Mean force based temperature accelerated sliced sampling: Efficient reconstruction of high dimensional free energy landscapes

Temperature accelerated sliced sampling (TASS) is an efficient method to compute high dimensional free energy landscapes. The original TASS method employs the weighted histogram analysis method (WHAM) which is an iterative post‐processing to reweight and stitch high dimensional probability distributions in sliced windows that are obtained in the presence of restraining biases. The WHAM necessitates that TASS windows lie close to each other for proper overlap of distributions and span the collective variable space of interest. On the other hand, increase in number of TASS windows implies more number of simulations, and thus it affects the efficiency of the method. To overcome this problem, we propose herein a new mean‐force (MF) based reweighting scheme called TASS‐MF, which enables accurate computation with a fewer number of windows devoid of the WHAM post‐processing. Application of the technique is demonstrated for alanine di‐ and tripeptides in vacuo to compute their two‐ and four‐dimensional free energy landscapes, the latter of which is formidable in conventional umbrella sampling and metadynamics. The landscapes are computed within a kcal mol−1 accuracy, ensuring a safe usage for broad applications in computational chemistry.

[1]  Michiel Sprik,et al.  Free energy from constrained molecular dynamics , 1998 .

[2]  Gabriel Stoltz,et al.  Smoothed Biasing Forces Yield Unbiased Free Energies with the Extended-System Adaptive Biasing Force Method , 2016, The journal of physical chemistry. B.

[3]  Gabriel Stoltz,et al.  Computation of free energy profiles with parallel adaptive dynamics. , 2007, The Journal of chemical physics.

[4]  G. Ciccotti,et al.  Theory and methods for rare events , 2012 .

[5]  C. Simmerling,et al.  ff14SB: Improving the Accuracy of Protein Side Chain and Backbone Parameters from ff99SB. , 2015, Journal of chemical theory and computation.

[6]  M. Tuckerman,et al.  Free Energy Reconstruction from Metadynamics or Adiabatic Free Energy Dynamics Simulations. , 2014, Journal of chemical theory and computation.

[7]  M. Tuckerman,et al.  Efficient and direct generation of multidimensional free energy surfaces via adiabatic dynamics without coordinate transformations. , 2008, The journal of physical chemistry. B.

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

[9]  Haruki Nakamura,et al.  Multidimensional virtual‐system coupled canonical molecular dynamics to compute free‐energy landscapes of peptide multimer assembly , 2019, J. Comput. Chem..

[10]  Michele Parrinello,et al.  Enhancing Important Fluctuations: Rare Events and Metadynamics from a Conceptual Viewpoint. , 2016, Annual review of physical chemistry.

[11]  Walter Thiel,et al.  Bridging the gap between thermodynamic integration and umbrella sampling provides a novel analysis method: "Umbrella integration". , 2005, The Journal of chemical physics.

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

[13]  M. Shiga,et al.  On the hierarchical parallelization of ab initio simulations , 2016, 1601.02713.

[14]  I. Tavernelli,et al.  A Novel Hamiltonian Replica Exchange MD Protocol to Enhance Protein Conformational Space Sampling. , 2006, Journal of chemical theory and computation.

[15]  Christopher B. Barnett,et al.  Free Energies from Adaptive Reaction Coordinate Forces (FEARCF): an application to ring puckering , 2009 .

[16]  Lula Rosso,et al.  Mapping the backbone dihedral free-energy surfaces in small peptides in solution using adiabatic free-energy dynamics. , 2005, The journal of physical chemistry. B.

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

[18]  E. Vanden-Eijnden,et al.  A temperature accelerated method for sampling free energy and determining reaction pathways in rare events simulations , 2006 .

[19]  N. N. Nair,et al.  Exploring high dimensional free energy landscapes: Temperature accelerated sliced sampling , 2016, 1612.08240.

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

[21]  Hisashi Okumura,et al.  Replica-Permutation Method with the Suwa-Todo Algorithm beyond the Replica-Exchange Method. , 2012, Journal of chemical theory and computation.

[22]  J Andrew McCammon,et al.  Computing accurate potentials of mean force in electrolyte solutions with the generalized gradient-augmented harmonic Fourier beads method. , 2008, The Journal of chemical physics.

[23]  B. Berne,et al.  Replica exchange with solute tempering: a method for sampling biological systems in explicit water. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

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

[25]  D. Frenkel Free-energy calculations , 1991 .

[26]  Harish Vashisth,et al.  Phase space and collective variable based simulation methods for studies of rare events , 2019, Molecular Simulation.

[27]  Eric Vanden-Eijnden,et al.  Some recent techniques for free energy calculations , 2009, J. Comput. Chem..

[28]  Shalini Awasthi,et al.  Exploring high‐dimensional free energy landscapes of chemical reactions , 2018, WIREs Computational Molecular Science.

[29]  M. Tuckerman,et al.  Heating and flooding: a unified approach for rapid generation of free energy surfaces. , 2012, The Journal of chemical physics.

[30]  Eric F Darve Thermodynamic Integration Using Constrained and Unconstrained Dynamics , 2007 .

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

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

[33]  Wilfred F. van Gunsteren,et al.  Basic ingredients of free energy calculations: A review , 2009, J. Comput. Chem..

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

[35]  J. Kästner Umbrella sampling , 2011 .

[36]  Tetsuya Morishita,et al.  Free Energy Reconstruction from Logarithmic Mean-Force Dynamics Using Multiple Nonequilibrium Trajectories. , 2017, Journal of chemical theory and computation.

[37]  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.

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

[39]  J. Mongan,et al.  Accelerated molecular dynamics: a promising and efficient simulation method for biomolecules. , 2004, The Journal of chemical physics.

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