The MUMO (minimal under-restraining minimal over-restraining) method for the determination of native state ensembles of proteins

While reliable procedures for determining the conformations of proteins are available, methods for generating ensembles of structures that also reflect their flexibility are much less well established. Here we present a systematic assessment of the ability of ensemble-averaged molecular dynamics simulations with ensemble-averaged NMR restraints to simultaneously reproduce the average structure of proteins and their associated dynamics. We discuss the effects that under-restraining (overfitting) and over-restraining (underfitting) have on the structures generated in ensemble-averaged molecular simulations. We then introduce the MUMO (minimal under-restraining minimal over-restraining) method, a procedure in which different observables are averaged over a different number of molecules. As both over-restraining and under-restraining are significantly reduced in the MUMO method, it is possible to generate ensembles of conformations that accurately characterize both the structure and the dynamics of native states of proteins. The application of the MUMO method to the protein ubiquitin yields a high-resolution structural ensemble with an RDC Q-factor of 0.19.

[1]  Martin Karplus,et al.  Vicinal Proton Coupling in Nuclear Magnetic Resonance , 1963 .

[2]  G. Ciccotti,et al.  Numerical Integration of the Cartesian Equations of Motion of a System with Constraints: Molecular Dynamics of n-Alkanes , 1977 .

[3]  G. Lipari.  Model-free approach to the interpretation of nuclear magnetic resonance relaxation in macromolecules , 1982 .

[4]  A. Szabó,et al.  Model-free approach to the interpretation of nuclear magnetic resonance relaxation in macromolecules. 1. Theory and range of validity , 1982 .

[5]  W. L. Jorgensen,et al.  Comparison of simple potential functions for simulating liquid water , 1983 .

[6]  M. Karplus,et al.  CHARMM: A program for macromolecular energy, minimization, and dynamics calculations , 1983 .

[7]  E. Henry,et al.  Influence of vibrational motion on solid state line shapes and NMR relaxation , 1985 .

[8]  K. Wüthrich.  NMR of proteins and nucleic acids , 1988 .

[9]  M Karplus,et al.  Effect of anisotropy and anharmonicity on protein crystallographic refinement. An evaluation by molecular dynamics. , 1986, Journal of molecular biology.

[10]  M Karplus,et al.  Three-dimensional structure of proteins determined by molecular dynamics with interproton distance restraints: application to crambin. , 1986, Proceedings of the National Academy of Sciences of the United States of America.

[11]  C. Bugg,et al.  Structure of ubiquitin refined at 1.8 A resolution. , 1987, Journal of molecular biology.

[12]  M. Mézard,et al.  Spin Glass Theory and Beyond , 1987 .

[13]  M. Karplus,et al.  Anisotropy and anharmonicity of atomic fluctuations in proteins: implications for X-ray analysis. , 1988, Biochemistry.

[14]  David Neuhaus,et al.  The Nuclear Overhauser Effect in Structural and Conformational Analysis , 1989 .

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

[16]  M. Karplus,et al.  Molecular dynamics simulations in biology , 1990, Nature.

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

[18]  A. Brünger.  Free R value: a novel statistical quantity for assessing the accuracy of crystal structures , 1992, Nature.

[19]  A. Gronenborn,et al.  Assessing the quality of solution nuclear magnetic resonance structures by complete cross-validation. , 1993, Science.

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

[21]  D. Beglov,et al.  Finite representation of an infinite bulk system: Solvent boundary potential for computer simulations , 1994 .

[22]  A. Bax,et al.  Rotational diffusion anisotropy of human ubiquitin from 15N NMR relaxation , 1995 .

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

[24]  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.

[25]  P. Kollman,et al.  A Second Generation Force Field for the Simulation of Proteins, Nucleic Acids, and Organic Molecules , 1995 .

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

[27]  A T Brünger,et al.  Do NOE distances contain enough information to assess the relative populations of multi-conformer structures? , 1996, Journal of biomolecular NMR.

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

[29]  Ad Bax,et al.  Validation of Protein Structure from Anisotropic Carbonyl Chemical Shifts in a Dilute Liquid Crystalline Phase , 1998 .

[30]  R J Read,et al.  Crystallography & NMR system: A new software suite for macromolecular structure determination. , 1998, Acta crystallographica. Section D, Biological crystallography.

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

[32]  Comparison of 2H and 13C NMR Relaxation Techniques for the Study of Protein Methyl Group Dynamics in Solution , 1999 .

[33]  G. Marius Clore,et al.  Improving the Packing and Accuracy of NMR Structures with a Pseudopotential for the Radius of Gyration , 1999 .

[34]  Andrew E. Torda,et al.  The GROMOS biomolecular simulation program package , 1999 .

[35]  S. Grzesiek,et al.  Direct Observation of Hydrogen Bonds in Proteins by Interresidue 3hJNC' Scalar Couplings , 1999 .

[36]  A T Brünger,et al.  Influence of internal dynamics on accuracy of protein NMR structures: derivation of realistic model distance data from a long molecular dynamics trajectory. , 1999, Journal of molecular biology.

[37]  M Karplus,et al.  Forced unfolding of fibronectin type 3 modules: an analysis by biased molecular dynamics simulations. , 1999, Journal of molecular biology.

[38]  Ad Bax,et al.  Prediction of Sterically Induced Alignment in a Dilute Liquid Crystalline Phase: Aid to Protein Structure Determination by NMR , 2000 .

[39]  B. X. Carlson,et al.  A single glycine residue at the entrance to the first membrane-spanning domain of the gamma-aminobutyric acid type A receptor beta(2) subunit affects allosteric sensitivity to GABA and anesthetics. , 2000, Molecular pharmacology.

[40]  J A McCammon,et al.  Accommodating protein flexibility in computational drug design. , 2000, Molecular pharmacology.

[41]  A. Joshua Wand,et al.  Dynamic activation of protein function: A view emerging from NMR spectroscopy , 2001, Nature Structural Biology.

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

[43]  S. Grzesiek,et al.  Temperature-dependence of protein hydrogen bond properties as studied by high-resolution NMR. , 2002, Journal of molecular biology.

[44]  H. Carlson.  Protein flexibility and drug design: how to hit a moving target. , 2002, Current opinion in chemical biology.

[45]  Nico Tjandra,et al.  NMR dipolar couplings for the structure determination of biopolymers in solution , 2002 .

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

[47]  R. Nussinov,et al.  Stabilities and conformations of Alzheimer's β-amyloid peptide oligomers (Aβ16–22, Aβ16–35, and Aβ10–35): Sequence effects , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[48]  M. Barfield,et al.  Structural dependencies of interresidue scalar coupling (h3)J(NC') and donor (1)H chemical shifts in the hydrogen bonding regions of proteins. , 2002, Journal of the American Chemical Society.

[49]  Michele Vendruscolo,et al.  Protein folding: bringing theory and experiment closer together. , 2003, Current opinion in structural biology.

[50]  E. Zuiderweg,et al.  Temperature dependence of anisotropic protein backbone dynamics. , 2003, Journal of the American Chemical Society.

[51]  Ad Bax,et al.  Insights into the mobility of methyl-bearing side chains in proteins from (3)J(CC) and (3)J(CN) couplings. , 2003, Journal of the American Chemical Society.

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

[53]  S. Teague.  Implications of protein flexibility for drug discovery , 2003, Nature Reviews Drug Discovery.

[54]  J Andrew McCammon,et al.  Protein flexibility and computer-aided drug design. , 2003, Annual review of pharmacology and toxicology.

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

[56]  Michele Vendruscolo,et al.  Towards complete descriptions of the free–energy landscapes of proteins , 2005, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[57]  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.

[58]  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 .

[59]  M. Nilges,et al.  Complementarity of structure ensembles in protein-protein binding. , 2004, Structure.

[60]  Gert Vriend,et al.  Validation of protein structures derived by NMR spectroscopy , 2004 .

[61]  J. Mccammon,et al.  HIV‐1 protease molecular dynamics of a wild‐type and of the V82F/I84V mutant: Possible contributions to drug resistance and a potential new target site for drugs , 2004, Protein science : a publication of the Protein Society.

[62]  M. Vendruscolo,et al.  Determination of protein structures consistent with NMR order parameters. , 2004, Journal of the American Chemical Society.

[63]  S. Grzesiek,et al.  Insights into biomolecular hydrogen bonds from hydrogen bond scalar couplings , 2004 .

[64]  Charles D Schwieters,et al.  Amplitudes of protein backbone dynamics and correlated motions in a small alpha/beta protein: correspondence of dipolar coupling and heteronuclear relaxation measurements. , 2004, Biochemistry.

[65]  Arthur G. Palmer,et al.  NMR Characterization of the Dynamics of Biomacromolecules , 2004 .

[66]  Peter E. Wright,et al.  Model-free Analysis of Protein Dynamics: Assessment of Accuracy and Model Selection Protocols Based on Molecular Dynamics Simulation , 2004, Journal of biomolecular NMR.

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

[68]  Michael Nilges,et al.  Materials and Methods Som Text Figs. S1 to S6 References Movies S1 to S5 Inferential Structure Determination , 2022 .

[69]  Nico Tjandra,et al.  Temperature dependence of protein backbone motion from carbonyl 13C and amide 15N NMR relaxation. , 2005, Journal of magnetic resonance.

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

[71]  A. Bonvin,et al.  NMR Relaxation and Internal Dynamics of Ubiquitin from a 0.2 μs MD Simulation. , 2005, Journal of chemical theory and computation.

[72]  G. Marius Clore,et al.  Using Xplor-NIH for NMR molecular structure determination , 2006 .

[73]  G. Clore,et al.  Concordance of residual dipolar couplings, backbone order parameters and crystallographic B-factors for a small alpha/beta protein: a unified picture of high probability, fast atomic motions in proteins. , 2006, Journal of molecular biology.

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

[75]  G. Marius Clore,et al.  Using Xplor‐NIH for NMR Molecular Structure Determination , 2006 .