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Dominic AJ, Cao S, Montoya-Castillo A, Huang X. Memory Unlocks the Future of Biomolecular Dynamics: Transformative Tools to Uncover Physical Insights Accurately and Efficiently. J Am Chem Soc 2023; 145:9916-9927. [PMID: 37104720 DOI: 10.1021/jacs.3c01095] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/29/2023]
Abstract
Conformational changes underpin function and encode complex biomolecular mechanisms. Gaining atomic-level detail of how such changes occur has the potential to reveal these mechanisms and is of critical importance in identifying drug targets, facilitating rational drug design, and enabling bioengineering applications. While the past two decades have brought Markov state model techniques to the point where practitioners can regularly use them to glimpse the long-time dynamics of slow conformations in complex systems, many systems are still beyond their reach. In this Perspective, we discuss how including memory (i.e., non-Markovian effects) can reduce the computational cost to predict the long-time dynamics in these complex systems by orders of magnitude and with greater accuracy and resolution than state-of-the-art Markov state models. We illustrate how memory lies at the heart of successful and promising techniques, ranging from the Fokker-Planck and generalized Langevin equations to deep-learning recurrent neural networks and generalized master equations. We delineate how these techniques work, identify insights that they can offer in biomolecular systems, and discuss their advantages and disadvantages in practical settings. We show how generalized master equations can enable the investigation of, for example, the gate-opening process in RNA polymerase II and demonstrate how our recent advances tame the deleterious influence of statistical underconvergence of the molecular dynamics simulations used to parameterize these techniques. This represents a significant leap forward that will enable our memory-based techniques to interrogate systems that are currently beyond the reach of even the best Markov state models. We conclude by discussing some current challenges and future prospects for how exploiting memory will open the door to many exciting opportunities.
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Affiliation(s)
- Anthony J Dominic
- Department of Chemistry, University of Colorado Boulder, Boulder, Colorado 80309, USA
| | - Siqin Cao
- Department of Chemistry, Theoretical Chemistry Institute, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA
| | | | - Xuhui Huang
- Department of Chemistry, Theoretical Chemistry Institute, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA
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Sayer T, Montoya-Castillo A. Compact and complete description of non-Markovian dynamics. J Chem Phys 2023; 158:014105. [PMID: 36610963 DOI: 10.1063/5.0132614] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023] Open
Abstract
Generalized master equations provide a theoretically rigorous framework to capture the dynamics of processes ranging from energy harvesting in plants and photovoltaic devices to qubit decoherence in quantum technologies and even protein folding. At their center is the concept of memory. The explicit time-nonlocal description of memory is both protracted and elaborate. When physical intuition is at a premium, one would desire a more compact, yet complete, description. Here, we demonstrate how and when the time-convolutionless formalism constitutes such a description. In particular, by focusing on the dissipative dynamics of the spin-boson and Frenkel exciton models, we show how to: easily construct the time-local generator from reference reduced dynamics, elucidate the dependence of its existence on the system parameters and the choice of reduced observables, identify the physical origin of its apparent divergences, and offer analysis tools to diagnose their severity and circumvent their deleterious effects. We demonstrate that, when applicable, the time-local approach requires as little information as the more commonly used time-nonlocal scheme, with the important advantages of providing a more compact description, greater algorithmic simplicity, and physical interpretability. We conclude by introducing the discrete-time analog and a straightforward protocol to employ it in cases where the reference dynamics have limited resolution. The insights we present here offer the potential for extending the reach of dynamical methods, reducing both their cost and conceptual complexity.
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Affiliation(s)
- Thomas Sayer
- Department of Chemistry, University of Colorado Boulder, Boulder, Colorado 80309, USA
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Cao S, Montoya-Castillo A, Wang W, Markland TE, Huang X. On the advantages of exploiting memory in Markov state models for biomolecular dynamics. J Chem Phys 2021; 153:014105. [PMID: 32640825 DOI: 10.1063/5.0010787] [Citation(s) in RCA: 31] [Impact Index Per Article: 10.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/24/2023] Open
Abstract
Biomolecular dynamics play an important role in numerous biological processes. Markov State Models (MSMs) provide a powerful approach to study these dynamic processes by predicting long time scale dynamics based on many short molecular dynamics (MD) simulations. In an MSM, protein dynamics are modeled as a kinetic process consisting of a series of Markovian transitions between different conformational states at discrete time intervals (called "lag time"). To achieve this, a master equation must be constructed with a sufficiently long lag time to allow interstate transitions to become truly Markovian. This imposes a major challenge for MSM studies of proteins since the lag time is bound by the length of relatively short MD simulations available to estimate the frequency of transitions. Here, we show how one can employ the generalized master equation formalism to obtain an exact description of protein conformational dynamics both at short and long time scales without the time resolution restrictions imposed by the MSM lag time. Using a simple kinetic model, alanine dipeptide, and WW domain, we demonstrate that it is possible to construct these quasi-Markov State Models (qMSMs) using MD simulations that are 5-10 times shorter than those required by MSMs. These qMSMs only contain a handful of metastable states and, thus, can greatly facilitate the interpretation of mechanisms associated with protein dynamics. A qMSM opens the door to the study of conformational changes of complex biomolecules where a Markovian model with a few states is often difficult to construct due to the limited length of available MD simulations.
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Affiliation(s)
- Siqin Cao
- Department of Chemistry, The Hong Kong University of Science and Technology, Kowloon, Hong Kong
| | | | - Wei Wang
- Department of Chemistry, The Hong Kong University of Science and Technology, Kowloon, Hong Kong
| | - Thomas E Markland
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
| | - Xuhui Huang
- Department of Chemistry, The Hong Kong University of Science and Technology, Kowloon, Hong Kong
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Kelly A, Montoya-Castillo A, Wang L, Markland TE. Generalized quantum master equations in and out of equilibrium: When can one win? J Chem Phys 2016; 144:184105. [DOI: 10.1063/1.4948612] [Citation(s) in RCA: 42] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023] Open
Affiliation(s)
- Aaron Kelly
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
| | | | - Lu Wang
- Department of Chemistry and Chemical Biology, Rutgers University, Piscataway, New Jersey 08854, USA
| | - Thomas E. Markland
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
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Sunthar P, Nguyen DA, Dubbelboer R, Prakash JR, Sridhar T. Measurement and Prediction of the Elongational Stress Growth in a Dilute Solution of DNA Molecules. Macromolecules 2005. [DOI: 10.1021/ma0511907] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- P. Sunthar
- Department of Chemical Engineering, Monash University, Melbourne VIC 3800, Australia
| | - Duc At Nguyen
- Department of Chemical Engineering, Monash University, Melbourne VIC 3800, Australia
| | - Roelf Dubbelboer
- Department of Chemical Engineering, Monash University, Melbourne VIC 3800, Australia
| | - J. Ravi Prakash
- Department of Chemical Engineering, Monash University, Melbourne VIC 3800, Australia
| | - Tam Sridhar
- Department of Chemical Engineering, Monash University, Melbourne VIC 3800, Australia
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Yang S, Witkoskie JB, Cao J. Single-molecule dynamics of semiflexible Gaussian chains. J Chem Phys 2002. [DOI: 10.1063/1.1521156] [Citation(s) in RCA: 20] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Koike A. Molecular Dynamics Study of Viscoelastic Properties of Confined Oligomer Melts. Macromolecules 1998. [DOI: 10.1021/ma971343t] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Asako Koike
- Hitachi Research Laboratory, Hitachi Ltd., 7-1-1 Omika, Hitachi, Ibaraki 319-1292, Japan
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Avalos JB. Dynamics of semiflexible and rigid particles. II. Derivation of the stress tensor and transport equations. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996; 54:3971-3983. [PMID: 9965545 DOI: 10.1103/physreve.54.3971] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Avalos JB. Dynamics of semiflexible and rigid particles. I. The velocity distribution and the Smoluchowski equation. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996; 54:3955-3970. [PMID: 9965544 DOI: 10.1103/physreve.54.3955] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Jorquera H, Dahler JS. A kinetic theory of suspensions. II. The steady flow of a hard‐sphere suspension. J Chem Phys 1994. [DOI: 10.1063/1.467763] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Stepanow S, Helmis G. On the dynamical viscosity of dilute polymer solutions in theta solvents. J Chem Phys 1988. [DOI: 10.1063/1.454863] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Wang S, Freed KF. Renormalization group theory of the Rouse–Zimm model of polymer dynamics to second order in ε. II. Dynamic intrinsic viscosity of Gaussian chains. J Chem Phys 1987. [DOI: 10.1063/1.452057] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Jagannathan A, Oono Y, Schaub B. Intrinsic viscosity from the Green–Kubo formula. J Chem Phys 1987. [DOI: 10.1063/1.452126] [Citation(s) in RCA: 20] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Bixon M, Zwanzig R. Hydrodynamic interaction and the dynamic intrinsic viscosity of a flexible polymer. J Chem Phys 1978. [DOI: 10.1063/1.435915] [Citation(s) in RCA: 33] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Bixon M, Kaldor U. The intrinsic viscosity of a suspension of nonharmonic dumbbells. J Chem Phys 1977. [DOI: 10.1063/1.433870] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Titulaer UM. The non‐Newtonian viscosity of dilute solutions of stiff polymers. J Chem Phys 1977. [DOI: 10.1063/1.434085] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Yamakawa H, Tanaka G. Some further comments on correlation‐function formulas for polymer intrinsic viscosity. J Chem Phys 1975. [DOI: 10.1063/1.431242] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Titulaer UM, Deutch JM. The intrinsic viscosity of dilute solutions of stiff polymers. J Chem Phys 1975. [DOI: 10.1063/1.431130] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Wilemski G. Intrinsic viscosity of stiff dumbbells from time correlation functions. J Chem Phys 1975. [DOI: 10.1063/1.431644] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Stockmayer WH, Wilemski G, Yamakawa H, Tanaka G. Some comments on correlation‐function formulas for polymer intrinsic viscosity. J Chem Phys 1975. [DOI: 10.1063/1.431402] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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