Biology, Chemistry, Pharmacy, Freie Universität Berlin, Takustraße 3, D-14195 Berlin, Germany
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7
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Abstract
Molecular dynamics simulations can now routinely access the microsecond timescale, making feasible direct sampling of ligand association events. While Markov State Model (MSM) approaches offer a useful framework for analyzing such trajectory data to gain insight into binding mechanisms, accurate modeling of ligand association pathways and kinetics must be done carefully. We describe methods and good practices for constructing MSMs of ligand binding from unbiased trajectory data and discuss how to use time-lagged independent component analysis (tICA) to build informative models, using as an example recent simulation work to model the binding of phenylalanine to the regulatory ACT domain dimer of phenylalanine hydroxylase. We describe a variety of methods for estimating association rates from MSMs and discuss how to distinguish between conformational selection and induced-fit mechanisms using MSMs. In addition, we review some examples of MSMs constructed to elucidate the mechanisms by which p53 transactivation domain (TAD) and related peptides bind the oncoprotein MDM2.
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Affiliation(s)
- Yunhui Ge
- Department of Chemistry, Temple University, Philadelphia, PA, USA
| | - Vincent A Voelz
- Department of Chemistry, Temple University, Philadelphia, PA, USA.
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8
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Abstract
Ever since Clausius in 1865 and Boltzmann in 1877, the concepts of entropy and of its maximization have been the foundations for predicting how material equilibria derive from microscopic properties. But, despite much work, there has been no equally satisfactory general variational principle for nonequilibrium situations. However, in 1980, a new avenue was opened by E.T. Jaynes and by Shore and Johnson. We review here maximum caliber, which is a maximum-entropy-like principle that can infer distributions of flows over pathways, given dynamical constraints. This approach is providing new insights, particularly into few-particle complex systems, such as gene circuits, protein conformational reaction coordinates, network traffic, bird flocking, cell motility, and neuronal firing.
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Affiliation(s)
- Kingshuk Ghosh
- Department of Physics and Astronomy, University of Denver, Denver, Colorado 80209, USA
| | - Purushottam D. Dixit
- Department of Systems Biology, Columbia University, New York, NY 10032, USA,Department of Physics, University of Florida, Gainesville, Florida 32611, USA
| | - Luca Agozzino
- Laufer Center for Physical and Quantitative Biology, Stony Brook University, Stony Brook, New York 11794, USA
| | - Ken A. Dill
- Laufer Center for Physical and Quantitative Biology, Stony Brook University, Stony Brook, New York 11794, USA
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9
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Matsunaga Y, Sugita Y. Use of single-molecule time-series data for refining conformational dynamics in molecular simulations. Curr Opin Struct Biol 2020; 61:153-159. [DOI: 10.1016/j.sbi.2019.12.022] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/30/2019] [Revised: 12/24/2019] [Accepted: 12/27/2019] [Indexed: 12/18/2022]
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10
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Wan H, Ge Y, Razavi A, Voelz VA. Reconciling Simulated Ensembles of Apomyoglobin with Experimental Hydrogen/Deuterium Exchange Data Using Bayesian Inference and Multiensemble Markov State Models. J Chem Theory Comput 2020; 16:1333-1348. [PMID: 31917926 DOI: 10.1021/acs.jctc.9b01240] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/08/2023]
Abstract
Hydrogen/deuterium exchange (HDX) is a powerful technique to investigate protein conformational dynamics at amino acid resolution. Because HDX provides a measurement of solvent exposure of backbone hydrogens, ensemble-averaged over potentially slow kinetic processes, it has been challenging to use HDX protection factors to refine structural ensembles obtained from molecular dynamics simulations. This entails dual challenges: (1) identifying structural observables that best correlate with backbone amide protection from exchange and (2) restraining these observables in molecular simulations to model ensembles consistent with experimental measurements. Here, we make significant progress on both fronts. First, we describe an improved predictor of HDX protection factors from structural observables in simulated ensembles, parametrized from ultralong molecular dynamics simulation trajectory data, with a Bayesian inference approach used to retain the full posterior distribution of model parameters. We next present a new method for obtaining simulated ensembles in agreement with experimental HDX protection factors, in which molecular simulations are performed at various temperatures and restraint biases and used to construct multiensemble Markov State Models (MSMs). Finally, the BICePs (Bayesian Inference of Conformational Populations) algorithm is then used with our HDX protection factor predictor to infer which thermodynamic ensemble agrees best with the experiment and estimate populations of each conformational state in the MSM. To illustrate the approach, we use a combination of HDX protection factor restraints and chemical shift restraints to model the conformational ensemble of apomyoglobin at pH 6. The resulting ensemble agrees well with the experiment and gives insight into the all-atom structure of disordered helices F and H in the absence of heme.
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Affiliation(s)
- Hongbin Wan
- Department of Chemistry , Temple University , Philadelphia , Pennsylvania 19122 , United States
| | - Yunhui Ge
- Department of Chemistry , Temple University , Philadelphia , Pennsylvania 19122 , United States
| | - Asghar Razavi
- 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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11
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Wan H, Voelz VA. Adaptive Markov state model estimation using short reseeding trajectories. J Chem Phys 2020; 152:024103. [PMID: 31941308 DOI: 10.1063/1.5142457] [Citation(s) in RCA: 21] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022] Open
Abstract
In the last decade, advances in molecular dynamics (MD) and Markov State Model (MSM) methodologies have made possible accurate and efficient estimation of kinetic rates and reactive pathways for complex biomolecular dynamics occurring on slow time scales. A promising approach to enhanced sampling of MSMs is to use "adaptive" methods, in which new MD trajectories are "seeded" preferentially from previously identified states. Here, we investigate the performance of various MSM estimators applied to reseeding trajectory data, for both a simple 1D free energy landscape and mini-protein folding MSMs of WW domain and NTL9(1-39). Our results reveal the practical challenges of reseeding simulations and suggest a simple way to reweight seeding trajectory data to better estimate both thermodynamic and kinetic quantities.
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Affiliation(s)
- Hongbin Wan
- Department of Chemistry, Temple University, Philadelphia, Pennsylvania 19122, USA
| | - Vincent A Voelz
- Department of Chemistry, Temple University, Philadelphia, Pennsylvania 19122, USA
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12
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Kieninger S, Donati L, Keller BG. Dynamical reweighting methods for Markov models. Curr Opin Struct Biol 2020; 61:124-131. [PMID: 31958761 DOI: 10.1016/j.sbi.2019.12.018] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/17/2019] [Revised: 12/13/2019] [Accepted: 12/26/2019] [Indexed: 12/21/2022]
Abstract
Conformational dynamics is essential to biomolecular processes. Markov State Models (MSMs) are widely used to elucidate dynamic properties of molecular systems from unbiased Molecular Dynamics (MD). However, the implementation of reweighting schemes for MSMs to analyze biased simulations is still at an early stage of development. Several dynamical reweighing approaches have been proposed, which can be classified as approaches based on (i) Kramers rate theory, (ii) rescaling of the probability density flux, (iii) reweighting by formulating a likelihood function, (iv) path reweighting. We present the state-of-the-art and discuss the methodological differences of these methods, their limitations and recent applications.
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Affiliation(s)
- Stefanie Kieninger
- Freie Universität Berlin, Department of Biology, Chemistry, Pharmacy, Arnimallee 22, D-14194 Berlin, Germany
| | - Luca Donati
- Freie Universität Berlin, Department of Biology, Chemistry, Pharmacy, Arnimallee 22, D-14194 Berlin, Germany
| | - Bettina G Keller
- Freie Universität Berlin, Department of Biology, Chemistry, Pharmacy, Arnimallee 22, D-14194 Berlin, Germany.
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13
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Smith CA, Mazur A, Rout AK, Becker S, Lee D, de Groot BL, Griesinger C. Enhancing NMR derived ensembles with kinetics on multiple timescales. JOURNAL OF BIOMOLECULAR NMR 2020; 74:27-43. [PMID: 31838619 PMCID: PMC7015964 DOI: 10.1007/s10858-019-00288-8] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/01/2019] [Accepted: 11/11/2019] [Indexed: 05/14/2023]
Abstract
Nuclear magnetic resonance (NMR) has the unique advantage of elucidating the structure and dynamics of biomolecules in solution at physiological temperatures, where they are in constant movement on timescales from picoseconds to milliseconds. Such motions have been shown to be critical for enzyme catalysis, allosteric regulation, and molecular recognition. With NMR being particularly sensitive to these timescales, detailed information about the kinetics can be acquired. However, nearly all methods of NMR-based biomolecular structure determination neglect kinetics, which introduces a large approximation to the underlying physics, limiting both structural resolution and the ability to accurately determine molecular flexibility. Here we present the Kinetic Ensemble approach that uses a hierarchy of interconversion rates between a set of ensemble members to rigorously calculate Nuclear Overhauser Effect (NOE) intensities. It can be used to simultaneously refine both temporal and structural coordinates. By generalizing ideas from the extended model free approach, the method can analyze the amplitudes and kinetics of motions anywhere along the backbone or side chains. Furthermore, analysis of a large set of crystal structures suggests that NOE data contains a surprising amount of high-resolution information that is better modeled using our approach. The Kinetic Ensemble approach provides the means to unify numerous types of experiments under a single quantitative framework and more fully characterize and exploit kinetically distinct protein states. While we apply the approach here to the protein ubiquitin and cross validate it with previously derived datasets, the approach can be applied to any protein for which NOE data is available.
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Affiliation(s)
- Colin A Smith
- Department for Theoretical and Computational Biophysics, Max Planck Institute for Biophysical Chemistry, Göttingen, Germany.
- Department for NMR-Based Structural Biology, Max Planck Institute for Biophysical Chemistry, Göttingen, Germany.
- Department of Chemistry, Wesleyan University, Middletown, USA.
| | - Adam Mazur
- Department for NMR-Based Structural Biology, Max Planck Institute for Biophysical Chemistry, Göttingen, Germany
- Biozentrum, University of Basel, Basel, Switzerland
| | - Ashok K Rout
- Department for NMR-Based Structural Biology, Max Planck Institute for Biophysical Chemistry, Göttingen, Germany
| | - Stefan Becker
- Department for NMR-Based Structural Biology, Max Planck Institute for Biophysical Chemistry, Göttingen, Germany
| | - Donghan Lee
- Department for NMR-Based Structural Biology, Max Planck Institute for Biophysical Chemistry, Göttingen, Germany.
- James Graham Brown Cancer Center, University of Louisville, Louisville, USA.
| | - Bert L de Groot
- Department for Theoretical and Computational Biophysics, Max Planck Institute for Biophysical Chemistry, Göttingen, Germany.
| | - Christian Griesinger
- Department for NMR-Based Structural Biology, Max Planck Institute for Biophysical Chemistry, Göttingen, Germany.
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14
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Bause M, Wittenstein T, Kremer K, Bereau T. Microscopic reweighting for nonequilibrium steady-state dynamics. Phys Rev E 2019; 100:060103. [PMID: 31962494 DOI: 10.1103/physreve.100.060103] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2019] [Indexed: 06/10/2023]
Abstract
Computer simulations generate trajectories at a single, well-defined thermodynamic state point. Statistical reweighting offers the means to reweight static and dynamical properties to different equilibrium state points by means of analytic relations. We extend these ideas to nonequilibrium steady states by relying on a maximum path entropy formalism subject to physical constraints. Stochastic thermodynamics analytically relates the forward and backward probabilities of any pathway through the external nonconservative force, enabling reweighting both in and out of equilibrium. We avoid the combinatorial explosion of microtrajectories by systematically constructing pathways through Markovian transitions. We further identify a quantity that is invariant to dynamical reweighting, analogous to the density of states in equilibrium reweighting.
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Affiliation(s)
- Marius Bause
- Max Planck Institute for Polymer Research, 55128 Mainz, Germany
| | | | - Kurt Kremer
- Max Planck Institute for Polymer Research, 55128 Mainz, Germany
| | - Tristan Bereau
- Max Planck Institute for Polymer Research, 55128 Mainz, Germany
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15
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Provasi D. Ligand-Binding Calculations with Metadynamics. METHODS IN MOLECULAR BIOLOGY (CLIFTON, N.J.) 2019; 2022:233-253. [PMID: 31396906 DOI: 10.1007/978-1-4939-9608-7_10] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
Abstract
All-atom molecular dynamics simulations can capture the dynamic degrees of freedom that characterize molecular recognition, the knowledge of which constitutes the cornerstone of rational approaches to drug design and optimization. In particular, enhanced sampling algorithms, such as metadynamics, are powerful tools to dramatically reduce the computational cost required for a mechanistic description of the binding process. Here, we describe the essential details characterizing these simulation strategies, focusing on the critical step of identifying suitable reaction coordinates, as well as on the different analysis algorithms to estimate binding affinity and residence times. We conclude with a survey of published applications that provides explicit examples of successful simulations for several targets.
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Affiliation(s)
- Davide Provasi
- Department of Pharmacological Sciences, Icahn School of Medicine at Mount Sinai, New York, NY, USA.
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16
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Scherer MK, Husic BE, Hoffmann M, Paul F, Wu H, Noé F. Variational selection of features for molecular kinetics. J Chem Phys 2019; 150:194108. [PMID: 31117766 DOI: 10.1063/1.5083040] [Citation(s) in RCA: 40] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022] Open
Abstract
The modeling of atomistic biomolecular simulations using kinetic models such as Markov state models (MSMs) has had many notable algorithmic advances in recent years. The variational principle has opened the door for a nearly fully automated toolkit for selecting models that predict the long time-scale kinetics from molecular dynamics simulations. However, one yet-unoptimized step of the pipeline involves choosing the features, or collective variables, from which the model should be constructed. In order to build intuitive models, these collective variables are often sought to be interpretable and familiar features, such as torsional angles or contact distances in a protein structure. However, previous approaches for evaluating the chosen features rely on constructing a full MSM, which in turn requires additional hyperparameters to be chosen, and hence leads to a computationally expensive framework. Here, we present a method to optimize the feature choice directly, without requiring the construction of the final kinetic model. We demonstrate our rigorous preprocessing algorithm on a canonical set of 12 fast-folding protein simulations and show that our procedure leads to more efficient model selection.
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Affiliation(s)
- Martin K Scherer
- Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
| | - Brooke E Husic
- Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
| | - Moritz Hoffmann
- 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
| | - Hao Wu
- School of Mathematical Sciences, Tongji University, Shanghai 200092, People's Republic of China
| | - Frank Noé
- Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
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17
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Dixit PD, Dill KA. Building Markov state models using optimal transport theory. J Chem Phys 2019; 150:054105. [DOI: 10.1063/1.5086681] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
Affiliation(s)
- Purushottam D. Dixit
- Department of Systems Biology, Columbia University, New York, New York 10032, USA
| | - Ken A. Dill
- Laufer Center for Physical and Quantitative Biology, Stony Brook University, Stony Brook, New York 11794, USA
- Department of Chemistry, Stony Brook University, Stony Brook, New York 11794, USA
- Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11794, USA
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18
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Davis S, González D, Gutiérrez G. Probabilistic Inference for Dynamical Systems. ENTROPY (BASEL, SWITZERLAND) 2018; 20:e20090696. [PMID: 33265785 PMCID: PMC7513225 DOI: 10.3390/e20090696] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/30/2018] [Revised: 09/05/2018] [Accepted: 09/06/2018] [Indexed: 06/12/2023]
Abstract
A general framework for inference in dynamical systems is described, based on the language of Bayesian probability theory and making use of the maximum entropy principle. Taking the concept of a path as fundamental, the continuity equation and Cauchy's equation for fluid dynamics arise naturally, while the specific information about the system can be included using the maximum caliber (or maximum path entropy) principle.
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Affiliation(s)
- Sergio Davis
- Comisión Chilena de Energía Nuclear, Casilla 188-D Santiago, Chile
- Departamento de Física, Facultad de Ciencias Exactas, Universidad Andres Bello, Sazié 2212, Piso 7, 8370136 Santiago, Chile
| | - Diego González
- Comisión Chilena de Energía Nuclear, Casilla 188-D Santiago, Chile
- Grupo de Nanomateriales, Departamento de Física, Facultad de Ciencias, Universidad de Chile, Casilla 653 Santiago, Chile
| | - Gonzalo Gutiérrez
- Grupo de Nanomateriales, Departamento de Física, Facultad de Ciencias, Universidad de Chile, Casilla 653 Santiago, Chile
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19
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Ahalawat N, Mondal J. Assessment and optimization of collective variables for protein conformational landscape: GB1 β-hairpin as a case study. J Chem Phys 2018; 149:094101. [PMID: 30195312 DOI: 10.1063/1.5041073] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Collective variables (CVs), when chosen judiciously, can play an important role in recognizing rate-limiting processes and rare events in any biomolecular systems. However, high dimensionality and inherent complexities associated with such biochemical systems render the identification of an optimal CV a challenging task, which in turn precludes the elucidation of an underlying conformational landscape in sufficient details. In this context, a relevant model system is presented by a 16-residue β-hairpin of GB1 protein. Despite being the target of numerous theoretical and computational studies for understanding the protein folding, the set of CVs optimally characterizing the conformational landscape of the β-hairpin of GB1 protein has remained elusive, resulting in a lack of consensus on its folding mechanism. Here we address this by proposing a pair of optimal CVs which can resolve the underlying free energy landscape of the GB1 hairpin quite efficiently. Expressed as a linear combination of a number of traditional CVs, the optimal CV for this system is derived by employing the recently introduced time-structured independent component analysis approach on a large number of independent unbiased simulations. By projecting the replica-exchange simulated trajectories along these pair of optimized CVs, the resulting free energy landscape of this system is able to resolve four distinct well-separated metastable states encompassing the extensive ensembles of folded, unfolded, and molten globule states. Importantly, the optimized CVs were found to be capable of automatically recovering a novel partial helical state of this protein, without needing to explicitly invoke helicity as a constituent CV. Furthermore, a quantitative sensitivity analysis of each constituent in the optimized CV provided key insights on the relative contributions of the constituent CVs in the overall free energy landscapes. Finally, the kinetic pathways connecting these metastable states, constructed using a Markov state model, provide an optimum description of the underlying folding mechanism of the peptide. Taken together, this work offers a quantitatively robust approach toward comprehensive mapping of the underlying folding landscape of a quintessential model system along its optimized CV.
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Affiliation(s)
- Navjeet Ahalawat
- Tata Institute of Fundamental Research, Center for Interdisciplinary Sciences, Hyderabad 500107, India
| | - Jagannath Mondal
- Tata Institute of Fundamental Research, Center for Interdisciplinary Sciences, Hyderabad 500107, India
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20
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Sultan MM, Kiss G, Pande VS. Towards simple kinetic models of functional dynamics for a kinase subfamily. Nat Chem 2018; 10:903-909. [PMID: 29988151 DOI: 10.1038/s41557-018-0077-9] [Citation(s) in RCA: 46] [Impact Index Per Article: 7.7] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/19/2017] [Accepted: 05/08/2018] [Indexed: 11/09/2022]
Abstract
Kinases are ubiquitous enzymes involved in the regulation of critical cellular pathways. However, in silico modelling of the conformational ensembles of these enzymes is difficult due to inherent limitations and the cost of computational approaches. Recent algorithmic advances combined with homology modelling and parallel simulations have enabled researchers to address this computational sampling bottleneck. Here, we present the results of molecular dynamics studies for seven Src family kinase (SFK) members: Fyn, Lyn, Lck, Hck, Fgr, Yes and Blk. We present a sequence invariant extension to Markov state models, which allows us to quantitatively compare the structural ensembles of the seven kinases. Our findings indicate that in the absence of their regulatory partners, SFK members have similar in silico dynamics with active state populations ranging from 4 to 40% and activation timescales in the hundreds of microseconds. Furthermore, we observe several potentially druggable intermediate states, including a pocket next to the adenosine triphosphate binding site that could potentially be targeted via a small-molecule inhibitor.
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Affiliation(s)
| | - Gert Kiss
- Department of Chemistry, Stanford University, Stanford, CA, USA.,Center for Molecular Analysis and Design, Stanford University, Stanford, CA, USA.,Revolution Medicines, Redwood City, CA, USA
| | - Vijay S Pande
- Department of Bioengineering, Stanford University, Stanford, CA, USA.
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21
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Dixit PD, Wagoner J, Weistuch C, Pressé S, Ghosh K, Dill KA. Perspective: Maximum caliber is a general variational principle for dynamical systems. J Chem Phys 2018; 148:010901. [PMID: 29306272 DOI: 10.1063/1.5012990] [Citation(s) in RCA: 60] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
Abstract
We review here Maximum Caliber (Max Cal), a general variational principle for inferring distributions of paths in dynamical processes and networks. Max Cal is to dynamical trajectories what the principle of maximum entropy is to equilibrium states or stationary populations. In Max Cal, you maximize a path entropy over all possible pathways, subject to dynamical constraints, in order to predict relative path weights. Many well-known relationships of non-equilibrium statistical physics-such as the Green-Kubo fluctuation-dissipation relations, Onsager's reciprocal relations, and Prigogine's minimum entropy production-are limited to near-equilibrium processes. Max Cal is more general. While it can readily derive these results under those limits, Max Cal is also applicable far from equilibrium. We give examples of Max Cal as a method of inference about trajectory distributions from limited data, finding reaction coordinates in bio-molecular simulations, and modeling the complex dynamics of non-thermal systems such as gene regulatory networks or the collective firing of neurons. We also survey its basis in principle and some limitations.
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Affiliation(s)
- Purushottam D Dixit
- Department of Systems Biology, Columbia University, New York, New York 10032, USA
| | - Jason Wagoner
- Laufer Center for Quantitative Biology, Stony Brook University, Stony Brook, New York 11794, USA
| | - Corey Weistuch
- Laufer Center for Quantitative Biology, Stony Brook University, Stony Brook, New York 11794, USA
| | - Steve Pressé
- Department of Physics and School of Molecular Sciences, Arizona State University, Tempe, Arizona 85281, USA
| | - Kingshuk Ghosh
- Department of Physics and Astronomy, University of Denver, Denver, Colorado 80208, USA
| | - Ken A Dill
- Laufer Center for Quantitative Biology, Stony Brook University, Stony Brook, New York 11794, USA
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22
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Capelli R, Tiana G, Camilloni C. An implementation of the maximum-caliber principle by replica-averaged time-resolved restrained simulations. J Chem Phys 2018; 148:184114. [PMID: 29764124 DOI: 10.1063/1.5030339] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
Abstract
Inferential methods can be used to integrate experimental informations and molecular simulations. The maximum entropy principle provides a framework for using equilibrium experimental data, and it has been shown that replica-averaged simulations, restrained using a static potential, are a practical and powerful implementation of such a principle. Here we show that replica-averaged simulations restrained using a time-dependent potential are equivalent to the principle of maximum caliber, the dynamic version of the principle of maximum entropy, and thus may allow us to integrate time-resolved data in molecular dynamics simulations. We provide an analytical proof of the equivalence as well as a computational validation making use of simple models and synthetic data. Some limitations and possible solutions are also discussed.
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Affiliation(s)
- Riccardo Capelli
- Center for Complexity and Biosystems and Department of Physics, Università degli Studi di Milano and INFN, Via Celoria 16, I-20133 Milano, Italy
| | - Guido Tiana
- Center for Complexity and Biosystems and Department of Physics, Università degli Studi di Milano and INFN, Via Celoria 16, I-20133 Milano, Italy
| | - Carlo Camilloni
- Dipartimento di Bioscienze, Università degli Studi di Milano, Via Celoria 26, I-20133 Milano, Italy
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23
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Matsunaga Y, Sugita Y. Linking time-series of single-molecule experiments with molecular dynamics simulations by machine learning. eLife 2018; 7:32668. [PMID: 29723137 PMCID: PMC5933924 DOI: 10.7554/elife.32668] [Citation(s) in RCA: 27] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/10/2017] [Accepted: 04/23/2018] [Indexed: 12/27/2022] Open
Abstract
Single-molecule experiments and molecular dynamics (MD) simulations are indispensable tools for investigating protein conformational dynamics. The former provide time-series data, such as donor-acceptor distances, whereas the latter give atomistic information, although this information is often biased by model parameters. Here, we devise a machine-learning method to combine the complementary information from the two approaches and construct a consistent model of conformational dynamics. It is applied to the folding dynamics of the formin-binding protein WW domain. MD simulations over 400 μs led to an initial Markov state model (MSM), which was then "refined" using single-molecule Förster resonance energy transfer (FRET) data through hidden Markov modeling. The refined or data-assimilated MSM reproduces the FRET data and features hairpin one in the transition-state ensemble, consistent with mutation experiments. The folding pathway in the data-assimilated MSM suggests interplay between hydrophobic contacts and turn formation. Our method provides a general framework for investigating conformational transitions in other proteins.
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Affiliation(s)
- Yasuhiro Matsunaga
- Computational Biophysics Research Team, RIKEN Center for Computational Science, Kobe, Japan.,JST PRESTO, Kawaguchi, Japan
| | - Yuji Sugita
- Computational Biophysics Research Team, RIKEN Center for Computational Science, Kobe, Japan.,Theoretical Molecular Science Laboratory, RIKEN Cluster for Pioneering Research, Wako, Japan.,Laboratory for Biomolecular Function Simulation, RIKEN Center for Biosystems Dynamics Research, Kobe, Japan
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24
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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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25
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Dixit PD. Communication: Introducing prescribed biases in out-of-equilibrium Markov models. J Chem Phys 2018. [DOI: 10.1063/1.5023232] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Purushottam D. Dixit
- Department of Systems Biology, Columbia University, New York, New York 10032, USA
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26
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Firman T, Wedekind S, McMorrow TJ, Ghosh K. Maximum Caliber Can Characterize Genetic Switches with Multiple Hidden Species. J Phys Chem B 2018; 122:5666-5677. [PMID: 29406749 DOI: 10.1021/acs.jpcb.7b12251] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022]
Abstract
Gene networks with feedback often involve interactions between multiple species of biomolecules, much more than experiments can actually monitor. Coupled with this is the challenge that experiments often measure gene expression in noisy fluorescence instead of protein numbers. How do we infer biophysical information and characterize the underlying circuits from this limited and convoluted data? We address this by building stochastic models using the principle of Maximum Caliber (MaxCal). MaxCal uses the basic information on synthesis, degradation, and feedback-without invoking any other auxiliary species and ad hoc reactions-to generate stochastic trajectories similar to those typically measured in experiments. MaxCal in conjunction with Maximum Likelihood (ML) can infer parameters of the model using fluctuating trajectories of protein expression over time. We demonstrate the success of the MaxCal + ML methodology using synthetic data generated from known circuits of different genetic switches: (i) a single-gene autoactivating circuit involving five species (including mRNA), (ii) a mutually repressing two-gene circuit (toggle switch) with seven species (including mRNA) considering stochastic time traces of two proteins, and (iii) the same toggle switch circuit considering stochastic time traces of only one of the two proteins. To further challenge the MaxCal + ML inference scheme, we repeat our analysis for the second and third scenario with traces expressed in noisy fluorescence instead of protein number to closely mimic typical experiments. We show that, for all of these models with increasing complexity and obfuscation, the minimal model of MaxCal is still able to capture the fluctuations of the trajectory and infer basic underlying rate parameters when benchmarked against the known values used to generate the synthetic data. Importantly, the model also yields an effective feedback parameter that can be used to quantify interactions within these circuits. These applications show the promise of MaxCal's ability to characterize circuits with limited data, and its utility to better understand evolution and advance design strategies for specific functions.
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Affiliation(s)
- Taylor Firman
- Molecular and Cellular Biophysics , University of Denver , Denver , Colorado 80209 , United States
| | - Stephen Wedekind
- Department of Physics and Astronomy , University of Denver , Denver , Colorado 80209 , United States
| | - T J McMorrow
- Department of Physics and Astronomy , University of Denver , Denver , Colorado 80209 , United States
| | - Kingshuk Ghosh
- Department of Physics and Astronomy , University of Denver , Denver , Colorado 80209 , United States
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27
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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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28
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Dixit PD, Dill KA. Caliber Corrected Markov Modeling (C 2M 2): Correcting Equilibrium Markov Models. J Chem Theory Comput 2018; 14:1111-1119. [PMID: 29323898 DOI: 10.1021/acs.jctc.7b01126] [Citation(s) in RCA: 25] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Rate processes are often modeled using Markov State Models (MSMs). Suppose you know a prior MSM and then learn that your prediction of some particular observable rate is wrong. What is the best way to correct the whole MSM? For example, molecular dynamics simulations of protein folding may sample many microstates, possibly giving correct pathways through them while also giving the wrong overall folding rate when compared to experiment. Here, we describe Caliber Corrected Markov Modeling (C2M2), an approach based on the principle of maximum entropy for updating a Markov model by imposing state- and trajectory-based constraints. We show that such corrections are equivalent to asserting position-dependent diffusion coefficients in continuous-time continuous-space Markov processes modeled by a Smoluchowski equation. We derive the functional form of the diffusion coefficient explicitly in terms of the trajectory-based constraints. We illustrate with examples of 2D particle diffusion and an overdamped harmonic oscillator.
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Affiliation(s)
- Purushottam D Dixit
- Department of Systems Biology, Columbia University , New York, New York 10032, United States
| | - Ken A Dill
- Laufer Center for Quantitative Biology, Department of Chemistry, and Department of Physics and Astronomy, Stony Brook University , Stony Brook, New York 11790, United States
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29
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Husic BE, McKiernan KA, Wayment-Steele HK, Sultan MM, Pande VS. A Minimum Variance Clustering Approach Produces Robust and Interpretable Coarse-Grained Models. J Chem Theory Comput 2018; 14:1071-1082. [PMID: 29253336 DOI: 10.1021/acs.jctc.7b01004] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Markov state models (MSMs) are a powerful framework for the analysis of molecular dynamics data sets, such as protein folding simulations, because of their straightforward construction and statistical rigor. The coarse-graining of MSMs into an interpretable number of macrostates is a crucial step for connecting theoretical results with experimental observables. Here we present the minimum variance clustering approach (MVCA) for the coarse-graining of MSMs into macrostate models. The method utilizes agglomerative clustering with Ward's minimum variance objective function, and the similarity of the microstate dynamics is determined using the Jensen-Shannon divergence between the corresponding rows in the MSM transition probability matrix. We first show that MVCA produces intuitive results for a simple tripeptide system and is robust toward long-duration statistical artifacts. MVCA is then applied to two protein folding simulations of the same protein in different force fields to demonstrate that a different number of macrostates is appropriate for each model, revealing a misfolded state present in only one of the simulations. Finally, we show that the same method can be used to analyze a data set containing many MSMs from simulations in different force fields by aggregating them into groups and quantifying their dynamical similarity in the context of force field parameter choices. The minimum variance clustering approach with the Jensen-Shannon divergence provides a powerful tool to group dynamics by similarity, both among model states and among dynamical models themselves.
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Affiliation(s)
- Brooke E Husic
- Department of Chemistry, Stanford University , Stanford, California 94305, United States
| | - Keri A McKiernan
- Department of Chemistry, Stanford University , Stanford, California 94305, United States
| | | | - Mohammad M Sultan
- 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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30
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Howard RJ, Carnevale V, Delemotte L, Hellmich UA, Rothberg BS. Permeating disciplines: Overcoming barriers between molecular simulations and classical structure-function approaches in biological ion transport. BIOCHIMICA ET BIOPHYSICA ACTA-BIOMEMBRANES 2017; 1860:927-942. [PMID: 29258839 DOI: 10.1016/j.bbamem.2017.12.013] [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: 09/16/2017] [Revised: 12/08/2017] [Accepted: 12/14/2017] [Indexed: 11/20/2022]
Abstract
Ion translocation across biological barriers is a fundamental requirement for life. In many cases, controlling this process-for example with neuroactive drugs-demands an understanding of rapid and reversible structural changes in membrane-embedded proteins, including ion channels and transporters. Classical approaches to electrophysiology and structural biology have provided valuable insights into several such proteins over macroscopic, often discontinuous scales of space and time. Integrating these observations into meaningful mechanistic models now relies increasingly on computational methods, particularly molecular dynamics simulations, while surfacing important challenges in data management and conceptual alignment. Here, we seek to provide contemporary context, concrete examples, and a look to the future for bridging disciplinary gaps in biological ion transport. This article is part of a Special Issue entitled: Beyond the Structure-Function Horizon of Membrane Proteins edited by Ute Hellmich, Rupak Doshi and Benjamin McIlwain.
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Affiliation(s)
- Rebecca J Howard
- Science for Life Laboratory, Department of Biochemistry and Biophysics, Stockholm University, Box 1031, 17121 Solna, Sweden.
| | - Vincenzo Carnevale
- Institute for Computational Molecular Science, Department of Chemistry, Temple University, Philadelphia, PA 19122, USA.
| | - Lucie Delemotte
- Science for Life Laboratory, Department of Theoretical Physics, KTH Royal Institute of Technology, Box 1031, 17121 Solna, Sweden.
| | - Ute A Hellmich
- Johannes Gutenberg University Mainz, Institute for Pharmacy and Biochemistry, Johann-Joachim-Becherweg 30, 55128 Mainz, Germany; Centre for Biomolecular Magnetic Resonance (BMRZ), Goethe University Frankfurt, Max-von-Laue Str. 9, 60438 Frankfurt, Germany.
| | - Brad S Rothberg
- Department of Medical Genetics and Molecular Biochemistry, Temple University Lewis Katz School of Medicine, Philadelphia, PA 19140, USA.
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31
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Firman T, Balázsi G, Ghosh K. Building Predictive Models of Genetic Circuits Using the Principle of Maximum Caliber. Biophys J 2017; 113:2121-2130. [PMID: 29117534 DOI: 10.1016/j.bpj.2017.08.057] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/30/2017] [Revised: 08/25/2017] [Accepted: 08/31/2017] [Indexed: 11/17/2022] Open
Abstract
Learning the underlying details of a gene network is a major challenge in cellular and synthetic biology. We address this challenge by building a chemical kinetic model that utilizes information encoded in the stochastic protein expression trajectories typically measured in experiments. The applicability of the proposed method is demonstrated in an auto-activating genetic circuit, a common motif in natural and synthetic gene networks. Our approach is based on the principle of maximum caliber (MaxCal)-a dynamical analog of the principle of maximum entropy-and builds a minimal model using only three constraints: 1) protein synthesis, 2) protein degradation, and 3) positive feedback. The MaxCal-generated model (described with four parameters) was benchmarked against synthetic data generated using a Gillespie algorithm on a known reaction network (with seven parameters). MaxCal accurately predicts underlying rate parameters of protein synthesis and degradation as well as experimental observables such as protein number and dwell-time distributions. Furthermore, MaxCal yields an effective feedback parameter that can be useful for circuit design. We also extend our methodology and demonstrate how to analyze trajectories that are not in protein numbers but in arbitrary fluorescence units, a more typical condition in experiments. This "top-down" methodology based on minimal information-in contrast to traditional "bottom-up" approaches that require ad hoc knowledge of circuit details-provides a powerful tool to accurately infer underlying details of feedback circuits that are not otherwise visible in experiments and to help guide circuit design.
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Affiliation(s)
- Taylor Firman
- Department of Physics and Astronomy, Molecular and Cellular Biophysics, University of Denver, Denver, Colorado
| | - Gábor Balázsi
- The Louis and Beatrice Laufer Center for Physical and Quantitative Biology, Stony Brook University, Stony Brook, New York; Department of Biomedical Engineering, Stony Brook University, Stony Brook, New York
| | - Kingshuk Ghosh
- Department of Physics and Astronomy, Molecular and Cellular Biophysics, University of Denver, Denver, Colorado.
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32
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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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33
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Meng L, Sheong FK, Zeng X, Zhu L, Huang X. Path lumping: An efficient algorithm to identify metastable path channels for conformational dynamics of multi-body systems. J Chem Phys 2017; 147:044112. [DOI: 10.1063/1.4995558] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023] Open
Affiliation(s)
- Luming Meng
- Department of Chemistry, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
| | - Fu Kit Sheong
- Department of Chemistry, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
| | - Xiangze Zeng
- Department of Chemistry, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
| | - Lizhe Zhu
- Department of Chemistry, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
- Center of Systems Biology and Human Health, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
| | - Xuhui Huang
- Department of Chemistry, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
- Center of Systems Biology and Human Health, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
- Hong Kong Branch of Chinese National Engineering Research Center for Tissue Restoration and Reconstruction, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
- HKUST-Shenzhen Research Institute, Hi-Tech Park, Nanshan, Shenzhen 518057, China
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34
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Ge Y, Kier BL, Andersen NH, Voelz VA. Computational and Experimental Evaluation of Designed β-Cap Hairpins Using Molecular Simulations and Kinetic Network Models. J Chem Inf Model 2017; 57:1609-1620. [PMID: 28614661 DOI: 10.1021/acs.jcim.7b00132] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
Abstract
Molecular simulation has been used to model the detailed folding properties of peptides, yet prospective computational peptide design by such approaches remains challenging and nontrivial. To test the accuracy of simulation-based hairpin design, we characterized the folding properties of a series of so-called β-cap hairpin peptides designed to mimic a conserved hairpin of LapD, a bacterial intracellular signaling protein, both experimentally by NMR spectroscopy and computationally by implicit-solvent replica-exchange molecular dynamics using three different AMBER force fields (ff96, ff99sb-ildn, and ff99sb-ildn-NMR). A unique challenge presented by these designs is the presence of both a terminal Trp-Trp capping motif and a conserved GWxQ motif in the hairpin turn required for binding to LapG. Consistent with previous studies, we found AMBER ff96 to be the most accurate when used with the OBC GBSA implicit solvent model, despite its known bias toward β-sheet conformations when used in explicit-solvent simulations. To gain microscopic insight into the folding landscape of the hairpin designs, we additionally performed parallel simulations on the Folding@home distributed computing platform using AMBER ff99sb-ildn-NMR with TIP3P explicit solvent. Markov state models (MSMs) built from trajectory data reveal a number of non-native interactions between Trp and other amino acid side chains, creating potential problems in achieving well-folded hairpin structures in solution.
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Affiliation(s)
- Yunhui Ge
- Department of Chemistry, Temple University , Philadelphia, Pennsylvania 19122, United States
| | - Brandon L Kier
- Department of Chemistry, University of Washington , Seattle, Washington 98195, United States
| | - Niels H Andersen
- Department of Chemistry, University of Washington , Seattle, Washington 98195, United States
| | - Vincent A Voelz
- Department of Chemistry, Temple University , Philadelphia, Pennsylvania 19122, United States
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