1
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Keller BG, Bolhuis PG. Dynamical Reweighting for Biased Rare Event Simulations. Annu Rev Phys Chem 2024; 75:137-162. [PMID: 38941527 DOI: 10.1146/annurev-physchem-083122-124538] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/30/2024]
Abstract
Dynamical reweighting techniques aim to recover the correct molecular dynamics from a simulation at a modified potential energy surface. They are important for unbiasing enhanced sampling simulations of molecular rare events. Here, we review the theoretical frameworks of dynamical reweighting for modified potentials. Based on an overview of kinetic models with increasing level of detail, we discuss techniques to reweight two-state dynamics, multistate dynamics, and path integrals. We explore the natural link to transition path sampling and how the effect of nonequilibrium forces can be reweighted. We end by providing an outlook on how dynamical reweighting integrates with techniques for optimizing collective variables and with modern potential energy surfaces.
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Affiliation(s)
- Bettina G Keller
- Department of Biology, Chemistry and Pharmacy, Freie Universität Berlin, Berlin, Germany;
| | - Peter G Bolhuis
- Van 't Hoff Institute for Molecular Sciences, University of Amsterdam, Amsterdam, The Netherlands
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2
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Torres A, Cockerell S, Phillips M, Balázsi G, Ghosh K. MaxCal can infer models from coupled stochastic trajectories of gene expression and cell division. Biophys J 2023; 122:2623-2635. [PMID: 37218129 PMCID: PMC10397576 DOI: 10.1016/j.bpj.2023.05.017] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/24/2023] [Revised: 05/03/2023] [Accepted: 05/18/2023] [Indexed: 05/24/2023] Open
Abstract
Gene expression is inherently noisy due to small numbers of proteins and nucleic acids inside a cell. Likewise, cell division is stochastic, particularly when tracking at the level of a single cell. The two can be coupled when gene expression affects the rate of cell division. Single-cell time-lapse experiments can measure both fluctuations by simultaneously recording protein levels inside a cell and its stochastic division. These information-rich noisy trajectory data sets can be harnessed to learn about the underlying molecular and cellular details that are often not known a priori. A critical question is: How can we infer a model given data where fluctuations at two levels-gene expression and cell division-are intricately convoluted? We show the principle of maximum caliber (MaxCal)-integrated within a Bayesian framework-can be used to infer several cellular and molecular details (division rates, protein production, and degradation rates) from these coupled stochastic trajectories (CSTs). We demonstrate this proof of concept using synthetic data generated from a known model. An additional challenge in data analysis is that trajectories are often not in protein numbers, but in noisy fluorescence that depends on protein number in a probabilistic manner. We again show that MaxCal can infer important molecular and cellular rates even when data are in fluorescence, another example of CST with three confounding factors-gene expression noise, cell division noise, and fluorescence distortion-all coupled. Our approach will provide guidance to build models in synthetic biology experiments as well as general biological systems where examples of CSTs are abundant.
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Affiliation(s)
- Andrew Torres
- Department of Physics and Astronomy, University of Denver, Denver, Colorado
| | - Spencer Cockerell
- Department of Physics and Astronomy, University of Denver, Denver, Colorado
| | - Michael Phillips
- Department of Physics and Astronomy, University of Denver, Denver, Colorado
| | - Gábor Balázsi
- Laufer Center for Physical and Quantitative Biology, Stony Brook University, Stony Brook, New York
| | - Kingshuk Ghosh
- Molecular and Cellular Biophysics, University of Denver, Denver, Colorado; Department of Physics and Astronomy, University of Denver, Denver, Colorado.
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3
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Capera-Aragones P, Tyson RC, Foxall E. The maximum entropy principle to predict forager spatial distributions: an alternate perspective for movement ecology. THEOR ECOL-NETH 2023. [DOI: 10.1007/s12080-023-00552-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/29/2023]
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4
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Pachter JA, Dill KA. Nonequilibrium statistical physics beyond the ideal heat bath approximation. Phys Rev E 2023; 107:014131. [PMID: 36797947 DOI: 10.1103/physreve.107.014131] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/29/2022] [Accepted: 01/09/2023] [Indexed: 06/18/2023]
Abstract
Important models of nonequilibrium statistical physics (NESP) are limited by a commonly used, but often unrecognized, near-equilibrium approximation. Fokker-Planck and Langevin equations, the Einstein and random-flight diffusion models, and the Schnakenberg model of biochemical networks suppose that fluctuations are due to an ideal equilibrium bath. But far from equilibrium, this perfect bath concept does not hold. A more principled approach should derive the rate fluctuations from an underlying dynamical model, rather than assuming a particular form. Here, using maximum caliber as the underlying principle, we derive corrections for NESP processes in an imperfect-but more realistic-environment, corrections which become particularly important for a system driven strongly away from equilibrium. Beyond characterizing a heat bath by the single equilibrium property of its temperature, the bath's speed and size must also be used to characterize the bath's ability to handle fast or large fluctuations.
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Affiliation(s)
- Jonathan Asher Pachter
- Laufer Center for Physical and Quantitative Biology, Stony Brook University, Stony Brook, New York 11794, USA
- Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11794, USA
| | - Ken A Dill
- Laufer Center for Physical and Quantitative Biology, Stony Brook University, Stony Brook, New York 11794, USA
- Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11794, USA
- Department of Chemistry, Stony Brook University, Stony Brook, New York 11794, USA
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5
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Rydzewski J, Chen M, Ghosh TK, Valsson O. Reweighted Manifold Learning of Collective Variables from Enhanced Sampling Simulations. J Chem Theory Comput 2022; 18:7179-7192. [PMID: 36367826 DOI: 10.1021/acs.jctc.2c00873] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/13/2022]
Abstract
Enhanced sampling methods are indispensable in computational chemistry and physics, where atomistic simulations cannot exhaustively sample the high-dimensional configuration space of dynamical systems due to the sampling problem. A class of such enhanced sampling methods works by identifying a few slow degrees of freedom, termed collective variables (CVs), and enhancing the sampling along these CVs. Selecting CVs to analyze and drive the sampling is not trivial and often relies on chemical intuition. Despite routinely circumventing this issue using manifold learning to estimate CVs directly from standard simulations, such methods cannot provide mappings to a low-dimensional manifold from enhanced sampling simulations, as the geometry and density of the learned manifold are biased. Here, we address this crucial issue and provide a general reweighting framework based on anisotropic diffusion maps for manifold learning that takes into account that the learning data set is sampled from a biased probability distribution. We consider manifold learning methods based on constructing a Markov chain describing transition probabilities between high-dimensional samples. We show that our framework reverts the biasing effect, yielding CVs that correctly describe the equilibrium density. This advancement enables the construction of low-dimensional CVs using manifold learning directly from the data generated by enhanced sampling simulations. We call our framework reweighted manifold learning. We show that it can be used in many manifold learning techniques on data from both standard and enhanced sampling simulations.
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Affiliation(s)
- Jakub Rydzewski
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, Grudziadzka 5, 87-100 Toruń, Poland
| | - Ming Chen
- Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, United States
| | - Tushar K Ghosh
- Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, United States
| | - Omar Valsson
- Department of Chemistry, University of North Texas, Denton, Texas 76201, United States
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6
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Tsai ST, Fields E, Xu Y, Kuo EJ, Tiwary P. Path sampling of recurrent neural networks by incorporating known physics. Nat Commun 2022; 13:7231. [PMID: 36433982 PMCID: PMC9700810 DOI: 10.1038/s41467-022-34780-x] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/29/2022] [Accepted: 11/07/2022] [Indexed: 11/27/2022] Open
Abstract
Recurrent neural networks have seen widespread use in modeling dynamical systems in varied domains such as weather prediction, text prediction and several others. Often one wishes to supplement the experimentally observed dynamics with prior knowledge or intuition about the system. While the recurrent nature of these networks allows them to model arbitrarily long memories in the time series used in training, it makes it harder to impose prior knowledge or intuition through generic constraints. In this work, we present a path sampling approach based on principle of Maximum Caliber that allows us to include generic thermodynamic or kinetic constraints into recurrent neural networks. We show the method here for a widely used type of recurrent neural network known as long short-term memory network in the context of supplementing time series collected from different application domains. These include classical Molecular Dynamics of a protein and Monte Carlo simulations of an open quantum system continuously losing photons to the environment and displaying Rabi oscillations. Our method can be easily generalized to other generative artificial intelligence models and to generic time series in different areas of physical and social sciences, where one wishes to supplement limited data with intuition or theory based corrections.
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Affiliation(s)
- Sun-Ting Tsai
- grid.164295.d0000 0001 0941 7177Department of Physics, University of Maryland, College Park, MD 20742 USA ,grid.164295.d0000 0001 0941 7177Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742 USA
| | - Eric Fields
- grid.164295.d0000 0001 0941 7177Department of Chemistry and Biochemistry, University of Maryland, College Park, MD 20742 USA ,grid.164295.d0000 0001 0941 7177Department of Computer Science, University of Maryland, College Park, MD 20742 USA
| | - Yijia Xu
- grid.164295.d0000 0001 0941 7177Department of Physics, University of Maryland, College Park, MD 20742 USA ,grid.164295.d0000 0001 0941 7177Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742 USA ,grid.94225.38000000012158463XJoint Quantum Institute and Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, MD 20742 USA
| | - En-Jui Kuo
- grid.164295.d0000 0001 0941 7177Department of Physics, University of Maryland, College Park, MD 20742 USA ,grid.94225.38000000012158463XJoint Quantum Institute and Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, MD 20742 USA
| | - Pratyush Tiwary
- grid.164295.d0000 0001 0941 7177Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742 USA ,grid.164295.d0000 0001 0941 7177Department of Chemistry and Biochemistry, University of Maryland, College Park, MD 20742 USA
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7
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Abstract
BACKGROUND Compositional systems, represented as parts of some whole, are ubiquitous. They encompass the abundances of proteins in a cell, the distribution of organisms in nature, and the stoichiometry of the most basic chemical reactions. Thus, a central goal is to understand how such processes emerge from the behaviors of their components and their pairwise interactions. Such a study, however, is challenging for two key reasons. Firstly, such systems are complex and depend, often stochastically, on their constituent parts. Secondly, the data lie on a simplex which influences their correlations. RESULTS To resolve both of these issues, we provide a general and data-driven modeling tool for compositional systems called Compositional Maximum Entropy (CME). By integrating the prior geometric structure of compositions with sample-specific information, CME infers the underlying multivariate relationships between the constituent components. We provide two proofs of principle. First, we measure the relative abundances of different bacteria and infer how they interact. Second, we show that our method outperforms a common alternative for the extraction of gene-gene interactions in triple-negative breast cancer. CONCLUSIONS CME provides novel and biologically-intuitive insights and is promising as a comprehensive quantitative framework for compositional data.
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8
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Qian H. Statistical Chemical Thermodynamics and Energetic Behavior of Counting: Gibbs’ Theory Revisited. J Chem Theory Comput 2022; 18:6421-6436. [DOI: 10.1021/acs.jctc.2c00783] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Hong Qian
- Department of Applied Mathematics, University of Washington, Seattle, Washington98195-3925, United States
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9
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A Hierarchy of Probability, Fluid and Generalized Densities for the Eulerian Velocivolumetric Description of Fluid Flow, for New Families of Conservation Laws. ENTROPY 2022; 24:1493. [PMCID: PMC9602039 DOI: 10.3390/e24101493] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/03/2022] [Accepted: 10/12/2022] [Indexed: 05/28/2023]
Abstract
The Reynolds transport theorem occupies a central place in continuum mechanics, providing a generalized integral conservation equation for the transport of any conserved quantity within a fluid or material volume, which can be connected to its corresponding differential equation. Recently, a more generalized framework was presented for this theorem, enabling parametric transformations between positions on a manifold or in any generalized coordinate space, exploiting the underlying continuous multivariate (Lie) symmetries of a vector or tensor field associated with a conserved quantity. We explore the implications of this framework for fluid flow systems, based on an Eulerian velocivolumetric (position-velocity) description of fluid flow. The analysis invokes a hierarchy of five probability density functions, which by convolution are used to define five fluid densities and generalized densities relevant to this description. We derive 11 formulations of the generalized Reynolds transport theorem for different choices of the coordinate space, parameter space and density, only the first of which is commonly known. These are used to generate a table of integral and differential conservation laws applicable to each formulation, for eight important conserved quantities (fluid mass, species mass, linear momentum, angular momentum, energy, charge, entropy and probability). The findings substantially expand the set of conservation laws for the analysis of fluid flow and dynamical systems.
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10
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Jadrich RB, Lindquist BA, Truskett TM. Treating random sequential addition via the replica method. J Chem Phys 2022; 157:084116. [DOI: 10.1063/5.0096276] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
While many physical processes are non-equilibrium in nature, the theory and modeling of such phenomena lag behind theoretical treatments of equilibrium systems. The diversity of powerful theoretical tools available to describe equilibrium systems has inspired strategies that map non-equilibrium systems onto equivalent equilibrium analogs so that interrogation with standard statistical mechanical approaches is possible. In this work, we revisit the mapping from the non-equilibrium random sequential addition process onto an equilibrium multi-component mixture via the replica method, allowing for theoretical predictions of non-equilibrium structural quantities. We validate the above approach by comparing the theoretical predictions to numerical simulations of random sequential addition.
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Affiliation(s)
| | | | - Thomas M. Truskett
- McKetta Department of Chemical Engineering, University of Texas at Austin, United States of America
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11
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Regarding Flows Under the Free Energy Principle. Phys Life Rev 2022; 42:25-28. [DOI: 10.1016/j.plrev.2022.05.009] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/16/2022] [Accepted: 05/23/2022] [Indexed: 11/19/2022]
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12
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A Maximum Caliber analysis of the Foldon Hypothesis. Proteins 2022; 90:1170-1178. [DOI: 10.1002/prot.26299] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/03/2021] [Revised: 12/17/2021] [Accepted: 01/06/2022] [Indexed: 01/28/2023]
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13
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Ge Y, Voelz VA. Estimation of binding rates and affinities from multiensemble Markov models and ligand decoupling. J Chem Phys 2022; 156:134115. [PMID: 35395889 PMCID: PMC8993428 DOI: 10.1063/5.0088024] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Accurate and efficient simulation of the thermodynamics and kinetics of protein-ligand interactions is crucial for computational drug discovery. Multiensemble Markov Model (MEMM) estimators can provide estimates of both binding rates and affinities from collections of short trajectories but have not been systematically explored for situations when a ligand is decoupled through scaling of non-bonded interactions. In this work, we compare the performance of two MEMM approaches for estimating ligand binding affinities and rates: (1) the transition-based reweighting analysis method (TRAM) and (2) a Maximum Caliber (MaxCal) based method. As a test system, we construct a small host-guest system where the ligand is a single uncharged Lennard-Jones (LJ) particle, and the receptor is an 11-particle icosahedral pocket made from the same atom type. To realistically mimic a protein-ligand binding system, the LJ ϵ parameter was tuned, and the system was placed in a periodic box with 860 TIP3P water molecules. A benchmark was performed using over 80 µs of unbiased simulation, and an 18-state Markov state model was used to estimate reference binding affinities and rates. We then tested the performance of TRAM and MaxCal when challenged with limited data. Both TRAM and MaxCal approaches perform better than conventional Markov state models, with TRAM showing better convergence and accuracy. We find that subsampling of trajectories to remove time correlation improves the accuracy of both TRAM and MaxCal and that in most cases, only a single biased ensemble to enhance sampled transitions is required to make accurate estimates.
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Affiliation(s)
- Yunhui Ge
- Department of Pharmaceutical Sciences, University of California, Irvine, California 92697, USA
| | - Vincent A Voelz
- Department of Chemistry, Temple University, Philadelphia, Pennsylvania 19122, USA
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14
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Tomkins M, Hughes A, Morris RJ. An update on passive transport in and out of plant cells. PLANT PHYSIOLOGY 2021; 187:1973-1984. [PMID: 35235675 PMCID: PMC8644452 DOI: 10.1093/plphys/kiab406] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/12/2021] [Accepted: 07/30/2021] [Indexed: 05/09/2023]
Abstract
Transport across membranes is critical for plant survival. Membranes are the interfaces at which plants interact with their environment. The transmission of energy and molecules into cells provides plants with the source material and power to grow, develop, defend, and move. An appreciation of the physical forces that drive transport processes is thus important for understanding the plant growth and development. We focus on the passive transport of molecules, describing the fundamental concepts and demonstrating how different levels of abstraction can lead to different interpretations of the driving forces. We summarize recent developments on quantitative frameworks for describing diffusive and bulk flow transport processes in and out of cells, with a more detailed focus on plasmodesmata, and outline open questions and challenges.
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Affiliation(s)
- Melissa Tomkins
- Computational and Systems Biology, John Innes Centre, Norwich Research Park, NR4 7UH Norwich, UK
| | - Aoife Hughes
- Computational and Systems Biology, John Innes Centre, Norwich Research Park, NR4 7UH Norwich, UK
| | - Richard J Morris
- Computational and Systems Biology, John Innes Centre, Norwich Research Park, NR4 7UH Norwich, UK
- Author for communication:
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15
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Zou Z, Tsai ST, Tiwary P. Toward Automated Sampling of Polymorph Nucleation and Free Energies with the SGOOP and Metadynamics. J Phys Chem B 2021; 125:13049-13056. [PMID: 34788047 DOI: 10.1021/acs.jpcb.1c07595] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Understanding the driving forces behind the nucleation of different polymorphs is of great importance for material sciences and the pharmaceutical industry. This includes understanding the reaction coordinate that governs the nucleation process and correctly calculating the relative free energies of different polymorphs. Here, we demonstrate, for the prototypical case of urea nucleation from the melt, how one can learn such a one-dimensional reaction coordinate as a function of prespecified order parameters and use it to perform efficient biased all-atom molecular dynamics simulations. The reaction coordinate is learnt as a function of the generic thermodynamic and structural order parameters using the "spectral gap optimization of order parameters (SGOOP)" approach [Tiwary, P. and Berne, B. J. Proc. Natl. Acad. Sci. U.S.A. (2016)] and is biased using well-tempered metadynamics simulations. The reaction coordinate gives insights into the role played by different structural and thermodynamics order parameters, and the biased simulations obtain accurate relative free energies for different polymorphs. This includes an accurate prediction of the approximate pressure at which urea undergoes a phase transition and one of the metastable polymorphs becomes the most stable conformation. We believe the ideas demonstrated in this work will facilitate efficient sampling of nucleation in complex, generic systems.
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Affiliation(s)
- Ziyue Zou
- Department of Chemistry and Biochemistry, University of Maryland, College Park, Maryland 20742, United States
| | - Sun-Ting Tsai
- Department of Physics, University of Maryland, College Park, Maryland 20742, United States.,Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, United States
| | - Pratyush Tiwary
- Department of Chemistry and Biochemistry, University of Maryland, College Park, Maryland 20742, United States.,Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, United States
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16
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Dynamic maximum entropy provides accurate approximation of structured population dynamics. PLoS Comput Biol 2021; 17:e1009661. [PMID: 34851948 PMCID: PMC8668141 DOI: 10.1371/journal.pcbi.1009661] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/14/2021] [Revised: 12/13/2021] [Accepted: 11/19/2021] [Indexed: 11/30/2022] Open
Abstract
Realistic models of biological processes typically involve interacting components on multiple scales, driven by changing environment and inherent stochasticity. Such models are often analytically and numerically intractable. We revisit a dynamic maximum entropy method that combines a static maximum entropy with a quasi-stationary approximation. This allows us to reduce stochastic non-equilibrium dynamics expressed by the Fokker-Planck equation to a simpler low-dimensional deterministic dynamics, without the need to track microscopic details. Although the method has been previously applied to a few (rather complicated) applications in population genetics, our main goal here is to explain and to better understand how the method works. We demonstrate the usefulness of the method for two widely studied stochastic problems, highlighting its accuracy in capturing important macroscopic quantities even in rapidly changing non-stationary conditions. For the Ornstein-Uhlenbeck process, the method recovers the exact dynamics whilst for a stochastic island model with migration from other habitats, the approximation retains high macroscopic accuracy under a wide range of scenarios in a dynamic environment. Complex processes in biology and physics have much in common. Collective motion of animals can be well described by models of interacting particles and emergent collective behavior can often be characterized as phase transitions of such a model. When the system is settled to a steady state, statistical physics connects random fluctuations of the process with key macroscopic quantities, using the maximum entropy method. It is thus not surprising that this method is in turn useful in understanding biological systems. However, realistic problems such as structured population dynamics, studied in our work, are set in dynamic environments, caused for instance by fluctuations in food supply. Therefore, we use the dynamical maximum entropy approximation, which allows us to reduce the full problem to simpler dynamics, without the need to track microscopic details. We focus on two processes (one in physics, one in biology) in our study: the motion of a charged particle and the dynamics of structured populations, both in a changing environment. We show that the method is extremely accurate even when the environmental changes are very fast, thus providing a powerful tool to study both biological and physical processes in changing environments.
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17
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Tsai ST, Smith Z, Tiwary P. SGOOP-d: Estimating Kinetic Distances and Reaction Coordinate Dimensionality for Rare Event Systems from Biased/Unbiased Simulations. J Chem Theory Comput 2021; 17:6757-6765. [PMID: 34662516 DOI: 10.1021/acs.jctc.1c00431] [Citation(s) in RCA: 17] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022]
Abstract
Understanding kinetics including reaction pathways and associated transition rates is an important yet difficult problem in numerous chemical and biological systems, especially in situations with multiple competing pathways. When these high-dimensional systems are projected on low-dimensional coordinates, which are often needed for enhanced sampling or for interpretation of simulations and experiments, one can end up losing the kinetic connectivity of the underlying high-dimensional landscape. Thus, in the low-dimensional projection, metastable states might appear closer or further than they actually are. To deal with this issue, in this work, we develop a formalism that learns a multidimensional yet minimally complex reaction coordinate (RC) for generic high-dimensional systems. When projected along this RC, all possible kinetically relevant pathways can be demarcated and the true high-dimensional connectivity is maintained. One of the defining attributes of our method lies in that it can work on long unbiased simulations as well as biased simulations often needed for rare event systems. We demonstrate the utility of the method by studying a range of model systems including conformational transitions in a small peptide Ace-Ala3-Nme, where we show how two-dimensional and three-dimensional RCs found by our previously published spectral gap optimization method "SGOOP" [Tiwary, P. and Berne, B. J. Proc. Natl. Acad. Sci. 2016, 113, 2839] can capture the kinetics for 23 and all 28 out of the 28 dominant state-to-state transitions, respectively.
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Affiliation(s)
- Sun-Ting Tsai
- Department of Physics and Institute for Physical Science and Technology, University of Maryland, College Park 20742, Maryland, United States
| | - Zachary Smith
- Biophysics Program and Institute for Physical Science and Technology, University of Maryland, College Park 20742, Maryland, United States
| | - Pratyush Tiwary
- Department of Chemistry and Biochemistry and Institute for Physical Science and Technology, University of Maryland, College Park 20742, Maryland, United States
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18
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Zuckerman DM, Russo JD. A gentle introduction to the non-equilibrium physics of trajectories: Theory, algorithms, and biomolecular applications. AMERICAN JOURNAL OF PHYSICS 2021; 89:1048-1061. [PMID: 35530173 PMCID: PMC9075726 DOI: 10.1119/10.0005603] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/20/2021] [Accepted: 06/25/2021] [Indexed: 06/14/2023]
Abstract
Despite the importance of non-equilibrium statistical mechanics in modern physics and related fields, the topic is often omitted from undergraduate and core-graduate curricula. Key aspects of non-equilibrium physics, however, can be understood with a minimum of formalism based on a rigorous trajectory picture. The fundamental object is the ensemble of trajectories, a set of independent time-evolving systems, which easily can be visualized or simulated (e.g., for protein folding) and which can be analyzed rigorously in analogy to an ensemble of static system configurations. The trajectory picture provides a straightforward basis for understanding first-passage times, "mechanisms" in complex systems, and fundamental constraints on the apparent reversibility of complex processes. Trajectories make concrete the physics underlying the diffusion and Fokker-Planck partial differential equations. Last but not least, trajectory ensembles underpin some of the most important algorithms that have provided significant advances in biomolecular studies of protein conformational and binding processes.
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19
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Mathematical Models with Nonlocal Initial Conditions: An Exemplification from Quantum Mechanics. MATHEMATICAL AND COMPUTATIONAL APPLICATIONS 2021. [DOI: 10.3390/mca26040073] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Abstract
Nonlocal models are ubiquitous in all branches of science and engineering, with a rapidly expanding range of mathematical and computational applications due to the ability of such models to capture effects and phenomena that traditional models cannot. While spatial nonlocalities have received considerable attention in the research community, the same cannot be said about nonlocality in time, in particular when nonlocal initial conditions are present. This paper aims at filling this gap, providing an overview of the current status of nonlocal models and focusing on the mathematical treatment of such models when nonlocal initial conditions are at the heart of the problem. Specifically, our representative example is given for a nonlocal-in-time problem for the abstract Schrödinger equation. By exploiting the linear nature of nonlocal conditions, we derive an exact representation of the solution operator under assumptions that the spectrum of Hamiltonian is contained in the horizontal strip of the complex plane. The derived representation permits us to establish the necessary and sufficient conditions for the problem’s well-posedness and the existence of its solution under different regularities. Furthermore, we present new sufficient conditions for the existence of the solution that extend the existing results in this field to the case when some nonlocal parameters are unbounded. Two further examples demonstrate the developed methodology and highlight the importance of its computer algebra component in the reduction procedures and parameter estimations for nonlocal models. Finally, a connection of the considered models and developed analysis is discussed in the context of other reduction techniques, concentrating on the most promising from the viewpoint of data-driven modelling environments, and providing directions for further generalizations.
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20
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Alston JJ, Soranno A, Holehouse AS. Integrating single-molecule spectroscopy and simulations for the study of intrinsically disordered proteins. Methods 2021; 193:116-135. [PMID: 33831596 PMCID: PMC8713295 DOI: 10.1016/j.ymeth.2021.03.018] [Citation(s) in RCA: 21] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/17/2020] [Revised: 03/25/2021] [Accepted: 03/31/2021] [Indexed: 12/21/2022] Open
Abstract
Over the last two decades, intrinsically disordered proteins and protein regions (IDRs) have emerged from a niche corner of biophysics to be recognized as essential drivers of cellular function. Various techniques have provided fundamental insight into the function and dysfunction of IDRs. Among these techniques, single-molecule fluorescence spectroscopy and molecular simulations have played a major role in shaping our modern understanding of the sequence-encoded conformational behavior of disordered proteins. While both techniques are frequently used in isolation, when combined they offer synergistic and complementary information that can help uncover complex molecular details. Here we offer an overview of single-molecule fluorescence spectroscopy and molecular simulations in the context of studying disordered proteins. We discuss the various means in which simulations and single-molecule spectroscopy can be integrated, and consider a number of studies in which this integration has uncovered biological and biophysical mechanisms.
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Affiliation(s)
- Jhullian J Alston
- Department of Biochemistry and Molecular Biophysics, Washington University School of Medicine, St. Louis 63110, MO, USA; Center for Science and Engineering of Living Systems (CSELS), Washington University in St. Louis, St. Louis 63130, MO, USA
| | - Andrea Soranno
- Department of Biochemistry and Molecular Biophysics, Washington University School of Medicine, St. Louis 63110, MO, USA; Center for Science and Engineering of Living Systems (CSELS), Washington University in St. Louis, St. Louis 63130, MO, USA.
| | - Alex S Holehouse
- Department of Biochemistry and Molecular Biophysics, Washington University School of Medicine, St. Louis 63110, MO, USA; Center for Science and Engineering of Living Systems (CSELS), Washington University in St. Louis, St. Louis 63130, MO, USA.
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21
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Barua A, Beygi A, Hatzikirou H. Close to Optimal Cell Sensing Ensures the Robustness of Tissue Differentiation Process: The Avian Photoreceptor Mosaic Case. ENTROPY 2021; 23:e23070867. [PMID: 34356408 PMCID: PMC8303396 DOI: 10.3390/e23070867] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/14/2021] [Revised: 07/05/2021] [Accepted: 07/05/2021] [Indexed: 12/22/2022]
Abstract
The way that progenitor cell fate decisions and the associated environmental sensing are regulated to ensure the robustness of the spatial and temporal order in which cells are generated towards a fully differentiating tissue still remains elusive. Here, we investigate how cells regulate their sensing intensity and radius to guarantee the required thermodynamic robustness of a differentiated tissue. In particular, we are interested in finding the conditions where dedifferentiation at cell level is possible (microscopic reversibility), but tissue maintains its spatial order and differentiation integrity (macroscopic irreversibility). In order to tackle this, we exploit the recently postulated Least microEnvironmental Uncertainty Principle (LEUP) to develop a theory of stochastic thermodynamics for cell differentiation. To assess the predictive and explanatory power of our theory, we challenge it against the avian photoreceptor mosaic data. By calibrating a single parameter, the LEUP can predict the cone color spatial distribution in the avian retina and, at the same time, suggest that such a spatial pattern is associated with quasi-optimal cell sensing. By means of the stochastic thermodynamics formalism, we find out that thermodynamic robustness of differentiated tissues depends on cell metabolism and cell sensing properties. In turn, we calculate the limits of the cell sensing radius that ensure the robustness of differentiated tissue spatial order. Finally, we further constrain our model predictions to the avian photoreceptor mosaic.
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Affiliation(s)
- Arnab Barua
- Centre for Information Services and High Performance Computing, Technische Universität Dresden, Nöthnitzer Straße 46, 01062 Dresden, Germany; (A.B.); (A.B.)
| | - Alireza Beygi
- Centre for Information Services and High Performance Computing, Technische Universität Dresden, Nöthnitzer Straße 46, 01062 Dresden, Germany; (A.B.); (A.B.)
| | - Haralampos Hatzikirou
- Centre for Information Services and High Performance Computing, Technische Universität Dresden, Nöthnitzer Straße 46, 01062 Dresden, Germany; (A.B.); (A.B.)
- Mathematics Department, Khalifa University, Abu Dhabi P.O. Box 127788, United Arab Emirates
- Correspondence:
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22
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Voelz VA, Ge Y, Raddi RM. Reconciling Simulations and Experiments With BICePs: A Review. Front Mol Biosci 2021; 8:661520. [PMID: 34046431 PMCID: PMC8144449 DOI: 10.3389/fmolb.2021.661520] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/30/2021] [Accepted: 04/12/2021] [Indexed: 02/04/2023] Open
Abstract
Bayesian Inference of Conformational Populations (BICePs) is an algorithm developed to reconcile simulated ensembles with sparse experimental measurements. The Bayesian framework of BICePs enables population reweighting as a post-simulation processing step, with several advantages over existing methods, including the proper use of reference potentials, and the estimation of a Bayes factor-like quantity called the BICePs score for model selection. Here, we summarize the theory underlying this method in context with related algorithms, review the history of BICePs applications to date, and discuss current shortcomings along with future plans for improvement.
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Affiliation(s)
- Vincent A. Voelz
- Department of Chemistry, Temple University, Philadelphia, PA, United States
| | - Yunhui Ge
- Department of Pharmaceutical Sciences, University of California, Irvine, Irvine, CA, United States
| | - Robert M. Raddi
- Department of Chemistry, Temple University, Philadelphia, PA, United States
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23
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Weistuch C, Mujica-Parodi LR, Dill K. The Refractory Period Matters: Unifying Mechanisms of Macroscopic Brain Waves. Neural Comput 2021; 33:1145-1163. [PMID: 33617741 DOI: 10.1162/neco_a_01371] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/14/2020] [Accepted: 11/16/2020] [Indexed: 11/04/2022]
Abstract
The relationship between complex brain oscillations and the dynamics of individual neurons is poorly understood. Here we utilize maximum caliber, a dynamical inference principle, to build a minimal yet general model of the collective (mean field) dynamics of large populations of neurons. In agreement with previous experimental observations, we describe a simple, testable mechanism, involving only a single type of neuron, by which many of these complex oscillatory patterns may emerge. Our model predicts that the refractory period of neurons, which has often been neglected, is essential for these behaviors.
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Affiliation(s)
- Corey Weistuch
- Laufer Center for Physical and Quantitative Biology and Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, NY 11794, U.S.A.
| | - Lilianne R Mujica-Parodi
- Laufer Center for Physical and Quantitative Biology, Departments of Biomedical Engineering and of Physics and Astronomy, Program in Neuroscience, and Department of Chemistry, Stony Brook University, Stony Brook, NY 11794, U.S.A., and Athinoula A. Martinos Center for Biomedical Imaging, Massachusetts General Hospital and Harvard Medical School, Boston, MA 02129, U.S.A.
| | - Ken Dill
- Laufer Center for Physical and Quantitative Biology, Department of Physics and Astronomy, and Department of Chemistry, Stony Brook University, Stony Brook, NY 11794, U.S.A.
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24
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Bause M, Bereau T. Reweighting non-equilibrium steady-state dynamics along collective variables. J Chem Phys 2021; 154:134105. [PMID: 33832234 DOI: 10.1063/5.0042972] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022] Open
Abstract
Computer simulations generate microscopic trajectories of complex systems at a single thermodynamic state point. We recently introduced a Maximum Caliber (MaxCal) approach for dynamical reweighting. Our approach mapped these trajectories to a Markovian description on the configurational coordinates and reweighted path probabilities as a function of external forces. Trajectory probabilities can be dynamically reweighted both from and to equilibrium or non-equilibrium steady states. As the system's dimensionality increases, an exhaustive description of the microtrajectories becomes prohibitive-even with a Markovian assumption. Instead, we reduce the dimensionality of the configurational space to collective variables (CVs). Going from configurational to CV space, we define local entropy productions derived from configurationally averaged mean forces. The entropy production is shown to be a suitable constraint on MaxCal for non-equilibrium steady states expressed as a function of CVs. We test the reweighting procedure on two systems: a particle subject to a two-dimensional potential and a coarse-grained peptide. Our CV-based MaxCal approach expands dynamical reweighting to larger systems, for both static and dynamical properties, and across a large range of driving forces.
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Affiliation(s)
- Marius Bause
- Max Planck Institute for Polymer Research, 55128 Mainz, Germany
| | - Tristan Bereau
- Max Planck Institute for Polymer Research, 55128 Mainz, Germany
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25
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Critical Comparison of MaxCal and Other Stochastic Modeling Approaches in Analysis of Gene Networks. ENTROPY 2021; 23:e23030357. [PMID: 33802879 PMCID: PMC8002683 DOI: 10.3390/e23030357] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Subscribe] [Scholar Register] [Received: 02/05/2021] [Revised: 03/09/2021] [Accepted: 03/10/2021] [Indexed: 11/24/2022]
Abstract
Learning the underlying details of a gene network with feedback is critical in designing new synthetic circuits. Yet, quantitative characterization of these circuits remains limited. This is due to the fact that experiments can only measure partial information from which the details of the circuit must be inferred. One potentially useful avenue is to harness hidden information from single-cell stochastic gene expression time trajectories measured for long periods of time—recorded at frequent intervals—over multiple cells. This raises the feasibility vs. accuracy dilemma while deciding between different models of mining these stochastic trajectories. We demonstrate that inference based on the Maximum Caliber (MaxCal) principle is the method of choice by critically evaluating its computational efficiency and accuracy against two other typical modeling approaches: (i) a detailed model (DM) with explicit consideration of multiple molecules including protein-promoter interaction, and (ii) a coarse-grain model (CGM) using Hill type functions to model feedback. MaxCal provides a reasonably accurate model while being significantly more computationally efficient than DM and CGM. Furthermore, MaxCal requires minimal assumptions since it is a top-down approach and allows systematic model improvement by including constraints of higher order, in contrast to traditional bottom-up approaches that require more parameters or ad hoc assumptions. Thus, based on efficiency, accuracy, and ability to build minimal models, we propose MaxCal as a superior alternative to traditional approaches (DM, CGM) when inferring underlying details of gene circuits with feedback from limited data.
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26
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Bhakat S. Pepsin-like aspartic proteases (PAPs) as model systems for combining biomolecular simulation with biophysical experiments. RSC Adv 2021; 11:11026-11047. [PMID: 35423571 PMCID: PMC8695779 DOI: 10.1039/d0ra10359d] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/08/2020] [Accepted: 02/21/2021] [Indexed: 01/26/2023] Open
Abstract
Pepsin-like aspartic proteases (PAPs) are a class of aspartic proteases which shares tremendous structural similarity with human pepsin. One of the key structural features of PAPs is the presence of a β-hairpin motif otherwise known as flap. The biological function of the PAPs is highly dependent on the conformational dynamics of the flap region. In apo PAPs, the conformational dynamics of the flap is dominated by the rotational degrees of freedom associated with χ1 and χ2 angles of conserved Tyr (or Phe in some cases). However it is plausible that dihedral order parameters associated with several other residues might play crucial roles in the conformational dynamics of apo PAPs. Due to their size, complexities associated with conformational dynamics and clinical significance (drug targets for malaria, Alzheimer's disease etc.), PAPs provide a challenging testing ground for computational and experimental methods focusing on understanding conformational dynamics and molecular recognition in biomolecules. The opening of the flap region is necessary to accommodate substrate/ligand in the active site of the PAPs. The BIG challenge is to gain atomistic details into how reversible ligand binding/unbinding (molecular recognition) affects the conformational dynamics. Recent reports of kinetics (K i, K d) and thermodynamic parameters (ΔH, TΔS, and ΔG) associated with macro-cyclic ligands bound to BACE1 (belongs to PAP family) provide a perfect challenge (how to deal with big ligands with multiple torsional angles and select optimum order parameters to study reversible ligand binding/unbinding) for computational methods to predict binding free energies and kinetics beyond typical test systems e.g. benzamide-trypsin. In this work, i reviewed several order parameters which were proposed to capture the conformational dynamics and molecular recognition in PAPs. I further highlighted how machine learning methods can be used as order parameters in the context of PAPs. I then proposed some open ideas and challenges in the context of molecular simulation and put forward my case on how biophysical experiments e.g. NMR, time-resolved FRET etc. can be used in conjunction with biomolecular simulation to gain complete atomistic insights into the conformational dynamics of PAPs.
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Affiliation(s)
- Soumendranath Bhakat
- Division of Biophysical Chemistry, Center for Molecular Protein Science, Department of Chemistry, Lund University P. O. Box 124 SE-22100 Lund Sweden +46-769608418
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27
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Abstract
Molecular dynamics simulations can now routinely access the microsecond timescale, making feasible direct sampling of ligand association events. While Markov State Model (MSM) approaches offer a useful framework for analyzing such trajectory data to gain insight into binding mechanisms, accurate modeling of ligand association pathways and kinetics must be done carefully. We describe methods and good practices for constructing MSMs of ligand binding from unbiased trajectory data and discuss how to use time-lagged independent component analysis (tICA) to build informative models, using as an example recent simulation work to model the binding of phenylalanine to the regulatory ACT domain dimer of phenylalanine hydroxylase. We describe a variety of methods for estimating association rates from MSMs and discuss how to distinguish between conformational selection and induced-fit mechanisms using MSMs. In addition, we review some examples of MSMs constructed to elucidate the mechanisms by which p53 transactivation domain (TAD) and related peptides bind the oncoprotein MDM2.
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Affiliation(s)
- Yunhui Ge
- Department of Chemistry, Temple University, Philadelphia, PA, USA
| | - Vincent A Voelz
- Department of Chemistry, Temple University, Philadelphia, PA, USA.
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28
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Pant S, Smith Z, Wang Y, Tajkhorshid E, Tiwary P. Confronting pitfalls of AI-augmented molecular dynamics using statistical physics. J Chem Phys 2020; 153:234118. [PMID: 33353347 PMCID: PMC7863682 DOI: 10.1063/5.0030931] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/25/2020] [Accepted: 11/29/2020] [Indexed: 12/31/2022] Open
Abstract
Artificial intelligence (AI)-based approaches have had indubitable impact across the sciences through the ability to extract relevant information from raw data. Recently, AI has also found use in enhancing the efficiency of molecular simulations, wherein AI derived slow modes are used to accelerate the simulation in targeted ways. However, while typical fields where AI is used are characterized by a plethora of data, molecular simulations, per construction, suffer from limited sampling and thus limited data. As such, the use of AI in molecular simulations can suffer from a dangerous situation where the AI-optimization could get stuck in spurious regimes, leading to incorrect characterization of the reaction coordinate (RC) for the problem at hand. When such an incorrect RC is then used to perform additional simulations, one could start to deviate progressively from the ground truth. To deal with this problem of spurious AI-solutions, here, we report a novel and automated algorithm using ideas from statistical mechanics. It is based on the notion that a more reliable AI-solution will be one that maximizes the timescale separation between slow and fast processes. To learn this timescale separation even from limited data, we use a maximum caliber-based framework. We show the applicability of this automatic protocol for three classic benchmark problems, namely, the conformational dynamics of a model peptide, ligand-unbinding from a protein, and folding/unfolding energy landscape of the C-terminal domain of protein G. We believe that our work will lead to increased and robust use of trustworthy AI in molecular simulations of complex systems.
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Affiliation(s)
- Shashank Pant
- NIH Center for Macromolecular Modeling and Bioinformatics, Beckman Institute for Advanced Science and Technology, Department of Biochemistry, Center for Biophysics and Quantitative Biology, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | | | | | - Emad Tajkhorshid
- NIH Center for Macromolecular Modeling and Bioinformatics, Beckman Institute for Advanced Science and Technology, Department of Biochemistry, Center for Biophysics and Quantitative Biology, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
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29
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Roach TNF. Use and Abuse of Entropy in Biology: A Case for Caliber. ENTROPY 2020; 22:e22121335. [PMID: 33266519 PMCID: PMC7760317 DOI: 10.3390/e22121335] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Subscribe] [Scholar Register] [Received: 10/07/2020] [Revised: 11/18/2020] [Accepted: 11/19/2020] [Indexed: 11/16/2022]
Abstract
Here, I discuss entropy and its use as a tool in fields of biology such as bioenergetics, ecology, and evolutionary biology. Statistical entropy concepts including Shannon's diversity, configurational entropy, and informational entropy are discussed in connection to their use in describing the diversity, heterogeneity, and spatial patterning of biological systems. The use of entropy as a measure of biological complexity is also discussed, and I explore the extension of thermodynamic entropy principles to open, nonequilibrium systems operating in finite time. I conclude with suggestions for use of caliber, a metric similar to entropy but for time-dependent trajectories rather than static distributions, and propose the complementary notion of path information.
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Affiliation(s)
- Ty N F Roach
- Hawai'i Institute of Marine Biology, University of Hawai'i at Mānoa, Kāne'ohe, HI 96744, USA
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30
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Weistuch C, Agozzino L, Mujica-Parodi LR, Dill KA. Inferring a network from dynamical signals at its nodes. PLoS Comput Biol 2020; 16:e1008435. [PMID: 33253160 PMCID: PMC7728228 DOI: 10.1371/journal.pcbi.1008435] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/07/2020] [Revised: 12/10/2020] [Accepted: 10/12/2020] [Indexed: 12/26/2022] Open
Abstract
We give an approximate solution to the difficult inverse problem of inferring the topology of an unknown network from given time-dependent signals at the nodes. For example, we measure signals from individual neurons in the brain, and infer how they are inter-connected. We use Maximum Caliber as an inference principle. The combinatorial challenge of high-dimensional data is handled using two different approximations to the pairwise couplings. We show two proofs of principle: in a nonlinear genetic toggle switch circuit, and in a toy neural network.
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Affiliation(s)
- Corey Weistuch
- Laufer Center for Physical and Quantitative Biology, Stony Brook University, Stony Brook, New York, USA
- Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, New York, USA
| | - Luca Agozzino
- Laufer Center for Physical and Quantitative Biology, Stony Brook University, Stony Brook, New York, USA
| | - Lilianne R. Mujica-Parodi
- Laufer Center for Physical and Quantitative Biology, Stony Brook University, Stony Brook, New York, USA
- Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York, USA
- Department of Biomedical Engineering, Stony Brook University, Stony Brook, New York, USA
- Program in Neuroscience, Stony Brook University, Stony Brook, New York, USA
- Athinoula A. Martinos Center for Biomedical Imaging, Massachusetts General Hospital and Harvard Medical School, Boston, Massachusetts, USA
| | - Ken A. Dill
- Laufer Center for Physical and Quantitative Biology, Stony Brook University, Stony Brook, New York, USA
- Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York, USA
- Department of Chemistry, Stony Brook University, Stony Brook, New York, USA
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