Extending the horizon: towards the efficient modeling of large biomolecular complexes in atomic detail

The application of evaluation of implicit solvent methods for the simulation of biomolecules is described. Detailed comparisons with explicit solvent are described for the modeling of peptide and proteins in continuum aqueous solvent. In addition, we are presenting new data on the simulation of DNA with implicit solvent and describe the development of a heterogeneous dielectric model for the simulation of integral membranes. The performance of implicit solvent simulations based on the GBMV generalized Born method is compared with explicit solvent simulations, and implications for the simulation of very large biomolecular complexes is discussed. We are anticipating that the work described herein will lead to new, efficient modeling tools that will allow the simulation of longer timescales and larger system sizes in order to meet current and future challenges by the experimental community.

[1]  T. Lazaridis.  Effective energy function for proteins in lipid membranes , 2003, Proteins.

[2]  Generalized Langevin models and condensed-phase chemical reaction dynamics , 1982 .

[3]  Samir Kumar Pal,et al.  Dynamics of water in biological recognition. , 2004, Chemical reviews.

[4]  Jacopo Tomasi,et al.  Evaluation of the dispersion contribution to the solvation energy. A simple computational model in the continuum approximation , 1989 .

[5]  M. Karplus,et al.  Effective energy functions for protein structure prediction. , 2000, Current opinion in structural biology.

[6]  U. Hansmann.  Parallel tempering algorithm for conformational studies of biological molecules , 1997, physics/9710041.

[7]  R. Constanciel,et al.  Self consistent field theory of solvent effects representation by continuum models: Introduction of desolvation contribution , 1984 .

[8]  V. Ramakrishnan,et al.  Atomic structures at last: the ribosome in 2000. , 2001, Current opinion in structural biology.

[9]  S. Harvey,et al.  Modeling large RNAs and ribonucleoprotein particles using molecular mechanics techniques. , 1994, Biophysical journal.

[10]  P. Kollman,et al.  Molecular Dynamics Simulations on Solvated Biomolecular Systems: The Particle Mesh Ewald Method Leads to Stable Trajectories of DNA, RNA, and Proteins , 1995 .

[11]  M Feig,et al.  Accurate reconstruction of all‐atom protein representations from side‐chain‐based low‐resolution models , 2000, Proteins.

[12]  Alexander D. MacKerell,et al.  Force field influence on the observation of π-helical protein structures in molecular dynamics simulations , 2003 .

[13]  Holger Gohlke,et al.  Converging free energy estimates: MM‐PB(GB)SA studies on the protein–protein complex Ras–Raf , 2004, J. Comput. Chem..

[14]  B. Pettitt,et al.  Experiment vs force fields: DNA conformation from molecular dynamics simulations , 1997 .

[15]  Tomasz Grycuk,et al.  Deficiency of the Coulomb-field approximation in the generalized Born model: An improved formula for Born radii evaluation , 2003 .

[16]  B. Roux,et al.  Implicit solvent models. , 1999, Biophysical chemistry.

[17]  A. Kolinski.  Protein modeling and structure prediction with a reduced representation. , 2004, Acta biochimica Polonica.

[18]  Alexander D. MacKerell,et al.  All‐atom empirical force field for nucleic acids: I. Parameter optimization based on small molecule and condensed phase macromolecular target data , 2000 .

[19]  Sandeep Patel,et al.  A nonadditive methanol force field: bulk liquid and liquid-vapor interfacial properties via molecular dynamics simulations using a fluctuating charge model. , 2005, The Journal of chemical physics.

[20]  M. Karplus,et al.  Discrimination of the native from misfolded protein models with an energy function including implicit solvation. , 1999, Journal of molecular biology.

[21]  J. Apostolakis,et al.  Evaluation of a fast implicit solvent model for molecular dynamics simulations , 2002, Proteins.

[22]  Ronald M. Levy,et al.  AGBNP: An analytic implicit solvent model suitable for molecular dynamics simulations and high‐resolution modeling , 2004, J. Comput. Chem..

[23]  Michael Feig,et al.  MMTSB Tool Set: enhanced sampling and multiscale modeling methods for applications in structural biology. , 2004, Journal of molecular graphics & modelling.

[24]  C. Brooks,et al.  First-principles calculation of the folding free energy of a three-helix bundle protein. , 1995, Science.

[25]  C. Brooks,et al.  Comparative Study of the Folding Free Energy Landscape of a Three-Stranded β-Sheet Protein with Explicit and Implicit Solvent Models , 2000 .

[26]  U. Hansmann.  Generalized ensemble techniques and protein folding simulations , 2002 .

[27]  Velin Z. Spassov,et al.  Introducing an Implicit Membrane in Generalized Born/Solvent Accessibility Continuum Solvent Models , 2002 .

[28]  J. Kirkwood,et al.  Theory of Solutions of Molecules Containing Widely Separated Charges with Special Application to Zwitterions , 1934 .

[29]  Richard A. Friesner,et al.  Solvent models for protein–ligand binding: Comparison of implicit solvent poisson and surface generalized born models with explicit solvent simulations , 2001, J. Comput. Chem..

[30]  S. Joseph,et al.  Understanding discrimination by the ribosome: stability testing and groove measurement of codon-anticodon pairs. , 2003, Journal of molecular biology.

[31]  T. Steitz,et al.  The complete atomic structure of the large ribosomal subunit at 2.4 A resolution. , 2000, Science.

[32]  R. Rittenhouse,et al.  Characterization of the active site of DNA polymerase β by molecular dynamics and quantum chemical calculation , 2003, Proteins.

[33]  M. Hao,et al.  Designing potential energy functions for protein folding. , 1999, Current opinion in structural biology.

[34]  Anastassis Perrakis,et al.  The crystal structure of DNA mismatch repair protein MutS binding to a G·T mismatch , 2000, Nature.

[35]  Joanna Trylska,et al.  Ribosome motions modulate electrostatic properties , 2004, Biopolymers.

[36]  P. Cramer,et al.  Structural Basis of Transcription: An RNA Polymerase II Elongation Complex at 3.3 Å Resolution , 2001, Science.

[37]  Alexander D. MacKerell,et al.  Extending the treatment of backbone energetics in protein force fields: Limitations of gas‐phase quantum mechanics in reproducing protein conformational distributions in molecular dynamics simulations , 2004, J. Comput. Chem..

[38]  Herman J. C. Berendsen,et al.  Permeation Process of Small Molecules across Lipid Membranes Studied by Molecular Dynamics Simulations , 1996 .

[39]  Charles L. Brooks,et al.  New analytic approximation to the standard molecular volume definition and its application to generalized Born calculations , 2003, J. Comput. Chem..

[40]  P. Kollman,et al.  Use of MM-PBSA in reproducing the binding free energies to HIV-1 RT of TIBO derivatives and predicting the binding mode to HIV-1 RT of efavirenz by docking and MM-PBSA. , 2001, Journal of the American Chemical Society.

[41]  R Reichelt,et al.  Scanning force microscopy at the air-water interface of an air bubble coated with pulmonary surfactant. , 2002, Biophysical journal.

[42]  Jung-Hsin Lin,et al.  Bridging implicit and explicit solvent approaches for membrane electrostatics. , 2002, Biophysical journal.

[43]  P. Cramer,et al.  Structural Basis of Transcription: RNA Polymerase II at 2.8 Ångstrom Resolution , 2001, Science.

[44]  Mariusz Milik,et al.  Algorithm for rapid reconstruction of protein backbone from alpha carbon coordinates , 1997 .

[45]  K. Sanbonmatsu,et al.  Structure of Met‐enkephalin in explicit aqueous solution using replica exchange molecular dynamics , 2002, Proteins.

[46]  Alexander D. MacKerell.  Empirical force fields for biological macromolecules: Overview and issues , 2004, J. Comput. Chem..

[47]  D. Case,et al.  Insights into protein-protein binding by binding free energy calculation and free energy decomposition for the Ras-Raf and Ras-RalGDS complexes. , 2003, Journal of molecular biology.

[48]  C. Brooks,et al.  Recent advances in the development and application of implicit solvent models in biomolecule simulations. , 2004, Current opinion in structural biology.

[49]  Michael Feig,et al.  Implicit solvation based on generalized Born theory in different dielectric environments. , 2004, The Journal of chemical physics.

[50]  P. Payne,et al.  Reconstruction of protein conformations from estimated positions of the Cα coordinates , 1993, Protein science : a publication of the Protein Society.

[51]  G. Torrie,et al.  Monte Carlo free energy estimates using non-Boltzmann sampling: Application to the sub-critical Lennard-Jones fluid , 1974 .

[52]  B. Pettitt,et al.  Solvation and hydration of proteins and nucleic acids: a theoretical view of simulation and experiment. , 2002, Accounts of chemical research.

[53]  T. Schlick,et al.  Extrapolation versus impulse in multiple-timestepping schemes. II. Linear analysis and applications to Newtonian and Langevin dynamics , 1998 .

[54]  B. Honig,et al.  The electrostatic contribution to the B to Z transition of DNA. , 1996, Biochemistry.

[55]  J. Troe.  Recent Advances in Statistical Adiabatic Channel Calculations of State‐Specific Dissociation Dynamics , 2007 .

[56]  Alexander D. MacKerell,et al.  Development and current status of the CHARMM force field for nucleic acids , 2000, Biopolymers.

[57]  Harry A. Stern,et al.  Calculation of the dielectric permittivity profile for a nonuniform system: Application to a lipid bilayer simulation , 2003 .

[58]  Alexander D. MacKerell,et al.  All-atom empirical potential for molecular modeling and dynamics studies of proteins. , 1998, The journal of physical chemistry. B.

[59]  D Thirumalai,et al.  Kinetics and thermodynamics of folding in model proteins. , 1993, Proceedings of the National Academy of Sciences of the United States of America.

[60]  S Gnanakaran,et al.  Peptide folding simulations. , 2003, Current opinion in structural biology.

[61]  Jiang Zhu,et al.  Parametrization of a Generalized Born/Solvent-Accessible Surface Area Model and Applications to the Simulation of Protein Dynamics , 2002 .

[62]  K. Dill,et al.  Cooperativity in protein-folding kinetics. , 1993, Proceedings of the National Academy of Sciences of the United States of America.

[63]  K. Morokuma,et al.  ONIOM: A Multilayered Integrated MO + MM Method for Geometry Optimizations and Single Point Energy Predictions. A Test for Diels−Alder Reactions and Pt(P(t-Bu)3)2 + H2 Oxidative Addition , 1996 .

[64]  Y. Sugita,et al.  Replica-exchange molecular dynamics method for protein folding , 1999 .

[65]  C. Brooks,et al.  Novel generalized Born methods , 2002 .

[66]  C. Cramer,et al.  Implicit Solvation Models: Equilibria, Structure, Spectra, and Dynamics. , 1999, Chemical reviews.

[67]  S. Hassan,et al.  A critical analysis of continuum electrostatics: The screened Coulomb potential–implicit solvent model and the study of the alanine dipeptide and discrimination of misfolded structures of proteins , 2002, Proteins.

[68]  Gregory D. Hawkins,et al.  Pairwise solute descreening of solute charges from a dielectric medium , 1995 .

[69]  Charles L. Brooks,et al.  Performance comparison of generalized born and Poisson methods in the calculation of electrostatic solvation energies for protein structures , 2004, J. Comput. Chem..

[70]  D. Beglov,et al.  Atomic Radii for Continuum Electrostatics Calculations Based on Molecular Dynamics Free Energy Simulations , 1997 .

[71]  Wei Zu Chen,et al.  Protein molecular dynamics with electrostatic force entirely determined by a single Poisson‐Boltzmann calculation , 2002, Proteins.

[72]  M. Feig,et al.  A generalized Born formalism for heterogeneous dielectric environments: application to the implicit modeling of biological membranes. , 2005, The Journal of chemical physics.

[73]  Ranbir Singh,et al.  J. Mol. Struct. (Theochem) , 1996 .

[74]  Anthony K. Felts,et al.  On the nonpolar hydration free energy of proteins: surface area and continuum solvent models for the solute-solvent interaction energy. , 2003, Journal of the American Chemical Society.

[75]  T. Darden,et al.  Toward the Accurate Modeling of DNA: The Importance of Long-Range Electrostatics , 1995 .

[76]  D. Bushnell,et al.  Structural Basis of Transcription: Separation of RNA from DNA by RNA Polymerase II , 2004, Science.

[77]  Alexander D. MacKerell,et al.  Improved treatment of the protein backbone in empirical force fields. , 2004, Journal of the American Chemical Society.

[78]  V. Pande,et al.  Multiplexed-replica exchange molecular dynamics method for protein folding simulation. , 2003, Biophysical journal.

[79]  Michael Feig,et al.  Evaluating CASP4 predictions with physical energy functions , 2002, Proteins.

[80]  Gregory D. Hawkins,et al.  Parametrized Models of Aqueous Free Energies of Solvation Based on Pairwise Descreening of Solute Atomic Charges from a Dielectric Medium , 1996 .

[81]  P. Beroza,et al.  Application of a pairwise generalized Born model to proteins and nucleic acids: inclusion of salt effects , 1999 .

[82]  Kim A. Sharp,et al.  Incorporating solvent and ion screening into molecular dynamics using the finite‐difference Poisson–Boltzmann method , 1991 .

[83]  B. Honig,et al.  Classical electrostatics in biology and chemistry. , 1995, Science.

[84]  U H Hansmann,et al.  New Monte Carlo algorithms for protein folding. , 1999, Current opinion in structural biology.

[85]  D. Truhlar,et al.  Quantum mechanical methods for enzyme kinetics. , 2003, Annual review of physical chemistry.

[86]  Atsushi Suenaga,et al.  Replica-exchange molecular dynamics simulations for a small-sized protein folding with implicit solvent , 2003 .

[87]  Mark A Olson,et al.  An efficient hybrid explicit/implicit solvent method for biomolecular simulations , 2004, J. Comput. Chem..

[88]  J. Skolnick,et al.  MONSSTER: a method for folding globular proteins with a small number of distance restraints. , 1997, Journal of molecular biology.

[89]  James A. Hutchby,et al.  Limits to binary logic switch scaling - a gedanken model , 2003, Proc. IEEE.

[90]  B. Lee,et al.  The interpretation of protein structures: estimation of static accessibility. , 1971, Journal of molecular biology.

[91]  R A Friesner,et al.  Prediction of loop geometries using a generalized born model of solvation effects , 1999, Proteins.

[92]  M. Karplus,et al.  A Comprehensive Analytical Treatment of Continuum Electrostatics , 1996 .

[93]  Klaus Gerwert,et al.  Dynamics of water molecules in the bacteriorhodopsin trimer in explicit lipid/water environment. , 2004, Biophysical journal.

[94]  C. Brooks,et al.  An implicit membrane generalized born theory for the study of structure, stability, and interactions of membrane proteins. , 2003, Biophysical journal.

[95]  M. L. Connolly.  Analytical molecular surface calculation , 1983 .

[96]  Ruhong Zhou,et al.  New Linear Interaction Method for Binding Affinity Calculations Using a Continuum Solvent Model , 2001 .

[97]  A. Roitberg,et al.  All-atom structure prediction and folding simulations of a stable protein. , 2002, Journal of the American Chemical Society.

[98]  Alexander D. MacKerell,et al.  All‐atom empirical force field for nucleic acids: II. Application to molecular dynamics simulations of DNA and RNA in solution , 2000 .

[99]  W. C. Still,et al.  The GB/SA Continuum Model for Solvation. A Fast Analytical Method for the Calculation of Approximate Born Radii , 1997 .

[100]  B. Montgomery Pettitt,et al.  Efficient Ewald electrostatic calculations for large systems , 1995 .

[101]  J. Skolnick,et al.  A new combination of replica exchange Monte Carlo and histogram analysis for protein folding and thermodynamics , 2001 .

[102]  Xiaojie Xu,et al.  Empirical Aqueous Solvation Models Based on Accessible Surface Areas with Implicit Electrostatics , 2002 .

[103]  Wei Zhang,et al.  Parameters for the generalized Born model consistent with RESP atomic partial charge assignment protocol , 2003 .

[104]  M. Born.  Volumen und Hydratationswärme der Ionen , 1920 .

[105]  A. Liwo,et al.  A united‐residue force field for off‐lattice protein‐structure simulations. II. Parameterization of short‐range interactions and determination of weights of energy terms by Z‐score optimization , 1997 .

[106]  W. Im,et al.  Continuum solvation model: Computation of electrostatic forces from numerical solutions to the Poisson-Boltzmann equation , 1998 .

[107]  Charles L. Brooks,et al.  Generalized born model with a simple smoothing function , 2003, J. Comput. Chem..

[108]  D. Case,et al.  Molecular Dynamics Simulations of Nucleic Acids with a Generalized Born Solvation Model , 2000 .

[109]  Gregory D. Hawkins,et al.  Modeling The Effect of Solvation on Structure, Reactivity, and Partitioning of Organic Solutes: Utility in Drug Design , 1999 .

[110]  T. Simonson,et al.  Protein molecular dynamics with the generalized born/ACE solvent model , 2001, Proteins.

[111]  Edward D Harder,et al.  Efficient multiple time step method for use with Ewald and particle mesh Ewald for large biomolecular systems , 2001 .

[112]  A. Warshel,et al.  Computer simulation studies of the fidelity of DNA polymerases , 2003, Biopolymers.

[113]  K. Sanbonmatsu,et al.  α-Helical stabilization by side chain shielding of backbone hydrogen bonds , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[114]  Jeffrey Skolnick,et al.  Efficient algorithm for the reconstruction of a protein backbone from the α‐carbon coordinates , 1992 .

[115]  Guohui Li,et al.  pKa calculations with QM/MM free energy perturbations , 2003 .

[116]  V S Pande,et al.  Molecular dynamics simulations of unfolding and refolding of a beta-hairpin fragment of protein G. , 1999, Proceedings of the National Academy of Sciences of the United States of America.

[117]  Wei Yang,et al.  Crystal structures of mismatch repair protein MutS and its complex with a substrate DNA , 2000, Nature.

[118]  K. Sharp,et al.  Accurate Calculation of Hydration Free Energies Using Macroscopic Solvent Models , 1994 .

[119]  K. Freed,et al.  Long time dynamics of Met-enkephalin: comparison of explicit and implicit solvent models. , 2002, Biophysical journal.

[120]  W. Olson,et al.  Electrostatic effects in short superhelical DNA. , 1994, Biophysical chemistry.

[121]  H. Nymeyer,et al.  Simulation of the folding equilibrium of α-helical peptides: A comparison of the generalized Born approximation with explicit solvent , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[122]  Ulrich H E Hansmann,et al.  Parallel tempering simulations of HP‐36 , 2003, Proteins.

[123]  W. C. Still,et al.  Semianalytical treatment of solvation for molecular mechanics and dynamics , 1990 .

[124]  Alessandro Laio,et al.  Reconstructing the density of states by history-dependent metadynamics. , 2004, Physical review letters.

[125]  M. Karplus,et al.  Effective energy function for proteins in solution , 1999, Proteins.

[126]  Herman J. C. Berendsen,et al.  Simulation of Water Transport through a Lipid Membrane , 1994 .

[127]  J. Langowski,et al.  DNA supercoiling, localized bending and thermal fluctuations. , 1996, Trends in biochemical sciences.

[128]  Eric J. Sorin,et al.  β-hairpin folding simulations in atomistic detail using an implicit solvent model1 , 2001 .

[129]  Bojan Zagrovic,et al.  Solvent viscosity dependence of the folding rate of a small protein: Distributed computing study , 2003, J. Comput. Chem..

[130]  D. Case,et al.  Generalized born models of macromolecular solvation effects. , 2000, Annual review of physical chemistry.

[131]  Hongyi Zhou,et al.  Stability scale and atomic solvation parameters extracted from 1023 mutation experiments , 2002, Proteins.

[132]  A. Liwo,et al.  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 , 1997 .

[133]  Charles L. Brooks,et al.  CHARMM fluctuating charge force field for proteins: I parameterization and application to bulk organic liquid simulations , 2004, J. Comput. Chem..

[134]  E I Shakhnovich,et al.  A test of lattice protein folding algorithms. , 1995, Proceedings of the National Academy of Sciences of the United States of America.

[135]  K. Sanbonmatsu,et al.  Exploring the energy landscape of a β hairpin in explicit solvent , 2001 .

[136]  B. Roux,et al.  Atomic Radii for Continuum Electrostatics Calculations on Nucleic Acids , 2002 .

[137]  M R Lee,et al.  Use of MM‐PB/SA in estimating the free energies of proteins: Application to native, intermediates, and unfolded villin headpiece , 2000, Proteins.

[138]  Roger D Kornberg,et al.  Complete, 12-subunit RNA polymerase II at 4.1-Å resolution: Implications for the initiation of transcription , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[139]  D. Thirumalai,et al.  Folding kinetics of proteins : a model study , 1992 .

[140]  M. Karplus,et al.  Dependence of DNA polymerase replication rate on external forces: a model based on molecular dynamics simulations. , 2004, Biophysical journal.

[141]  K. Dill.  Theory for the folding and stability of globular proteins. , 1985, Biochemistry.

[142]  Thomas B Woolf,et al.  Discrimination of native loop conformations in membrane proteins: Decoy library design and evaluation of effective energy scoring functions , 2003, Proteins.

[143]  Yong Duan,et al.  Distinguish protein decoys by Using a scoring function based on a new AMBER force field, short molecular dynamics simulations, and the generalized born solvent model , 2004, Proteins.

[144]  M. Levitt,et al.  A lattice model for protein structure prediction at low resolution. , 1992, Proceedings of the National Academy of Sciences of the United States of America.

[145]  Junmei Wang,et al.  Development and testing of a general amber force field , 2004, J. Comput. Chem..

[146]  C. Brooks,et al.  De novo folding of membrane proteins: an exploration of the structure and NMR properties of the fd coat protein. , 2004, Journal of molecular biology.

[147]  M K Gilson,et al.  Interpreting trends in the binding of cyclic ureas to HIV-1 protease. , 2001, Journal of molecular biology.

[148]  B. Dominy,et al.  Development of a generalized Born model parameterization for proteins and nucleic acids , 1999 .

[149]  Franca Fraternali,et al.  Conformational transitions of a dipeptide in water: Effects of imposed pathways using umbrella sampling techniques , 1994 .

[150]  Emil Alexov,et al.  Comparative study of generalized born models: Born radii and peptide folding. , 2005, The journal of physical chemistry. B.

[151]  Marcin Król,et al.  Comparison of various implicit solvent models in molecular dynamics simulations of immunoglobulin G light chain dimer , 2003, J. Comput. Chem..

[152]  Themis Lazaridis,et al.  Distance and exposure dependent effective dielectric function , 2002, J. Comput. Chem..

[153]  Chris Oostenbrink,et al.  A biomolecular force field based on the free enthalpy of hydration and solvation: The GROMOS force‐field parameter sets 53A5 and 53A6 , 2004, J. Comput. Chem..

[154]  C L Brooks,et al.  Simulations of protein folding and unfolding. , 1998, Current opinion in structural biology.

[155]  J. C. Phillips,et al.  Molecular Dynamics Study of Bacteriorhodopsin and the Purple Membrane , 2001 .

[156]  M R Lee,et al.  Free-energy calculations highlight differences in accuracy between X-ray and NMR structures and add value to protein structure prediction. , 2001, Structure.

[157]  Viktor Hornak,et al.  Development of softcore potential functions for overcoming steric barriers in molecular dynamics simulations. , 2004, Journal of molecular graphics & modelling.

[158]  D. Eisenberg,et al.  Atomic solvation parameters applied to molecular dynamics of proteins in solution , 1992, Protein science : a publication of the Protein Society.

[159]  J. Skolnick,et al.  Monte carlo simulations of protein folding. I. Lattice model and interaction scheme , 1994, Proteins.

[160]  Soonmin Jang,et al.  Molecular Dynamics Study of Peptides in Implicit Water: Ab Initio Folding of β-Hairpin, β-Sheet, and ββα-motif , 2002 .

[161]  M Feig,et al.  Modeling high-resolution hydration patterns in correlation with DNA sequence and conformation. , 1999, Journal of molecular biology.

[162]  Yuko Okamoto,et al.  Generalized-ensemble algorithms: enhanced sampling techniques for Monte Carlo and molecular dynamics simulations. , 2003, Journal of molecular graphics & modelling.

[163]  R. Dickerson,et al.  DNA bending: the prevalence of kinkiness and the virtues of normality. , 1998, Nucleic acids research.

[164]  Charles L. Brooks,et al.  Identifying native‐like protein structures using physics‐based potentials , 2002, J. Comput. Chem..

[165]  B. Roux.  Influence of the membrane potential on the free energy of an intrinsic protein. , 1997, Biophysical journal.

[166]  Peijuan Zhu,et al.  Implementation and testing of stable, fast implicit solvation in molecular dynamics using the smooth‐permittivity finite difference Poisson–Boltzmann method , 2004, J. Comput. Chem..

[167]  P A Kollman,et al.  Continuum solvent studies of the stability of RNA hairpin loops and helices. , 1998, Journal of biomolecular structure & dynamics.

[168]  William Swope,et al.  Understanding folding and design: Replica-exchange simulations of ``Trp-cage'' miniproteins , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[169]  John W. Brady,et al.  Use of Umbrella Sampling in the Calculation of the Potential of Mean Force for Maltose in Vacuum From Molecular Dynamics Simulations , 1995 .

[170]  J. Skolnick,et al.  Monte Carlo simulations on an equilibrium globular protein folding model. , 1986, Proceedings of the National Academy of Sciences of the United States of America.

[171]  Anthony K. Felts,et al.  Distinguishing native conformations of proteins from decoys with an effective free energy estimator based on the OPLS all‐atom force field and the surface generalized born solvent model , 2002, Proteins.

[172]  F. Rao,et al.  Replica exchange molecular dynamics simulations of reversible folding , 2003 .

[173]  Alexander D. MacKerell,et al.  CHARMM fluctuating charge force field for proteins: II Protein/solvent properties from molecular dynamics simulations using a nonadditive electrostatic model , 2004, J. Comput. Chem..

[174]  Viktor Hornak,et al.  Improved conformational sampling through an efficient combination of mean-field simulation approaches , 2004 .

[175]  Donald G. Truhlar,et al.  Improved methods for semiempirical solvation models , 1995, J. Comput. Chem..

[176]  T Schlick,et al.  Biomolecular dynamics at long timesteps: bridging the timescale gap between simulation and experimentation. , 1997, Annual review of biophysics and biomolecular structure.

[177]  H. Berman.  Hydration of DNA: take 2 , 1994 .

[178]  Wilfred F. van Gunsteren,et al.  The computation of a potential of mean force: Choice of the biasing potential in the umbrella sampling technique , 1994 .

[179]  Charles L Brooks,et al.  Protein and peptide folding explored with molecular simulations. , 2002, Accounts of chemical research.

[180]  P. Kollman,et al.  Continuum Solvent Studies of the Stability of DNA, RNA, and Phosphoramidate−DNA Helices , 1998 .

[181]  R. Zhou.  Free energy landscape of protein folding in water: Explicit vs. implicit solvent , 2003, Proteins.

[182]  M Feig,et al.  Structural equilibrium of DNA represented with different force fields. , 1998, Biophysical journal.

[183]  David A. Case,et al.  Effective Born radii in the generalized Born approximation: The importance of being perfect , 2002, J. Comput. Chem..

[184]  A. Fersht,et al.  Protein folding and unfolding in microseconds to nanoseconds by experiment and simulation. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[185]  Wilfred F. van Gunsteren,et al.  A Comparison of Particle-Particle, Particle-Mesh and Ewald Methods for Calculating Electrostatic Interactions in Periodic Molecular Systems , 1994 .

[186]  Ray Luo,et al.  Accelerated Poisson–Boltzmann calculations for static and dynamic systems , 2002, J. Comput. Chem..

[187]  R. Friesner,et al.  Generalized Born Model Based on a Surface Integral Formulation , 1998 .

[188]  B. Berne,et al.  The free energy landscape for β hairpin folding in explicit water , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[189]  K. Sharp,et al.  Electrostatic interactions in macromolecules: theory and applications. , 1990, Annual review of biophysics and biophysical chemistry.

[190]  Barry Honig,et al.  Electrostatic Potentials near the Surface of DNA: Comparing Theory and Experiment , 1995 .

[191]  A. Kidera,et al.  Multicanonical Ensemble Generated by Molecular Dynamics Simulation for Enhanced Conformational Sampling of Peptides , 1997 .

[192]  Federico Fogolari,et al.  Protocol for MM/PBSA molecular dynamics simulations of proteins. , 2003, Biophysical journal.