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Chen YT, Yang H, Chu JW. Trajectory Statistical Learning of the Potential Mean of Force and Diffusion Coefficient from Molecular Dynamics Simulations. J Phys Chem B 2024; 128:56-66. [PMID: 38165090 DOI: 10.1021/acs.jpcb.3c05245] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2024]
Abstract
Central to studying the conformational changes of a complex protein is understanding the dynamics and energetics involved. Phenomenologically, structural dynamics can be formulated using an overdamped Langevin model along an observable, e.g., the distance between two residues in the protein. The Langevin model is specified by the deterministic force (the potential of mean force, PMF) and stochastic force (characterized by the diffusion coefficient, D). It is therefore of great interest to be able to extract both PMF and D from an observable time series but under the same computational framework. Here, we approach this challenge in molecular dynamics (MD) simulations by treating it as a missing-data Bayesian estimation problem. An important distinction in our methodology is that the entire MD trajectory, as opposed to the individual data elements, is used as the statistical variable in Bayesian imputation. This idea is implemented through an eigen-decomposition procedure for a time-symmetrized Fokker-Planck equation, followed by maximizing the likelihood for parameter estimation. The mathematical expressions for the functional derivatives used in learning PMF and D also provide new physical insights for the manner by which the information on both the deterministic and stochastic forces is encoded in the dynamics data. An all-atom MD simulation of a nontrivial biomolecule case is used to illustrate the application of this approach. We show that, interestingly, the results of trajectory statistical learning can motivate new order parameters for an improved description of the kinetic bottlenecks in conformational changes. Complementing purely data-driven or black-box methods, this work underscores the advantages of physics-based machine learning in gaining chemical insights from quantitative parameter estimation.
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Affiliation(s)
- Yi-Tsao Chen
- Institute of Bioinformatics and Systems Biology, National Yang Ming Chiao Tung University, Hsinchu 30010, Taiwan, Republic of China
| | - Haw Yang
- Department of Chemistry, Princeton University, Princeton, New Jersey 08544, United States
| | - Jhih-Wei Chu
- Institute of Bioinformatics and Systems Biology, Department of Biological Science and Technology, Institute of Molecular Medicine and Bioengineering, and Center for Intelligent Drug Systems and Smart Bio-Devices (IDS2B), National Yang Ming Chiao Tung University, Hsinchu 30010, Taiwan, Republic of China
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2
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Blöchliger N, Caflisch A, Vitalis A. Weighted Distance Functions Improve Analysis of High-Dimensional Data: Application to Molecular Dynamics Simulations. J Chem Theory Comput 2015; 11:5481-92. [DOI: 10.1021/acs.jctc.5b00618] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Nicolas Blöchliger
- Department of Biochemistry, University of Zurich, Winterthurerstrasse
190, CH-8057 Zurich, Zurich, Switzerland
| | - Amedeo Caflisch
- Department of Biochemistry, University of Zurich, Winterthurerstrasse
190, CH-8057 Zurich, Zurich, Switzerland
| | - Andreas Vitalis
- Department of Biochemistry, University of Zurich, Winterthurerstrasse
190, CH-8057 Zurich, Zurich, Switzerland
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3
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Chekmarev SF. Equilibration of Protein States: A Time Dependent Free-Energy Disconnectivity Graph. J Phys Chem B 2015; 119:8340-8. [PMID: 26068182 DOI: 10.1021/acs.jpcb.5b04336] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The process of equilibration of protein states in a three-stranded antiparallel β-sheet miniprotein is studied using a time-dependent free energy disconnectivity graph. To determine the rates of transitions, the molecular dynamics simulation results of a recent work (Kalgin, I. V.; J. Phys. Chem. B 2013, 117, 6092) are employed. The vertices of the graph are the free energies of characteristic states of the protein, and the edges are the transition state free energies. To determine the latter, the "complete" partition function (Eyring, 1935) is used, which includes the translational partition function corresponding to the ballistic motion of the system along the reaction coordinate. The distance along the reaction coordinate that enters the translational partition function is taken to be proportional to the observation time and thus measures the number of representative points that cross the transition state surface during given time. As the time increases, the free energy barriers between the clusters of characteristic conformations (native-like, helical, and β-sheet conformations of different degree of organization) decrease and (local) equilibrium between the clusters is established. With time, these clusters are grouped into larger clusters, extending the equilibrium to a larger portion of protein states.
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Affiliation(s)
- Sergei F Chekmarev
- †Institute of Thermophysics, SB RAS, 630090 Novosibirsk, Russia.,‡Department of Physics, Novosibirsk State University, 630090 Novosibirsk, Russia
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4
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Wales DJ. Perspective: Insight into reaction coordinates and dynamics from the potential energy landscape. J Chem Phys 2015; 142:130901. [DOI: 10.1063/1.4916307] [Citation(s) in RCA: 73] [Impact Index Per Article: 8.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2023] Open
Affiliation(s)
- D. J. Wales
- University Chemical Laboratories, Lensfield Road, Cambridge CB2 1EW, United Kingdom
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5
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Kalgin IV, Chekmarev SF. Folding of a β-sheet miniprotein: probability fluxes, streamlines, and the potential for the driving force. J Phys Chem B 2015; 119:1380-7. [PMID: 25544646 DOI: 10.1021/jp5112795] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
In this work we continue the study of the first-passage folding of an antiparallel β-sheet miniprotein (beta3s) that was initiated in the previous work [Kalgin et al. J. Phys. Chem. B, 2014, 118, 4287]. We consider a larger ensemble of folding trajectories, which allows us to gain a closer insight into the folding dynamics. In particular, we calculate the potential for the driving force of folding in a reduced space of collective variables. The potential has two components. One component (Φ) is responsible for the source and sink of the folding flow, which are formed, respectively, in the regions of the unfolded and native states of the protein, and the other (Ψ) accounts for the flow vorticity inherently generated at the sides of the reaction channel and provides the canalization of the folding flow between the source and sink. We show that both components obey Poisson's equations with the corresponding source/sink terms. The resulting components have a very simple form: the Φ-surface consists of two well-defined peaks of different signs, which correspond, respectively, to the source and sink of the folding flow, and the Ψ-surface consists of two ridges of different signs that connect the source and sink of the flow.
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Affiliation(s)
- Igor V Kalgin
- Institute of Thermophysics, Siberian Branch of the Russian Academy of Sciences, 630090 Novosibirsk, Russia
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6
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Zheng W, Vargiu AV, Vargiu AV, Rohrdanz MA, Carloni P, Clementi C. Molecular recognition of DNA by ligands: roughness and complexity of the free energy profile. J Chem Phys 2014; 139:145102. [PMID: 24116648 DOI: 10.1063/1.4824106] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Understanding the molecular mechanism by which probes and chemotherapeutic agents bind to nucleic acids is a fundamental issue in modern drug design. From a computational perspective, valuable insights are gained by the estimation of free energy landscapes as a function of some collective variables (CVs), which are associated with the molecular recognition event. Unfortunately the choice of CVs is highly non-trivial because of DNA's high flexibility and the presence of multiple association-dissociation events at different locations and/or sliding within the grooves. Here we have applied a modified version of Locally-Scaled Diffusion Map (LSDMap), a nonlinear dimensionality reduction technique for decoupling multiple-timescale dynamics in macromolecular systems, to a metadynamics-based free energy landscape calculated using a set of intuitive CVs. We investigated the binding of the organic drug anthramycin to a DNA 14-mer duplex. By performing an extensive set of metadynamics simulations, we observed sliding of anthramycin along the full-length DNA minor groove, as well as several detachments from multiple sites, including the one identified by X-ray crystallography. As in the case of equilibrium processes, the LSDMap analysis is able to extract the most relevant collective motions, which are associated with the slow processes within the system, i.e., ligand diffusion along the minor groove and dissociation from it. Thus, LSDMap in combination with metadynamics (and possibly every equivalent method) emerges as a powerful method to describe the energetics of ligand binding to DNA without resorting to intuitive ad hoc reaction coordinates.
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Affiliation(s)
- Wenwei Zheng
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
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7
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Kalgin IV, Chekmarev SF, Karplus M. First passage analysis of the folding of a β-sheet miniprotein: is it more realistic than the standard equilibrium approach? J Phys Chem B 2014; 118:4287-99. [PMID: 24669953 PMCID: PMC4002127 DOI: 10.1021/jp412729r] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
![]()
Simulations of first-passage folding
of the antiparallel β-sheet
miniprotein beta3s, which has been intensively studied under equilibrium
conditions by A. Caflisch and co-workers, show that the kinetics and
dynamics are significantly different from those for equilibrium folding.
Because the folding of a protein in a living system generally corresponds
to the former (i.e., the folded protein is stable and unfolding is
a rare event), the difference is of interest. In contrast to equilibrium
folding, the Ch-curl conformations become very rare because they contain
unfavorable parallel β-strand arrangements, which are difficult
to form dynamically due to the distant N- and C-terminal strands.
At the same time, the formation of helical conformations becomes much
easier (particularly in the early stage of folding) due to short-range
contacts. The hydrodynamic descriptions of the folding reaction have
also revealed that while the equilibrium flow field presented a collection
of local vortices with closed ”streamlines”, the first-passage
folding is characterized by a pronounced overall flow from the unfolded
states to the native state. The flows through the locally stable structures
Cs-or and Ns-or, which are conformationally close to the native state,
are negligible due to detailed balance established between these structures
and the native state. Although there are significant differences in
the general picture of the folding process from the equilibrium and
first-passage folding simulations, some aspects of the two are in
agreement. The rate of transitions between the clusters of characteristic
protein conformations in both cases decreases approximately exponentially
with the distance between the clusters in the hydrogen bond distance
space of collective variables, and the folding time distribution in
the first-passage segments of the equilibrium trajectory is in good
agreement with that for the first-passage folding simulations.
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Affiliation(s)
- Igor V Kalgin
- Department of Physics, Novosibirsk State University , 630090 Novosibirsk, Russia
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8
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Li W, Ma A. Recent developments in methods for identifying reaction coordinates. MOLECULAR SIMULATION 2014; 40:784-793. [PMID: 25197161 PMCID: PMC4152980 DOI: 10.1080/08927022.2014.907898] [Citation(s) in RCA: 44] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
Abstract
In the study of rare events in complex systems with many degrees of freedom, a key element is to identify the reaction coordinates of a given process. Over recent years, a number of methods and protocols have been developed to extract the reaction coordinates based on limited information from molecular dynamics simulations. In this review, we provide a brief survey over a number of major methods developed in the past decade, some of which are discussed in greater detail, to provide an overview of the problems that are partially solved and challenges that still remain. A particular emphasis has been placed on methods for identifying reaction coordinates that are related to the committor.
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Affiliation(s)
- Wenjin Li
- Department of Bioengineering, The University of Illinois at Chicago, 851 South Morgan Street, Chicago, IL 60607, USA
| | - Ao Ma
- Department of Bioengineering, The University of Illinois at Chicago, 851 South Morgan Street, Chicago, IL 60607, USA
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9
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Mori T, Hamers RJ, Pedersen JA, Cui Q. An Explicit Consideration of Desolvation is Critical to Binding Free Energy Calculations of Charged Molecules at Ionic Surfaces. J Chem Theory Comput 2013; 9:5059-69. [DOI: 10.1021/ct400487e] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023]
Affiliation(s)
- Toshifumi Mori
- Department
of Chemistry and Theoretical Chemistry Institute, University of Wisconsin—Madison, 1101 University Avenue, Madison, Wisconsin 53706, United States
| | - Robert J. Hamers
- Department of Chemistry, University of Wisconsin—Madison, 1101 University Avenue, Madison, Wisconsin 53706, United States
| | - Joel A. Pedersen
- Department of Soil Science, Civil & Environmental Engineering, and Chemistry, University of Wisconsin—Madison, 1525 Observatory Drive, Madison, Wisconsin 53706, United States
| | - Qiang Cui
- Department
of Chemistry and Theoretical Chemistry Institute, University of Wisconsin—Madison, 1101 University Avenue, Madison, Wisconsin 53706, United States
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10
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Kalgin IV, Caflisch A, Chekmarev SF, Karplus M. New insights into the folding of a β-sheet miniprotein in a reduced space of collective hydrogen bond variables: application to a hydrodynamic analysis of the folding flow. J Phys Chem B 2013; 117:6092-105. [PMID: 23621790 DOI: 10.1021/jp401742y] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
A new analysis of the 20 μs equilibrium folding/unfolding molecular dynamics simulations of the three-stranded antiparallel β-sheet miniprotein (beta3s) in implicit solvent is presented. The conformation space is reduced in dimensionality by introduction of linear combinations of hydrogen bond distances as the collective variables making use of a specially adapted principal component analysis (PCA); i.e., to make structured conformations more pronounced, only the formed bonds are included in determining the principal components. It is shown that a three-dimensional (3D) subspace gives a meaningful representation of the folding behavior. The first component, to which eight native hydrogen bonds make the major contribution (four in each beta hairpin), is found to play the role of the reaction coordinate for the overall folding process, while the second and third components distinguish the structured conformations. The representative points of the trajectory in the 3D space are grouped into conformational clusters that correspond to locally stable conformations of beta3s identified in earlier work. A simplified kinetic network based on the three components is constructed, and it is complemented by a hydrodynamic analysis. The latter, making use of "passive tracers" in 3D space, indicates that the folding flow is much more complex than suggested by the kinetic network. A 2D representation of streamlines shows there are vortices which correspond to repeated local rearrangement, not only around minima of the free energy surface but also in flat regions between minima. The vortices revealed by the hydrodynamic analysis are apparently not evident in folding pathways generated by transition-path sampling. Making use of the fact that the values of the collective hydrogen bond variables are linearly related to the Cartesian coordinate space, the RMSD between clusters is determined. Interestingly, the transition rates show an approximate exponential correlation with distance in the hydrogen bond subspace. Comparison with the many published studies shows good agreement with the present analysis for the parts that can be compared, supporting the robust character of our understanding of this "hydrogen atom" of protein folding.
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Affiliation(s)
- Igor V Kalgin
- Department of Physics, Novosibirsk State University, 630090 Novosibirsk, Russia
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11
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Dama JF, Sinitskiy AV, McCullagh M, Weare J, Roux B, Dinner AR, Voth GA. The Theory of Ultra-Coarse-Graining. 1. General Principles. J Chem Theory Comput 2013; 9:2466-80. [PMID: 26583735 DOI: 10.1021/ct4000444] [Citation(s) in RCA: 117] [Impact Index Per Article: 10.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/02/2023]
Abstract
Coarse-grained (CG) models provide a computationally efficient means to study biomolecular and other soft matter processes involving large numbers of atoms correlated over distance scales of many covalent bond lengths and long time scales. Variational methods based on information from simulations of finer-grained (e.g., all-atom) models, for example the multiscale coarse-graining (MS-CG) and relative entropy minimization methods, provide attractive tools for the systematic development of CG models. However, these methods have important drawbacks when used in the "ultra-coarse-grained" (UCG) regime, e.g., at a resolution level coarser or much coarser than one amino acid residue per effective CG particle in proteins. This is due to the possible existence of multiple metastable states "within" the CG sites for a given UCG model configuration. In this work, systematic variational UCG methods are presented that are specifically designed to CG entire protein domains and subdomains into single effective CG particles. This is accomplished by augmenting existing effective particle CG schemes to allow for discrete state transitions and configuration-dependent resolution. Additionally, certain conclusions of this work connect back to single-state force matching and open up new avenues for method development in that area. These results provide a formal statistical mechanical basis for UCG methods related to force matching and relative entropy CG methods and suggest practical algorithms for constructing optimal approximate UCG models from fine-grained simulation data.
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Affiliation(s)
- James F Dama
- Department of Chemistry and Institute for Biophysical Dynamics, ‡Computation Institute, §James Franck Institute, ∥Department of Mathematics, ⊥Department of Biochemistry and Molecular Biology, University of Chicago , Chicago, Illinois 60637, United States
| | - Anton V Sinitskiy
- Department of Chemistry and Institute for Biophysical Dynamics, ‡Computation Institute, §James Franck Institute, ∥Department of Mathematics, ⊥Department of Biochemistry and Molecular Biology, University of Chicago , Chicago, Illinois 60637, United States
| | - Martin McCullagh
- Department of Chemistry and Institute for Biophysical Dynamics, ‡Computation Institute, §James Franck Institute, ∥Department of Mathematics, ⊥Department of Biochemistry and Molecular Biology, University of Chicago , Chicago, Illinois 60637, United States
| | - Jonathan Weare
- Department of Chemistry and Institute for Biophysical Dynamics, ‡Computation Institute, §James Franck Institute, ∥Department of Mathematics, ⊥Department of Biochemistry and Molecular Biology, University of Chicago , Chicago, Illinois 60637, United States
| | - Benoît Roux
- Department of Chemistry and Institute for Biophysical Dynamics, ‡Computation Institute, §James Franck Institute, ∥Department of Mathematics, ⊥Department of Biochemistry and Molecular Biology, University of Chicago , Chicago, Illinois 60637, United States
| | - Aaron R Dinner
- Department of Chemistry and Institute for Biophysical Dynamics, ‡Computation Institute, §James Franck Institute, ∥Department of Mathematics, ⊥Department of Biochemistry and Molecular Biology, University of Chicago , Chicago, Illinois 60637, United States
| | - Gregory A Voth
- Department of Chemistry and Institute for Biophysical Dynamics, ‡Computation Institute, §James Franck Institute, ∥Department of Mathematics, ⊥Department of Biochemistry and Molecular Biology, University of Chicago , Chicago, Illinois 60637, United States
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12
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Guttenberg N, Dama JF, Saunders MG, Voth GA, Weare J, Dinner AR. Minimizing memory as an objective for coarse-graining. J Chem Phys 2013; 138:094111. [DOI: 10.1063/1.4793313] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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13
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Zhou T, Caflisch A. Distribution of Reciprocal of Interatomic Distances: A Fast Structural Metric. J Chem Theory Comput 2012; 8:2930-7. [PMID: 26592131 DOI: 10.1021/ct3003145] [Citation(s) in RCA: 38] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/08/2023]
Abstract
We present a structural metric based on the Distribution of Reciprocal of Interatomic Distances (DRID) for evaluating geometrical similarity between two conformations of a molecule. A molecular conformation is described by a vector of 3N orientation-independent DRID descriptors where N is the number of molecular centroids, for example, the non-hydrogen atoms in all nonsymmetric groups of a peptide. For two real-world applications (pairwise comparison of snapshots from an explicit solvent simulation of a protease/peptide substrate complex and implicit solvent simulations of reversible folding of a 20-residue β-sheet peptide), the DRID-based metric is shown to be about 5 and 15 times faster than coordinate root-mean-square deviation (cRMSD) and distance root-mean-square deviation (dRMSD), respectively. A single core of a mainstream processor can perform about 10(8) DRID comparisons in one-half a minute. Importantly, the DRID metric has closer similarity to kinetic distance than does either cRMSD or dRMSD. Therefore, DRID is suitable for clustering molecular dynamics trajectories for kinetic analysis, for example, by Markov state models. Moreover, conformational space networks and free energy profiles derived by DRID-based clustering preserve the kinetic information.
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Affiliation(s)
- Ting Zhou
- Department of Biochemistry, University of Zurich , CH-8057 Zurich, Switzerland
| | - Amedeo Caflisch
- Department of Biochemistry, University of Zurich , CH-8057 Zurich, Switzerland
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14
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Abstract
A free energy-guided sampling (FEGS) method is proposed for accelerating exploration of conformational space in unbiased molecular dynamics. Using the cut-based free energy profile and Markov state models, FEGS speeds up sampling of the canonical ensemble by iteratively restarting multiple short simulations in parallel from regions of the free energy surface visited rarely. This exploration stage is followed by a refinement stage in which multiple independent runs are initiated from Boltzmann distributed conformations. Notably, FEGS does not require either collective variables or reaction coordinates and can control the kinetic distance from the starting conformation. We applied FEGS to the alanine dipeptide, which has a human-comprehensible two-dimensional free energy landscape, and a three-stranded antiparallel β-sheet peptide of 20 residues whose folding/unfolding process is governed by a delicate interplay of enthalpy and entropy. For these two systems, FEGS speeds up the exploration of conformational space by 1 to 2 orders of magnitude with respect to conventional sampling and preserves the basins and barriers on the free energy profile.
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Affiliation(s)
- Ting Zhou
- Department of Biochemistry, University of Zurich, CH-8057 Zurich, Switzerland
| | - Amedeo Caflisch
- Department of Biochemistry, University of Zurich, CH-8057 Zurich, Switzerland
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15
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16
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Zheng W, Qi B, Rohrdanz MA, Caflisch A, Dinner AR, Clementi C. Delineation of folding pathways of a β-sheet miniprotein. J Phys Chem B 2011; 115:13065-74. [PMID: 21942785 DOI: 10.1021/jp2076935] [Citation(s) in RCA: 41] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Several methods have been developed in the past few years for the analysis of molecular dynamics simulations of biological (macro)molecules whose complexity is difficult to capture by simple projections of the free-energy surface onto one or two geometric variables. The locally scaled diffusion map (LSDMap) method is a nonlinear dimensionality reduction technique for describing the dynamics of complex systems in terms of a few collective coordinates. Here, we compare LSDMap to two previously developed approaches for the characterization of the configurational landscape associated with the folding dynamics of a three-stranded antiparallel β-sheet peptide, termed Beta3s. The analysis is aided by an improved procedure for extracting pathways from the equilibrium transition network, which enables calculation of pathway-specific cut-based free energy profiles. We find that the results from LSDMap are consistent with analysis based on transition networks and allow a coherent interpretation of metastable states and folding pathways in terms of different time scales of transitions between minima on the free energy projections.
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Affiliation(s)
- Wenwei Zheng
- Department of Chemistry, Rice University, Houston, Texas 77005, United States
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17
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Rohrdanz MA, Zheng W, Maggioni M, Clementi C. Determination of reaction coordinates via locally scaled diffusion map. J Chem Phys 2011; 134:124116. [DOI: 10.1063/1.3569857] [Citation(s) in RCA: 194] [Impact Index Per Article: 14.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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18
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Pellarin R, Schuetz P, Guarnera E, Caflisch A. Amyloid Fibril Polymorphism Is under Kinetic Control. J Am Chem Soc 2010; 132:14960-70. [DOI: 10.1021/ja106044u] [Citation(s) in RCA: 102] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Riccardo Pellarin
- Department of Biochemistry, University of Zurich, Winterthurerstrasse 190, CH-8057 Zurich, Switzerland
| | - Philipp Schuetz
- Department of Biochemistry, University of Zurich, Winterthurerstrasse 190, CH-8057 Zurich, Switzerland
| | - Enrico Guarnera
- Department of Biochemistry, University of Zurich, Winterthurerstrasse 190, CH-8057 Zurich, Switzerland
| | - Amedeo Caflisch
- Department of Biochemistry, University of Zurich, Winterthurerstrasse 190, CH-8057 Zurich, Switzerland
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19
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Buchner GS, Murphy RD, Buchete NV, Kubelka J. Dynamics of protein folding: probing the kinetic network of folding-unfolding transitions with experiment and theory. BIOCHIMICA ET BIOPHYSICA ACTA-PROTEINS AND PROTEOMICS 2010; 1814:1001-20. [PMID: 20883829 DOI: 10.1016/j.bbapap.2010.09.013] [Citation(s) in RCA: 44] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/2010] [Revised: 09/14/2010] [Accepted: 09/16/2010] [Indexed: 10/19/2022]
Abstract
The problem of spontaneous folding of amino acid chains into highly organized, biologically functional three-dimensional protein structures continues to challenge the modern science. Understanding how proteins fold requires characterization of the underlying energy landscapes as well as the dynamics of the polypeptide chains in all stages of the folding process. In recent years, important advances toward these goals have been achieved owing to the rapidly growing interdisciplinary interest and significant progress in both experimental techniques and theoretical methods. Improvements in the experimental time resolution led to determination of the timescales of the important elementary events in folding, such as formation of secondary structure and tertiary contacts. Sensitive single molecule methods made possible probing the distributions of the unfolded and folded states and following the folding reaction of individual protein molecules. Discovery of proteins that fold in microseconds opened the possibility of atomic-level theoretical simulations of folding and their direct comparisons with experimental data, as well as of direct experimental observation of the barrier-less folding transition. The ultra-fast folding also brought new questions, concerning the intrinsic limits of the folding rates and experimental signatures of barrier-less "downhill" folding. These problems will require novel approaches for even more detailed experimental investigations of the folding dynamics as well as for the analysis of the folding kinetic data. For theoretical simulations of folding, a main challenge is how to extract the relevant information from overwhelmingly detailed atomistic trajectories. New theoretical methods have been devised to allow a systematic approach towards a quantitative analysis of the kinetic network of folding-unfolding transitions between various configuration states of a protein, revealing the transition states and the associated folding pathways at multiple levels, from atomistic to coarse-grained representations. This article is part of a Special Issue entitled: Protein Dynamics: Experimental and Computational Approaches.
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Affiliation(s)
- Ginka S Buchner
- Department of Chemistry, University of Wyoming, Laramie, WY 82071, USA; Universität Würzbug, Würzburg, Germany
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