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Brooks CL, MacKerell AD, Post CB, Nilsson L. Biomolecular dynamics in the 21st century. Biochim Biophys Acta Gen Subj 2024; 1868:130534. [PMID: 38065235 PMCID: PMC10842176 DOI: 10.1016/j.bbagen.2023.130534] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/26/2023] [Revised: 11/28/2023] [Accepted: 11/29/2023] [Indexed: 01/03/2024]
Abstract
The relevance of motions in biological macromolecules has been clear since the early structural analyses of proteins by X-ray crystallography. Computer simulations have been applied to provide a deeper understanding of the dynamics of biological macromolecules since 1976, and are now a standard tool in many labs working on the structure and function of biomolecules. In this mini-review we highlight some areas of current interest and active development for simulations, in particular all-atom molecular dynamics simulations.
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Affiliation(s)
- Charles L Brooks
- University of Michigan, Department of Chemistry, Ann Arbor, MI 48109, USA.
| | | | - Carol B Post
- Purdue University, Department of Medicinal Chemistry and Molecular Pharmacology, West Lafayette, IN 47907-2091, USA.
| | - Lennart Nilsson
- Karolinska Institutet, Department of Biosciences and Nutrition, SE-14183 Huddinge, Sweden.
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2
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Nagel D, Sartore S, Stock G. Toward a Benchmark for Markov State Models: The Folding of HP35. J Phys Chem Lett 2023; 14:6956-6967. [PMID: 37504674 DOI: 10.1021/acs.jpclett.3c01561] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/29/2023]
Abstract
Adopting a 300 μs long MD trajectory of the folding of villin headpiece (HP35) by D. E. Shaw Research, we recently constructed a Markov state model (MSM) based on inter-residue contacts. The model reproduces the folding time and predicts that the native basin and unfolded region consist of metastable substates that are structurally well-characterized. Recognizing the need to establish well-defined benchmark problems, we study to what extent and in what sense this MSM can be employed as a reference model. Hence, we test the robustness of the MSM by comparing it to models that use alternative combinations of features, dimensionality reduction methods, and clustering schemes. The study suggests some main characteristics of the folding of HP35 that should be reproduced by other competitive models. Moreover, the discussion reveals which parts of the MSM workflow matter most for the considered problem and illustrates the promises and pitfalls of state-based models for the interpretation of biomolecular simulations.
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Affiliation(s)
- Daniel Nagel
- Biomolecular Dynamics, Institute of Physics, University of Freiburg, 79104 Freiburg, Germany
| | - Sofia Sartore
- Biomolecular Dynamics, Institute of Physics, University of Freiburg, 79104 Freiburg, Germany
| | - Gerhard Stock
- Biomolecular Dynamics, Institute of Physics, University of Freiburg, 79104 Freiburg, Germany
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3
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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: 14] [Impact Index Per Article: 14.0] [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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4
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Sharpe DJ, Wales DJ. Nearly reducible finite Markov chains: Theory and algorithms. J Chem Phys 2021; 155:140901. [PMID: 34654307 DOI: 10.1063/5.0060978] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023] Open
Abstract
Finite Markov chains, memoryless random walks on complex networks, appear commonly as models for stochastic dynamics in condensed matter physics, biophysics, ecology, epidemiology, economics, and elsewhere. Here, we review exact numerical methods for the analysis of arbitrary discrete- and continuous-time Markovian networks. We focus on numerically stable methods that are required to treat nearly reducible Markov chains, which exhibit a separation of characteristic timescales and are therefore ill-conditioned. In this metastable regime, dense linear algebra methods are afflicted by propagation of error in the finite precision arithmetic, and the kinetic Monte Carlo algorithm to simulate paths is unfeasibly inefficient. Furthermore, iterative eigendecomposition methods fail to converge without the use of nontrivial and system-specific preconditioning techniques. An alternative approach is provided by state reduction procedures, which do not require additional a priori knowledge of the Markov chain. Macroscopic dynamical quantities, such as moments of the first passage time distribution for a transition to an absorbing state, and microscopic properties, such as the stationary, committor, and visitation probabilities for nodes, can be computed robustly using state reduction algorithms. The related kinetic path sampling algorithm allows for efficient sampling of trajectories on a nearly reducible Markov chain. Thus, all of the information required to determine the kinetically relevant transition mechanisms, and to identify the states that have a dominant effect on the global dynamics, can be computed reliably even for computationally challenging models. Rare events are a ubiquitous feature of realistic dynamical systems, and so the methods described herein are valuable in many practical applications.
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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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5
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Li Y, Wang T, Zhang J, Shao B, Gong H, Wang Y, He X, Liu S, Liu T. Exploring the Regulatory Function of the N-terminal Domain of SARS-CoV-2 Spike Protein through Molecular Dynamics Simulation. ADVANCED THEORY AND SIMULATIONS 2021; 4:2100152. [PMID: 34901736 PMCID: PMC8646686 DOI: 10.1002/adts.202100152] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/26/2021] [Revised: 07/28/2021] [Indexed: 12/18/2022]
Abstract
SARS-CoV-2 is what has caused the COVID-19 pandemic. Early viral infection is mediated by the SARS-CoV-2 homo-trimeric Spike (S) protein with its receptor binding domains (RBDs) in the receptor-accessible state. Molecular dynamics simulation on the S protein with a focus on the function of its N-terminal domains (NTDs) is performed. The study reveals that the NTD acts as a "wedge" and plays a crucial regulatory role in the conformational changes of the S protein. The complete RBD structural transition is allowed only when the neighboring NTD that typically prohibits the RBD's movements as a wedge detaches and swings away. Based on this NTD "wedge" model, it is proposed that the NTD-RBD interface should be a potential drug target.
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Affiliation(s)
- Yao Li
- MOE Key Laboratory of BioinformaticsSchool of Life SciencesTsinghua UniversityBeijing100084China
- Beijing Advanced Innovation Center for Structural BiologyTsinghua UniversityBeijing100084China
- Microsoft Research AsiaBeijing100080China
| | - Tong Wang
- Microsoft Research AsiaBeijing100080China
| | - Juanrong Zhang
- MOE Key Laboratory of BioinformaticsSchool of Life SciencesTsinghua UniversityBeijing100084China
- Beijing Advanced Innovation Center for Structural BiologyTsinghua UniversityBeijing100084China
- Microsoft Research AsiaBeijing100080China
| | - Bin Shao
- Microsoft Research AsiaBeijing100080China
| | - Haipeng Gong
- MOE Key Laboratory of BioinformaticsSchool of Life SciencesTsinghua UniversityBeijing100084China
- Beijing Advanced Innovation Center for Structural BiologyTsinghua UniversityBeijing100084China
| | | | - Xinheng He
- Microsoft Research AsiaBeijing100080China
- The CAS Key Laboratory of Receptor ResearchShanghai Institute of Materia MedicaChinese Academy of SciencesShanghai201203China
| | - Siyuan Liu
- Microsoft Research AsiaBeijing100080China
- School of Data and Computer ScienceSun Yat‐sen UniversityGuangzhou510006China
- Guangdong Key Laboratory of Big Data Analysis and ProcessingGuangzhou510006China
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6
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Konovalov K, Unarta IC, Cao S, Goonetilleke EC, Huang X. Markov State Models to Study the Functional Dynamics of Proteins in the Wake of Machine Learning. JACS AU 2021; 1:1330-1341. [PMID: 34604842 PMCID: PMC8479766 DOI: 10.1021/jacsau.1c00254] [Citation(s) in RCA: 47] [Impact Index Per Article: 15.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/07/2021] [Indexed: 05/19/2023]
Abstract
Markov state models (MSMs) based on molecular dynamics (MD) simulations are routinely employed to study protein folding, however, their application to functional conformational changes of biomolecules is still limited. In the past few years, the field of computational chemistry has experienced a surge of advancements stemming from machine learning algorithms, and MSMs have not been left out. Unlike global processes, such as protein folding, the application of MSMs to functional conformational changes is challenging because they mostly consist of localized structural transitions. Therefore, it is critical to properly select a subset of structural features that can describe the slowest dynamics of these functional conformational changes. To address this challenge, we recommend several automatic feature selection methods such as Spectral-OASIS. To identify states in MSMs, the chosen features can be subject to dimensionality reduction methods such as TICA or deep learning based VAMPNets to project MD conformations onto a few collective variables for subsequent clustering. Another challenge for the application of MSMs to the study of functional conformational changes is the ability to comprehend their biophysical mechanisms, as MSMs built for these processes often require a large number of states. We recommend the recently developed quasi-MSMs (qMSMs) to address this issue. Compared to MSMs, qMSMs encode the non-Markovian dynamics via the generalized master equation and can significantly reduce the number of states. As a result, qMSMs can be built with a handful of states to facilitate the interpretation of functional conformational changes. In the wake of machine learning, we believe that the rapid advancement in the MSM methodology will lead to their wider application in studying functional conformational changes of biomolecules.
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Affiliation(s)
- Kirill
A. Konovalov
- Department
of Chemistry, State Key Laboratory of Molecular Neuroscience, The Hong Kong University of Science and Technology, Kowloon, Hong Kong
- Hong
Kong Center for Neurodegenerative Diseases, Hong Kong Science Park, Hong Kong
| | - Ilona Christy Unarta
- Department
of Chemical and Biological Engineering, The Hong Kong University of Science and Technology, Kowloon, Hong Kong
- Hong
Kong Center for Neurodegenerative Diseases, Hong Kong Science Park, Hong Kong
| | - Siqin Cao
- Department
of Chemistry, State Key Laboratory of Molecular Neuroscience, The Hong Kong University of Science and Technology, Kowloon, Hong Kong
- Hong
Kong Center for Neurodegenerative Diseases, Hong Kong Science Park, Hong Kong
| | - Eshani C. Goonetilleke
- Department
of Chemistry, State Key Laboratory of Molecular Neuroscience, The Hong Kong University of Science and Technology, Kowloon, Hong Kong
- Hong
Kong Center for Neurodegenerative Diseases, Hong Kong Science Park, Hong Kong
| | - Xuhui Huang
- Department
of Chemistry, State Key Laboratory of Molecular Neuroscience, The Hong Kong University of Science and Technology, Kowloon, Hong Kong
- Department
of Chemical and Biological Engineering, The Hong Kong University of Science and Technology, Kowloon, Hong Kong
- Hong
Kong Center for Neurodegenerative Diseases, Hong Kong Science Park, Hong Kong
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7
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Sharpe DJ, Wales DJ. Graph transformation and shortest paths algorithms for finite Markov chains. Phys Rev E 2021; 103:063306. [PMID: 34271741 DOI: 10.1103/physreve.103.063306] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/25/2021] [Accepted: 04/29/2021] [Indexed: 12/20/2022]
Abstract
The graph transformation (GT) algorithm robustly computes the mean first-passage time to an absorbing state in a finite Markov chain. Here we present a concise overview of the iterative and block formulations of the GT procedure and generalize the GT formalism to the case of any path property that is a sum of contributions from individual transitions. In particular, we examine the path action, which directly relates to the path probability, and analyze the first-passage path ensemble for a model Markov chain that is metastable and therefore numerically challenging. We compare the mean first-passage path action, obtained using GT, with the full path action probability distribution simulated efficiently using kinetic path sampling, and with values for the highest-probability paths determined by the recursive enumeration algorithm (REA). In Markov chains representing realistic dynamical processes, the probability distributions of first-passage path properties are typically fat-tailed and therefore difficult to converge by sampling, which motivates the use of exact and numerically stable approaches to compute the expectation. We find that the kinetic relevance of the set of highest-probability paths depends strongly on the metastability of the Markov chain, and so the properties of the dominant first-passage paths may be unrepresentative of the global dynamics. Use of a global measure for edge costs in the REA, based on net productive fluxes, allows the total reactive flux to be decomposed into a finite set of contributions from simple flux paths. By considering transition flux paths, a detailed quantitative analysis of the relative importance of competing dynamical processes is possible even in the metastable regime.
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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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8
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Trozzi F, Wang F, Verkhivker G, Zoltowski BD, Tao P. Dimeric allostery mechanism of the plant circadian clock photoreceptor ZEITLUPE. PLoS Comput Biol 2021; 17:e1009168. [PMID: 34310591 PMCID: PMC8341706 DOI: 10.1371/journal.pcbi.1009168] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/02/2021] [Revised: 08/05/2021] [Accepted: 06/10/2021] [Indexed: 11/19/2022] Open
Abstract
In Arabidopsis thaliana, the Light-Oxygen-Voltage (LOV) domain containing protein ZEITLUPE (ZTL) integrates light quality, intensity, and duration into regulation of the circadian clock. Recent structural and biochemical studies of ZTL indicate that the protein diverges from other members of the LOV superfamily in its allosteric mechanism, and that the divergent allosteric mechanism hinges upon conservation of two signaling residues G46 and V48 that alter dynamic motions of a Gln residue implicated in signal transduction in all LOV proteins. Here, we delineate the allosteric mechanism of ZTL via an integrated computational approach that employs atomistic simulations of wild type and allosteric variants of ZTL in the functional dark and light states, together with Markov state and supervised machine learning classification models. This approach has unveiled key factors of the ZTL allosteric mechanisms, and identified specific interactions and residues implicated in functional allosteric changes. The final results reveal atomic level insights into allosteric mechanisms of ZTL function that operate via a non-trivial combination of population-shift and dynamics-driven allosteric pathways.
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Affiliation(s)
- Francesco Trozzi
- Department of Chemistry, Center for Research Computing, Center for Drug Discovery, Design, and Delivery (CD4), Southern Methodist University, Dallas, Texas, United States of America
| | - Feng Wang
- Department of Chemistry, Center for Research Computing, Center for Drug Discovery, Design, and Delivery (CD4), Southern Methodist University, Dallas, Texas, United States of America
| | - Gennady Verkhivker
- Graduate Program in Computational and Data Sciences, Schmid College of Science and Technology, Chapman University, Orange, California, United States of America
- Chapman University School of Pharmacy, Irvine, California, United States of America
| | - Brian D. Zoltowski
- Department of Chemistry, Center for Research Computing, Center for Drug Discovery, Design, and Delivery (CD4), Southern Methodist University, Dallas, Texas, United States of America
| | - Peng Tao
- Department of Chemistry, Center for Research Computing, Center for Drug Discovery, Design, and Delivery (CD4), Southern Methodist University, Dallas, Texas, United States of America
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9
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Jiang H, Fan X. The Two-Step Clustering Approach for Metastable States Learning. Int J Mol Sci 2021; 22:6576. [PMID: 34205252 PMCID: PMC8233889 DOI: 10.3390/ijms22126576] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/31/2021] [Revised: 06/14/2021] [Accepted: 06/14/2021] [Indexed: 01/20/2023] Open
Abstract
Understanding the energy landscape and the conformational dynamics is crucial for studying many biological or chemical processes, such as protein-protein interaction and RNA folding. Molecular Dynamics (MD) simulations have been a major source of dynamic structure. Although many methods were proposed for learning metastable states from MD data, some key problems are still in need of further investigation. Here, we give a brief review on recent progresses in this field, with an emphasis on some popular methods belonging to a two-step clustering framework, and hope to draw more researchers to contribute to this area.
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Affiliation(s)
- Hangjin Jiang
- Center for Data Science, Zhejiang University, Hangzhou 310058, China;
| | - Xiaodan Fan
- Department of Statistics, The Chinese University of Hong Kong, Hong Kong, China
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10
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Lickert B, Stock G. Modeling non-Markovian data using Markov state and Langevin models. J Chem Phys 2020; 153:244112. [DOI: 10.1063/5.0031979] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Benjamin Lickert
- Biomolecular Dynamics, Institute of Physics, Albert Ludwigs University, 79104 Freiburg, Germany
| | - Gerhard Stock
- Biomolecular Dynamics, Institute of Physics, Albert Ludwigs University, 79104 Freiburg, Germany
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11
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Wang Z, Zhou X, Zuo G. EspcTM: Kinetic Transition Network Based on Trajectory Mapping in Effective Energy Rescaling Space. Front Mol Biosci 2020; 7:589718. [PMID: 33195438 PMCID: PMC7653181 DOI: 10.3389/fmolb.2020.589718] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/31/2020] [Accepted: 09/24/2020] [Indexed: 11/27/2022] Open
Abstract
The transition network provides a key to reveal the thermodynamic and kinetic properties of biomolecular systems. In this paper, we introduce a new method, named effective energy rescaling space trajectory mapping (EspcTM), to detect metastable states and construct transition networks based on the simulation trajectories of the complex biomolecular system. It mapped simulation trajectories into an orthogonal function space, whose bases were rescaled by effective energy, and clustered the interrelation between these trajectories to locate metastable states. By using the EspcTM method, we identified the metastable states and elucidated interstate transition kinetics of a Brownian particle and a dodecapeptide. It was found that the scaling parameters of effective energy also provided a clue to the dominating factors in dynamics. We believe that the EspcTM method is a useful tool for the studies of dynamics of the complex system and may provide new insight into the understanding of thermodynamics and kinetics of biomolecular systems.
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Affiliation(s)
- Zhenyu Wang
- T-Life Research Center, State Key Laboratory of Surface Physics, Department of Physics, Fudan University, Shanghai, China
| | - Xin Zhou
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, China
| | - Guanghong Zuo
- T-Life Research Center, State Key Laboratory of Surface Physics, Department of Physics, Fudan University, Shanghai, China
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12
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Nagel D, Weber A, Stock G. MSMPathfinder: Identification of Pathways in Markov State Models. J Chem Theory Comput 2020; 16:7874-7882. [PMID: 33141565 DOI: 10.1021/acs.jctc.0c00774] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Abstract
Markov state models represent a popular means to interpret biomolecular processes in terms of memoryless transitions between metastable conformational states. To gain insight into the underlying mechanism, it is instructive to determine all relevant pathways between initial and final states of the process. Currently available methods, such as Markov chain Monte Carlo and transition path theory, are convenient for identifying the most frequented pathways. They are less suited to account for the typically huge amount of pathways with low probability which, though, may dominate the cumulative flux of the reaction. On the basis of a systematic construction of all possible pathways, the here proposed method MSMPathfinder is able to characterize the multitude of unique pathways (say, up to 1010) in a complex system and to quantitatively calculate their correct weights and associated waiting times with predefined accuracy. Adopting the chiral transitions of a peptide helix and the folding of the villin headpiece as model problems, mechanisms and associated waiting times of these processes are discussed using a kinetic network representation. The analysis reveals that the waiting time distribution may yield only little insight into the diversity of pathways, because the measured folding times do typically not reflect the most probable path lengths but rather the cumulative effect of many different pathways.
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Affiliation(s)
- Daniel Nagel
- Biomolecular Dynamics, Institute of Physics, Albert Ludwigs University, 79104 Freiburg, Germany
| | - Anna Weber
- Biomolecular Dynamics, Institute of Physics, Albert Ludwigs University, 79104 Freiburg, Germany
| | - Gerhard Stock
- Biomolecular Dynamics, Institute of Physics, Albert Ludwigs University, 79104 Freiburg, Germany
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13
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Swinburne TD, Kannan D, Sharpe DJ, Wales DJ. Rare events and first passage time statistics from the energy landscape. J Chem Phys 2020; 153:134115. [PMID: 33032418 DOI: 10.1063/5.0016244] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022] Open
Abstract
We analyze the probability distribution of rare first passage times corresponding to transitions between product and reactant states in a kinetic transition network. The mean first passage times and the corresponding rate constants are analyzed in detail for two model landscapes and the double funnel landscape corresponding to an atomic cluster. Evaluation schemes based on eigendecomposition and kinetic path sampling, which both allow access to the first passage time distribution, are benchmarked against mean first passage times calculated using graph transformation. Numerical precision issues severely limit the useful temperature range for eigendecomposition, but kinetic path sampling is capable of extending the first passage time analysis to lower temperatures, where the kinetics of interest constitute rare events. We then investigate the influence of free energy based state regrouping schemes for the underlying network. Alternative formulations of the effective transition rates for a given regrouping are compared in detail to determine their numerical stability and capability to reproduce the true kinetics, including recent coarse-graining approaches that preserve occupancy cross correlation functions. We find that appropriate regrouping of states under the simplest local equilibrium approximation can provide reduced transition networks with useful accuracy at somewhat lower temperatures. Finally, a method is provided to systematically interpolate between the local equilibrium approximation and exact intergroup dynamics. Spectral analysis is applied to each grouping of states, employing a moment-based mode selection criterion to produce a reduced state space, which does not require any spectral gap to exist, but reduces to gap-based coarse graining as a special case. Implementations of the developed methods are freely available online.
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Affiliation(s)
- Thomas D Swinburne
- Aix-Marseille Université, CNRS, CINaM UMR 7325, Campus de Luminy, 13288 Marseille, France
| | - Deepti Kannan
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - 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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14
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Affiliation(s)
- Francesco Cocina
- Biochemistry Department, University of Zurich, Zurich CH-8057, Switzerland
| | - Andreas Vitalis
- Biochemistry Department, University of Zurich, Zurich CH-8057, Switzerland
| | - Amedeo Caflisch
- Biochemistry Department, University of Zurich, Zurich CH-8057, Switzerland
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15
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Wolfe DK, Persichetti JR, Sharma AK, Hudson PS, Woodcock HL, O'Brien EP. Hierarchical Markov State Model Building to Describe Molecular Processes. J Chem Theory Comput 2020; 16:1816-1826. [PMID: 32011146 DOI: 10.1021/acs.jctc.9b00955] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
Abstract
Markov state models can describe ensembles of pathways via kinetic networks but are difficult to create when large free-energy barriers limit unbiased sampling. Chain-of-states simulations allow sampling over large free-energy barriers but are often constructed using a single pathway that is unlikely to thermodynamically average over orthogonal degrees of freedom in complex systems. Here, we combine the advantages of these two approaches in the form of a Markov state model of Markov state models, which we call a Hierarchical Markov state model. In this approach, independent Markov models are constructed in regions of configuration space that are locally well sampled but are separated by large free-energy barriers from other regions. A string method is used to construct an ensemble of pathways connecting the states of these different local Markov models, and the rate through each pathway is then estimated. These rates are then combined with the rate information from the local Markov models in a master equation to predict global rates, fluxes, and populations. By applying this hierarchical approach to tractable systems, a toy potential and dipeptides, we demonstrate that it is more accurate than the conventional single-pathway description. The advantages of this approach are that it (i) is more realistic than the conventional chain-of-states approach, as an ensemble of pathways rather than a single pathway is used to describe processes in high-dimensional systems, and (ii) it resolves the issue of poor sampling in Markov State model building when large free-energy barriers are present. The divide-and-conquer strategy inherent to this approach should make this procedure straightforward to apply to more complex systems.
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Affiliation(s)
| | | | - Ajeet K Sharma
- Department of Physics, Indian Institute of Technology, Jammu 181221, India
| | - Phillip S Hudson
- Department of Chemistry, University of South Florida, Tampa, Florida 33620, United States
| | - H Lee Woodcock
- Department of Chemistry, University of South Florida, Tampa, Florida 33620, United States
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16
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Nagel D, Weber A, Lickert B, Stock G. Dynamical coring of Markov state models. J Chem Phys 2019; 150:094111. [DOI: 10.1063/1.5081767] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023] Open
Affiliation(s)
- Daniel Nagel
- Biomolecular Dynamics, Institute of Physics, Albert Ludwigs University, 79104 Freiburg, Germany
| | - Anna Weber
- Biomolecular Dynamics, Institute of Physics, Albert Ludwigs University, 79104 Freiburg, Germany
| | - Benjamin Lickert
- Biomolecular Dynamics, Institute of Physics, Albert Ludwigs University, 79104 Freiburg, Germany
| | - Gerhard Stock
- Biomolecular Dynamics, Institute of Physics, Albert Ludwigs University, 79104 Freiburg, Germany
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17
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Sittel F, Stock G. Perspective: Identification of collective variables and metastable states of protein dynamics. J Chem Phys 2018; 149:150901. [PMID: 30342445 DOI: 10.1063/1.5049637] [Citation(s) in RCA: 84] [Impact Index Per Article: 14.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023] Open
Abstract
The statistical analysis of molecular dynamics simulations requires dimensionality reduction techniques, which yield a low-dimensional set of collective variables (CVs) {x i } = x that in some sense describe the essential dynamics of the system. Considering the distribution P( x ) of the CVs, the primal goal of a statistical analysis is to detect the characteristic features of P( x ), in particular, its maxima and their connection paths. This is because these features characterize the low-energy regions and the energy barriers of the corresponding free energy landscape ΔG( x ) = -k B T ln P( x ), and therefore amount to the metastable states and transition regions of the system. In this perspective, we outline a systematic strategy to identify CVs and metastable states, which subsequently can be employed to construct a Langevin or a Markov state model of the dynamics. In particular, we account for the still limited sampling typically achieved by molecular dynamics simulations, which in practice seriously limits the applicability of theories (e.g., assuming ergodicity) and black-box software tools (e.g., using redundant input coordinates). We show that it is essential to use internal (rather than Cartesian) input coordinates, employ dimensionality reduction methods that avoid rescaling errors (such as principal component analysis), and perform density based (rather than k-means-type) clustering. Finally, we briefly discuss a machine learning approach to dimensionality reduction, which highlights the essential internal coordinates of a system and may reveal hidden reaction mechanisms.
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Affiliation(s)
- Florian Sittel
- Biomolecular Dynamics, Institute of Physics, Albert Ludwigs University, 79104 Freiburg, Germany
| | - Gerhard Stock
- Biomolecular Dynamics, Institute of Physics, Albert Ludwigs University, 79104 Freiburg, Germany
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18
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Wang W, Liang T, Sheong FK, Fan X, Huang X. An efficient Bayesian kinetic lumping algorithm to identify metastable conformational states via Gibbs sampling. J Chem Phys 2018; 149:072337. [PMID: 30134698 DOI: 10.1063/1.5027001] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023] Open
Abstract
Markov State Model (MSM) has become a popular approach to study the conformational dynamics of complex biological systems in recent years. Built upon a large number of short molecular dynamics simulation trajectories, MSM is able to predict the long time scale dynamics of complex systems. However, to achieve Markovianity, an MSM often contains hundreds or thousands of states (microstates), hindering human interpretation of the underlying system mechanism. One way to reduce the number of states is to lump kinetically similar states together and thus coarse-grain the microstates into macrostates. In this work, we introduce a probabilistic lumping algorithm, the Gibbs lumping algorithm, to assign a probability to any given kinetic lumping using the Bayesian inference. In our algorithm, the transitions among kinetically distinct macrostates are modeled by Poisson processes, which will well reflect the separation of time scales in the underlying free energy landscape of biomolecules. Furthermore, to facilitate the search for the optimal kinetic lumping (i.e., the lumped model with the highest probability), a Gibbs sampling algorithm is introduced. To demonstrate the power of our new method, we apply it to three systems: a 2D potential, alanine dipeptide, and a WW protein domain. In comparison with six other popular lumping algorithms, we show that our method can persistently produce the lumped macrostate model with the highest probability as well as the largest metastability. We anticipate that our Gibbs lumping algorithm holds great promise to be widely applied to investigate conformational changes in biological macromolecules.
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Affiliation(s)
- Wei Wang
- HKUST-Shenzhen Research Institute, Hi-Tech Park, Nanshan, Shenzhen 518057, China
| | - Tong Liang
- Department of Statistics, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong
| | - Fu Kit Sheong
- Department of Chemistry, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
| | - Xiaodan Fan
- Department of Statistics, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong
| | - Xuhui Huang
- HKUST-Shenzhen Research Institute, Hi-Tech Park, Nanshan, Shenzhen 518057, China
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19
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Peng JH, Wang W, Yu YQ, Gu HL, Huang X. Clustering algorithms to analyze molecular dynamics simulation trajectories for complex chemical and biological systems. CHINESE J CHEM PHYS 2018. [DOI: 10.1063/1674-0068/31/cjcp1806147] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Affiliation(s)
- Jun-hui Peng
- HKUST-Shenzhen Research Institute, Hi-Tech Park, Nanshan, Shenzhen 518057, China
- Department of Chemistry, The Hong Kong University of Science and Technology, Kowloon, Hong Kong
| | - Wei Wang
- HKUST-Shenzhen Research Institute, Hi-Tech Park, Nanshan, Shenzhen 518057, China
- Department of Chemistry, The Hong Kong University of Science and Technology, Kowloon, Hong Kong
| | - Ye-qing Yu
- HKUST-Shenzhen Research Institute, Hi-Tech Park, Nanshan, Shenzhen 518057, China
- Department of Chemistry, The Hong Kong University of Science and Technology, Kowloon, Hong Kong
| | - Han-lin Gu
- Department of Mathematics, The Hong Kong University of Science and Technology, Kowloon, Hong Kong
| | - Xuhui Huang
- HKUST-Shenzhen Research Institute, Hi-Tech Park, Nanshan, Shenzhen 518057, China
- Department of Chemistry, The Hong Kong University of Science and Technology, Kowloon, Hong Kong
- Center of Systems Biology and Human Health, The Hong Kong University of Science and Technology, Kowloon, Hong Kong
- State Key Laboratory of Molecular Neuroscience, The Hong Kong University of Science and Technology, Kowloon, Hong Kong
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20
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Brandt S, Sittel F, Ernst M, Stock G. Machine Learning of Biomolecular Reaction Coordinates. J Phys Chem Lett 2018; 9:2144-2150. [PMID: 29630378 DOI: 10.1021/acs.jpclett.8b00759] [Citation(s) in RCA: 44] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
We present a systematic approach to reduce the dimensionality of a complex molecular system. Starting with a data set of molecular coordinates (obtained from experiment or simulation) and an associated set of metastable conformational states (obtained from clustering the data), a supervised machine learning model is trained to assign unknown molecular structures to the set of metastable states. In this way, the model learns to determine the features of the molecular coordinates that are most important to discriminate the states. Using a new algorithm that exploits this feature importance via an iterative exclusion principle, we identify the essential internal coordinates (such as specific interatomic distances or dihedral angles) of the system, which are shown to represent versatile reaction coordinates that account for the dynamics of the slow degrees of freedom and explain the mechanism of the underlying processes. Moreover, these coordinates give rise to a free energy landscape that may reveal previously hidden intermediate states of the system.
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Affiliation(s)
- Simon Brandt
- Biomolecular Dynamics, Institute of Physics , Albert Ludwigs University , 79104 Freiburg , Germany
| | - Florian Sittel
- Biomolecular Dynamics, Institute of Physics , Albert Ludwigs University , 79104 Freiburg , Germany
| | - Matthias Ernst
- Biomolecular Dynamics, Institute of Physics , Albert Ludwigs University , 79104 Freiburg , Germany
| | - Gerhard Stock
- Biomolecular Dynamics, Institute of Physics , Albert Ludwigs University , 79104 Freiburg , Germany
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21
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Optimal Data-Driven Estimation of Generalized Markov State Models for Non-Equilibrium Dynamics. COMPUTATION 2018. [DOI: 10.3390/computation6010022] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
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22
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Zheng Y, Cui Q. Multiple Pathways and Time Scales for Conformational Transitions in apo-Adenylate Kinase. J Chem Theory Comput 2018; 14:1716-1726. [PMID: 29378407 DOI: 10.1021/acs.jctc.7b01064] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022]
Abstract
The open/close transition in adenylate kinase (AK) is regarded as a representative example for large-scale conformational transition in proteins, yet its mechanism remains unclear despite numerous experimental and computational studies. Using extensive (∼50 μs) explicit solvent atomistic simulations and Markov state analysis, we shed new lights on the mechanism of this transition in the apo form of AK. The closed basin of apo AK features an open NMP domain while the LID domain closes and rotates toward it. Therefore, although the computed structural properties of the closed ensemble are consistent with previously reported FRET and PRE measurements, our simulations suggest that NMP closure is likely to follow AMP binding, in contrast to the previous interpretation of FRET and PRE data that the apo state was able to sample the fully closed conformation for "ligand selection". The closed state ensemble is found to be kinetically heterogeneous; multiple pathways and time scales are associated with the open/close transition, providing new clues to the disparate time scales observed in different experiments. Besides interdomain interactions, a novel mutual information analysis identifies specific intradomain interactions that correlate strongly to transition kinetics, supporting observations from previous chimera experiments. While our results underscore the role of internal domain properties in determining the kinetics of open/close transition in apo AK, no evidence is observed for any significant degree of local unfolding during the transition. These observations about AK have general implications to our view of conformational states, transition pathways, and time scales of conformational changes in proteins. The key features and time scales of observed transition pathways are robust and similar from simulations using two popular fixed charge force fields.
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Affiliation(s)
- Yuqing Zheng
- Graduate Program in Biophysics and Department of Chemistry , University of Wisconsin-Madison , 1101 University Avenue , Madison , Wisconsin 53706 , United States
| | - Qiang Cui
- Graduate Program in Biophysics and Department of Chemistry , University of Wisconsin-Madison , 1101 University Avenue , Madison , Wisconsin 53706 , United States
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23
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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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24
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Wang W, Cao S, Zhu L, Huang X. Constructing Markov State Models to elucidate the functional conformational changes of complex biomolecules. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2017. [DOI: 10.1002/wcms.1343] [Citation(s) in RCA: 52] [Impact Index Per Article: 7.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
Affiliation(s)
- Wei Wang
- Department of ChemistryThe Hong Kong University of Science and Technology Kowloon Hong Kong
- Center of Systems Biology and Human HealthThe Hong Kong University of Science and Technology Kowloon Hong Kong
| | - Siqin Cao
- Department of ChemistryThe Hong Kong University of Science and Technology Kowloon Hong Kong
| | - Lizhe Zhu
- Department of ChemistryThe Hong Kong University of Science and Technology Kowloon Hong Kong
- Center of Systems Biology and Human HealthThe Hong Kong University of Science and Technology Kowloon Hong Kong
| | - Xuhui Huang
- Department of ChemistryThe Hong Kong University of Science and Technology Kowloon Hong Kong
- Center of Systems Biology and Human HealthThe Hong Kong University of Science and Technology Kowloon Hong Kong
- Hong Kong Branch of Chinese National Engineering Research Center for Tissue Restoration & ReconstructionThe Hong Kong University of Science and Technology Kowloon Hong Kong
- HKUST‐Shenzhen Research Institute Shenzhen China
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25
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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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26
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Zhang C, Yu J, Zhou X. Imaging Metastable States and Transitions in Proteins by Trajectory Map. J Phys Chem B 2017; 121:4678-4686. [PMID: 28425289 DOI: 10.1021/acs.jpcb.7b00664] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/03/2023]
Abstract
It has been a long-standing and intriguing issue to develop robust methods to identify metastable states and interstate transitions from simulations or experimental data to understand the functional conformational changes of proteins. It is usually hard to define the complicated boundaries of the states in the conformational space using most of the existing methods, and they often lead to parameter-sensitive results. Here, we present a new approach, visualized Trajectory Map (vTM), to identify the metastable states and the rare interstate transitions, by considering both the conformational similarity and the temporal successiveness of conformations. The vTM is able to give a nonambiguous description of slow dynamics. The case study of a β-hairpin peptide shows that the vTM can reveal the states and transitions from all-atom MD trajectory data even when a single observable (i.e, one-dimensional reaction coordinate) is used. We also use the vTM to refine the folding/unfolding mechanism of HP35 in explicit water by analyzing a 125 μs all-atom MD trajectory and obtain folding/unfolding rates of about 1/μs, which are in good agreement with the experimental values.
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Affiliation(s)
- Chuanbiao Zhang
- School of Physical Sciences, University of Chinese Academy of Sciences , Beijing 100049, China
| | - Jin Yu
- Beijing Computer Science Research Center , Beijing 100193, China
| | - Xin Zhou
- School of Physical Sciences, University of Chinese Academy of Sciences , Beijing 100049, China
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27
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Melvin RL, Godwin RC, Xiao J, Thompson WG, Berenhaut KS, Salsbury FR. Uncovering Large-Scale Conformational Change in Molecular Dynamics without Prior Knowledge. J Chem Theory Comput 2016; 12:6130-6146. [PMID: 27802394 PMCID: PMC5719493 DOI: 10.1021/acs.jctc.6b00757] [Citation(s) in RCA: 32] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
Abstract
As the length of molecular dynamics (MD) trajectories grows with increasing computational power, so does the importance of clustering methods for partitioning trajectories into conformational bins. Of the methods available, the vast majority require users to either have some a priori knowledge about the system to be clustered or to tune clustering parameters through trial and error. Here we present non-parametric uses of two modern clustering techniques suitable for first-pass investigation of an MD trajectory. Being non-parametric, these methods require neither prior knowledge nor parameter tuning. The first method, HDBSCAN, is fast-relative to other popular clustering methods-and is able to group unstructured or intrinsically disordered systems (such as intrinsically disordered proteins, or IDPs) into bins that represent global conformational shifts. HDBSCAN is also useful for determining the overall stability of a system-as it tends to group stable systems into one or two bins-and identifying transition events between metastable states. The second method, iMWK-Means, with explicit rescaling followed by K-Means, while slower than HDBSCAN, performs well with stable, structured systems such as folded proteins and is able to identify higher resolution details such as changes in relative position of secondary structural elements. Used in conjunction, these clustering methods allow a user to discern quickly and without prior knowledge the stability of a simulated system and identify both local and global conformational changes.
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Affiliation(s)
- Ryan L. Melvin
- Department of Physics, Wake Forest University, Winston-Salem, North Carolina 27109, United States
| | - Ryan C. Godwin
- Department of Physics, Wake Forest University, Winston-Salem, North Carolina 27109, United States
| | - Jiajie Xiao
- Department of Physics, Wake Forest University, Winston-Salem, North Carolina 27109, United States
| | - William G. Thompson
- Department of Physics, Wake Forest University, Winston-Salem, North Carolina 27109, United States
| | - Kenneth S. Berenhaut
- Department of Mathematics & Statistics, Wake Forest University, Winston-Salem, North Carolina 27109, United States
| | - Freddie R. Salsbury
- Department of Physics, Wake Forest University, Winston-Salem, North Carolina 27109, United States
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28
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Koltai P, Ciccotti G, Schütte C. On metastability and Markov state models for non-stationary molecular dynamics. J Chem Phys 2016; 145:174103. [DOI: 10.1063/1.4966157] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/17/2023] Open
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29
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Orioli S, Faccioli P. Dimensional reduction of Markov state models from renormalization group theory. J Chem Phys 2016; 145:124120. [DOI: 10.1063/1.4963196] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022] Open
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30
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Li Y, Dong Z. Effect of Clustering Algorithm on Establishing Markov State Model for Molecular Dynamics Simulations. J Chem Inf Model 2016; 56:1205-15. [DOI: 10.1021/acs.jcim.6b00181] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Yan Li
- The Hormel Institute, University of Minnesota, Austin, Minnesota 55912, United States
| | - Zigang Dong
- The Hormel Institute, University of Minnesota, Austin, Minnesota 55912, United States
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31
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Sittel F, Stock G. Robust Density-Based Clustering To Identify Metastable Conformational States of Proteins. J Chem Theory Comput 2016; 12:2426-35. [PMID: 27058020 DOI: 10.1021/acs.jctc.5b01233] [Citation(s) in RCA: 56] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Abstract
A density-based clustering method is proposed that is deterministic, computationally efficient, and self-consistent in its parameter choice. By calculating a geometric coordinate space density for every point of a given data set, a local free energy is defined. On the basis of these free energy estimates, the frames are lumped into local free energy minima, ultimately forming microstates separated by local free energy barriers. The algorithm is embedded into a complete workflow to robustly generate Markov state models from molecular dynamics trajectories. It consists of (i) preprocessing of the data via principal component analysis in order to reduce the dimensionality of the problem, (ii) proposed density-based clustering to generate microstates, and (iii) dynamical clustering via the most probable path algorithm to construct metastable states. To characterize the resulting state-resolved conformational distribution, dihedral angle content color plots are introduced which identify structural differences of protein states in a concise way. To illustrate the performance of the method, three well-established model problems are adopted: conformational transitions of hepta-alanine, folding of villin headpiece, and functional dynamics of bovine pancreatic trypsin inhibitor.
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Affiliation(s)
- Florian Sittel
- Biomolecular Dynamics, Institute of Physics, Albert Ludwigs University , 79104 Freiburg, Germany
| | - Gerhard Stock
- Biomolecular Dynamics, Institute of Physics, Albert Ludwigs University , 79104 Freiburg, Germany
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32
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Zhang L, Pardo-Avila F, Unarta IC, Cheung PPH, Wang G, Wang D, Huang X. Elucidation of the Dynamics of Transcription Elongation by RNA Polymerase II using Kinetic Network Models. Acc Chem Res 2016; 49:687-94. [PMID: 26991064 DOI: 10.1021/acs.accounts.5b00536] [Citation(s) in RCA: 39] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/22/2023]
Abstract
RNA polymerase II (Pol II) is an essential enzyme that catalyzes transcription with high efficiency and fidelity in eukaryotic cells. During transcription elongation, Pol II catalyzes the nucleotide addition cycle (NAC) to synthesize mRNA using DNA as the template. The transitions between the states of the NAC require conformational changes of both the protein and nucleotides. Although X-ray structures are available for most of these states, the dynamics of the transitions between states are largely unknown. Molecular dynamics (MD) simulations can predict structure-based molecular details and shed light on the mechanisms of these dynamic transitions. However, the employment of MD simulations on a macromolecule (tens to hundreds of nanoseconds) such as Pol II is challenging due to the difficulty of reaching biologically relevant timescales (tens of microseconds or even longer). For this challenge to be overcome, kinetic network models (KNMs), such as Markov State Models (MSMs), have become a popular approach to access long-timescale conformational changes using many short MD simulations. We describe here our application of KNMs to characterize the molecular mechanisms of the NAC of Pol II. First, we introduce the general background of MSMs and further explain procedures for the construction and validation of MSMs by providing some technical details. Next, we review our previous studies in which we applied MSMs to investigate the individual steps of the NAC, including translocation and pyrophosphate ion release. In particular, we describe in detail how we prepared the initial conformations of Pol II elongation complex, performed MD simulations, extracted MD conformations to construct MSMs, and further validated them. We also summarize our major findings on molecular mechanisms of Pol II elongation based on these MSMs. In addition, we have included discussions regarding various key points and challenges for applications of MSMs to systems as large as the Pol II elongation complex. Finally, to study the overall NAC, we combine the individual steps of the NAC into a five-state KNM based on a nonbranched Brownian ratchet scheme to explain the single-molecule optical tweezers experimental data. The studies complement experimental observations and provide molecular mechanisms for the transcription elongation cycle. In the long term, incorporation of sequence-dependent kinetic parameters into KNMs has great potential for identifying error-prone sequences and predicting transcription dynamics in genome-wide transcriptomes.
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Affiliation(s)
- Lu Zhang
- Department
of Chemistry and State Key Laboratory of Molecular Neuroscience, Center
for System Biology and Human Health, School of Science, and IAS, The Hong Kong University of Science and Technology, Kowloon, Hong Kong
| | - Fátima Pardo-Avila
- Department
of Chemistry and State Key Laboratory of Molecular Neuroscience, Center
for System Biology and Human Health, School of Science, and IAS, The Hong Kong University of Science and Technology, Kowloon, Hong Kong
| | - Ilona Christy Unarta
- Department
of Chemistry and State Key Laboratory of Molecular Neuroscience, Center
for System Biology and Human Health, School of Science, and IAS, The Hong Kong University of Science and Technology, Kowloon, Hong Kong
| | - Peter Pak-Hang Cheung
- Department
of Chemistry and State Key Laboratory of Molecular Neuroscience, Center
for System Biology and Human Health, School of Science, and IAS, The Hong Kong University of Science and Technology, Kowloon, Hong Kong
| | - Guo Wang
- Department
of Chemistry and State Key Laboratory of Molecular Neuroscience, Center
for System Biology and Human Health, School of Science, and IAS, The Hong Kong University of Science and Technology, Kowloon, Hong Kong
| | - Dong Wang
- Department
of Cellular and Molecular Medicine, Skaggs School of Pharmacy and
Pharmaceutical Sciences, University of California, San Diego, La Jolla, California 92093, United States
| | - Xuhui Huang
- Department
of Chemistry and State Key Laboratory of Molecular Neuroscience, Center
for System Biology and Human Health, School of Science, and IAS, The Hong Kong University of Science and Technology, Kowloon, Hong Kong
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33
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Zhou G, Voelz VA. Using Kinetic Network Models To Probe Non-Native Salt-Bridge Effects on α-Helix Folding. J Phys Chem B 2016; 120:926-35. [PMID: 26769494 DOI: 10.1021/acs.jpcb.5b11767] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023]
Abstract
Salt-bridge interactions play an important role in stabilizing many protein structures, and have been shown to be designable features for protein design. In this work, we study the effects of non-native salt bridges on the folding of a soluble alanine-based peptide (Fs peptide) using extensive all-atom molecular dynamics simulations performed on the Folding@home distributed computing platform. Using Markov State Models, we show how non-native salt-bridges affect the folding kinetics of Fs peptide by perturbing specific conformational states. Furthermore, we present methods for the automatic detection and analysis of such states. These results provide insight into helix folding mechanisms and useful information to guide simulation-based computational protein design.
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Affiliation(s)
- Guangfeng Zhou
- Department of Chemistry, Temple University , 1901 North 13th Street, Beury Hall, Philadelphia, Pennsylvania 19122, United States
| | - Vincent A Voelz
- Department of Chemistry, Temple University , 1901 North 13th Street, Beury Hall, Philadelphia, Pennsylvania 19122, United States
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34
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Zhang L, Jiang H, Sheong F, Pardo-Avila F, Cheung PH, Huang X. Constructing Kinetic Network Models to Elucidate Mechanisms of Functional Conformational Changes of Enzymes and Their Recognition with Ligands. Methods Enzymol 2016; 578:343-71. [DOI: 10.1016/bs.mie.2016.05.026] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
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35
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Systematically constructing kinetic transition network in polypeptide from top to down: trajectory mapping. PLoS One 2015; 10:e0125932. [PMID: 25962177 PMCID: PMC4427365 DOI: 10.1371/journal.pone.0125932] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/14/2014] [Accepted: 03/24/2015] [Indexed: 11/23/2022] Open
Abstract
Molecular dynamics (MD) simulation is an important tool for understanding bio-molecules in microscopic temporal/spatial scales. Besides the demand in improving simulation techniques to approach experimental scales, it becomes more and more crucial to develop robust methodology for precisely and objectively interpreting massive MD simulation data. In our previous work [J Phys Chem B 114, 10266 (2010)], the trajectory mapping (TM) method was presented to analyze simulation trajectories then to construct a kinetic transition network of metastable states. In this work, we further present a top-down implementation of TM to systematically detect complicate features of conformational space. We first look at longer MD trajectory pieces to get a coarse picture of transition network at larger time scale, and then we gradually cut the trajectory pieces in shorter for more details. A robust clustering algorithm is designed to more effectively identify the metastable states and transition events. We applied this TM method to detect the hierarchical structure in the conformational space of alanine-dodeca-peptide from microsecond to nanosecond time scales. The results show a downhill folding process of the peptide through multiple pathways. Even in this simple system, we found that single common-used order parameter is not sufficient either in distinguishing the metastable states or predicting the transition kinetics among these states.
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36
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Zheng Y, Cui Q. The histone H3 N-terminal tail: a computational analysis of the free energy landscape and kinetics. Phys Chem Chem Phys 2015; 17:13689-98. [DOI: 10.1039/c5cp01858g] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022]
Abstract
Extensive molecular dynamics simulations and Markov State models are used to characterize the free energy landscape and kinetics of the histone H3 N-terminal tail, which plays a critical role in regulating chromatin dynamics and gene activity.
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Affiliation(s)
- Yuqing Zheng
- Graduate Program in Biophysics
- University of Wisconsin-Madison
- Madison
- USA
| | - Qiang Cui
- Graduate Program in Biophysics
- University of Wisconsin-Madison
- Madison
- USA
- Department of Chemistry and Theoretical Chemistry Institute
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37
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Sheong FK, Silva DA, Meng L, Zhao Y, Huang X. Automatic state partitioning for multibody systems (APM): an efficient algorithm for constructing Markov state models to elucidate conformational dynamics of multibody systems. J Chem Theory Comput 2014; 11:17-27. [PMID: 26574199 DOI: 10.1021/ct5007168] [Citation(s) in RCA: 32] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Abstract
The conformational dynamics of multibody systems plays crucial roles in many important problems. Markov state models (MSMs) are powerful kinetic network models that can predict long-time-scale dynamics using many short molecular dynamics simulations. Although MSMs have been successfully applied to conformational changes of individual proteins, the analysis of multibody systems is still a challenge because of the complexity of the dynamics that occur on a mixture of drastically different time scales. In this work, we have developed a new algorithm, automatic state partitioning for multibody systems (APM), for constructing MSMs to elucidate the conformational dynamics of multibody systems. The APM algorithm effectively addresses different time scales in the multibody systems by directly incorporating dynamics into geometric clustering when identifying the metastable conformational states. We have applied the APM algorithm to a 2D potential that can mimic a protein-ligand binding system and the aggregation of two hydrophobic particles in water and have shown that it can yield tremendous enhancements in the computational efficiency of MSM construction and the accuracy of the models.
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Affiliation(s)
- Fu Kit Sheong
- HKUST Shenzhen Research Institute , Nanshan, Shenzhen 518057, China
| | | | - Luming Meng
- HKUST Shenzhen Research Institute , Nanshan, Shenzhen 518057, China
| | | | - Xuhui Huang
- HKUST Shenzhen Research Institute , Nanshan, Shenzhen 518057, China
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Schwantes CR, McGibbon RT, Pande VS. Perspective: Markov models for long-timescale biomolecular dynamics. J Chem Phys 2014; 141:090901. [PMID: 25194354 PMCID: PMC4156582 DOI: 10.1063/1.4895044] [Citation(s) in RCA: 70] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/08/2014] [Accepted: 08/27/2014] [Indexed: 01/24/2023] Open
Abstract
Molecular dynamics simulations have the potential to provide atomic-level detail and insight to important questions in chemical physics that cannot be observed in typical experiments. However, simply generating a long trajectory is insufficient, as researchers must be able to transform the data in a simulation trajectory into specific scientific insights. Although this analysis step has often been taken for granted, it deserves further attention as large-scale simulations become increasingly routine. In this perspective, we discuss the application of Markov models to the analysis of large-scale biomolecular simulations. We draw attention to recent improvements in the construction of these models as well as several important open issues. In addition, we highlight recent theoretical advances that pave the way for a new generation of models of molecular kinetics.
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Affiliation(s)
- C R Schwantes
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
| | - R T McGibbon
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
| | - V S Pande
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
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39
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Gu S, Silva DA, Meng L, Yue A, Huang X. Quantitatively characterizing the ligand binding mechanisms of choline binding protein using Markov state model analysis. PLoS Comput Biol 2014; 10:e1003767. [PMID: 25101697 PMCID: PMC4125059 DOI: 10.1371/journal.pcbi.1003767] [Citation(s) in RCA: 54] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/29/2013] [Accepted: 06/22/2014] [Indexed: 01/05/2023] Open
Abstract
Protein-ligand recognition plays key roles in many biological processes. One of the most fascinating questions about protein-ligand recognition is to understand its underlying mechanism, which often results from a combination of induced fit and conformational selection. In this study, we have developed a three-pronged approach of Markov State Models, Molecular Dynamics simulations, and flux analysis to determine the contribution of each model. Using this approach, we have quantified the recognition mechanism of the choline binding protein (ChoX) to be ∼90% conformational selection dominant under experimental conditions. This is achieved by recovering all the necessary parameters for the flux analysis in combination with available experimental data. Our results also suggest that ChoX has several metastable conformational states, of which an apo-closed state is dominant, consistent with previous experimental findings. Our methodology holds great potential to be widely applied to understand recognition mechanisms underlining many fundamental biological processes.
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Affiliation(s)
- Shuo Gu
- Department of Chemistry, Institute for Advance Study and School of Science, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
| | - Daniel-Adriano Silva
- Department of Chemistry, Institute for Advance Study and School of Science, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
- Department of Biochemistry, University of Washington, Seattle, Washington, United States of America
| | - Luming Meng
- Department of Chemistry, Institute for Advance Study and School of Science, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
| | - Alexander Yue
- Department of Chemistry, Institute for Advance Study and School of Science, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
| | - Xuhui Huang
- Department of Chemistry, Institute for Advance Study and School of Science, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
- Division of Biomedical Engineering, Institute for Advance Study and School of Science, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
- Center of Systems Biology and Human Health, Institute for Advance Study and School of Science, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
- * E-mail:
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40
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Chodera JD, Noé F. Markov state models of biomolecular conformational dynamics. Curr Opin Struct Biol 2014; 25:135-44. [PMID: 24836551 DOI: 10.1016/j.sbi.2014.04.002] [Citation(s) in RCA: 502] [Impact Index Per Article: 50.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/11/2014] [Revised: 04/08/2014] [Accepted: 04/12/2014] [Indexed: 10/25/2022]
Abstract
It has recently become practical to construct Markov state models (MSMs) that reproduce the long-time statistical conformational dynamics of biomolecules using data from molecular dynamics simulations. MSMs can predict both stationary and kinetic quantities on long timescales (e.g. milliseconds) using a set of atomistic molecular dynamics simulations that are individually much shorter, thus addressing the well-known sampling problem in molecular dynamics simulation. In addition to providing predictive quantitative models, MSMs greatly facilitate both the extraction of insight into biomolecular mechanism (such as folding and functional dynamics) and quantitative comparison with single-molecule and ensemble kinetics experiments. A variety of methodological advances and software packages now bring the construction of these models closer to routine practice. Here, we review recent progress in this field, considering theoretical and methodological advances, new software tools, and recent applications of these approaches in several domains of biochemistry and biophysics, commenting on remaining challenges.
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Affiliation(s)
- John D Chodera
- Computational Biology Program, Sloan Kettering Institute, Memorial Sloan Kettering Cancer Center, New York, NY 10065, USA.
| | - Frank Noé
- Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany.
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41
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McGibbon RT, Schwantes CR, Pande VS. Statistical model selection for Markov models of biomolecular dynamics. J Phys Chem B 2014; 118:6475-81. [PMID: 24738580 DOI: 10.1021/jp411822r] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Abstract
Markov state models provide a powerful framework for the analysis of biomolecular conformation dynamics in terms of their metastable states and transition rates. These models provide both a quantitative and comprehensible description of the long-time scale dynamics of large molecular dynamics with a Master equation and have been successfully used to study protein folding, protein conformational change, and protein-ligand binding. However, to achieve satisfactory performance, existing methodologies often require expert intervention when defining the model's discrete state space. While standard model selection methodologies focus on the minimization of systematic bias and disregard statistical error, we show that by consideration of the states' conditional distribution over conformations, both sources of error can be balanced evenhandedly. Application of techniques that consider both systematic bias and statistical error on two 100 μs molecular dynamics trajectories of the Fip35 WW domain shows agreement with existing techniques based on self-consistency of the model's relaxation time scales with more suitable results in regimes in which those time scale-based techniques encourage overfitting. By removing the need for expert tuning, these methods should reduce modeling bias and lower the barriers to entry in Markov state model construction.
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Affiliation(s)
- Robert T McGibbon
- Department of Chemistry, ‡Biophysics Program, §Department of Computer Science, and ∥Department of Structural Biology, Stanford University , Stanford, California 94305, United States
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42
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Jain A, Stock G. Hierarchical Folding Free Energy Landscape of HP35 Revealed by Most Probable Path Clustering. J Phys Chem B 2014; 118:7750-60. [DOI: 10.1021/jp410398a] [Citation(s) in RCA: 33] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Affiliation(s)
- Abhinav Jain
- Biomolecular
Dynamics, Institute
of Physics and Freiburg Institute for Advanced Studies (FRIAS), Albert Ludwigs University, 79104 Freiburg, Germany
| | - Gerhard Stock
- Biomolecular
Dynamics, Institute
of Physics and Freiburg Institute for Advanced Studies (FRIAS), Albert Ludwigs University, 79104 Freiburg, Germany
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Gruebele M, Thirumalai D. Perspective: Reaches of chemical physics in biology. J Chem Phys 2013; 139:121701. [PMID: 24089712 PMCID: PMC5942441 DOI: 10.1063/1.4820139] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/14/2013] [Accepted: 08/20/2013] [Indexed: 01/09/2023] Open
Abstract
Chemical physics as a discipline contributes many experimental tools, algorithms, and fundamental theoretical models that can be applied to biological problems. This is especially true now as the molecular level and the systems level descriptions begin to connect, and multi-scale approaches are being developed to solve cutting edge problems in biology. In some cases, the concepts and tools got their start in non-biological fields, and migrated over, such as the idea of glassy landscapes, fluorescence spectroscopy, or master equation approaches. In other cases, the tools were specifically developed with biological physics applications in mind, such as modeling of single molecule trajectories or super-resolution laser techniques. In this introduction to the special topic section on chemical physics of biological systems, we consider a wide range of contributions, all the way from the molecular level, to molecular assemblies, chemical physics of the cell, and finally systems-level approaches, based on the contributions to this special issue. Chemical physicists can look forward to an exciting future where computational tools, analytical models, and new instrumentation will push the boundaries of biological inquiry.
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Affiliation(s)
- Martin Gruebele
- Departments of Chemistry and Physics, and Center for Biophysics and Computational Biology, University of Illinois, Urbana, Illinois 61801, USA
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