Elastic network normal modes provide a basis for protein structure refinement.

It is well recognized that thermal motions of atoms in the protein native state, the fluctuations about the minimum of the global free energy, are well reproduced by the simple elastic network models (ENMs) such as the anisotropic network model (ANM). Elastic network models represent protein dynamics as vibrations of a network of nodes (usually represented by positions of the heavy atoms or by the C(α) atoms only for coarse-grained representations) in which the spatially close nodes are connected by harmonic springs. These models provide a reliable representation of the fluctuational dynamics of proteins and RNA, and explain various conformational changes in protein structures including those important for ligand binding. In the present paper, we study the problem of protein structure refinement by analyzing thermal motions of proteins in non-native states. We represent the conformational space close to the native state by a set of decoys generated by the I-TASSER protein structure prediction server utilizing template-free modeling. The protein substates are selected by hierarchical structure clustering. The main finding is that thermal motions for some substates, overlap significantly with the deformations necessary to reach the native state. Additionally, more mobile residues yield higher overlaps with the required deformations than do the less mobile ones. These findings suggest that structural refinement of poorly resolved protein models can be significantly enhanced by reduction of the conformational space to the motions imposed by the dominant normal modes.

[1]  P. Wolynes,et al.  Spin glasses and the statistical mechanics of protein folding. , 1987, Proceedings of the National Academy of Sciences of the United States of America.

[2]  Ron Elber,et al.  A method for determining reaction paths in large molecules: application to myoglobin , 1987 .

[3]  P. Wolynes,et al.  Intermediates and barrier crossing in a random energy model , 1989 .

[4]  N. Go,et al.  Structural basis of hierarchical multiple substates of a protein. V: Nonlocal deformations , 1989, Proteins.

[5]  O. Ptitsyn,et al.  Molten globule and protein folding. , 1995, Advances in protein chemistry.

[6]  Y. Sanejouand,et al.  Hinge‐bending motion in citrate synthase arising from normal mode calculations , 1995, Proteins.

[7]  David Pérahia,et al.  Computation of Low-frequency Normal Modes in Macromolecules: Improvements to the Method of Diagonalization in a Mixed Basis and Application to Hemoglobin , 1995, Comput. Chem..

[8]  W. L. Jorgensen,et al.  Development and Testing of the OPLS All-Atom Force Field on Conformational Energetics and Properties of Organic Liquids , 1996 .

[9]  J. Onuchic,et al.  Theory of protein folding: the energy landscape perspective. , 1997, Annual review of physical chemistry.

[10]  B. Erman,et al.  Efficient characterization of collective motions and interresidue correlations in proteins by low-resolution simulations. , 1997, Biochemistry.

[11]  A. Atilgan,et al.  Direct evaluation of thermal fluctuations in proteins using a single-parameter harmonic potential. , 1997, Folding & design.

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

[13]  D. Baker,et al.  Clustering of low-energy conformations near the native structures of small proteins. , 1998, Proceedings of the National Academy of Sciences of the United States of America.

[14]  R. J. Dwayne Miller,et al.  Ultrafast Phase Grating Studies of Heme Proteins: Observation of the Low-Frequency Modes Directing Functionally Important Protein Motions , 1998 .

[15]  R. Nussinov,et al.  Folding and binding cascades: shifts in energy landscapes. , 1999, Proceedings of the National Academy of Sciences of the United States of America.

[16]  D T Jones,et al.  Protein secondary structure prediction based on position-specific scoring matrices. , 1999, Journal of molecular biology.

[17]  David S. Cafiso,et al.  Identifying conformational changes with site-directed spin labeling , 2000, Nature Structural Biology.

[18]  Y. Sanejouand,et al.  Conformational change of proteins arising from normal mode calculations. , 2001, Protein engineering.

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

[20]  G. Chirikjian,et al.  Elastic models of conformational transitions in macromolecules. , 2002, Journal of molecular graphics & modelling.

[21]  G. Chirikjian,et al.  Efficient generation of feasible pathways for protein conformational transitions. , 2002, Biophysical journal.

[22]  Dror Tobi,et al.  Allosteric changes in protein structure computed by a simple mechanical model: hemoglobin T<-->R2 transition. , 2003, Journal of molecular biology.

[23]  Jens Meiler,et al.  Rosetta predictions in CASP5: Successes, failures, and prospects for complete automation , 2003, Proteins.

[24]  A. Elofsson,et al.  Can correct protein models be identified? , 2003, Protein science : a publication of the Protein Society.

[25]  M. Delarue,et al.  On the use of low-frequency normal modes to enforce collective movements in refining macromolecular structural models. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

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

[27]  Yang Zhang,et al.  Scoring function for automated assessment of protein structure template quality , 2004, Proteins.

[28]  Robert L Jernigan,et al.  Rigid-cluster models of conformational transitions in macromolecular machines and assemblies. , 2005, Biophysical journal.

[29]  Dominik Gront,et al.  HCPM - program for hierarchical clustering of protein models , 2005, Bioinform..

[30]  Jianpeng Ma,et al.  Usefulness and limitations of normal mode analysis in modeling dynamics of biomolecular complexes. , 2005, Structure.

[31]  Eric J. Sorin,et al.  Exploring the helix-coil transition via all-atom equilibrium ensemble simulations. , 2005, Biophysical journal.

[32]  L. Kay,et al.  Intrinsic dynamics of an enzyme underlies catalysis , 2005, Nature.

[33]  Taner Z Sen,et al.  The Extent of Cooperativity of Protein Motions Observed with Elastic Network Models Is Similar for Atomic and Coarser-Grained Models. , 2006, Journal of chemical theory and computation.

[34]  Ivet Bahar,et al.  Anisotropic network model: systematic evaluation and a new web interface , 2006, Bioinform..

[35]  Michael Feig,et al.  A correlation‐based method for the enhancement of scoring functions on funnel‐shaped energy landscapes , 2006, Proteins.

[36]  D. Cafiso,et al.  Recent advances and applications of site-directed spin labeling. , 2006, Current opinion in structural biology.

[37]  Guang Song,et al.  How well can we understand large-scale protein motions using normal modes of elastic network models? , 2007, Biophysical journal.

[38]  Yang Zhang,et al.  I-TASSER server for protein 3D structure prediction , 2008, BMC Bioinformatics.

[39]  C Micheletti,et al.  Anharmonicity and self-similarity of the free energy landscape of protein G. , 2006, Physical review letters.

[40]  C. Chennubhotla,et al.  Intrinsic dynamics of enzymes in the unbound state and relation to allosteric regulation. , 2007, Current opinion in structural biology.

[41]  R. Jernigan,et al.  The ribosome structure controls and directs mRNA entry, translocation and exit dynamics , 2008, Physical biology.

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

[43]  J. I. Sulkowska,et al.  Predicting the order in which contacts are broken during single molecule protein stretching experiments , 2008, Proteins.

[44]  Christopher M. Summa,et al.  Solvent dramatically affects protein structure refinement , 2008, Proceedings of the National Academy of Sciences.

[45]  Cristian Micheletti,et al.  Small- and large-scale conformational changes of adenylate kinase: a molecular dynamics study of the subdomain motion and mechanics. , 2008, Biophysical journal.

[46]  Michael Feig,et al.  Sampling of near‐native protein conformations during protein structure refinement using a coarse‐grained model, normal modes, and molecular dynamics simulations , 2007, Proteins.

[47]  R. Jernigan,et al.  Effects of protein subunits removal on the computed motions of partial 30S structures of the ribosome. , 2008, Journal of chemical theory and computation.

[48]  K. Dill,et al.  The protein folding problem. , 1993, Annual review of biophysics.

[49]  Michal Brylinski,et al.  FINDSITE: a combined evolution/structure-based approach to protein function prediction , 2009, Briefings Bioinform..

[50]  Michal Brylinski,et al.  FINDSITELHM: A Threading-Based Approach to Ligand Homology Modeling , 2009, PLoS Comput. Biol..

[51]  K. Dill,et al.  Assessment of the protein‐structure refinement category in CASP8 , 2009, Proteins.

[52]  R. Jernigan,et al.  The energy profiles of atomic conformational transition intermediates of adenylate kinase , 2009, Proteins.

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

[54]  Yang Zhang,et al.  How significant is a protein structure similarity with TM-score = 0.5? , 2010, Bioinform..

[55]  I. Bahar,et al.  Normal mode analysis of biomolecular structures: functional mechanisms of membrane proteins. , 2010, Chemical reviews.

[56]  Yang Zhang,et al.  I-TASSER: a unified platform for automated protein structure and function prediction , 2010, Nature Protocols.

[57]  Yang Zhang,et al.  A Novel Side-Chain Orientation Dependent Potential Derived from Random-Walk Reference State for Protein Fold Selection and Structure Prediction , 2010, PloS one.

[58]  I. Bahar,et al.  Global dynamics of proteins: bridging between structure and function. , 2010, Annual review of biophysics.

[59]  Andrzej Kloczkowski,et al.  MAVENs: Motion analysis and visualization of elastic networks and structural ensembles , 2011, BMC Bioinformatics.

[60]  Andrzej Kloczkowski,et al.  Free energies for coarse-grained proteins by integrating multibody statistical contact potentials with entropies from elastic network models , 2011, Journal of Structural and Functional Genomics.

[61]  Benjamin A. Lewis,et al.  Human telomerase model shows the role of the TEN domain in advancing the double helix for the next polymerization step , 2011, Proceedings of the National Academy of Sciences.

[62]  R. Jernigan,et al.  Immunoglobulin Structure Exhibits Control over CDR Motion , 2014, Immunome research.

[63]  Matthew P Jacobson,et al.  Assessment of protein structure refinement in CASP9 , 2011, Proteins.

[64]  Andrzej Kloczkowski,et al.  How noise in force fields can affect the structural refinement of protein models? , 2012, Proteins.

[65]  Sumudu P. Leelananda,et al.  The importance of slow motions for protein functional loops , 2012, Physical biology.