Coarse-grained representation of protein flexibility. Foundations, successes, and shortcomings.

Flexibility is the key magnitude to understand the variety of functions of proteins. Unfortunately, its experimental study is quite difficult, and in fact, most experimental procedures are designed to reduce flexibility and allow a better definition of the structure. Theoretical approaches have become then the alternative but face serious timescale problems, since many biologically relevant deformation movements happen in a timescale that is far beyond the possibility of current atomistic models. In this complex scenario, coarse-grained simulation methods have emerged as a powerful and inexpensive alternative. Along this chapter, we will review these coarse-grained methods, and explain their physical foundations and their range of applicability.

[1]  Kyle A. Beauchamp,et al.  Molecular simulation of ab initio protein folding for a millisecond folder NTL9(1-39). , 2010, Journal of the American Chemical Society.

[2]  Modesto Orozco,et al.  Approaching Elastic Network Models to Molecular Dynamics Flexibility. , 2010, Journal of chemical theory and computation.

[3]  Modesto Orozco,et al.  FlexServ: an integrated tool for the analysis of protein flexibility , 2009, Bioinform..

[4]  R. Abseher,et al.  Essential spaces defined by NMR structure ensembles and molecular dynamics simulation show significant overlap , 1998, Proteins.

[5]  Modesto Orozco,et al.  United-Atom Discrete Molecular Dynamics of Proteins Using Physics-Based Potentials. , 2008, Journal of chemical theory and computation.

[6]  Mark Gerstein,et al.  Normal mode analysis of macromolecular motions in a database framework: Developing mode concentration as a useful classifying statistic , 2002, Proteins.

[7]  Modesto Orozco,et al.  Protein flexibility from discrete molecular dynamics simulations using quasi‐physical potentials , 2010, Proteins.

[8]  J. Onuchic,et al.  Interplay among tertiary contacts, secondary structure formation and side-chain packing in the protein folding mechanism: all-atom representation study of protein L. , 2003, Journal of molecular biology.

[9]  K. Hinsen,et al.  Harmonicity in slow protein dynamics , 2000 .

[10]  D. Lemons,et al.  Paul Langevin’s 1908 paper “On the Theory of Brownian Motion” [“Sur la théorie du mouvement brownien,” C. R. Acad. Sci. (Paris) 146, 530–533 (1908)] , 1997 .

[11]  Ruben Abagyan,et al.  Consistent Improvement of Cross-Docking Results Using Binding Site Ensembles Generated with Elastic Network Normal Modes , 2009, J. Chem. Inf. Model..

[12]  Y. Sanejouand,et al.  Building‐block approach for determining low‐frequency normal modes of macromolecules , 2000, Proteins.

[13]  Modesto Orozco,et al.  A consensus view of protein dynamics , 2007, Proceedings of the National Academy of Sciences.

[14]  M. Karplus,et al.  The allosteric mechanism of yeast chorismate mutase: a dynamic analysis. , 2006, Journal of molecular biology.

[15]  M. Kim,et al.  A connection rule for alpha-carbon coarse-grained elastic network models using chemical bond information. , 2006, Journal of molecular graphics & modelling.

[16]  N. Go,et al.  Studies on protein folding, unfolding and fluctuations by computer simulation. I. The effect of specific amino acid sequence represented by specific inter-unit interactions. , 2009 .

[17]  Raymond J. Seeger,et al.  Lectures in Theoretical Physics , 1962 .

[18]  J. Sorenson,et al.  Toward minimalist models of larger proteins: A ubiquitin‐like protein , 2002, Proteins.

[19]  Klaus Schulten,et al.  Coarse-grained molecular dynamics simulations of a rotating bacterial flagellum. , 2006, Biophysical journal.

[20]  M J Harvey,et al.  ACEMD: Accelerating Biomolecular Dynamics in the Microsecond Time Scale. , 2009, Journal of chemical theory and computation.

[21]  Carsten Kutzner,et al.  GROMACS 4:  Algorithms for Highly Efficient, Load-Balanced, and Scalable Molecular Simulation. , 2008, Journal of chemical theory and computation.

[22]  R. Abagyan,et al.  Predictions of protein flexibility: First‐order measures , 2004, Proteins.

[23]  Alexander D. MacKerell,et al.  An all-atom empirical energy function for the simulation of nucleic acids , 1995 .

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

[25]  G. Voth Coarse-Graining of Condensed Phase and Biomolecular Systems , 2008 .

[26]  Modesto Orozco,et al.  MoDEL (Molecular Dynamics Extended Library): a database of atomistic molecular dynamics trajectories. , 2010, Structure.

[27]  Laxmikant V. Kalé,et al.  Scalable molecular dynamics with NAMD , 2005, J. Comput. Chem..

[28]  Robert L. Jernigan,et al.  Optimizing the Parameters of the Gaussian Network Model for ATP-Binding Proteins , 2005 .

[29]  N. Go Protein folding as a stochastic process , 1983 .

[30]  T. N. Bhat,et al.  The Protein Data Bank , 2000, Nucleic Acids Res..

[31]  M. Karplus,et al.  Interpreting the folding kinetics of helical proteins , 1999, Nature.

[32]  M. Karplus Molecular Dynamics Simulations of Proteins , 1987 .

[33]  Tirion,et al.  Large Amplitude Elastic Motions in Proteins from a Single-Parameter, Atomic Analysis. , 1996, Physical review letters.

[34]  C. W. Gardiner,et al.  Handbook of stochastic methods - for physics, chemistry and the natural sciences, Second Edition , 1986, Springer series in synergetics.

[35]  G. Phillips,et al.  Optimization and evaluation of a coarse-grained model of protein motion using x-ray crystal data. , 2006, Biophysical journal.

[36]  A. Liwo,et al.  Modification and optimization of the united-residue (UNRES) potential energy function for canonical simulations. I. Temperature dependence of the effective energy function and tests of the optimization method with single training proteins. , 2007, The journal of physical chemistry. B.

[37]  B. Montgomery Pettitt,et al.  Dynamical Simulation Methods , 1988 .

[38]  M. Karplus,et al.  Dynamics of folded proteins , 1977, Nature.

[39]  I. Bahar,et al.  Normal mode analysis : theory and applications to biological and chemical systems , 2005 .

[40]  R Dustin Schaeffer,et al.  Dynameomics: a comprehensive database of protein dynamics. , 2010, Structure.

[41]  N. Kampen,et al.  Stochastic processes in physics and chemistry , 1981 .

[42]  D. Tieleman,et al.  The MARTINI force field: coarse grained model for biomolecular simulations. , 2007, The journal of physical chemistry. B.

[43]  J. Onuchic,et al.  Topological and energetic factors: what determines the structural details of the transition state ensemble and "en-route" intermediates for protein folding? An investigation for small globular proteins. , 2000, Journal of molecular biology.

[44]  William L. Jorgensen,et al.  Monte Carlo backbone sampling for polypeptides with variable bond angles and dihedral angles using concerted rotations and a Gaussian bias , 2003 .

[45]  Julian Tirado-Rives,et al.  Molecular modeling of organic and biomolecular systems using BOSS and MCPRO , 2005, J. Comput. Chem..

[46]  Ugo Bastolla,et al.  Torsional network model: normal modes in torsion angle space better correlate with conformation changes in proteins. , 2010, Physical review letters.

[47]  S. Marrink,et al.  The MARTINI force field , 2008 .

[48]  Klaus Schulten,et al.  Coarse grained protein-lipid model with application to lipoprotein particles. , 2006, The journal of physical chemistry. B.

[49]  A. Liwo,et al.  Kinetic studies of folding of the B-domain of staphylococcal protein A with molecular dynamics and a united-residue (UNRES) model of polypeptide chains. , 2006, Journal of molecular biology.

[50]  Jeremy C. Smith,et al.  Coarse-grained biomolecular simulation with REACH: realistic extension algorithm via covariance Hessian. , 2007, Biophysical journal.

[51]  P. Chacón,et al.  Thorough validation of protein normal mode analysis: a comparative study with essential dynamics. , 2007, Structure.

[52]  Feng Ding,et al.  Dynamical roles of metal ions and the disulfide bond in Cu, Zn superoxide dismutase folding and aggregation , 2008, Proceedings of the National Academy of Sciences.

[53]  S. Buldyrev,et al.  Folding Trp-cage to NMR resolution native structure using a coarse-grained protein model. , 2004, Biophysical journal.

[54]  C. Chennubhotla,et al.  Insights into equilibrium dynamics of proteins from comparison of NMR and X-ray data with computational predictions. , 2007, Structure.

[55]  R. Jernigan,et al.  Anisotropy of fluctuation dynamics of proteins with an elastic network model. , 2001, Biophysical journal.

[56]  M. Sternberg,et al.  Insights into protein flexibility: The relationship between normal modes and conformational change upon protein–protein docking , 2008, Proceedings of the National Academy of Sciences.

[57]  Klaus Schulten,et al.  Stability and dynamics of virus capsids described by coarse-grained modeling. , 2006, Structure.

[58]  P. Mazur On the theory of brownian motion , 1959 .

[59]  Modesto Orozco,et al.  Exploring the suitability of coarse-grained techniques for the representation of protein dynamics. , 2008, Biophysical journal.