New advances in metadynamics

Metadynamics is an algorithm for accelerating rare events and reconstructing the associated free energy surface. It works by biasing the evolution of the system by a history‐dependent potential that is adaptively constructed in the space of a suitably chosen set of collective variables. Since its first appearance, the method has been successfully applied in several domains of science. Its widespread adoption is not only due to its efficiency, flexibility, and availability but also to its continuous evolution and its combination with complementary enhanced sampling algorithms. Here, we focus on the progress made in the development of more general and powerful collective variables and on the very recent and exciting evolutions of the method. © 2012 John Wiley & Sons, Ltd.

[1]  M. Karplus,et al.  A hierarchy of timescales in protein dynamics is linked to enzyme catalysis , 2007, Nature.

[2]  Massimiliano Bonomi,et al.  Reconstructing the equilibrium Boltzmann distribution from well‐tempered metadynamics , 2009, J. Comput. Chem..

[3]  Alessandro Laio,et al.  METAGUI. A VMD interface for analyzing metadynamics and molecular dynamics simulations , 2012, Comput. Phys. Commun..

[4]  Alessandro Laio,et al.  A Collective Variable for the Efficient Exploration of Protein Beta-Sheet Structures: Application to SH3 and GB1. , 2009, Journal of chemical theory and computation.

[5]  M. Parrinello,et al.  Well-tempered metadynamics: a smoothly converging and tunable free-energy method. , 2008, Physical review letters.

[6]  Alessandro Laio,et al.  A VMD interface for analyzing metadynamics and molecular dynamics simulations ✩ , 2011 .

[7]  F. Pederiva,et al.  On the calculation of puckering free energy surfaces. , 2009, The Journal of chemical physics.

[8]  Gregory A Voth,et al.  A Combined Metadynamics and Umbrella Sampling Method for the Calculation of Ion Permeation Free Energy Profiles. , 2011, Journal of chemical theory and computation.

[9]  Francesco Luigi Gervasio,et al.  The role of the peripheral anionic site and cation-pi interactions in the ligand penetration of the human AChE gorge. , 2005, Journal of the American Chemical Society.

[10]  Alessandro Laio,et al.  Finite temperature properties of clusters by replica exchange metadynamics: the water nonamer. , 2011, Journal of the American Chemical Society.

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

[12]  U. Hansmann.  Parallel tempering algorithm for conformational studies of biological molecules , 1997, physics/9710041.

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

[14]  J. Tenenbaum,et al.  A global geometric framework for nonlinear dimensionality reduction. , 2000, Science.

[15]  Michele Parrinello,et al.  A self-learning algorithm for biased molecular dynamics , 2010, Proceedings of the National Academy of Sciences.

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

[17]  Francesco L Gervasio,et al.  The different flexibility of c-Src and c-Abl kinases regulates the accessibility of a druggable inactive conformation. , 2012, Journal of the American Chemical Society.

[18]  Fabio Pietrucci,et al.  Graph theory meets ab initio molecular dynamics: atomic structures and transformations at the nanoscale. , 2011, Physical review letters.

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

[20]  A. Laio,et al.  Assessing the accuracy of metadynamics. , 2005, The journal of physical chemistry. B.

[21]  K. Schulten,et al.  Reconstructing Potentials of Mean Force through Time Series Analysis of Steered Molecular Dynamics Simulations , 1999 .

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

[23]  Haruki Nakamura,et al.  Multicanonical molecular dynamics simulations combined with Metadynamics for the free energy landscape of a biomolecular system with high energy barriers , 2011 .

[24]  Vojtěch Spiwok,et al.  Metadynamics in the conformational space nonlinearly dimensionally reduced by Isomap. , 2011, The Journal of chemical physics.

[25]  Charles L. Brooks,et al.  λ‐dynamics: A new approach to free energy calculations , 1996 .

[26]  A. Laio,et al.  Free-energy landscape for beta hairpin folding from combined parallel tempering and metadynamics. , 2006, Journal of the American Chemical Society.

[27]  Massimiliano Bonomi,et al.  Assessing the Quality of the OPEP Coarse-Grained Force Field. , 2011, Journal of chemical theory and computation.

[28]  A. Laio,et al.  Escaping free-energy minima , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[29]  Sergei V Krivov,et al.  Diffusive reaction dynamics on invariant free energy profiles , 2008, Proceedings of the National Academy of Sciences.

[30]  M. Tuckerman,et al.  On the use of the adiabatic molecular dynamics technique in the calculation of free energy profiles , 2002 .

[31]  Berend Smit,et al.  Understanding Molecular Simulations: from Algorithms to Applications , 2002 .

[32]  Juan J. de Pablo,et al.  Flux Tempered Metadynamics , 2011 .

[33]  P. A. Bash,et al.  Calculation of the relative change in binding free energy of a protein-inhibitor complex. , 1987, Science.

[34]  Francesco Luigi Gervasio,et al.  Comparing the Efficiency of Biased and Unbiased Molecular Dynamics in Reconstructing the Free Energy Landscape of Met-Enkephalin , 2010 .

[35]  Grubmüller,et al.  Predicting slow structural transitions in macromolecular systems: Conformational flooding. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[36]  M J Harvey,et al.  ACEMD: Accelerating Biomolecular Dynamics in the Microsecond Time Scale. , 2009, Journal of chemical theory and computation.

[37]  Francesco Luigi Gervasio,et al.  A Hybrid All-Atom Structure-Based Model for Protein Folding and Large Scale Conformational Transitions. , 2011, Journal of chemical theory and computation.

[38]  Xiangqian Hu,et al.  λ-Meta Dynamics Approach To Compute Absolute Solvation Free Energy. , 2011, The journal of physical chemistry letters.

[39]  V. Pande,et al.  Rapid equilibrium sampling initiated from nonequilibrium data , 2009, Proceedings of the National Academy of Sciences.

[40]  Carlo Camilloni,et al.  Energy landscape of the prion protein helix 1 probed by metadynamics and NMR. , 2012, Biophysical journal.

[41]  Michele Parrinello,et al.  Simplifying the representation of complex free-energy landscapes using sketch-map , 2011, Proceedings of the National Academy of Sciences.

[42]  Vojtech Spiwok,et al.  Metadynamics in essential coordinates: free energy simulation of conformational changes. , 2007, The journal of physical chemistry. B.

[43]  D. Huse,et al.  Optimizing the ensemble for equilibration in broad-histogram Monte Carlo simulations. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[44]  Massimiliano Bonomi,et al.  A chirality‐based metrics for free‐energy calculations in biomolecular systems , 2011, J. Comput. Chem..

[45]  E. M.,et al.  Statistical Mechanics , 2021, Manual for Theoretical Chemistry.

[46]  V. Pande,et al.  Multiplexed-replica exchange molecular dynamics method for protein folding simulation. , 2003, Biophysical journal.

[47]  Francesco Luigi Gervasio,et al.  Conformational selection versus induced fit in kinases: the case of PI3K-γ. , 2012, Angewandte Chemie.

[48]  Vojtěch Spiwok,et al.  Continuous metadynamics in essential coordinates as a tool for free energy modelling of conformational changes , 2008, Journal of molecular modeling.

[49]  A. Laio,et al.  Equilibrium free energies from nonequilibrium metadynamics. , 2006, Physical Review Letters.

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

[51]  M. Parrinello,et al.  Targeting biomolecular flexibility with metadynamics. , 2010, Current opinion in structural biology.

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

[53]  A. Laio,et al.  A bias-exchange approach to protein folding. , 2007, The journal of physical chemistry. B.

[54]  Andrew E. Torda,et al.  Local elevation: A method for improving the searching properties of molecular dynamics simulation , 1994, J. Comput. Aided Mol. Des..

[55]  Alan M. Ferrenberg,et al.  Optimized Monte Carlo data analysis. , 1989, Physical review letters.

[56]  Jirí Vondrásek,et al.  Metadynamics as a tool for mapping the conformational and free-energy space of peptides--the alanine dipeptide case study. , 2010, The journal of physical chemistry. B.

[57]  A. Laio,et al.  Substrate binding mechanism of HIV-1 protease from explicit-solvent atomistic simulations. , 2009, Journal of the American Chemical Society.

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

[59]  M. Parrinello,et al.  The unfolded ensemble and folding mechanism of the C-terminal GB1 beta-hairpin. , 2008, Journal of the American Chemical Society.

[60]  G. Grisetti,et al.  Further Reading , 1984, IEEE Spectrum.

[61]  A. Laio,et al.  Metadynamics: a method to simulate rare events and reconstruct the free energy in biophysics, chemistry and material science , 2008 .

[62]  K Schulten,et al.  VMD: visual molecular dynamics. , 1996, Journal of molecular graphics.

[63]  J. Valleau,et al.  A Monte Carlo method for obtaining the interionic potential of mean force in ionic solution , 1975 .

[64]  Joseph A. Bank,et al.  Supporting Online Material Materials and Methods Figs. S1 to S10 Table S1 References Movies S1 to S3 Atomic-level Characterization of the Structural Dynamics of Proteins , 2022 .

[65]  Matthias Troyer,et al.  Feedback-optimized parallel tempering Monte Carlo , 2006, cond-mat/0602085.

[66]  Massimiliano Bonomi,et al.  PLUMED: A portable plugin for free-energy calculations with molecular dynamics , 2009, Comput. Phys. Commun..

[67]  G. Ciccotti,et al.  Constrained reaction coordinate dynamics for the simulation of rare events , 1989 .

[68]  M. Parrinello,et al.  Enhanced sampling in the well-tempered ensemble. , 2009, Physical review letters.