Weighted ensemble: Recent mathematical developments

Weighted ensemble (WE) is an enhanced sampling method based on periodically replicating and pruning trajectories generated in parallel. WE has grown increasingly popular for computational biochemistry problems due, in part, to improved hardware and accessible software implementations. Algorithmic and analytical improvements have played an important role, and progress has accelerated in recent years. Here, we discuss and elaborate on the WE method from a mathematical perspective, highlighting recent results that enhance the computational efficiency. The mathematical theory reveals a new strategy for optimizing trajectory management that approaches the best possible variance while generalizing to systems of arbitrary dimension.

[1]  David N. LeBard,et al.  WESTPA 2.0: High-performance upgrades for weighted ensemble simulations and analysis of longer-timescale applications , 2021, bioRxiv.

[2]  Rommie E. Amaro,et al.  Gaussian-Accelerated Molecular Dynamics with the Weighted Ensemble Method: A Hybrid Method Improves Thermodynamic and Kinetic Sampling. , 2021, Journal of chemical theory and computation.

[3]  I. Andricioaei,et al.  Markovian Weighted Ensemble Milestoning (M-WEM): Long-time Kinetics from Short Trajectories , 2021, bioRxiv.

[4]  D. Abbot,et al.  Rare Event Sampling Improves Mercury Instability Statistics , 2021, The Astrophysical Journal.

[5]  Rommie E. Amaro,et al.  A glycan gate controls opening of the SARS-CoV-2 spike protein , 2021, bioRxiv.

[6]  Robert J. Webber,et al.  Learning forecasts of rare stratospheric transitions from short simulations , 2021, Monthly Weather Review.

[7]  Robert J. Webber,et al.  A splitting method to reduce MCMC variance , 2020, ArXiv.

[8]  Daniel M. Zuckerman,et al.  Accelerated estimation of long-timescale kinetics from weighted ensemble simulation via non-Markovian "microbin" analysis. , 2020, Journal of chemical theory and computation.

[9]  Ron Elber,et al.  The value of temporal information when analyzing reaction coordinates. , 2020, Journal of chemical theory and computation.

[10]  Samuel D. Lotz,et al.  Wepy: A Flexible Software Framework for Simulating Rare Events with Weighted Ensemble Resampling , 2020, ACS omega.

[11]  Ioan Andricioaei,et al.  Weighted ensemble milestoning (WEM): A combined approach for rare event simulations. , 2019, The Journal of chemical physics.

[12]  David Aristoff,et al.  An ergodic theorem for the weighted ensemble method , 2019, Journal of Applied Probability.

[13]  D. Zuckerman,et al.  Computational Estimation of Microsecond to Second Atomistic Folding Times. , 2019, Journal of the American Chemical Society.

[14]  Daniel M. Zuckerman,et al.  Optimizing Weighted Ensemble Sampling of Steady States , 2018, Multiscale Model. Simul..

[15]  Alex J. DeGrave,et al.  Large enhancement of response times of a protein conformational switch by computational design , 2018, Nature Communications.

[16]  Samuel D. Lotz,et al.  Unbiased Molecular Dynamics of 11 min Timescale Drug Unbinding Reveals Transition State Stabilizing Interactions. , 2018, Journal of the American Chemical Society.

[17]  Daniel M Zuckerman,et al.  Weighted Ensemble Simulation: Review of Methodology, Applications, and Software. , 2017, Annual review of biophysics.

[18]  David Aristoff,et al.  Analysis and optimization of weighted ensemble sampling , 2016, ESAIM: Mathematical Modelling and Numerical Analysis.

[19]  Robert F. Murphy,et al.  Unbiased Rare Event Sampling in Spatial Stochastic Systems Biology Models Using a Weighted Ensemble of Trajectories , 2016, PLoS Comput. Biol..

[20]  Eric Darve,et al.  A comparison of weighted ensemble and Markov state model methodologies. , 2015, The Journal of chemical physics.

[21]  Juan M. Bello-Rivas,et al.  A Mathematical Framework for Exact Milestoning , 2015, Multiscale Model. Simul..

[22]  Joshua L Adelman,et al.  WESTPA: an interoperable, highly scalable software package for weighted ensemble simulation and analysis. , 2015, Journal of chemical theory and computation.

[23]  Douglas Thain,et al.  AWE-WQ: Fast-Forwarding Molecular Dynamics Using the Accelerated Weighted Ensemble , 2014, J. Chem. Inf. Model..

[24]  Frank Noé,et al.  Markov state models of biomolecular conformational dynamics. , 2014, Current opinion in structural biology.

[25]  Alex Dickson,et al.  WExplore: hierarchical exploration of high-dimensional spaces using the weighted ensemble algorithm. , 2014, The journal of physical chemistry. B.

[26]  James R Faeder,et al.  Efficient stochastic simulation of chemical kinetics networks using a weighted ensemble of trajectories. , 2013, The Journal of chemical physics.

[27]  Jianfeng Lu,et al.  Reactive trajectories and the transition path process , 2013, 1303.1744.

[28]  Joshua L Adelman,et al.  Simulating rare events using a weighted ensemble-based string method. , 2012, The Journal of chemical physics.

[29]  L. Chong,et al.  Simultaneous Computation of Dynamical and Equilibrium Information Using a Weighted Ensemble of Trajectories , 2012, Journal of chemical theory and computation.

[30]  Ernest K. Ryu,et al.  Computing reaction rates in bio-molecular systems using discrete macro-states , 2012, 1307.0763.

[31]  Divesh Bhatt,et al.  Simulations of the alternating access mechanism of the sodium symporter Mhp1. , 2011, Biophysical journal.

[32]  Divesh Bhatt,et al.  Beyond microscopic reversibility: Are observable non-equilibrium processes precisely reversible? , 2011, Journal of chemical theory and computation.

[33]  L. Chong,et al.  Efficient Explicit-Solvent Molecular Dynamics Simulations of Molecular Association Kinetics: Methane/Methane, Na(+)/Cl(-), Methane/Benzene, and K(+)/18-Crown-6 Ether. , 2011, Journal of chemical theory and computation.

[34]  Bin W. Zhang,et al.  Steady-state simulations using weighted ensemble path sampling. , 2009, The Journal of chemical physics.

[35]  Daniel M Zuckerman,et al.  The "weighted ensemble" path sampling method is statistically exact for a broad class of stochastic processes and binning procedures. , 2008, The Journal of chemical physics.

[36]  Bin W. Zhang,et al.  Efficient and verified simulation of a path ensemble for conformational change in a united-residue model of calmodulin , 2007, Proceedings of the National Academy of Sciences.

[37]  Aaron R Dinner,et al.  Umbrella sampling for nonequilibrium processes. , 2007, The Journal of chemical physics.

[38]  R. Pinsky,et al.  Spectral analysis of a family of second-order elliptic operators with nonlocal boundary condition indexed by a probability measure , 2007, 0707.0612.

[39]  F. Cérou,et al.  Adaptive Multilevel Splitting for Rare Event Analysis , 2007 .

[40]  P. R. ten Wolde,et al.  Sampling rare switching events in biochemical networks. , 2004, Physical review letters.

[41]  William Swope,et al.  Describing Protein Folding Kinetics by Molecular Dynamics Simulations. 1. Theory , 2004 .

[42]  P. Bolhuis,et al.  A novel path sampling method for the calculation of rate constants , 2002, cond-mat/0210614.

[43]  S. Orszag,et al.  Advanced Mathematical Methods For Scientists And Engineers , 1979 .

[44]  Jonathan Weare,et al.  Exploring stratospheric rare events with transition path theory and short simulations , 2021 .

[45]  Ron Elber,et al.  Exact milestoning. , 2015, The Journal of chemical physics.

[46]  G. Huber,et al.  Weighted-ensemble Brownian dynamics simulations for protein association reactions. , 1996, Biophysical journal.