Nonlinear relaxation dynamics in elastic networks and design principles of molecular machines

Analyzing nonlinear conformational relaxation dynamics in elastic networks corresponding to two classical motor proteins, we find that they respond by well defined internal mechanical motions to various initial deformations and that these motions are robust against external perturbations. We show that this behavior is not characteristic for random elastic networks. However, special network architectures with such properties can be designed by evolutionary optimization methods. Using them, an example of an artificial elastic network, operating as a cyclic machine powered by ligand binding, is constructed.

[1]  J. Onuchic,et al.  Nonlinear elasticity, proteinquakes, and the energy landscapes of functional transitions in proteins , 2003, Proceedings of the National Academy of Sciences of the United States of America.

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

[3]  James A. Spudich,et al.  How molecular motors work , 1994, Nature.

[4]  A. Lesk,et al.  Structural mechanisms for domain movements in proteins. , 1994, Biochemistry.

[5]  G. A. Scarborough.  Structure and function of the P-type ATPases. , 1999, Current opinion in cell biology.

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

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

[8]  P. Boyer.  The ATP synthase--a splendid molecular machine. , 1997, Annual review of biochemistry.

[9]  S. Taylor,et al.  Structure-function relationships in lactate dehydrogenase. , 1973, Proceedings of the National Academy of Sciences of the United States of America.

[10]  Qiang Cui,et al.  Analysis of functional motions in Brownian molecular machines with an efficient block normal mode approach: myosin-II and Ca2+ -ATPase. , 2004, Biophysical journal.

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

[12]  M. Levitt,et al.  Protein normal-mode dynamics: trypsin inhibitor, crambin, ribonuclease and lysozyme. , 1985, Journal of molecular biology.

[13]  L. A. Bli︠u︡menfelʹd,et al.  Biophysical Thermodynamics of Intracellular Processes: Molecular Machines of the Living Cell , 1994 .

[14]  Functional conformational motions in the turnover cycle of cholesterol oxidase. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[15]  M. Irving,et al.  Dynamic measurement of myosin light-chain-domain tilt and twist in muscle contraction , 1999, Nature.

[16]  Sebastian Doniach,et al.  A comparative study of motor-protein motions by using a simple elastic-network model , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[17]  R. MacKinnon,et al.  Principles of Selective Ion Transport in Channels and Pumps , 2005, Science.

[18]  Alexander S. Mikhailov,et al.  Conformational-relaxation models of single-enzyme kinetics , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[19]  David N Beratan,et al.  How does protein architecture facilitate the transduction of ATP chemical-bond energy into mechanical work? The cases of nitrogenase and ATP binding-cassette proteins. , 2004, Biophysical journal.

[20]  M. Karplus,et al.  Normal modes for specific motions of macromolecules: application to the hinge-bending mode of lysozyme. , 1985, Proceedings of the National Academy of Sciences of the United States of America.

[21]  I. Bahar,et al.  Coupling between catalytic site and collective dynamics: a requirement for mechanochemical activity of enzymes. , 2005, Structure.

[22]  Toshio Yanagida,et al.  Mechanism of muscle contraction based on stochastic properties of single actomyosin motors observed in vitro , 2005, Biophysics.

[23]  Hiromi Nomura,et al.  Structural changes in the calcium pump accompanying the dissociation of calcium , 2002, Nature.

[24]  E. Perozo,et al.  Structural rearrangements underlying K+-channel activation gating. , 1999, Science.

[25]  C. Cohen,et al.  Crystallographic findings on the internally uncoupled and near-rigor states of myosin: Further insights into the mechanics of the motor , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[26]  T. Aida,et al.  Toward intelligent molecular machines: directed motions of biological and artificial molecules and assemblies. , 2005, Chemical reviews.

[27]  I. Bahar,et al.  Gaussian Dynamics of Folded Proteins , 1997 .

[28]  L. Reed,et al.  Structure-function relationships in dihydrolipoamide acyltransferases. , 1990, The Journal of biological chemistry.

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

[30]  A. Leslie,et al.  The structure and nucleotide occupancy of bovine mitochondrial F1‐ATPase are not influenced by crystallisation at high concentrations of nucleotide , 2001, FEBS letters.

[31]  Ivet Bahar,et al.  Elastic network models for understanding biomolecular machinery: from enzymes to supramolecular assemblies , 2005, Physical biology.

[32]  F. Jülicher,et al.  Modeling molecular motors , 1997 .

[33]  L. Amos,et al.  Structure and dynamics of molecular motors. , 1997, Current opinion in structural biology.

[34]  P. Rios,et al.  Slow energy relaxation of macromolecules and nanoclusters in solution. , 2005, Physical review letters.