Functionally relevant protein motions: extracting basin-specific collective coordinates from molecular dynamics trajectories.

Functionally relevant motion of proteins has been associated with a number of atoms moving in a concerted fashion along so-called "collective coordinates." We present an approach to extract collective coordinates from conformations obtained from molecular dynamics simulations. The power of this technique for differentiating local structural fluctuations between classes of conformers obtained by clustering is illustrated by analyzing nanosecond-long trajectories for the response regulator protein Spo0F of Bacillus subtilis, generated both in vacuo and using an implicit-solvent representation. Conformational clustering is performed using automated histogram filtering of the inter-C(alpha) distances. Orthogonal (varimax) rotation of the vectors obtained by principal component analysis of these interresidue distances for the members of individual clusters is key to the interpretation of collective coordinates dominating each conformational class. The rotated loadings plots isolate significant variation in interresidue distances, and these are associated with entire mobile secondary structure elements. From this we infer concerted motions of these structural elements. For the Spo0F simulations employing an implicit-solvent representation, collective coordinates obtained in this fashion are consistent with the location of the protein's known active sites and experimentally determined mobile regions.

[1]  Takashi Amisaki,et al.  Development of MD Engine: High‐speed accelerator with parallel processor design for molecular dynamics simulations , 1999 .

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

[3]  A. C. Rencher.  Methods of multivariate analysis , 1995 .

[4]  J M Whiteley,et al.  High-resolution NMR structure and backbone dynamics of the Bacillus subtilis response regulator, Spo0F: implications for phosphorylation and molecular recognition. , 1997, Biochemistry.

[5]  Richard A. Johnson,et al.  Applied Multivariate Statistical Analysis , 1983 .

[6]  A. R. Srinivasan,et al.  Quasi‐harmonic method for studying very low frequency modes in proteins , 1984, Biopolymers.

[8]  A. D. McLachlan,et al.  Solvation energy in protein folding and binding , 1986, Nature.

[9]  P. Weiner,et al.  Computer Simulation of Biomolecular Systems , 1997 .

[10]  A Kitao,et al.  Energy landscape of a native protein: Jumping‐among‐minima model , 1998, Proteins.

[11]  Stuart M. Rothstein,et al.  Efficient generation of low-energy folded states of a model protein. II. Automated histogram filtering , 2003 .

[12]  F E Cohen,et al.  Protein conformational landscapes: Energy minimization and clustering of a long molecular dynamics trajectory , 1995, Proteins.

[13]  M L Teodoro,et al.  Conformational flexibility models for the receptor in structure based drug design. , 2003, Current pharmaceutical design.

[14]  H. Frauenfelder,et al.  Conformational substates in proteins. , 1988, Annual review of biophysics and biophysical chemistry.

[15]  M. Karplus,et al.  Evaluation of the configurational entropy for proteins: application to molecular dynamics simulations of an α-helix , 1984 .

[16]  Robert J. Wherry,et al.  Multiple Factor Analysis: A Development and Expansion of "The Vectors of the Mind" , 1948 .

[17]  Fumio Hirata,et al.  The effects of solvent on the conformation and the collective motions of protein: normal mode analysis and molecular dynamics simulations of melittin in water and in vacuum , 1991 .

[18]  H. Berendsen,et al.  Essential dynamics of proteins , 1993, Proteins.

[19]  H. Berendsen,et al.  Molecular dynamics with coupling to an external bath , 1984 .

[20]  J. Thornton,et al.  PROCHECK: a program to check the stereochemical quality of protein structures , 1993 .

[21]  Victoria A. Feher,et al.  Millisecond-timescale motions contribute to the function of the bacterial response regulator protein Spo0F , 1999, Nature.

[22]  H. Harman.  Modern factor analysis , 1961 .

[23]  A. Garcia,et al.  Simulations of CRP:(cAMP)2 in noncrystalline environments show a subunit transition from the open to the closed conformation , 1996, Protein science : a publication of the Protein Society.

[24]  J. Hoch,et al.  Molecular recognition in signal transduction: the interaction surfaces of the Spo0F response regulator with its cognate phosphorelay proteins revealed by alanine scanning mutagenesis. , 1997, Journal of molecular biology.

[25]  R. Rummel.  Applied Factor Analysis , 1970 .

[26]  Lydia E. Kavraki,et al.  Understanding Protein Flexibility through Dimensionality Reduction , 2003, J. Comput. Biol..

[27]  M. Karplus,et al.  Collective motions in proteins: A covariance analysis of atomic fluctuations in molecular dynamics and normal mode simulations , 1991, Proteins.

[28]  Julia M. Goodfellow,et al.  Simulated dynamics and biological macromolecules , 2003 .

[29]  N Go,et al.  Collective variable description of native protein dynamics. , 1995, Annual review of physical chemistry.

[30]  M. Tatsuoka.  Multivariate Analysis Techniques for Educational and Psychological Research , 1971 .

[31]  Stuart M. Rothstein,et al.  Histogram filtering: A technique to optimize wave functions for use in Monte Carlo simulations , 1999 .

[32]  P. Kraulis.  A program to produce both detailed and schematic plots of protein structures , 1991 .

[33]  M. Karplus,et al.  Method for estimating the configurational entropy of macromolecules , 1981 .

[34]  N. Go,et al.  Investigating protein dynamics in collective coordinate space. , 1999, Current opinion in structural biology.

[35]  H J Berendsen,et al.  An efficient method for sampling the essential subspace of proteins. , 1996, Journal of biomolecular structure & dynamics.

[36]  R. Berry,et al.  Principal coordinate analysis on a protein model , 1999 .