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Okamoto Y. Protein structure predictions by enhanced conformational sampling methods. Biophys Physicobiol 2019; 16:344-366. [PMID: 31984190 PMCID: PMC6976031 DOI: 10.2142/biophysico.16.0_344] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/05/2019] [Accepted: 08/07/2019] [Indexed: 12/01/2022] Open
Abstract
In this Special Festschrift Issue for the celebration of Professor Nobuhiro Gō's 80th birthday, we review enhanced conformational sampling methods for protein structure predictions. We present several generalized-ensemble algorithms such as multicanonical algorithm, replica-exchange method, etc. and parallel Monte Carlo or molecular dynamics method with genetic crossover. Examples of the results of these methods applied to the predictions of protein tertiary structures are also presented.
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Affiliation(s)
- Yuko Okamoto
- Department of Physics, Graduate School of Science, Nagoya University, Nagoya, Aichi 464-8602, Japan
- Structural Biology Research Center, Graduate School of Science, Nagoya University, Nagoya, Aichi 464-8602, Japan
- Center for Computational Science, Graduate School of Engineering, Nagoya University, Nagoya, Aichi 464-8603, Japan
- Information Technology Center, Nagoya University, Nagoya, Aichi 464-8601, Japan
- JST-CREST, Nagoya, Aichi 464-8602, Japan
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Ruggiero F, Aruta R, Netti PA, Torino E. Confinement of a polymer chain: An entropic study by Monte Carlo method. AIChE J 2017. [DOI: 10.1002/aic.15951] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
Affiliation(s)
- Flavia Ruggiero
- Center for Advanced Biomaterials for HealthCare; IIT@CRIB, Istituto Italiano di Tecnologia; Naples Italy
- Dept. of Chemical, Materials and Industrial Production Engineering; University of Naples Federico II; Naples Italy
| | - Rosaria Aruta
- Center for Advanced Biomaterials for HealthCare; IIT@CRIB, Istituto Italiano di Tecnologia; Naples Italy
- Dept. of Chemical, Materials and Industrial Production Engineering; University of Naples Federico II; Naples Italy
| | - Paolo Antonio Netti
- Center for Advanced Biomaterials for HealthCare; IIT@CRIB, Istituto Italiano di Tecnologia; Naples Italy
- Dept. of Chemical, Materials and Industrial Production Engineering; University of Naples Federico II; Naples Italy
- Interdisciplinary Research Center of Biomaterials, University of Naples Federico II; Naples Italy
| | - Enza Torino
- Center for Advanced Biomaterials for HealthCare; IIT@CRIB, Istituto Italiano di Tecnologia; Naples Italy
- Interdisciplinary Research Center of Biomaterials, University of Naples Federico II; Naples Italy
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Abstract
In biomolecular systems (especially all-atom models) with many degrees of freedom such as proteins and nucleic acids, there exist an astronomically large number of local-minimum-energy states. Conventional simulations in the canonical ensemble are of little use, because they tend to get trapped in states of these energy local minima. Enhanced conformational sampling techniques are thus in great demand. A simulation in generalized ensemble performs a random walk in potential energy space and can overcome this difficulty. From only one simulation run, one can obtain canonical-ensemble averages of physical quantities as functions of temperature by the single-histogram and/or multiple-histogram reweighting techniques. In this article we review uses of the generalized-ensemble algorithms in biomolecular systems. Three well-known methods, namely, multicanonical algorithm, simulated tempering, and replica-exchange method, are described first. Both Monte Carlo and molecular dynamics versions of the algorithms are given. We then present various extensions of these three generalized-ensemble algorithms. The effectiveness of the methods is tested with short peptide and protein systems.
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Affiliation(s)
- Ayori Mitsutake
- Department of Physics, Keio University, Yokohama, Kanagawa, Japan
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Vitalis A, Caflisch A. 50 Years of Lifson-Roig Models: Application to Molecular Simulation Data. J Chem Theory Comput 2011; 8:363-73. [PMID: 26592894 DOI: 10.1021/ct200744s] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Simple helix-coil transition theories have been indispensable tools in the analysis of data reporting on the reversible folding of α-helical polypeptides. They provide a transferable means to not only characterize different systems but to also compare different techniques, viz., experimental probes monitoring helix-coil transitions in vitro or biomolecular force fields in silico. This article addresses several issues with the application of Lifson-Roig theory to helix-coil transition data. We use computer simulation to generate two sets of ensembles for the temperature-controlled, reversible folding of the 21-residue, alanine-rich FS peptide. Ensembles differ in the rigidity of backbone bond angles and are analyzed using two distinct descriptors of helicity. The analysis unmasks an underlying phase diagram that is surprisingly complex. The complexities give rise to fitted nucleation and propagation parameters that are difficult to interpret and that are inconsistent with the distribution of isolated residues in the α-helical basin. We show that enthalpies of helix formation are more robustly determined using van't Hoff analysis of simple measures of helicity rather than fitted propagation parameters. To overcome some of these issues, we design a simple variant of the Lifson-Roig model that recovers physical interpretability of the obtained parameters by allowing bundle formation to be described in simple fashion. The relevance of our results is discussed in relation to the applicability of Lifson-Roig models to both in silico and in vitro data.
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Affiliation(s)
- Andreas Vitalis
- 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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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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Nowicki W, Nowicka G, Narkiewicz-Michałek J. Influence of confinement on conformational entropy of a polymer chain and structure of polymer–nanoparticles complexes. POLYMER 2009. [DOI: 10.1016/j.polymer.2009.02.044] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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8
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9
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Sikorski A. The Structure and Thermodynamics of a Heteropolymer Chain in Confinement – Computer Simulation Studies. MACROMOL THEOR SIMUL 2007. [DOI: 10.1002/mats.200700020] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
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Nowak C, Rostiashvili VG, Vilgis TA. Globular structures of a helix-coil copolymer: Self-consistent treatment. J Chem Phys 2007; 126:034902. [PMID: 17249898 DOI: 10.1063/1.2403868] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A self-consistent-field theory was developed in the grand canonical ensemble formulation to study transitions in a helix-coil multiblock globule. Helical and coil parts are treated as stiff rods and self-avoiding walks of variable lengths correspondingly. The resulting field theory takes, in addition to the conventional Zimm-Bragg, [J. Chem. Phys. 31, 526 (1959)] parameters, also three-dimensional interaction terms into account. The appropriate differential equations which determine the self-consistent fields were solved numerically with finite element method. Three different phase states are found: open chain, amorphous globule, and nematic liquid-crystalline (LC) globule. The LC-globule formation is driven by the interplay between the hydrophobic helical segment attraction and the anisotropic globule surface energy of an entropic nature. The full phase diagram of the helix-coil copolymer was calculated and thoroughly discussed. The suggested theory shows a clear interplay between secondary and tertiary structures in globular homopolypeptides.
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Affiliation(s)
- C Nowak
- Max-Planck-Institut für Polymerforschung, Ackermannweg 10, 55128 Mainz, Germany
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Sikorski A, Romiszowski P. Computer simulation of polypeptides in a confinement. J Mol Model 2006; 13:327-33. [PMID: 16977342 DOI: 10.1007/s00894-006-0147-6] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/30/2005] [Accepted: 06/27/2006] [Indexed: 10/24/2022]
Abstract
A coarse-grained model of polypeptide chains confined in a slit formed by two parallel impenetrable surfaces was studied. The chains were flexible heteropolymers (polypeptides) built of two kinds of united atoms-hydrophobic and hydrophilic. The positions of the united atoms were restricted to the vertices of a [310] lattice. The force field consisted of a rigorous excluded volume, a long-distance potential between a pair of amino-acid residues and a local preference for forming secondary structure (helices). The properties of the chains were studied at a wide range of temperatures from good to bad solvent conditions. Monte-Carlo simulations were carried out using the algorithm based on the chain's local changes of conformation and employing the Replica Exchange technique. The influence of the chain length, the distances between the confining surfaces, the temperature and the force field on the dimension and the structure of chains were studied. It was shown that the presence of the confinement chain complicates the process of the chain collapse to low-temperature structures. For some conditions, one can find a rapid decrease of chain size and a second transition indicated by the rapid decrease of the total energy of the system.
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Affiliation(s)
- Andrzej Sikorski
- Department of Chemistry, University of Warsaw, Pasteura 1, 02-093, Warsaw, Poland.
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Sikorski A, Romiszowski P. Folding Behavior of Polypeptides. A Monte Carlo Study of Simplified Models. MONATSHEFTE FUR CHEMIE 2006. [DOI: 10.1007/s00706-006-0485-1] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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13
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Sikorski A, Romiszowski P. Computer simulation of polypeptide translocation through a nanopore. J Mol Model 2005; 11:379-84. [PMID: 15806388 DOI: 10.1007/s00894-005-0254-9] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/02/2004] [Accepted: 02/07/2005] [Indexed: 11/26/2022]
Abstract
A simplified model of polypeptide chains was designed and studied by means of computer simulations. Chains were represented by a sequence of united atoms located at the positions of the alpha-carbons. A further assumption was the lattice approximation for the chains. We used a (310) lattice, which was found useful for studying properties of proteins. The force field used consisted of a long-range contact potential between amino-acid residues and a local preference for forming alpha-helical states. The chain consisted of two kinds of residues: hydrophilic (P) and hydrophobic (H) ones forming model helical septets--HHPPHPP--in a sequence. The chains were placed near an impenetrable surface with a square hole in it. The size of the hole was comparable or smaller than the size of a chain. The properties of these model chains were determined using the Monte-Carlo simulation method. During the simulations, translocation of the chain through the hole in the wall was observed. The influence of the chain length, the temperature differences on both sides of the wall and the force field on the chain properties were investigated. It was shown that the translocation time scales as N(2.2) and it was found that the presence of the local helical potential significantly slows down the process of translocation. [Figure: see text]. The snapshots of typical chain's conformation obtained during the simulation for chain consisted of N = 60. The values of the local potential epsilon(loc) = -8.
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Affiliation(s)
- Andrzej Sikorski
- Department of Chemistry, University of Warsaw, Pasteura 1, 02-093, Warszawa, Poland
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Okamoto Y. Generalized-ensemble algorithms: enhanced sampling techniques for Monte Carlo and molecular dynamics simulations. J Mol Graph Model 2004; 22:425-39. [PMID: 15099838 DOI: 10.1016/j.jmgm.2003.12.009] [Citation(s) in RCA: 272] [Impact Index Per Article: 13.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
In complex systems with many degrees of freedom such as spin glass and biomolecular systems, conventional simulations in canonical ensemble suffer from the quasi-ergodicity problem. A simulation in generalized ensemble performs a random walk in potential energy space and overcomes this difficulty. From only one simulation run, one can obtain canonical ensemble averages of physical quantities as functions of temperature by the single-histogram and/or multiple-histogram reweighting techniques. In this article we review the generalized ensemble algorithms. Three well-known methods, namely, multicanonical algorithm (MUCA), simulated tempering (ST), and replica-exchange method (REM), are described first. Both Monte Carlo (MC) and molecular dynamics (MD) versions of the algorithms are given. We then present five new generalized-ensemble algorithms which are extensions of the above methods.
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Affiliation(s)
- Yuko Okamoto
- Department of Theoretical Studies, Institute for Molecular Science, Okazaki, Aichi, Japan.
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Sikorski A, Romiszowski P. Properties of grafted amphiphilic chains. A computer simulation study. JOURNAL OF CHEMICAL INFORMATION AND COMPUTER SCIENCES 2004; 44:387-92. [PMID: 15032516 DOI: 10.1021/ci0304066] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
The model of a heteropolymer film formed by polypeptide chains was used for theoretical considerations. The linear chains consisting of amino acid residues were approximated by alpha carbon chains. Each chain was constructed on a very flexible [310] lattice. The inter- and intramolecular interactions consisted of the long-range contact potential between residues. The chains were built of hydrophilic and hydrophobic residues. Chains were terminally attached to an impenetrable surface with lateral motions possible. The Monte Carlo simulations of this model were carried out by using the Metropolis algorithm. The influence of the grafting density, the sequence of the amino acid residues, and the temperature on the static properties of the formed layer were studied and discussed. It was shown that homopolymer chains collapsed at higher temperature than the heteropolymers. The size of the polymers forming brush was smaller for homopolymers than for heteropolymers. The structure of the resulting polymer film and of its external surface was determined. The block copolymers formed well defined hydrophobic and hydrophilic layers, while for the amphiphilic case the composition of the brush layers changed continuously at high temperature. It was observed that the latter effect vanished at the collapsed amphiphilic copolymer.
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Affiliation(s)
- Andrzej Sikorski
- Department of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warszawa, Poland
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