Methodology for the Simulation of Molecular Motors at Different Scales.

Millisecond-scale conformational transitions represent a seminal challenge for traditional molecular dynamics simulations, even with the help of high-end supercomputer architectures. Such events are particularly relevant to the study of molecular motors-proteins or abiological constructs that convert chemical energy into mechanical work. Here, we present a hybrid-simulation scheme combining an array of methods including elastic network models, transition path sampling, and advanced free-energy methods, possibly in conjunction with generalized-ensemble schemes to deliver a viable option for capturing the millisecond-scale motor steps of biological motors. The methodology is already implemented in large measure in popular molecular dynamics programs, and it can leverage the massively parallel capabilities of petascale computers. The applicability of the hybrid method is demonstrated with two examples, namely cyclodextrin-based motors and V-type ATPases.

[1]  P. Boyer,et al.  Molecular motors: What makes ATP synthase spin? , 1999, Nature.

[2]  Alexander D. MacKerell,et al.  Force field influence on the observation of π-helical protein structures in molecular dynamics simulations , 2003 .

[3]  C. Chipot,et al.  Solvent-Controlled Shuttling in a Molecular Switch , 2012 .

[4]  J. Abrahams,et al.  The structure of bovine mitochondrial F1-ATPase: an example of rotary catalysis. , 1999, Biochemical Society transactions.

[5]  James A. Spudich,et al.  The myosin superfamily at a glance , 2012, Journal of Cell Science.

[6]  C. Jarzynski Nonequilibrium Equality for Free Energy Differences , 1996, cond-mat/9610209.

[7]  Giacomo Fiorin,et al.  Using collective variables to drive molecular dynamics simulations , 2013 .

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

[9]  K. Schulten,et al.  Flexibility Coexists with Shape-Persistence in Cyanostar Macrocycles. , 2016, Journal of the American Chemical Society.

[10]  Hsian-Rong Tseng,et al.  A reversible molecular valve. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[11]  R. Elber,et al.  Computing time scales from reaction coordinates by milestoning. , 2004, The Journal of chemical physics.

[12]  Ivet Bahar,et al.  Exploring the Conformational Transitions of Biomolecular Systems Using a Simple Two-State Anisotropic Network Model , 2014, PLoS Comput. Biol..

[13]  Eric F Darve,et al.  Calculating free energies using average force , 2001 .

[14]  Y. Sugita,et al.  Replica-exchange molecular dynamics method for protein folding , 1999 .

[15]  Toshio Yanagida,et al.  Chemomechanical coupling of the forward and backward steps of single kinesin molecules , 2002, Nature Cell Biology.

[16]  K. Sutoh,et al.  The 2.8 Å crystal structure of the dynein motor domain , 2012, Nature.

[17]  Y. Sugita,et al.  Multidimensional replica-exchange method for free-energy calculations , 2000, cond-mat/0009120.

[18]  R. Zwanzig High‐Temperature Equation of State by a Perturbation Method. I. Nonpolar Gases , 1954 .

[19]  P. Boyer New insights into one of nature's remarkable catalysts, the ATP synthase. , 2001, Molecular cell.

[20]  H. Noji,et al.  A rotary molecular motor that can work at near 100% efficiency. , 2000, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[21]  Mahmoud Moradi,et al.  Computational Recipe for Efficient Description of Large-Scale Conformational Changes in Biomolecular Systems , 2014, Journal of chemical theory and computation.

[22]  C. Chipot,et al.  Unveiling the Underlying Mechanism for Compression and Decompression Strokes of a Molecular Engine , 2014 .

[23]  Charles H. Bennett,et al.  Efficient estimation of free energy differences from Monte Carlo data , 1976 .

[24]  N. Perzov,et al.  The cellular biology of proton-motive force generation by V-ATPases. , 2000, The Journal of experimental biology.

[25]  Mahmoud Moradi,et al.  Mechanistic picture for conformational transition of a membrane transporter at atomic resolution , 2013, Proceedings of the National Academy of Sciences.

[26]  Yilin Meng,et al.  Self-Learning Adaptive Umbrella Sampling Method for the Determination of Free Energy Landscapes in Multiple Dimensions. , 2013, Journal of chemical theory and computation.

[27]  Bao-hang Han,et al.  Cyclodextrin Rotaxanes and Polyrotaxanes , 2006 .

[28]  G. Hummer,et al.  Elasticity, friction, and pathway of γ-subunit rotation in FoF1-ATP synthase , 2015, Proceedings of the National Academy of Sciences.

[29]  N. Perzov,et al.  Features of V‐ATPases that distinguish them from F‐ATPases , 2001, FEBS letters.

[30]  A. Harada,et al.  Cyclodextrin-based molecular machines. , 2001, Accounts of chemical research.

[31]  Alexander D. MacKerell,et al.  CHARMM general force field: A force field for drug‐like molecules compatible with the CHARMM all‐atom additive biological force fields , 2009, J. Comput. Chem..

[32]  Christophe Chipot,et al.  The Adaptive Biasing Force Method: Everything You Always Wanted To Know but Were Afraid To Ask , 2014, The journal of physical chemistry. B.

[33]  Arieh Warshel,et al.  Electrostatic origin of the mechanochemical rotary mechanism and the catalytic dwell of F1-ATPase , 2011, Proceedings of the National Academy of Sciences.

[34]  B. Roux,et al.  Calculation of absolute protein-ligand binding free energy from computer simulations. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[35]  M. Garcia‐Garibay,et al.  Crystalline molecular machines: a quest toward solid-state dynamics and function. , 2006, Accounts of chemical research.

[36]  Michael Habeck,et al.  Bayesian estimation of free energies from equilibrium simulations. , 2012, Physical review letters.

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

[38]  Christophe Chipot,et al.  Good practices in free-energy calculations. , 2010, The journal of physical chemistry. B.

[39]  E. Vanden-Eijnden,et al.  String method for the study of rare events , 2002, cond-mat/0205527.

[40]  Christophe Chipot,et al.  Potential of Mean Force Calculations: A Multiple-Walker Adaptive Biasing Force Approach , 2010 .

[41]  Klaus Schulten,et al.  Multiple-Replica Strategies for Free-Energy Calculations in NAMD: Multiple-Walker Adaptive Biasing Force and Walker Selection Rules. , 2014, Journal of chemical theory and computation.

[42]  Car,et al.  Unified approach for molecular dynamics and density-functional theory. , 1985, Physical review letters.

[43]  He Tian,et al.  Recent progress on switchable rotaxanes. , 2006, Chemical Society reviews.

[44]  Lei Huang,et al.  Generalized scalable multiple copy algorithms for molecular dynamics simulations in NAMD , 2014, Comput. Phys. Commun..

[45]  Roger J. Coulston,et al.  Harnessing the energy of molecular recognition in a nanomachine having a photochemical on/off switch. , 2006, Journal of the American Chemical Society.

[46]  E. Mandelkow,et al.  Kinesin motors and disease. , 2002, Trends in cell biology.

[47]  Simone Marsili,et al.  Self-healing umbrella sampling: a non-equilibrium approach for quantitative free energy calculations. , 2006, The journal of physical chemistry. B.

[48]  Masasuke Yoshida,et al.  Chemomechanical coupling of human mitochondrial F1-ATPase motor. , 2014, Nature chemical biology.

[49]  P. Pedersen,et al.  ATP Synthase and the Actions of Inhibitors Utilized To Study Its Roles in Human Health, Disease, and Other Scientific Areas , 2008, Microbiology and Molecular Biology Reviews.

[50]  Michael Y. Galperin,et al.  Inventing the dynamo machine: the evolution of the F-type and V-type ATPases , 2007, Nature Reviews Microbiology.

[51]  Klaus Schulten,et al.  Mechanism of substrate translocation by a ring-shaped ATPase motor at millisecond resolution. , 2015, Journal of the American Chemical Society.

[52]  Francesco Luigi Gervasio,et al.  From A to B in free energy space. , 2007, The Journal of chemical physics.

[53]  J. Abrahams,et al.  The structure of bovine F1-ATPase complexed with the antibiotic inhibitor aurovertin B. , 1996, Proceedings of the National Academy of Sciences of the United States of America.

[54]  T. E. Thompson,et al.  Lipid diffusion, free area, and molecular dynamics simulations. , 2005, Biophysical journal.

[55]  Christophe Chipot,et al.  Standard binding free energies from computer simulations: What is the best strategy? , 2013, Journal of chemical theory and computation.

[56]  R. Swendsen,et al.  THE weighted histogram analysis method for free‐energy calculations on biomolecules. I. The method , 1992 .

[57]  E Weinan,et al.  Transition pathways in complex systems: Reaction coordinates, isocommittor surfaces, and transition tubes , 2005 .

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

[59]  Gerhard Hummer,et al.  Position-dependent diffusion coefficients and free energies from Bayesian analysis of equilibrium and replica molecular dynamics simulations , 2005 .

[60]  Kevin J. Naidoo,et al.  Carbohydrate solution simulations: Producing a force field with experimentally consistent primary alcohol rotational frequencies and populations , 2002, J. Comput. Chem..

[61]  Wesley R Browne,et al.  Making molecular machines work , 2006, Nature nanotechnology.

[62]  C. Dellago,et al.  Transition path sampling and the calculation of rate constants , 1998 .

[63]  R. Pomès,et al.  Equilibrium exchange enhances the convergence rate of umbrella sampling , 2008 .

[64]  Masasuke Yoshida,et al.  ATP Hydrolysis and Synthesis of a Rotary Motor V-ATPase from Thermus thermophilus* , 2008, Journal of Biological Chemistry.

[65]  Albert C. Pan,et al.  Finding transition pathways using the string method with swarms of trajectories. , 2008, The journal of physical chemistry. B.

[66]  Francesco Zerbetto,et al.  Synthetic molecular motors and mechanical machines. , 2007, Angewandte Chemie.

[67]  Christophe Chipot,et al.  Efficient determination of protein-protein standard binding free energies from first principles. , 2013, Journal of chemical theory and computation.

[68]  Christophe Chipot,et al.  Calculating Position-Dependent Diffusivity in Biased Molecular Dynamics Simulations. , 2013, Journal of chemical theory and computation.

[69]  P. Krüger,et al.  Targeted molecular dynamics: a new approach for searching pathways of conformational transitions. , 1994, Journal of molecular graphics.

[70]  Helmut Grubmüller,et al.  Torsional elasticity and energetics of F1-ATPase , 2011, Proceedings of the National Academy of Sciences.

[71]  J. Berger,et al.  Running in Reverse: The Structural Basis for Translocation Polarity in Hexameric Helicases , 2009, Cell.

[72]  E. Tajkhorshid,et al.  Atomic-level characterization of transport cycle thermodynamics in the glycerol-3-phosphate:phosphate antiporter , 2015, Nature Communications.

[73]  Francesco Zerbetto,et al.  Macroscopic transport by synthetic molecular machines , 2005, Nature materials.

[74]  Bao-hang Han,et al.  Cyclodextrin rotaxanes and polyrotaxanes. , 2006, Chemical reviews.

[75]  G. Torrie,et al.  Nonphysical sampling distributions in Monte Carlo free-energy estimation: Umbrella sampling , 1977 .

[76]  A. Szabó,et al.  Role of diffusion in ligand binding to macromolecules and cell-bound receptors. , 1982, Biophysical journal.

[77]  V. Pande,et al.  On the transition coordinate for protein folding , 1998 .

[78]  Klaus Schulten,et al.  First passage time approach to diffusion controlled reactions , 1980 .

[79]  Alexander D. MacKerell,et al.  All-atom empirical potential for molecular modeling and dynamics studies of proteins. , 1998, The journal of physical chemistry. B.

[80]  D. N. Card,et al.  Monte Carlo Estimation of the Free Energy by Multistage Sampling , 1972 .

[81]  Benoît Roux,et al.  Conformational Flexibility of o-Phosphorylcholine and o-Phosphorylethanolamine: A Molecular Dynamics Study of Solvation Effects , 1994 .

[82]  Leemor Joshua-Tor,et al.  On helicases and other motor proteins. , 2008, Current opinion in structural biology.

[83]  S. Woutersen,et al.  Water lubricates hydrogen-bonded molecular machines. , 2013, Nature chemistry.

[84]  S. Arai,et al.  Rotation mechanism of Enterococcus hirae V1-ATPase based on asymmetric crystal structures , 2013, Nature.

[85]  Christophe Chipot,et al.  Thermodynamic Insights into the Dynamic Switching of a Cyclodextrin in a Bistable Molecular Shuttle , 2010 .

[86]  J. Kirkwood Statistical Mechanics of Fluid Mixtures , 1935 .

[87]  Belén Ferrer,et al.  Autonomous artificial nanomotor powered by sunlight , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[88]  David Chandler,et al.  Transition path sampling: throwing ropes over rough mountain passes, in the dark. , 2002, Annual review of physical chemistry.

[89]  M. Delarue,et al.  Simplified normal mode analysis of conformational transitions in DNA-dependent polymerases: the elastic network model. , 2002, Journal of molecular biology.

[90]  G. Hummer,et al.  Phosphate release coupled to rotary motion of F1-ATPase , 2013, Proceedings of the National Academy of Sciences.

[91]  Arieh Warshel,et al.  Realistic simulations of the coupling between the protomotive force and the mechanical rotation of the F0-ATPase , 2012, Proceedings of the National Academy of Sciences.

[92]  Yosuke Tanaka,et al.  Molecular Motors in Neurons: Transport Mechanisms and Roles in Brain Function, Development, and Disease , 2010, Neuron.

[93]  A. Warshel,et al.  Dissecting the role of the γ-subunit in the rotary–chemical coupling and torque generation of F1-ATPase , 2015, Proceedings of the National Academy of Sciences.

[94]  H. Grubmüller,et al.  Rotation triggers nucleotide-independent conformational transition of the empty β subunit of F₁-ATPase. , 2014, Journal of the American Chemical Society.

[95]  Christian Bartels,et al.  Multidimensional adaptive umbrella sampling: Applications to main chain and side chain peptide conformations , 1997 .

[96]  Christophe Chipot,et al.  Frontiers in free‐energy calculations of biological systems , 2014 .

[97]  J. Fraser Stoddart,et al.  Cyclodextrin-Based Catenanes and Rotaxanes. , 1998, Chemical reviews.

[98]  L. Joshua-Tor,et al.  Mechanism of DNA translocation in a replicative hexameric helicase , 2006, Nature.

[99]  Herman J. C. Berendsen,et al.  Simulation of Water Transport through a Lipid Membrane , 1994 .

[100]  Michael R. Shirts,et al.  Statistically optimal analysis of samples from multiple equilibrium states. , 2008, The Journal of chemical physics.

[101]  C. Bartels Analyzing biased Monte Carlo and molecular dynamics simulations , 2000 .