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Annual Review of Biophysics

Volume 46, 2017

Weighted Ensemble Simulation: Review of Methodology, Applications, and Software

Abstract

The weighted ensemble (WE) methodology orchestrates quasi-independent parallel simulations run with intermittent communication that can enhance sampling of rare events such as protein conformational changes, folding, and binding. The WE strategy can achieve superlinear scaling—the unbiased estimation of key observables such as rate constants and equilibrium state populations to greater precision than would be possible with ordinary parallel simulation. WE software can be used to control any dynamics engine, such as standard molecular dynamics and cell-modeling packages. This article reviews the theoretical basis of WE and goes on to describe successful applications to a number of complex biological processes—protein conformational transitions, (un)binding, and assembly processes, as well as cell-scale processes in systems biology. We furthermore discuss the challenges that need to be overcome in the next phase of WE methodological development. Overall, the combined advances in WE methodology and software have enabled the simulation of long-timescale processes that would otherwise not be practical on typical computing resources using standard simulation.

Keyword(s): cell modeling, kinetics, molecular dynamics, path sampling, rare events, weighted ensemble
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2017-05-22
2025-04-19
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Literature Cited

  1. Abdul-Wahid B, Feng H, Rajan D, Costaouec R, Darve E. 1.  et al. 2014. AWE-WQ: fast-forwarding molecular dynamics using the accelerated weighted ensemble. J. Chem. Inf. Model. 54:3033–43 [Google Scholar]
  2. Adelman JL, Dale AL, Zwier MC, Bhatt D, Chong LT. 2.  et al. 2011. Simulations of the alternating access mechanism of the sodium symporter Mhp1. Biophys. J. 101:2399–407 [Google Scholar]
  3. Adelman JL, Grabe M. 3.  2013. Simulating rare events using a weighted ensemble-based string method. J. Chem. Phys. 138:044105 [Google Scholar]
  4. Adelman JL, Grabe M. 4.  2015. Simulating current-voltage relationships for a narrow ion channel using the weighted ensemble method. J. Chem. Theory Comput. 11:1907–18 [Google Scholar]
  5. Allen RJ, Warren PB, ten Wolde PR. 5.  2005. Sampling rare switching events in biochemical networks. Phys. Rev. Lett. 94:4 [Google Scholar]
  6. Au S-K, Beck JL. 6.  2001. Estimation of small failure probabilities in high dimensions by subset simulation. Probab. Eng. Mech. 16:263–77 [Google Scholar]
  7. Basconi JE, Shirts MR. 7.  2013. Effects of temperature control algorithms on transport properties and kinetics in molecular dynamics simulations. J. Chem. Theory Comput. 9:2887–99 [Google Scholar]
  8. Becker NB, Allen RJ, ten Wolde PR. 8.  2012. Non-stationary forward flux sampling. J. Chem. Phys. 136:18 [Google Scholar]
  9. Bhatt D, Bahar I. 9.  2012. An adaptive weighted ensemble procedure for efficient computation of free energies and first passage rates. J. Chem. Phys. 137:104101 [Google Scholar]
  10. Bhatt D, Zhang BW, Zuckerman DM. 10.  2010. Steady-state simulations using weighted ensemble path sampling. J. Chem. Phys. 133:014110 [Google Scholar]
  11. Blinov ML, Faeder JR, Goldstein B, Hlavacek WS. 11.  2004. BioNetGen: software for rule-based modeling of signaling transduction based on the interactions of molecular domains. Bioinformatics 20:3289–91 [Google Scholar]
  12. Case DA, Cheatham I, Darden TETA, Gohlke H, Luo R. 12.  et al. 2005. The Amber biomolecular simulation programs. J. Comp. Chem. 26:1668–88 [Google Scholar]
  13. Cerou F. 13.  2007. Adaptive multilevel splitting for rare event analysis. Stochastic Anal. Appl. 25:417–43 [Google Scholar]
  14. Darve E, Rodriguez-Gomez D, Pohorille A. 14.  2008. Adaptive biasing force method for scalar and vector free energy calculations. J. Chem. Phys. 128:144120 [Google Scholar]
  15. Darve E, Ryu E. 15.  2012. Computing reaction rates in bio-molecular systems using discrete macro-states. Innovations in Biomolecular Modeling and Simulations 1 T Schlick 138–206 London: R. Soc. Chem. [Google Scholar]
  16. Dickson A, Brooks CL. 16.  2014. WExplore: hierarchical exploration of high-dimensional spaces using the weighted ensemble algorithm. J. Phys. Chem. B 118:3532–42 [Google Scholar]
  17. Dickson A, Lotz SD. 17.  2016. Ligand release pathways obtained with WExplore: residence times and mechanisms. J. Phys. Chem. B 120:5377–85 [Google Scholar]
  18. Dickson A, Maienschein-Cline M, Tovo-Dwyer A, Hammond JR, Dinner AR. 18.  2011. Flow-dependent unfolding and refolding of an RNA by nonequilibrium umbrella sampling. J. Chem. Theory Comput. 7:2710–20 [Google Scholar]
  19. Dickson A, Mustoe AM, Salmon L, Brooks CL. 19.  2014. Efficient in silico exploration of RNA interhelical conformations using Euler angles and WExplore. Nucleic Acids Res 42:12126–37Demonstrates the power of WE for conformational sampling of RNA molecules. [Google Scholar]
  20. Dickson A, Warmflash A, Dinner AR. 20.  2009. Separating forward and backward pathways in nonequilibrium umbrella sampling. J. Chem. Phys. 131:10 [Google Scholar]
  21. Donovan RM, Sedgewick AJ, Faeder JR, Zuckerman DM. 21.  2013. Efficient stochastic simulation of chemical kinetics networks using a weighted ensemble of trajectories. J. Chem. Phys. 139:115105 [Google Scholar]
  22. Donovan RM, Tapia J-J, Sullivan DP, Faeder JR, Murphy RF. 22.  et al. 2016. Unbiased rare event sampling in spatial stochastic systems biology models using a weighted ensemble of trajectories. PLOS Comput. Biol. 12:e1004611Application of WE to cellular-scale systems, including complex biochemical networks embedded in inhomogeneous spatial environments. [Google Scholar]
  23. Eastman P, Friedrichs MS, Chodera JD, Radmer RJ, Bruns CM. 23.  et al. 2013. OpenMM 4: a reusable, extensible, hardware independent library for high performance molecular simulation. J. Chem. Theory Comput. 9:461–69 [Google Scholar]
  24. Efron BYB, Tibshirani R. 24.  1986. Bootstrap methods for standard errors, confidence intervals, and other measures of statistical accuracy. Stat. Sci. 1:54–75 [Google Scholar]
  25. Elcock AH. 25.  2006. Molecular simulations of cotranslational protein folding: fragment stabilities, folding cooperativity, and trapping in the ribosome. PLOS Comput. Biol. 2:e98 [Google Scholar]
  26. Faeder JR, Blinov ML, Hlavacek WS. 26.  2009. Rule-based modeling of biochemical systems with BioNetGen. Methods Mol. Biol. 500:113–67 [Google Scholar]
  27. Faradjian AK, Elber R. 27.  2004. Computing time scales from reaction coordinates by milestoning. J. Chem. Phys. 120:10880–89 [Google Scholar]
  28. Feng HY, Costaouec R, Darve E, Izaguirre JA. 28.  2015. A comparison of weighted ensemble and Markov state model methodologies. J. Chem. Phys. 142:214113 [Google Scholar]
  29. Flyvbjerg H, Peterson HG. 29.  1989. Error estimates on averages of correlated data. J. Chem. Phys. 91:461 [Google Scholar]
  30. Frembgen-Kesner T, Elcock AH. 30.  2009. Striking effects of hydrodynamic interactions on the simulated diffusion and folding of proteins. J. Chem. Theory Comput. 5:242–56 [Google Scholar]
  31. Frenkel D, Smit B. 31.  2001. Understanding Molecular Simulation. Orlando, FL: Academic [Google Scholar]
  32. Gardiner C. 32.  2010. Stochastic Methods. Berlin: Springer-Verlag [Google Scholar]
  33. Grossfield A, Zuckerman DM. 33.  2009. Quantifying uncertainty and sampling quality in biomolecular simulations. Annu. Rep. Comput. Chem. 5:23–48 [Google Scholar]
  34. Hamelberg D, Mongan J, McCammon JA. 34.  2004. Accelerated molecular dynamics: a promising and efficient simulation method for biomolecules. J. Chem. Phys. 120:11919–29 [Google Scholar]
  35. Hansmann U. 35.  1997. Parallel tempering algorithm for conformational studies of biological macromolecules. Chem. Phys. Lett. 281:140–50 [Google Scholar]
  36. Hess B, Kutzner C, van der Spoel D, Lindahl E. 36.  2008. GROMACS 4: algorithms for highly efficient, load balanced, and scalable molecular simulation. J. Chem. Theory Comput. 4:435–47 [Google Scholar]
  37. Huber GA, Kim S. 37.  1996. Weighted-ensemble Brownian dynamics simulations of protein association reactions. Biophys. J. 70:97–110The original WE algorithm paper, which clearly describes and applies the simple, powerful strategy. [Google Scholar]
  38. Kahn H, Harris TE. 38.  1951. Estimation of particle transmission by random sampling. Natl. Bur. Stand. Appl. Math. Ser. 12:27–30The earliest known description of the splitting idea, which is the essence of WE. [Google Scholar]
  39. Kerr R, Bartol TM, Kaminsky B, Dittrich M, Chang JCJ. 39.  et al. 2008. Fast Monte Carlo simulation methods for biological reaction-diffusion systems in solution and on surfaces. SIAM J. Sci. Comput. 30:3126–49 [Google Scholar]
  40. Kiefhaber T, Bachmann A, Jensen KS. 40.  2012. Dynamics and mechanisms of coupled protein folding and binding reactions. Curr. Opin. Struct. Biol. 22:21–29 [Google Scholar]
  41. Kitano H. 41.  2002. Computational systems biology. Nature 420:206–10 [Google Scholar]
  42. Kratz EG, Duke RE, Cisneros GA. 42.  2016. Long-range electrostatic corrections in multipolar/polarizable QM/MM simulations. Theor. Chem. Acc. 135:166 [Google Scholar]
  43. Laio A, Parrinello M. 43.  2002. Escaping free-energy minima. PNAS 99:12562–66 [Google Scholar]
  44. Le Grand S, Gotz AW, Walker RC. 44.  2013. SPFP: speed without compromise—a mixed precision model for GPU accelerated molecular dynamics simulations. Comput. Phys. Commun. 184:374–80 [Google Scholar]
  45. Liu JS. 45.  Monte Carlo Strategies in Scientific Computing. New York: Springer-Verlag [Google Scholar]
  46. Metzner P, Schutte C, Vanden-Eijnden E. 46.  2006. Illustration of transition path theory on a collection of simple examples. J. Chem. Phys. 125:084110 [Google Scholar]
  47. Mitsutake A, Sugita Y, Okamoto Y. 47.  2001. Generalized-ensemble algorithms for molecular simulations of biopolymers. Biopolymers 60:96–123 [Google Scholar]
  48. Northrup SH, Allison SA, McCammon JA. 48.  1984. Brownian dynamics simulation of diffusion-influenced bimolecular reactions. J. Chem. Phys. 80:1517–24 [Google Scholar]
  49. Phillips JC, Braun R, Wang W, Gumbart J, Tajkhorshid E. 49.  et al. 2005. Scalable molecular dynamics with NAMD. J. Comp. Chem. 26:1781–802 [Google Scholar]
  50. Preto J, Clementi C. 50.  2014. Fast recovery of free energy landscapes via diffusion-map-directed molecular dynamics. Phys. Chem. Chem. Phys. 16:19181–91 [Google Scholar]
  51. Risken H, Frank T. 51.  1996. The Fokker-Planck Equation: Methods of Solution and Applications. Berlin: Springer-Verlag, 2nd ed.. [Google Scholar]
  52. Rojnuckarin A, Kim S, Subramaniam S. 52.  1998. Brownian dynamics simulations of protein folding: access to milliseconds time scale and beyond. PNAS 95:4288–92 [Google Scholar]
  53. Rojnuckarin A, Livesay DR, Subramaniam S. 53.  2000. Bimolecular reaction simulation using weighted ensemble Brownian dynamics and the University of Houston Brownian dynamics program. Biophys. J. 79:686–93 [Google Scholar]
  54. Rubino G, Tuffin B. 54.  2009. Rare Event Simulation using Monte Carlo Methods Chichester, UK: Wiley [Google Scholar]
  55. Saglam AS, Chong LT. 55.  2016. Highly efficient computation of the basal kon using direct simulation of protein–protein association with flexible molecular models. J. Phys. Chem. B 120:117–22Demonstrates the power of WE for even highly coarse-grained simulations of protein–protein association. [Google Scholar]
  56. Shaw DE, Deneroff MM, Dror RO, Kuskin JS, Larson RH. 56.  et al. 2008. Anton, a special-purpose machine for molecular dynamics simulation. Commun ACM 51:91–97 [Google Scholar]
  57. Shaw DE, Maragakis P, Lindorff-Larsen K, Piana S, Dror RO. 57.  et al. 2010. Atomic-level characterization of the structural dynamics of proteins. Science 330:341–46 [Google Scholar]
  58. Shi Y, Xia Z, Zhang J, Best R, Wu C. 58.  et al. 2013. The polarizable atomic multipole-based AMOEBA force field for proteins. J. Chem. Theory Comput. 9:4046–63 [Google Scholar]
  59. Spiriti J, Zuckerman DM. 59.  2015. Tabulation as a high-resolution alternative to coarse-graining protein interactions: initial application to virus capsid subunits. J. Chem. Phys. 143:243159 [Google Scholar]
  60. Stone JE, Hardy DJ, Ufimtsev IS, Schulten K. 60.  2010. GPU-accelerated molecular modeling coming of age. J. Mol. Graph. Model. 29:116–25 [Google Scholar]
  61. Suarez E, Adelman JL, Zuckerman DM. 61.  2016. Accurate estimation of protein folding and unfolding times: beyond Markov state models. J. Chem. Theory Comput. 12:3473–81 [Google Scholar]
  62. Suarez E, Lettieri S, Zwier MC, Stringer CA, Subramanian SR. 62.  et al. 2014. Simultaneous computation of dynamical and equilibrium information using a weighted ensemble of trajectories. J. Chem. Theory Comput. 10:2658–67Introduction of the non-Markovian analysis of WE trajectories, which is essential for unbiased kinetics when continuous trajectories are mapped to a discrete bin space. [Google Scholar]
  63. Suarez E, Pratt AJ, Chong LT, Zuckerman DM. 63.  2016. Estimating first-passage time distributions from weighted ensemble simulations and non-Markovian analyses. Protein Sci 25:67–78 [Google Scholar]
  64. Tse MJ, Chu BK, Roy M, Read EL. 64.  2015. DNA-binding kinetics determines the mechanism of noise-induced switching in gene networks. Biophys. J. 109:1746–57 [Google Scholar]
  65. van Erp TS, Moroni D, Bolhuis PG. 65.  2003. A novel path sampling method for the calculation of rate constants. J. Chem. Phys. 118:7762 [Google Scholar]
  66. Vanden-Eijnden E, Venturoli M. 66.  2009. Exact rate calculations by trajectory parallelization and tilting. J. Chem. Phys. 131:7 [Google Scholar]
  67. Villen-Altamirano M, Villen-Altamirano J. 67.  1994. RESTART: a straightforward method for fast simulation of rare events. Proc. Winter Simul. Conf.282–89 New York: IEEE [Google Scholar]
  68. Wall FT, Erpenbeck JJ. 68.  1959. New method for the statistical computation of polymer dimensions. J. Chem. Phys. 30:634–37 [Google Scholar]
  69. Zhang BW, Jasnow D, Zuckerman DM. 69.  2007. Efficient and verified simulation of a path ensemble for conformational change in a united-residue model of calmodulin. PNAS 104:18043–48 [Google Scholar]
  70. Zhang BW, Jasnow D, Zuckerman DM. 70.  2010. The “weighted ensemble” path sampling method is statistically exact for a broad class of stochastic processes and binning procedures. J. Chem. Phys. 132:054107 [Google Scholar]
  71. Zhao G, Perilla JR, Yufenyuy EL, Meng X, Chen B. 71.  et al. 2013. Mature HIV-1 capsid structure by cryo-electron microscopy and all-atom molecular dynamics. Nature 497:643–46 [Google Scholar]
  72. Zimmerman MI, Bowman GR. 72.  2015. FAST conformational searches by balancing exploration/exploitation trade-offs. J. Chem. Theory Comput. 11:5747–57 [Google Scholar]
  73. Zuckerman DM. 73.  2010. Statistical Physics of Biomolecules: An Introduction. Boca Raton, FL: CRC Press [Google Scholar]
  74. Zwier MC, Adelman JL, Kaus JW, Pratt AJ, Wong KF. 74.  et al. 2015. WESTPA: an interoperable, highly scalable software package for weighted ensemble simulation and analysis. J. Chem. Theory Comput. 11:800–9A freely available, highly scalable WE software package that interfaces with any dynamics engine. [Google Scholar]
  75. Zwier MC, Kaus JW, Chong LT. 75.  2011. Efficient explicit-solvent molecular dynamics simulations of molecular association kinetics: methane-methane, Na+/Cl−, methane/benzene, and K+/18-crown-6 ether. J. Chem. Theory Comput. 7:1189–97 [Google Scholar]
  76. Zwier MC, Pratt AJ, Adelman JL, Kaus JW, Zuckerman DM, Chong LT. 76.  2016. Efficient atomistic simulation of pathways and calculation of rate constants for a protein-peptide binding process: application to the MDM2 protein and an intrinsically disordered p53 peptide. J. Phys. Chem. Lett. 7:3440–45The largest-scale atomistic WE simulation to date, yielding the first atomistic simulations of complete pathways for a protein–peptide binding process with rigorous rate constants. [Google Scholar]
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Weighted Ensemble Simulation: Review of Methodology, Applications, and Software
Annual Review of Biophysics 46, 43 (2017); https://doi.org/10.1146/annurev-biophys-070816-033834
/content/journals/10.1146/annurev-biophys-070816-033834
/content/journals/10.1146/annurev-biophys-070816-033834
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