Combine umbrella sampling with integrated tempering method for efficient and accurate calculation of free energy changes of complex energy surface.

Umbrella sampling is an efficient method for the calculation of free energy changes of a system along well-defined reaction coordinates. However, when there exist multiple parallel channels along the reaction coordinate or hidden barriers in directions perpendicular to the reaction coordinate, it is difficult for conventional umbrella sampling to reach convergent sampling within limited simulation time. Here, we propose an approach to combine umbrella sampling with the integrated tempering sampling method. The umbrella sampling method is applied to chemically more relevant degrees of freedom that possess significant barriers. The integrated tempering sampling method is used to facilitate the sampling of other degrees of freedom which may possess statistically non-negligible barriers. The combined method is applied to two model systems, butane and ACE-NME molecules, and shows significantly improved sampling efficiencies as compared to standalone conventional umbrella sampling or integrated tempering sampling approaches. Further analyses suggest that the enhanced performance of the new method come from the complemented advantages of umbrella sampling with a well-defined reaction coordinate and integrated tempering sampling in orthogonal space. Therefore, the combined approach could be useful in the simulation of biomolecular processes, which often involves sampling of complex rugged energy landscapes.

[1]  Efthimios Kaxiras,et al.  A Self-Consistent Charge Density-Functional Based Tight-Binding Scheme for Large Biomolecules , 2000 .

[2]  B. Berg,et al.  Multicanonical algorithms for first order phase transitions , 1991 .

[3]  Hao Hu,et al.  Free energies of chemical reactions in solution and in enzymes with ab initio quantum mechanics/molecular mechanics methods. , 2008, Annual review of physical chemistry.

[4]  Lijiang Yang,et al.  Thermodynamics and kinetics simulations of multi-time-scale processes for complex systems , 2008 .

[5]  G. Torrie,et al.  Monte Carlo free energy estimates using non-Boltzmann sampling: Application to the sub-critical Lennard-Jones fluid , 1974 .

[6]  Qiang Shao,et al.  Structure change of β-hairpin induced by turn optimization: an enhanced sampling molecular dynamics simulation study. , 2011, The Journal of chemical physics.

[7]  Lijiang Yang,et al.  A selective integrated tempering method. , 2009, The Journal of chemical physics.

[8]  Tai-Sung Lee,et al.  A New Maximum Likelihood Approach for Free Energy Profile Construction from Molecular Simulations. , 2013, Journal of chemical theory and computation.

[9]  Qiang Shao,et al.  The relative helix and hydrogen bond stability in the B domain of protein A as revealed by integrated tempering sampling molecular dynamics simulation. , 2011, The Journal of chemical physics.

[10]  KumarShankar,et al.  The weighted histogram analysis method for free-energy calculations on biomolecules. I , 1992 .

[11]  Wei Hong,et al.  Temperature-Accelerated Sampling and Amplified Collective Motion with Adiabatic Reweighting to Obtain Canonical Distributions and Ensemble Averages. , 2012, Journal of chemical theory and computation.

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

[13]  A. Kidera,et al.  Multicanonical Ensemble Generated by Molecular Dynamics Simulation for Enhanced Conformational Sampling of Peptides , 1997 .

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

[15]  R. Hooft,et al.  An adaptive umbrella sampling procedure in conformational analysis using molecular dynamics and its application to glycol , 1992 .

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

[17]  M. Mezei.  Adaptive umbrella sampling: Self-consistent determination of the non-Boltzmann bias , 1987 .

[18]  Berg,et al.  Multicanonical ensemble: A new approach to simulate first-order phase transitions. , 1992, Physical review letters.

[19]  Wonpil Im,et al.  Transmembrane helix assembly by window exchange umbrella sampling. , 2012, Physical review letters.

[20]  Enhanced Conformational Sampling in Molecular Dynamics Simulations of Solvated Peptides: Fragment-Based Local Elevation Umbrella Sampling. , 2010, Journal of chemical theory and computation.

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

[22]  Y. Gao.  An integrate-over-temperature approach for enhanced sampling. , 2008, The Journal of chemical physics.

[23]  Yuko Okamoto,et al.  From multidimensional replica-exchange method to multidimensional multicanonical algorithm and simulated tempering. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  C. Dellago,et al.  Reaction coordinates of biomolecular isomerization. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[25]  Qiang Shao,et al.  Comparison between integrated and parallel tempering methods in enhanced sampling simulations. , 2009, The Journal of chemical physics.

[26]  Eric Darve,et al.  Adaptive biasing force method for scalar and vector free energy calculations. , 2008, The Journal of chemical physics.

[27]  Benoît Roux,et al.  Extension to the weighted histogram analysis method: combining umbrella sampling with free energy calculations , 2001 .

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

[29]  An efficient umbrella potential for the accurate calculation of free energies by molecular simulation. , 2010, The Journal of chemical physics.

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

[31]  Weiliang Zhu,et al.  Robustness in protein folding revealed by thermodynamics calculations. , 2012, The journal of physical chemistry. B.

[32]  Alessandro Laio,et al.  Reconstructing the density of states by history-dependent metadynamics. , 2004, Physical review letters.

[33]  Jan Hermans,et al.  Reversibility of Free Energy Simulations∶ Slow Growth May Have a Unique Advantage. (With a Note on Use of Ewald Summation) , 2002 .

[34]  Yuko Okamoto,et al.  Multidimensional generalized-ensemble algorithms for complex systems. , 2009, The Journal of chemical physics.

[35]  Zhiqiang Tan,et al.  On a Likelihood Approach for Monte Carlo Integration , 2004 .

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

[37]  Sándor Suhai,et al.  Self-consistent-charge density-functional tight-binding method for simulations of complex materials properties , 1998 .

[38]  Martin Karplus,et al.  Probability Distributions for Complex Systems: Adaptive Umbrella Sampling of the Potential Energy , 1998 .

[39]  Yi Qin Gao,et al.  Self-adaptive enhanced sampling in the energy and trajectory spaces: accelerated thermodynamics and kinetic calculations. , 2008, The Journal of chemical physics.

[40]  Jan Hermans,et al.  Simple analysis of noise and hysteresis in (slow-growth) free energy simulations , 1991 .

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

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

[43]  Free-energy analyses of a proton transfer reaction by simulated-tempering umbrella sampling and first-principles molecular dynamics simulations. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[44]  B. Roux.  The calculation of the potential of mean force using computer simulations , 1995 .

[45]  Wei Yang,et al.  Random walk in orthogonal space to achieve efficient free-energy simulation of complex systems , 2008, Proceedings of the National Academy of Sciences.

[46]  Alan M. Ferrenberg,et al.  Optimized Monte Carlo data analysis. , 1989, Physical Review Letters.

[47]  Jiye Shi,et al.  Enhanced sampling molecular dynamics simulation captures experimentally suggested intermediate and unfolded states in the folding pathway of Trp-cage miniprotein. , 2012, The Journal of chemical physics.

[48]  A. Lyubartsev,et al.  New approach to Monte Carlo calculation of the free energy: Method of expanded ensembles , 1992 .

[49]  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.

[50]  A Singharoy,et al.  Order parameters for macromolecules: application to multiscale simulation. , 2011, The Journal of chemical physics.

[51]  M. Zacharias,et al.  Enhanced conformational sampling of nucleic acids by a new Hamiltonian replica exchange molecular dynamics approach. , 2009, The Journal of chemical physics.

[52]  H. Berendsen,et al.  A LEAP-FROG ALGORITHM FOR STOCHASTIC DYNAMICS , 1988 .

[53]  Philippe H. Hünenberger,et al.  Using the local elevation method to construct optimized umbrella sampling potentials: Calculation of the relative free energies and interconversion barriers of glucopyranose ring conformers in water , 2010, J. Comput. Chem..

[54]  G. Parisi,et al.  Simulated tempering: a new Monte Carlo scheme , 1992, hep-lat/9205018.

[55]  J. Kästner.  Umbrella sampling , 2011 .