Simulating Protein Motions with Rigidity Analysis

Protein motions, ranging from molecular flexibility to large-scale conformational change, play an essential role in many biochemical processes. Despite the explosion in our knowledge of structural and functional data, our understanding of protein movement is still very limited. In previous work, we developed and validated a motion planning based method for mapping protein folding pathways from unstructured conformations to the native state. In this paper, we propose a novel method based on rigidity theory to sample conformation space more effectively, and we describe extensions of our framework to automate the process and to map transitions between specified conformations. Our results show that these additions both improve the accuracy of our maps and enable us to study a broader range of motions for larger proteins. For example, we show that rigidity-based sampling results in maps that capture subtle folding differences between protein G and its mutants, NuG1 and NuG2, and we illustrate how our technique can be used to study large-scale conformational changes in calmodulin, a 148 residue signaling protein known to undergo conformational changes when binding to Ca(2+). Finally, we announce our web-based protein folding server which includes a publicly available archive of protein motions: (http://parasol.tamu.edu/foldingserver/).

[1]  Walter Whiteley,et al.  Some matroids from discrete applied geometry , 1996 .

[2]  G. Rose,et al.  Rigid domains in proteins: An algorithmic approach to their identification , 1995, Proteins.

[3]  Tomás Lozano-Pérez,et al.  Spatial Planning: A Configuration Space Approach , 1983, IEEE Transactions on Computers.

[4]  D Baker,et al.  A breakdown of symmetry in the folding transition state of protein L. , 2000, Journal of molecular biology.

[5]  Jean-Claude Latombe,et al.  A Motion Planning Approach to Flexible Ligand Binding , 1999, ISMB.

[6]  G. Rose,et al.  Compact units in proteins. , 1986, Biochemistry.

[7]  B. Faverjon,et al.  Probabilistic Roadmaps for Path Planning in High-Dimensional Con(cid:12)guration Spaces , 1996 .

[8]  Donald J. Jacobs,et al.  Generic rigidity in three-dimensional bond-bending networks , 1998 .

[9]  Daniel Vallejo,et al.  OBPRM: an obstacle-based PRM for 3D workspaces , 1998 .

[10]  D. Baker,et al.  A surprising simplicity to protein folding , 2000, Nature.

[11]  Thierry Siméon,et al.  Geometric algorithms for the conformational analysis of long protein loops , 2004, J. Comput. Chem..

[12]  K. Dill,et al.  A simple protein folding algorithm using a binary code and secondary structure constraints. , 1995, Protein engineering.

[13]  G J Barton,et al.  Continuous and discontinuous domains: An algorithm for the automatic generation of reliable protein domain definitions , 1995, Protein science : a publication of the Protein Society.

[14]  M Gerstein,et al.  Analysis of protein loop closure. Two types of hinges produce one motion in lactate dehydrogenase. , 1991, Journal of molecular biology.

[15]  M. Gerstein,et al.  A database of macromolecular motions. , 1998, Nucleic acids research.

[16]  M. Sternberg.  Protein Structure Prediction: A Practical Approach , 1997 .

[17]  Ming Lei,et al.  Sampling protein conformations and pathways , 2004, J. Comput. Chem..

[18]  P. Karplus,et al.  Prediction of chain flexibility in proteins , 1985, Naturwissenschaften.

[19]  J. Skolnick,et al.  Monte carlo simulations of protein folding. I. Lattice model and interaction scheme , 1994, Proteins.

[20]  P. Kollman,et al.  Pathways to a protein folding intermediate observed in a 1-microsecond simulation in aqueous solution. , 1998, Science.

[21]  Leslie A. Kuhn,et al.  Flexible and Rigid Regions in Proteins , 2002 .

[22]  W. Chazin,et al.  An interaction‐based analysis of calcium‐induced conformational changes in Ca2+ sensor proteins , 1998, Protein science : a publication of the Protein Society.

[23]  Nancy M. Amato,et al.  A Path Planning-Based Study of Protein Folding with a Case Study of Hairpin Formation in Protein G and L , 2002, Pacific Symposium on Biocomputing.

[24]  B. Hendrickson,et al.  An Algorithm for Two-Dimensional Rigidity Percolation , 1997 .

[25]  V. Muñoz,et al.  A statistical mechanical model for β-hairpin kinetics , 1998 .

[26]  N. Amato,et al.  A motion planning approach to protein folding , 2003 .

[27]  B. Hendrickson,et al.  Regular ArticleAn Algorithm for Two-Dimensional Rigidity Percolation: The Pebble Game , 1997 .

[28]  R Abagyan,et al.  A new method for modeling large‐scale rearrangements of protein domains , 1997, Proteins.

[29]  M. Levitt.  Protein folding by restrained energy minimization and molecular dynamics. , 1983, Journal of molecular biology.

[30]  J. Janin,et al.  Structural domains in proteins and their role in the dynamics of protein function. , 1983, Progress in biophysics and molecular biology.

[31]  David Baker,et al.  Computer-based redesign of a protein folding pathway , 2001, Nature Structural Biology.

[32]  Daniel M. Zuckerman,et al.  Simulation of an Ensemble of Conformational Transitions in a United-Residue Model of Calmodulin , 2004 .

[33]  Sergei V. Krivov,et al.  Free energy disconnectivity graphs: Application to peptide models , 2002 .

[34]  J. Jung,et al.  Protein structure prediction. , 2001, Current opinion in chemical biology.

[35]  J. M. Haile,et al.  Molecular dynamics simulation : elementary methods / J.M. Haile , 1992 .

[36]  J. Collinge.  Prion diseases of humans and animals: their causes and molecular basis. , 2001, Annual review of neuroscience.

[37]  Nancy M. Amato,et al.  Using Motion Planning to Study Protein Folding Pathways , 2002, J. Comput. Biol..

[38]  M Ikura,et al.  Backbone dynamics of calmodulin studied by 15N relaxation using inverse detected two-dimensional NMR spectroscopy: the central helix is flexible. , 1992, Biochemistry.

[39]  Jean-Claude Latombe,et al.  Capturing molecular energy landscapes with probabilistic conformational roadmaps , 2001, Proceedings 2001 ICRA. IEEE International Conference on Robotics and Automation (Cat. No.01CH37164).

[40]  R. Schulz,et al.  Protein Structure Prediction , 2020, Methods in Molecular Biology.

[41]  Mark Gerstein,et al.  MolMovDB: analysis and visualization of conformational change and structural flexibility , 2003, Nucleic Acids Res..

[42]  Hans J. Vogel,et al.  Calmodulin: a versatile calcium mediator protein , 1994 .

[43]  J A McCammon,et al.  Large‐amplitude bending motions in phenylalanine transfer RNA , 1984, Biopolymers.

[44]  Nancy M. Amato,et al.  Ligand Binding with OBPRM and Haptic User Input: Enhancing Automatic Motion Planning with Virtual Touch , 2000 .

[45]  Arthur M. Lesk,et al.  Protein Architecture: A Practical Approach , 1991 .

[46]  Jacobs,et al.  Generic rigidity percolation: The pebble game. , 1995, Physical review letters.

[47]  R. Li,et al.  The hydrogen exchange core and protein folding , 1999, Protein science : a publication of the Protein Society.

[48]  M Karplus,et al.  The allosteric mechanism of the chaperonin GroEL: a dynamic analysis. , 1998, Proceedings of the National Academy of Sciences of the United States of America.

[49]  M Ikura,et al.  Molecular and structural basis of target recognition by calmodulin. , 1995, Annual review of biophysics and biomolecular structure.

[50]  Nancy M. Amato,et al.  Using Motion Planning to Study RNA Folding Kinetics , 2005, J. Comput. Biol..

[51]  M. Levitt,et al.  Computer simulation of protein folding , 1975, Nature.

[52]  J. Skolnick,et al.  Monte carlo simulations of protein folding. II. Application to protein A, ROP, and crambin , 1994, Proteins.

[53]  R. Jernigan,et al.  Proteins with similar architecture exhibit similar large-scale dynamic behavior. , 2000, Biophysical journal.

[54]  G. Laman.  On graphs and rigidity of plane skeletal structures , 1970 .

[55]  Marco R. Celio,et al.  Guidebook to the calcium-binding proteins , 1996 .

[56]  Stanley B. Prusiner,et al.  Nobel Lecture: Prions , 1998 .

[57]  Jean-Claude Latombe,et al.  Stochastic roadmap simulation: an efficient representation and algorithm for analyzing molecular motion , 2002, RECOMB '02.

[58]  M. Gerstein,et al.  Conformational changes associated with protein-protein interactions. , 2004, Current opinion in structural biology.

[59]  E. Alm,et al.  Prediction of protein-folding mechanisms from free-energy landscapes derived from native structures. , 1999, Proceedings of the National Academy of Sciences of the United States of America.

[60]  A. Rader,et al.  Identifying protein folding cores from the evolution of flexible regions during unfolding. , 2002, Journal of molecular graphics & modelling.

[61]  Leslie A Kuhn,et al.  Protein unfolding: Rigidity lost , 2002, Proceedings of the National Academy of Sciences of the United States of America.

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

[63]  Jacobs,et al.  Generic rigidity percolation in two dimensions. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[64]  M J Rooman,et al.  Automatic analysis of protein conformational changes by multiple linkage clustering. , 1995, Journal of molecular biology.

[65]  S. Linse,et al.  Calcium binding to calmodulin and its globular domains. , 1991, The Journal of biological chemistry.

[66]  D. Jacobs,et al.  Protein flexibility predictions using graph theory , 2001, Proteins.

[67]  D. Baker,et al.  Critical role of β-hairpin formation in protein G folding , 2000, Nature Structural Biology.

[68]  J. Onuchic,et al.  Funnels, pathways, and the energy landscape of protein folding: A synthesis , 1994, Proteins.

[69]  Nancy M. Amato,et al.  Incremental Map Generation (IMG) , 2006, WAFR.

[70]  M. Gerstein,et al.  The morph server: a standardized system for analyzing and visualizing macromolecular motions in a database framework. , 2000, Nucleic acids research.

[71]  David A. Case,et al.  Molecular Dynamics and Normal Mode Analysis of Biomolecular Rigidity , 2002 .

[72]  Nancy M. Amato,et al.  Using Motion Planning to Map Protein Folding Landscapes and Analyze Folding Kinetics of Known Native Structures , 2003, J. Comput. Biol..

[73]  A. Gronenborn,et al.  Solution structure of a calmodulin-target peptide complex by multidimensional NMR. , 1994, Science.

[74]  C. Sander,et al.  Parser for protein folding units , 1994, Proteins.

[75]  D. Covell.  Folding protein α‐carbon chains into compact forms by monte carlo methods , 1992 .