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Yaoqi Zhou - One of the best experts on this subject based on the ideXlab platform.
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Assembly and kinetic folding pathways of a tetrameric beta-sheet complex: molecular dynamics simulations on simplified off-Lattice Protein models.
Biophysical journal, 2004Co-Authors: Hyunbum Jang, Carol K Hall, Yaoqi ZhouAbstract:We have performed discontinuous molecular dynamic simulations of the assembly and folding kinetics of a tetrameric beta-sheet complex that contains four identical four-stranded antiparallel beta-sheet peptides. The potential used in the simulation is a hybrid Go-type potential characterized by the bias gap parameter g, an artificial measure of a model Protein's preference for its native state, and the intermolecular contact parameter eta, which measures the ratio of intermolecular to intramolecular native attractions. The formation of the beta-sheet complex and its equilibrium properties strongly depend on the size of the intermolecular contact parameter eta. The ordered beta-sheet complex in the folded state and nonaligned beta-sheets or tangled chains in the misfolded state are distinguished by measuring the squared radius of gyration Rg2 and the fraction of native contacts Q. The folding yield for the folded state is high at intermediate values of eta, but is low at both small and large values of eta. The folded state at small eta is liquid-like, but is solid-like at both intermediate and large eta. The misfolded state at small eta contains nonaligned beta-sheets and tangled chains with poor secondary structure at large eta. Various folding pathways via dimeric and trimeric intermediates are observed, depending on eta. Comparison with experimental results on Protein aggregation indicates that intermediate eta values are most appropriate for modeling fibril formation and small eta values are most appropriate for modeling the formation of amorphous aggregates.
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assembly and kinetic folding pathways of a tetrameric β sheet complex molecular dynamics simulations on simplified off Lattice Protein models
Biophysical Journal, 2004Co-Authors: Hyunbum Jang, Carol K Hall, Yaoqi ZhouAbstract:We have performed discontinuous molecular dynamic simulations of the assembly and folding kinetics of a tetrameric beta-sheet complex that contains four identical four-stranded antiparallel beta-sheet peptides. The potential used in the simulation is a hybrid Go-type potential characterized by the bias gap parameter g, an artificial measure of a model Protein's preference for its native state, and the intermolecular contact parameter eta, which measures the ratio of intermolecular to intramolecular native attractions. The formation of the beta-sheet complex and its equilibrium properties strongly depend on the size of the intermolecular contact parameter eta. The ordered beta-sheet complex in the folded state and nonaligned beta-sheets or tangled chains in the misfolded state are distinguished by measuring the squared radius of gyration Rg2 and the fraction of native contacts Q. The folding yield for the folded state is high at intermediate values of eta, but is low at both small and large values of eta. The folded state at small eta is liquid-like, but is solid-like at both intermediate and large eta. The misfolded state at small eta contains nonaligned beta-sheets and tangled chains with poor secondary structure at large eta. Various folding pathways via dimeric and trimeric intermediates are observed, depending on eta. Comparison with experimental results on Protein aggregation indicates that intermediate eta values are most appropriate for modeling fibril formation and small eta values are most appropriate for modeling the formation of amorphous aggregates.
Hyunbum Jang - One of the best experts on this subject based on the ideXlab platform.
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Assembly and kinetic folding pathways of a tetrameric beta-sheet complex: molecular dynamics simulations on simplified off-Lattice Protein models.
Biophysical journal, 2004Co-Authors: Hyunbum Jang, Carol K Hall, Yaoqi ZhouAbstract:We have performed discontinuous molecular dynamic simulations of the assembly and folding kinetics of a tetrameric beta-sheet complex that contains four identical four-stranded antiparallel beta-sheet peptides. The potential used in the simulation is a hybrid Go-type potential characterized by the bias gap parameter g, an artificial measure of a model Protein's preference for its native state, and the intermolecular contact parameter eta, which measures the ratio of intermolecular to intramolecular native attractions. The formation of the beta-sheet complex and its equilibrium properties strongly depend on the size of the intermolecular contact parameter eta. The ordered beta-sheet complex in the folded state and nonaligned beta-sheets or tangled chains in the misfolded state are distinguished by measuring the squared radius of gyration Rg2 and the fraction of native contacts Q. The folding yield for the folded state is high at intermediate values of eta, but is low at both small and large values of eta. The folded state at small eta is liquid-like, but is solid-like at both intermediate and large eta. The misfolded state at small eta contains nonaligned beta-sheets and tangled chains with poor secondary structure at large eta. Various folding pathways via dimeric and trimeric intermediates are observed, depending on eta. Comparison with experimental results on Protein aggregation indicates that intermediate eta values are most appropriate for modeling fibril formation and small eta values are most appropriate for modeling the formation of amorphous aggregates.
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assembly and kinetic folding pathways of a tetrameric β sheet complex molecular dynamics simulations on simplified off Lattice Protein models
Biophysical Journal, 2004Co-Authors: Hyunbum Jang, Carol K Hall, Yaoqi ZhouAbstract:We have performed discontinuous molecular dynamic simulations of the assembly and folding kinetics of a tetrameric beta-sheet complex that contains four identical four-stranded antiparallel beta-sheet peptides. The potential used in the simulation is a hybrid Go-type potential characterized by the bias gap parameter g, an artificial measure of a model Protein's preference for its native state, and the intermolecular contact parameter eta, which measures the ratio of intermolecular to intramolecular native attractions. The formation of the beta-sheet complex and its equilibrium properties strongly depend on the size of the intermolecular contact parameter eta. The ordered beta-sheet complex in the folded state and nonaligned beta-sheets or tangled chains in the misfolded state are distinguished by measuring the squared radius of gyration Rg2 and the fraction of native contacts Q. The folding yield for the folded state is high at intermediate values of eta, but is low at both small and large values of eta. The folded state at small eta is liquid-like, but is solid-like at both intermediate and large eta. The misfolded state at small eta contains nonaligned beta-sheets and tangled chains with poor secondary structure at large eta. Various folding pathways via dimeric and trimeric intermediates are observed, depending on eta. Comparison with experimental results on Protein aggregation indicates that intermediate eta values are most appropriate for modeling fibril formation and small eta values are most appropriate for modeling the formation of amorphous aggregates.
Adam Liwo - One of the best experts on this subject based on the ideXlab platform.
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united residue force field for off Lattice Protein structure simulations iii origin of backbone hydrogen bonding cooperativity in united residue potentials
Journal of Computational Chemistry, 1998Co-Authors: Adam Liwo, Rajmund Kazmierkiewicz, Cezary Czaplewski, Malgorzata Groth, Stanislaw Oldziej, Ryszard J Wawak, S Rackovsky, Matthew R PincusAbstract:Based on the dipole model of peptide groups developed in our earlier work [Liwo et al., Prot. Sci.,2, 1697 (1993)], a cumulant expansion of the average free energy of the system of freely rotating peptide-group dipoles tethered to a fixed α-carbon trace is derived. A graphical approach is presented to find all nonvanishing terms in the cumulants. In particular, analytical expressions for three- and four-body (correlation) terms in the averaged interaction potential of united peptide groups are derived. These expressions are similar to the cooperative forces in hydrogen bonding introduced by Kolinski and Skolnick [J. Chem. Phys.,97, 9412 (1992)]. The cooperativity arises here naturally from the higher order terms in the power-series expansion (in the inverse of the temperature) for the average energy. Test calculations have shown that addition of the derived four-body term to the statistical united-residue potential of our earlier work [Liwo et al., J. Comput. Chem.,18, 849, 874 (1997)] greatly improves its performance in folding poly-l-alanine into an α-helix. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 259–276, 1998
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a united residue force field for off Lattice Protein structure simulations i functional forms and parameters of long range side chain interaction potentials from Protein crystal data
Journal of Computational Chemistry, 1997Co-Authors: Adam Liwo, Stanislaw Oldziej, Ryszard J Wawak, S Rackovsky, Matthew R Pincus, Harold A ScheragaAbstract:A two-stage procedure for the determination of a united-residue potential designed for Protein simulations is outlined. In the first stage, the long-range and local-interaction energy terms of the total energy of a polypeptide chain are determined by analyzing Protein-crystal data and averaging the all-atom energy surfaces. In the second stage (described in the accompanying article), the relative weights of the energy terms are optimized so as to locate the native structures of selected test Proteins as the lowest energy structures. The goal of the work in the present study is to parameterize physically reasonable functional forms of the potentials of mean force for side-chain interactions. The potentials are of both radial and anisotropic type. Radial potentials include the Lennard-Jones and the shifted Lennard-Jones potential (with the shift parameter independent of orientation). To treat the angular dependence of side-chain interactions, three functional forms of the potential that were designed previously to describe anisotropic systems are evaluated: Berne-Pechukas (dilated Lennard-Jones); Gay-Berne (shifted Lennard-Jones with orientation-dependent shift parameters); and Gay-Berne-Vorobjev (the same as the preceding one, but with one more set of variable parameters). These functional forms were used to parameterize, within a short-distance range, the potentials of mean force for side-chain pair interactions that are related by the Boltzmann principle to the pair correlation functions determined from Protein-crystal data. Parameter determination was formulated as a generalized nonlinear least-squares problem with the target function being the weighted sum of squares of the differences between calculated and “experimental” (i.e., estimated from Protein-crystal data) angular, radial-angular, and radial pair correlation functions, as well as contact free energies. A set of 195 high-resolution nonhomologous structures from the Protein Data Bank was used to calculate the “experimental” values. The contact free energies were scaled by the slope of the correlation line between side-chain hydrophobicities, calculated from the contact free energies, and those determined by Fauchere and Pliska from the partition coefficients of amino acids between water and n-octanol. The methylene group served to define the reference contact free energy corresponding to that between the glycine methylene groups of backbone residues. Statistical analysis of the goodness of fit revealed that the Gay-Berne-Vorobjev anisotropic potential fits best to the experimental radial and angular correlation functions and contact free energies and therefore represents the free-energy surface of side-chain-side-chain interactions most accurately. Thus, its choice for simulations of Protein structure is probably the most appropriate. However, the use of simpler functional forms is recommended, if the speed of computations is an issue. © 1997 by John Wiley & Sons, Inc. J Comput Chem 18: 849–873, 1997
Fernando A. Escobedo - One of the best experts on this subject based on the ideXlab platform.
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folding kinetics of a Lattice Protein via a forward flux sampling approach
Journal of Chemical Physics, 2006Co-Authors: Ernesto E Borrero, Fernando A. EscobedoAbstract:We implement a forward flux sampling approach [R. J. Allen et al., J. Chem. Phys. 124, 194111 (2006)] for calculating transition rate constants and for sampling paths of Protein folding events. The algorithm generates trajectories for the transition between the unfolded and folded states as chains of partially connected paths, which can be used to obtain the transition-state ensemble and the properties that characterize these intermediates. We apply this approach to Monte Carlo simulations of a model Lattice Protein in open space and in confined spaces of varying dimensions. We study the effect of confinement on both Protein thermodynamic stability and folding kinetics; the former by mapping free-energy landscapes and the latter by the determination of rate constants and mechanistic details of the folding pathway. Our results show that, for the range of temperatures where the native state is stable, confinement of a Protein destabilizes the unfolded state by reducing its entropy, resulting in increased th...
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Expanded ensemble and replica exchange methods for simulation of Protein-like systems
Journal of Chemical Physics, 2003Co-Authors: Michael K. Fenwick, Fernando A. EscobedoAbstract:Extended state methods are powerful tools for studying the conformational equilibria of Proteins. This study focuses on three aspects of their implementation. First, existing approaches for determining importance weights (namely, recursion, random walk, and transition probability schemes) are compared in the context of their use with the method of expanded ensembles (EXE). Second, a combined scheme (REXE) involving EXE and replica exchange (REX) updates is developed for simulating a small number of replicas within a much larger macrostate space. Finally, variants of the extended state methods are considered for accelerating folding, either through special-purpose ensembles which target specific force-field parameters, or through biased sampling of extended macrostates that favor structural fluctuations. All methods are applied to a three-dimensional Lattice Protein model. Overall, it is found that transition probability approaches employing multiple system replicas perform naturally better than methods that intrinsically require macrostate equilibration by a single replica; the transition probability approaches need about an order of magnitude fewer steps to reach the same degree of convergence in the importance weights. The specific REXE protocol implemented is observed to have an efficiency intermediate to that of EXE and REX schemes at high temperatures, but to outperform them at more glassy conditions. Finally, special-purpose and locally enhanced tempering ensembles are shown to promote faster folding than conventional tempering.
Eugene I Shakhnovich - One of the best experts on this subject based on the ideXlab platform.
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identifying the Protein folding nucleus using molecular dynamics
Journal of Molecular Biology, 2000Co-Authors: Sergey V Buldyrev, Nikolay V Dokholyan, Eugene H Stanley, Eugene I ShakhnovichAbstract:Molecular dynamics simulations of folding in an off-Lattice Protein model reveal a nucleation scenario, in which a few well-defined contacts are formed with high probability in the transition state ensemble of conformations. Their appearance determines folding cooperativity and drives the model Protein into its folded conformation. Amino acid residues participating in those contacts may serve as "accelerator pedals" used by molecular evolution to control Protein folding rate.
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identifying the Protein folding nucleus using molecular dynamics
arXiv: Statistical Mechanics, 1998Co-Authors: Nikolay V Dokholyan, Sergey V Buldyrev, Eugene H Stanley, Eugene I ShakhnovichAbstract:Molecular dynamics simulations of folding in an off-Lattice Protein model reveal a nucleation scenario, in which a few well-defined contacts are formed with high probability in the transition state ensemble of conformations. Their appearance determines folding cooperativity and drives the model Protein into its folded conformation.
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a test of Lattice Protein folding algorithms
Proceedings of the National Academy of Sciences of the United States of America, 1995Co-Authors: Kaizhi Yue, Klaus M Fiebig, Paul D Thomas, Hue Sun Chan, Eugene I Shakhnovich, Ken A DillAbstract:We report a blind test of Lattice-model-based search strategies for finding global minima of model Protein chains. One of us (E.I.S.) selected 10 compact conformations of 48-mer chains on the three-dimensional cubic Lattice and used their inverse folding algorithm to design HP (H, hydrophobic; P, polar) sequences that should fold to those "target" structures. The sequences, but not the structures, were sent to the UCSF group (K.Y., K.M.F., P.D.T., H.S.C., and K.A.D.), who used two methods to attempt to find the globally optimal conformations: "hydrophobic zippers" and a constraint-based hydrophobic core construction (CHCC) method. The CHCC method found global minima in all cases, and the hydrophobic zippers method found global minima in some cases, in minutes to hours on workstations. In 9 out of 10 sequences, the CHCC method found lower energy conformations than the 48-mers were designed to fold to. Thus the search strategies succeed for the HP model but the design strategy does not. For every sequence the global energy minimum was found to have multiple degeneracy with 10(3) to 10(6) conformations. We discuss the implications of these results for (i) searching conformational spaces of simple models of Proteins and (ii) how these simple models relate to Proteins.