Molecular dynamics simulations with replica-averaged structural restraints generate structural ensembles according to the maximum entropy principle.

In order to characterise the dynamics of proteins, a well-established method is to incorporate experimental parameters as replica-averaged structural restraints into molecular dynamics simulations. Here, we justify this approach in the case of interproton distance information provided by nuclear Overhauser effects by showing that it generates ensembles of conformations according to the maximum entropy principle. These results indicate that the use of replica-averaged structural restraints in molecular dynamics simulations, given a force field and a set of experimental data, can provide an accurate approximation of the unknown Boltzmann distribution of a system.

[1]  A. Cavalli,et al.  Analysis of the distributed computing approach applied to the folding of a small β peptide , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[2]  Levi C. T. Pierce,et al.  Multi-Timescale Conformational Dynamics of the SH3 Domain of CD2-Associated Protein using NMR Spectroscopy and Accelerated Molecular Dynamics** , 2012, Angewandte Chemie.

[3]  M. Karplus,et al.  Molecular dynamics and protein function. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[4]  J. Pitera,et al.  Assessing the effect of conformational averaging on the measured values of observables , 2001, Journal of biomolecular NMR.

[5]  Jane R. Allison,et al.  Probing the Structure and Dynamics of Proteins by Combining Molecular Dynamics Simulations and Experimental NMR Data. , 2012, Journal of chemical theory and computation.

[6]  X. Salvatella,et al.  Toward an accurate determination of free energy landscapes in solution states of proteins. , 2009, Journal of the American Chemical Society.

[7]  Lewis E. Kay,et al.  New Tools Provide New Insights in NMR Studies of Protein Dynamics , 2006, Science.

[8]  F. Young Biochemistry , 1955, The Indian Medical Gazette.

[9]  John D Chodera,et al.  On the Use of Experimental Observations to Bias Simulated Ensembles. , 2012, Journal of chemical theory and computation.

[10]  R. Best Atomistic molecular simulations of protein folding. , 2012, Current opinion in structural biology.

[11]  A. Bax Weak alignment offers new NMR opportunities to study protein structure and dynamics , 2003, Protein science : a publication of the Protein Society.

[12]  宁北芳,et al.  疟原虫var基因转换速率变化导致抗原变异[英]/Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A , 2005 .

[13]  Berend Smit,et al.  Accelerating Monte Carlo Sampling , 2002 .

[14]  A. Palmer,et al.  NMR characterization of the dynamics of biomacromolecules. , 2004, Chemical reviews.

[15]  B. Zagrovic,et al.  Comparing atomistic simulation data with the NMR experiment: How much can NOEs actually tell us? , 2006, Proteins.

[16]  A. Brünger,et al.  Conformational variability of solution nuclear magnetic resonance structures. , 1995, Journal of molecular biology.

[17]  R. Brunne,et al.  Structure refinement using time-averaged J-coupling constant restraints , 1993, Journal of biomolecular NMR.

[18]  Michele Vendruscolo,et al.  Rare fluctuations of native proteins sampled by equilibrium hydrogen exchange. , 2003, Journal of the American Chemical Society.

[19]  K. Lindorff-Larsen,et al.  How robust are protein folding simulations with respect to force field parameterization? , 2011, Biophysical journal.

[20]  G. Daughdrill,et al.  Understanding the structural ensembles of a highly extended disordered protein. , 2012, Molecular bioSystems.

[21]  K. Wüthrich Protein structure determination in solution by nuclear magnetic resonance spectroscopy. , 1989, Science.

[22]  P. Wolynes,et al.  The energy landscapes and motions of proteins. , 1991, Science.

[23]  M. Plischke,et al.  Equilibrium statistical physics , 1988 .

[24]  W. Scott,et al.  On using time-averaging restraints in molecular dynamics simulation , 1998, Journal of biomolecular NMR.

[25]  R. Bruccoleri,et al.  Structural and Dynamic Properties of a .beta.-Hairpin-Forming Linear Peptide. 1. Modeling Using Ensemble-Averaged Constraints , 1995 .

[26]  B. Hess,et al.  Orientation restraints in molecular dynamics simulations using time and ensemble averaging. , 2003, Journal of magnetic resonance.

[27]  R. Rosenfeld Nature , 2009, Otolaryngology--head and neck surgery : official journal of American Academy of Otolaryngology-Head and Neck Surgery.

[28]  W. F. Gunsteren,et al.  Structure refinement with molecular dynamics and a Boltzmann-weighted ensemble , 1995, Journal of biomolecular NMR.

[29]  X. Salvatella,et al.  The MUMO (minimal under-restraining minimal over-restraining) method for the determination of native state ensembles of proteins , 2007, Journal of biomolecular NMR.

[30]  C. Kalodimos NMR reveals novel mechanisms of protein activity regulation , 2011, Protein science : a publication of the Protein Society.

[31]  C. Dobson,et al.  Protein Dynamics: Moore's Law in Molecular Biology , 2011, Current Biology.

[32]  C. Dobson,et al.  Mapping long-range interactions in alpha-synuclein using spin-label NMR and ensemble molecular dynamics simulations. , 2005, Journal of the American Chemical Society.

[33]  Michele Vendruscolo,et al.  Determination of conformationally heterogeneous states of proteins. , 2007, Current opinion in structural biology.

[34]  W. V. van Gunsteren,et al.  Time-averaged nuclear Overhauser effect distance restraints applied to tendamistat. , 1990, Journal of molecular biology.

[35]  A. Fersht Structure and mechanism in protein science , 1998 .

[36]  J. Forman-Kay,et al.  Atomic-level characterization of disordered protein ensembles. , 2007, Current opinion in structural biology.

[37]  B. Alberts,et al.  Molecular Biology of the Cell (Fifth Edition) , 2008 .

[38]  R. A. Leibler,et al.  On Information and Sufficiency , 1951 .

[39]  J. Berg,et al.  Molecular dynamics simulations of biomolecules , 2002, Nature Structural Biology.

[40]  M. DePristo,et al.  Simultaneous determination of protein structure and dynamics , 2005, Nature.

[41]  Michele Vendruscolo,et al.  Comparison of sequence-based and structure-based energy functions for the reversible folding of a peptide. , 2005, Biophysical journal.

[42]  G. Marius Clore,et al.  Amplitudes of Protein Backbone Dynamics and Correlated Motions in a Small α/β Protein: Correspondence of Dipolar Coupling and Heteronuclear Relaxation Measurements† , 2004 .

[43]  Berend Smit,et al.  Understanding Molecular Simulation , 2001 .

[44]  R. Kaptein,et al.  Time- and ensemble-averaged direct NOE restraints , 1994, Journal of biomolecular NMR.

[45]  Michael Nilges,et al.  Computational approaches to the interpretation of NMR data for studying protein dynamics , 2012 .

[46]  J. Kemmink,et al.  Dynamic modelling of a helical peptide in solution using NMR data: Multiple conformations and multi-spin effects , 1995, Journal of biomolecular NMR.

[47]  W. Vangunsteren,et al.  CONFORMATIONAL DYNAMICS DETECTED BY NUCLEAR MAGNETIC-RESONANCE NOE VALUES AND J-COUPLING CONSTANTS , 1988 .

[48]  Joseph A. Bank,et al.  Supporting Online Material Materials and Methods Figs. S1 to S10 Table S1 References Movies S1 to S3 Atomic-level Characterization of the Structural Dynamics of Proteins , 2022 .

[49]  G. Clore,et al.  How much backbone motion in ubiquitin is required to account for dipolar coupling data measured in multiple alignment media as assessed by independent cross-validation? , 2004, Journal of the American Chemical Society.

[50]  E. Jaynes Information Theory and Statistical Mechanics , 1957 .

[51]  Michele Vendruscolo,et al.  Determination of Conformational Equilibria in Proteins Using Residual Dipolar Couplings , 2011, Journal of chemical theory and computation.

[52]  W. Bialek,et al.  Statistical mechanics for natural flocks of birds , 2011, Proceedings of the National Academy of Sciences.

[53]  R. Nussinov,et al.  The role of dynamic conformational ensembles in biomolecular recognition. , 2009, Nature chemical biology.

[54]  W. F. Gunsteren,et al.  Time-dependent distance restraints in molecular dynamics simulations , 1989 .

[55]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

[56]  Martin Blackledge,et al.  Conformational distributions of unfolded polypeptides from novel NMR techniques. , 2008, The Journal of chemical physics.