1
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Mukuta N, Miura S. Potential energy landscape and thermodynamic transitions of coarse-grained protein models revealed by the multicanonical generalized hybrid Monte Carlo method. Biophys Physicobiol 2020; 17:14-24. [PMID: 32509490 PMCID: PMC7246090 DOI: 10.2142/biophysico.bsj-2019051] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/18/2019] [Accepted: 01/23/2020] [Indexed: 12/01/2022] Open
Abstract
In the present study, thermodynamic properties of coarse-grained protein models have been studied by an extended ensemble method. Two types of protein model were analyzed; one is categorized into a fast folder and the other into a slow folder. Both models exhibit the following thermodynamic transitions: the collapse transition between random coil states and spatially compact, but non-native states and the folding transition between the collapsed states and the folded native states. Caloric curve for the fast folder shows strong statistical ensemble dependence, while almost no ensemble dependence is found for the slow folder. Microcanonical caloric curve for the fast folder exhibits S-shaped temperature dependence on the internal energy around the collapse transition which is reminiscent of the van der Waals loop observed for the first order transition; at the transition temperature, the collapsed and random coil states coexist dynamically. The corresponding microcanonical heat capacity is found to have negative region around the transition. This kind of exotic behaviors could be utilized to distinguish fast folding proteins.
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Affiliation(s)
- Natsuki Mukuta
- Division of Mathematical and Physical Sciences, Graduate School of Natural Science and Technology, Kanazawa University, Kakuma, Kanazawa, Ishikawa 920-1192, Japan
| | - Shinichi Miura
- Faculty of Mathematics and Physics, Kanazawa University, Kakuma, Kanazawa, Ishikawa 920-1192, Japan
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2
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Takeuchi H. Two Perturbations for Geometry Optimization of Off-lattice Bead Protein Models. Mol Inform 2017; 36. [PMID: 28452128 DOI: 10.1002/minf.201600096] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/11/2016] [Accepted: 04/05/2017] [Indexed: 12/22/2022]
Abstract
Referring to the optimization algorithm previously developed for atomic clusters, the present author develops an efficient method for geometry optimization of a coarse-grained protein model expressed with two kinds of beads (hydrophilic and hydrophobic ones). In the method, two types of geometrical perturbations, center-directed bead move and one bead rotation, are used to explore new configurations and local optimizations are performed after the perturbations. The center-directed bead move is used for hydrophobic beads and the one bead rotation is performed for both hydrophobic and hydrophilic beads. The optimization method was applied to protein models consisting of 13, 20, 21, and 34 beads. The present method produced the global minima of the 13-, 21-, and 34-bead models reported in the literature and updated the lowest energies of the protein models with 20 beads. These results indicate that the present method is efficient for searching for optimal structures of proteins.
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Affiliation(s)
- Hiroshi Takeuchi
- Division of Chemistry, Graduate School of Science, Hokkaido University, Sapporo, 060-0810, Japan
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3
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Lammert H, Noel JK, Haglund E, Schug A, Onuchic JN. Constructing a folding model for protein S6 guided by native fluctuations deduced from NMR structures. J Chem Phys 2015; 143:243141. [DOI: 10.1063/1.4936881] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023] Open
Affiliation(s)
- Heiko Lammert
- Center for Theoretical Biological Physics and Department of Physics, Rice University, Houston, Texas 77005, USA
| | - Jeffrey K. Noel
- Center for Theoretical Biological Physics and Department of Physics, Rice University, Houston, Texas 77005, USA
| | - Ellinor Haglund
- Center for Theoretical Biological Physics and Department of Physics, Rice University, Houston, Texas 77005, USA
| | - Alexander Schug
- Steinbuch Centre for Computing, Karlsruhe Institute of Technology, Karlsruhe, Germany
| | - José N. Onuchic
- Center for Theoretical Biological Physics and Department of Physics, Rice University, Houston, Texas 77005, USA
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4
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Affiliation(s)
- Edyta Małolepsza
- Department
of Chemistry, Boston University, Boston, Massachusetts 02215-2521, United States
| | - Tom Keyes
- Department
of Chemistry, Boston University, Boston, Massachusetts 02215-2521, United States
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5
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Macdonald B, McCarley S, Noeen S, van Giessen AE. Protein–Protein Interactions Affect Alpha Helix Stability in Crowded Environments. J Phys Chem B 2015; 119:2956-67. [DOI: 10.1021/jp512630s] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Affiliation(s)
- Bryanne Macdonald
- Department of Chemistry, Mount Holyoke College, 50 College Street, South
Hadley, Massachusetts 01075, United States
| | - Shannon McCarley
- Department of Chemistry, Mount Holyoke College, 50 College Street, South
Hadley, Massachusetts 01075, United States
| | - Sundus Noeen
- Department of Chemistry, Mount Holyoke College, 50 College Street, South
Hadley, Massachusetts 01075, United States
| | - Alan E. van Giessen
- Department of Chemistry, Mount Holyoke College, 50 College Street, South
Hadley, Massachusetts 01075, United States
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6
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Gridnev DK, Ojeda-May P, Garcia ME. Selecting fast-folding proteins by their rate of convergence. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:012714. [PMID: 23410366 DOI: 10.1103/physreve.87.012714] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/20/2012] [Revised: 11/26/2012] [Indexed: 06/01/2023]
Abstract
We propose a general method for predicting potentially good folders from a given number of amino acid sequences. Our approach is based on the calculation of the rate of convergence of each amino acid chain towards the native structure using only the very initial parts of the dynamical trajectories. It does not require any preliminary knowledge of the native state and can be applied to different kinds of models, including atomistic descriptions. We tested the method within both the lattice and off-lattice model frameworks and obtained several so far unknown good folders. The unbiased algorithm also allows one to determine the optimal folding temperature and takes at least 3-4 orders of magnitude fewer time steps than those needed to compute folding times.
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7
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Oladepo SA, Xiong K, Hong Z, Asher SA, Handen J, Lednev IK. UV resonance Raman investigations of peptide and protein structure and dynamics. Chem Rev 2012; 112:2604-28. [PMID: 22335827 PMCID: PMC3349015 DOI: 10.1021/cr200198a] [Citation(s) in RCA: 139] [Impact Index Per Article: 11.6] [Reference Citation Analysis] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023]
Affiliation(s)
| | - Kan Xiong
- Department of Chemistry, University of Pittsburgh, Pittsburgh, PA 15260 USA
| | - Zhenmin Hong
- Department of Chemistry, University of Pittsburgh, Pittsburgh, PA 15260 USA
| | - Sanford A. Asher
- Department of Chemistry, University of Pittsburgh, Pittsburgh, PA 15260 USA
| | - Joseph Handen
- Department of Chemistry, University at Albany, SUNY, 1400 Washington Ave., Albany, NY 12222
| | - Igor K. Lednev
- Department of Chemistry, University at Albany, SUNY, 1400 Washington Ave., Albany, NY 12222
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8
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Kim J, Keyes T, Straub JE. Communication: Iteration-free, weighted histogram analysis method in terms of intensive variables. J Chem Phys 2012; 135:061103. [PMID: 21842919 DOI: 10.1063/1.3626150] [Citation(s) in RCA: 35] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present an iteration-free weighted histogram method in terms of intensive variables that directly determines the inverse statistical temperature, β(S) = ∂S/∂E, with S the microcanonical entropy. The method eliminates iterative evaluations of the partition functions intrinsic to the conventional approach and leads to a dramatic acceleration of the posterior analysis of combining statistically independent simulations with no loss in accuracy. The synergistic combination of the method with generalized ensemble weights provides insights into the nature of the underlying phase transitions via signatures in β(S) characteristic of finite size systems. The versatility and accuracy of the method is illustrated for the Ising and Potts models.
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Affiliation(s)
- Jaegil Kim
- Department of Chemistry, Boston University, Boston, Massachusetts 02215, USA.
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9
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Oakley MT, Wales DJ, Johnston RL. Energy landscape and global optimization for a frustrated model protein. J Phys Chem B 2011; 115:11525-9. [PMID: 21866973 PMCID: PMC3182752 DOI: 10.1021/jp207246m] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/29/2011] [Revised: 08/25/2011] [Indexed: 11/29/2022]
Abstract
The three-color (BLN) 69-residue model protein was designed to exhibit frustrated folding. We investigate the energy landscape of this protein using disconnectivity graphs and compare it to a Gō model, which is designed to reduce the frustration by removing all non-native attractive interactions. Finding the global minimum on a frustrated energy landscape is a good test of global optimization techniques, and we present calculations evaluating the performance of basin-hopping and genetic algorithms for this system. Comparisons are made with the widely studied 46-residue BLN protein. We show that the energy landscape of the 69-residue BLN protein contains several deep funnels, each of which corresponds to a different β-barrel structure.
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Affiliation(s)
- Mark T. Oakley
- School of Chemistry, University of Birmingham, Edgbaston, Birmingham, B15 2TT, U.K
| | - David J. Wales
- University Chemical Laboratories, Lensfield Road, Cambridge CB2 1EW, U.K
| | - Roy L. Johnston
- School of Chemistry, University of Birmingham, Edgbaston, Birmingham, B15 2TT, U.K
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Bereau T, Deserno M, Bachmann M. Structural basis of folding cooperativity in model proteins: insights from a microcanonical perspective. Biophys J 2011; 100:2764-72. [PMID: 21641322 PMCID: PMC3117192 DOI: 10.1016/j.bpj.2011.03.056] [Citation(s) in RCA: 30] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/09/2010] [Revised: 03/30/2011] [Accepted: 03/31/2011] [Indexed: 11/26/2022] Open
Abstract
Two-state cooperativity is an important characteristic in protein folding. It is defined by a depletion of states that lie energetically between folded and unfolded conformations. There are different ways to test for two-state cooperativity; however, most of these approaches probe indirect proxies of this depletion. Generalized-ensemble computer simulations allow us to unambiguously identify this transition by a microcanonical analysis on the basis of the density of states. Here, we present a detailed characterization of several helical peptides obtained by coarse-grained simulations. The level of resolution of the coarse-grained model allowed to study realistic structures ranging from small α-helices to a de novo three-helix bundle without biasing the force field toward the native state of the protein. By linking thermodynamic and structural features, we are able to show that whereas short α-helices exhibit two-state cooperativity, the type of transition changes for longer chain lengths because the chain forms multiple helix nucleation sites, stabilizing a significant population of intermediate states. The helix bundle exhibits signs of two-state cooperativity owing to favorable helix-helix interactions, as predicted from theoretical models. A detailed analysis of secondary and tertiary structure formation fits well into the framework of several folding mechanisms and confirms features that up to now have been observed only in lattice models.
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Affiliation(s)
- Tristan Bereau
- Department of Physics, Carnegie Mellon University, Pittsburgh, Pennsylvania
| | - Markus Deserno
- Department of Physics, Carnegie Mellon University, Pittsburgh, Pennsylvania
| | - Michael Bachmann
- Center for Simulational Physics, Department of Physics and Astronomy, University of Georgia, Athens, Georgia
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11
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Kim J, Straub JE. Generalized simulated tempering for exploring strong phase transitions. J Chem Phys 2011; 133:154101. [PMID: 20969364 DOI: 10.1063/1.3503503] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
An extension of the simulation tempering algorithm is proposed. It is shown to be particularly suited to the exploration of first-order phase transition systems characterized by the backbending or S-loop in the statistical temperature or a microcanonical caloric curve. A guided Markov process in an auxiliary parameter space systematically combines a set of parametrized Tsallis-weight ensemble simulations, which are targeted to transform unstable or metastable energy states of canonical ensembles into stable ones and smoothly join ordered and disordered phases across phase transition regions via a succession of unimodal energy distributions. The inverse mapping between the sampling weight and the effective temperature enables an optimal selection of relevant Tsallis-weight parameters. A semianalytic expression for the biasing weight in parameter space is adaptively updated "on the fly" during the simulation to achieve rapid convergence. Accelerated tunneling transitions with a comprehensive sampling for phase-coexistent states are explicitly demonstrated in systems subject to strong hysteresis including Potts and Ising spin models and a 147 atom Lennard-Jones cluster.
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Affiliation(s)
- Jaegil Kim
- Department of Chemistry, Boston University, Boston, Massachusetts 02215, USA.
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12
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Kim J, Keyes T, Straub JE. Generalized replica exchange method. J Chem Phys 2010; 132:224107. [PMID: 20550390 PMCID: PMC2896417 DOI: 10.1063/1.3432176] [Citation(s) in RCA: 74] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/24/2010] [Accepted: 04/30/2010] [Indexed: 01/28/2023] Open
Abstract
We present a powerful replica exchange method, particularly suited to first-order phase transitions associated with the backbending in the statistical temperature, by merging an optimally designed generalized ensemble sampling with replica exchanges. The key ingredients of our method are parametrized effective sampling weights, smoothly joining ordered and disordered phases with a succession of unimodal energy distributions by transforming unstable or metastable energy states of canonical ensembles into stable ones. The inverse mapping between the sampling weight and the effective temperature provides a systematic way to design the effective sampling weights and determine a dynamic range of relevant parameters. Illustrative simulations on Potts spins with varying system size and simulation conditions demonstrate a comprehensive sampling for phase-coexistent states with a dramatic acceleration of tunneling transitions. A significant improvement over the power-law slowing down of mean tunneling times with increasing system size is obtained, and the underlying mechanism for accelerated tunneling is discussed.
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Affiliation(s)
- Jaegil Kim
- Department of Chemistry, Boston University, Boston, Massachusetts 02215, USA.
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13
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Abstract
Molecular dynamics (MD) simulations provide essential information about the thermodynamics and dynamics of proteins. To construct the free-energy surface from equilibrium trajectories, it is necessary to group the individual snapshots in a meaningful way. The inherent structures (IS) are shown to provide an appropriate discretization of the trajectory and to avoid problems that can arise in clustering algorithms that have been employed previously. The IS-based approach is illustrated with a 30-ns room temperature "native" state MD simulation of a 10-residue peptide in a beta-hairpin conformation. The transitions between the IS are used to construct a configuration space network from which a one-dimensional free-energy profile is obtained with the mincut method. The results demonstrate that the IS approach is useful and that even for this simple system, there exists a nontrivial organization of the native state into several valleys separated by barriers as high as 3 kcal/mol. Further, by introducing a coarse-grained network, it is demonstrated that there are multiple pathways connecting the valleys. This scenario is hidden when the snapshots of the trajectory are used directly with rmsd clustering to compute the free-energy profile. Application of the IS approach to the native state of the PDZ2 signaling domain indicates its utility for the study of biologically relevant systems.
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Affiliation(s)
- Francesco Rao
- Laboratoire de Chimie Biophysique, Institut de Science et d’Ingénierie Supramoléculaires, Université de Strasbourg, 67000 Strasbourg, France; and
| | - Martin Karplus
- Laboratoire de Chimie Biophysique, Institut de Science et d’Ingénierie Supramoléculaires, Université de Strasbourg, 67000 Strasbourg, France; and
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA 02138
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