1932

Abstract

Recent advances in theory and algorithms for atomically detailed simulations open the way to the study of the kinetics of a wide range of molecular processes in biophysics. The theories propose a shift from the traditionally very long molecular dynamic trajectories, which are exact but may not be efficient in the study of kinetics, to the use of a large number of short trajectories. The short trajectories exploit a mapping to a mesh in coarse space and allow for efficient calculations of kinetics and thermodynamics. In this review, I focus on one theory: Milestoning is a theory and an algorithm that offers a hierarchical calculation of properties of interest, such as the free energy profile and the mean first passage time. Approximations to the true long-time dynamics can be computed efficiently and assessed at different steps of the investigation. The theory is discussed and illustrated using two biophysical examples: ion permeation through a phospholipid membrane and protein translocation through a channel.

Loading

Article metrics loading...

/content/journals/10.1146/annurev-biophys-121219-081528
2020-05-06
2024-10-14
Loading full text...

Full text loading...

/deliver/fulltext/biophys/49/1/annurev-biophys-121219-081528.html?itemId=/content/journals/10.1146/annurev-biophys-121219-081528&mimeType=html&fmt=ahah

Literature Cited

  1. 1. 
    Allen MP, Tildesley DJ. 1987. Computer Simulation of Liquids Oxford, UK: Oxford Univ. Press
    [Google Scholar]
  2. 2. 
    Allen RJ, Frenkel D, ten Wolde PR 2006. Forward flux sampling-type schemes for simulating rare events: efficiency analysis. J. Chem. Phys. 124:19194111
    [Google Scholar]
  3. 3. 
    Aristoff D, Bello-Rivas JM, Elber R 2016. A mathematical framework for exact milestoning. Multiscale Model. Simul. 14:1301–22
    [Google Scholar]
  4. 4. 
    Bahar I, Lezon TR, Yang LW, Eyal E 2010. Global dynamics of proteins: bridging between structure and function. Annu. Rev. Biophys. 39:23–42
    [Google Scholar]
  5. 5. 
    Bello-Rivas JM, Elber R. 2015. Exact milestoning. J. Chem. Phys. 142:9094102
    [Google Scholar]
  6. 6. 
    Bello-Rivas JM, Elber R. 2016. Simulations of thermodynamics and kinetics on rough energy landscapes with milestoning. J. Comput. Chem. 37:6602–13
    [Google Scholar]
  7. 7. 
    Bolhuis PG, Chandler D, Dellago C, Geissler PL 2002. Transition path sampling: throwing ropes over rough mountain passes, in the dark. Annu. Rev. Phys. Chem. 53:291–318
    [Google Scholar]
  8. 8. 
    Bowman GR, Pande VS. 2014. An Introduction to Markov State Models and Their Applications to Long Timescale Molecular Simulations Berlin: Springer
    [Google Scholar]
  9. 9. 
    Cardenas AE, Elber R. 2013. Computational study of peptide permeation through membrane: searching for hidden slow variables. Mol. Phys. 111:22–233565–78
    [Google Scholar]
  10. 10. 
    Cardenas AE, Elber R. 2014. Modeling kinetics and equilibrium of membranes with fields: milestoning analysis and implication to permeation. J. Chem. Phys. 141:5054101
    [Google Scholar]
  11. 11. 
    Cardenas AE, Jas GS, DeLeon KY, Hegefeld WA, Kuczera K, Elber R 2012. Unassisted transport of N-acetyl-L-tryptophanamide through membrane: experiment and simulation of kinetics. J. Phys. Chem. B 116:92739–50
    [Google Scholar]
  12. 12. 
    Chandler D. 1978. Statistical mechanics of isomerization dynamics in liquids and transition state approximation. J. Chem. Phys. 68:62959–70
    [Google Scholar]
  13. 13. 
    Chen Y, Lagerholm BC, Yang B, Jacobson K 2006. Methods to measure the lateral diffusion of membrane lipids and proteins. Methods 39:2147–53
    [Google Scholar]
  14. 14. 
    Cho SS, Levy Y, Wolynes PG 2006. P versus Q: Structural reaction coordinates capture protein folding on smooth landscapes. PNAS 103:3586–91
    [Google Scholar]
  15. 15. 
    Dickson A, Warmflash A, Dinner AR 2009. Separating forward and backward pathways in nonequilibrium umbrella sampling. J. Chem. Phys. 131:15154104
    [Google Scholar]
  16. 16. 
    Dinner AR, Mattingly JC, Tempkin JOB, van Koten B, Weare J 2018. Trajectory stratification of stochastic dynamics. SIAM Rev 60:4909–38
    [Google Scholar]
  17. 17. 
    E W. 2011. Principles of Multiscale Modeling Cambridge, UK: Cambridge Univ. Press
    [Google Scholar]
  18. 18. 
    E W, Ren WQ, Vanden-Eijnden E 2002. String method for the study of rare events. Phys. Rev. B 66:5052301
    [Google Scholar]
  19. 19. 
    E W, Vanden-Eijnden E. 2010. Transition-path theory and path-finding algorithms for the study of rare events. Annu. Rev. Phys. Chem. 61:391–420
    [Google Scholar]
  20. 20. 
    Elber R. 2007. A milestoning study of the kinetics of an allosteric transition: atomically detailed simulations of deoxy Scapharca hemoglobin. Biophys. J. 92:9L85–87
    [Google Scholar]
  21. 21. 
    Elber R. 2017. A new paradigm for atomically detailed simulations of kinetics in biophysical systems. Q. Rev. Biophys. 50:e8
    [Google Scholar]
  22. 22. 
    Elber R, Karplus M. 1987. Multiple conformational states of proteins: a molecular dynamics analysis of myoglobin. Science 235:4786318–21
    [Google Scholar]
  23. 23. 
    Faradjian AK, Elber R. 2004. Computing time scales from reaction coordinates by milestoning. J. Chem. Phys. 120:2310880–89
    [Google Scholar]
  24. 24. 
    Fathizadeh A, Elber R. 2019. Ion permeation through a phospholipid membrane: transition state, path splitting, and calculation of permeability. J. Chem. Theory Comput. 15:1720–30
    [Google Scholar]
  25. 25. 
    Frenkel D, Berend S. 1996. Understanding Molecular Simulation: From Algorithms to Applications San Diego, CA: Academic
    [Google Scholar]
  26. 26. 
    Frishman A, Pollak E. 1992. Canonical variational transition-state theory for dissipative systems: application to generalized Langevin equations. J. Chem. Phys. 96:128877–88
    [Google Scholar]
  27. 27. 
    Gaspar D, Veiga AS, Castanho MARB 2013. From antimicrobial to anticancer peptides: a review. Front. Microbiol. 4:294
    [Google Scholar]
  28. 28. 
    Hanggi P, Talkner P, Borkovec M 1990. Reaction-rate theory: 50 years after Kramers. Rev. Mod. Phys. 62:2251–341
    [Google Scholar]
  29. 29. 
    Harger M, Li D, Wang Z, Dalby K, Lagardere L et al. 2017. Tinker-OpenMM: absolute and relative alchemical free energies using AMOEBA on GPUs. J. Comput. Chem. 38:232047–55
    [Google Scholar]
  30. 30. 
    Harrison WA. 1980. Solid State Theory New York: Dover:
    [Google Scholar]
  31. 31. 
    Hijon C, Espanol P, Vanden-Eijnden E, Delgado-Buscalioni R 2010. Mori-Zwanzig formalism as a practical computational tool. Faraday Discuss 144:301–22
    [Google Scholar]
  32. 32. 
    Hille B. 2001. Ion Channels of Excitable Membranes Sunderland, UK: Sinauer Assoc.
    [Google Scholar]
  33. 33. 
    Hoch DH, Romero-Mira M, Ehrlich BE, Finkelstein A, Dasgupta BR, Simpson LL 1985. Channels formed by botulinum, tetanus, and diphtheria toxins in planar lipid bilayers: relevance to translocations of proteins across membranes. PNAS 82:61692–96
    [Google Scholar]
  34. 34. 
    Huang J, Lemkul JA, Eastman PK, MacKerell AD 2018. Molecular dynamics simulations using the drude polarizable force field on GPUs with OpenMM: implementation, validation, and benchmarks. J. Comput. Chem. 39:211682–89
    [Google Scholar]
  35. 35. 
    Huber GA, Kim S. 1996. Weighted-ensemble Brownian dynamics simulations for protein association reactions. Biophys. J. 70:197–110
    [Google Scholar]
  36. 36. 
    Izvekov S, Voth GA. 2005. A multiscale coarse-graining method for biomolecular systems. J. Phys. Chem. B 109:72469–73
    [Google Scholar]
  37. 37. 
    Jiang JS, Pentelute BL, Collier RJ, Zhou ZH 2015. Atomic structure of anthrax protective antigen pore elucidates toxin translocation. Nature 521:7553545–49
    [Google Scholar]
  38. 38. 
    Kirmizialtin S, Elber R. 2011. Revisiting and computing reaction coordinates with directional milestoning. J. Phys. Chem. A 115:236137–48
    [Google Scholar]
  39. 39. 
    Kirmizialtin S, Johnson KA, Elber R 2016. Enzyme selectivity of HIV reverse transcriptase: conformations, ligands and free energy partitions. Biophys. J. 110:311513–26
    [Google Scholar]
  40. 40. 
    Kirmizialtin S, Nguyen V, Johnson KA, Elber R 2012. How conformational dynamics of DNA polymerase select correct substrates: experiments and simulations. Structure 20:4618–27
    [Google Scholar]
  41. 41. 
    Kuczera K, Jas GS, Elber R 2009. Kinetics of helix unfolding: molecular dynamics simulations with milestoning. J. Phys. Chem. A 113:267461–73
    [Google Scholar]
  42. 42. 
    Lee TS, Cerutti DS, Mermelstein D, Lin C, LeGrand S et al. 2018. GPU-accelerated molecular dynamics and free energy methods in Amber18: performance enhancements and new features. J. Chem. Inform. Model. 58:102043–50
    [Google Scholar]
  43. 43. 
    Leimkuhler B, Matthews C. 2015. Molecular Dynamics with Deterministic and Stochastic Numerical Methods Berlin: Springer
    [Google Scholar]
  44. 44. 
    Li LB, Vorobyov I, Allen TW 2012. The role of membrane thickness in charged protein-lipid interactions. Biochim. Biophys. Acta Biomembr. 1818 2:135–45
    [Google Scholar]
  45. 45. 
    Lopes LJS, Lelievre T. 2019. Analysis of the adaptive multilevel splitting method on the isomerization of alanine dipeptide. J. Comput. Chem. 40:111198–208
    [Google Scholar]
  46. 46. 
    Ma P, Cardenas AE, Chaudhari MI, Elber R, Rempe SB 2018. Probing translocation in mutants of the anthrax channel: atomically detailed simulations with milestoning. J. Phys. Chem. B 122:4510296–305
    [Google Scholar]
  47. 47. 
    Ma W, Schulten K. 2015. Mechanism of substrate translocation by a ring-shaped ATPase motor at millisecond resolution. J. Am. Chem. Soc. 137:83031–40
    [Google Scholar]
  48. 48. 
    Majek P, Elber R. 2010. Milestoning without a reaction coordinate. J. Chem. Theory Comput. 6:61805–17
    [Google Scholar]
  49. 49. 
    Maragliano L, Cottone G, Ciccotti G, Vanden-Eijnden E 2010. Mapping the network of pathways of CO diffusion in myoglobin. J. Am. Chem. Soc. 132:31010–17
    [Google Scholar]
  50. 50. 
    Maragliano L, Vanden-Eijnden E. 2007. On-the-fly string method for minimum free energy paths calculation. Chem. Phys. Lett. 446:1–3182–90
    [Google Scholar]
  51. 51. 
    Marrink SJ, Berendsen HJC. 1996. Permeation process of small molecules across lipid membranes studied by molecular dynamics simulations. J. Phys. Chem. 100:4116729–38
    [Google Scholar]
  52. 52. 
    Marrink SJ, Risselada HJ, Yefimov S, Tieleman DP, de Vries AH 2007. The MARTINI force field: coarse grained model for biomolecular simulations. J. Phys. Chem. B 111:277812–24
    [Google Scholar]
  53. 53. 
    Mori T, Miyashita N, Im W, Feig M, Sugita Y 2016. Molecular dynamics simulations of biological membranes and membrane proteins using enhanced conformational sampling algorithms. Biochim. Biophys. Acta Biomembr. 1858:71635–51
    [Google Scholar]
  54. 54. 
    Moroni D, Bolhuis PG, van Erp TS 2004. Rate constants for diffusive processes by partial path sampling. J. Chem. Phys. 120:94055–65
    [Google Scholar]
  55. 55. 
    Nelson MT, Humphrey W, Gursoy A, Dalke A, Kale LV et al. 1996. NAMD: a parallel, object oriented molecular dynamics program. Int. J. Supercomput. Appl. High Perform. Comput. 10:4251–68
    [Google Scholar]
  56. 56. 
    Ovchinnikov V, Karplus M, Vanden-Eijnden E 2011. Free energy of conformational transition paths in biomolecules: the string method and its application to myosin VI. J. Chem. Phys. 134:8085103
    [Google Scholar]
  57. 57. 
    Pannifer AD, Wong TY, Schwarzenbacher R, Renatus M, Petosa C et al. 2001. Crystal structure of the anthrax lethal factor. Nature 414:6860229–33
    [Google Scholar]
  58. 58. 
    Paula S, Volkov AG, VanHoek AN, Haines TH, Deamer DW 1996. Permeation of protons, potassium ions, and small polar molecules through phospholipid bilayers as a function of membrane thickness. Biophys. J. 70:1339–48
    [Google Scholar]
  59. 59. 
    Phillips JC, Braun R, Wang W, Gumbart J, Tajkhorshid E et al. 2005. Scalable molecular dynamics with NAMD. J. Comput. Chem. 26:161781–802
    [Google Scholar]
  60. 60. 
    Ruymgaart AP, Cardenas AE, Elber R 2011. MOIL-opt: energy-conserving molecular dynamics on a GPU/CPU system. J. Chem. Theory Comput. 7:103072–82
    [Google Scholar]
  61. 61. 
    Ruymgaart AP, Elber R. 2012. Revisiting molecular dynamics on a CPU/GPU system: water kernel and SHAKE parallelization. J. Chem. Theory Comput. 8:114624–36
    [Google Scholar]
  62. 62. 
    Sanderson JM. 2012. Resolving the kinetics of lipid, protein and peptide diffusion in membranes. Mol. Membr. Biol. 29:5118–43
    [Google Scholar]
  63. 63. 
    Sarich M, Noe F, Schutte C 2010. On the approximation quality of the Markov state models. Multiscale Model. Simul. 8:41154–77
    [Google Scholar]
  64. 64. 
    Schlick T. 2002. Molecular Modeling and Simulation: An Interdisciplinary Guide Berlin: Springer
    [Google Scholar]
  65. 65. 
    Shaw DE, Deneroff MM, Dror RO, Kuskin JS, Larson RH et al. 2008. Anton, a special-purpose machine for molecular dynamics simulation. Commun. ACM 51:791–97
    [Google Scholar]
  66. 66. 
    Stone JE, Phillips JC, Freddolino PL, Hardy DJ, Trabuco LG, Schulten K 2007. Accelerating molecular modeling applications with graphics processors. J. Comput. Chem. 28:162618–40
    [Google Scholar]
  67. 67. 
    Sun J, Lang AE, Aktories K, Collier RJ 2008. Phenylalanine-427 of anthrax protective antigen functions in both pore formation and protein translocation. PNAS 105:114346–51
    [Google Scholar]
  68. 68. 
    Swenson DWH, Bolhuis PG. 2014. A replica exchange transition interface sampling method with multiple interface sets for investigating networks of rare events. J. Chem. Phys. 141:4044101
    [Google Scholar]
  69. 69. 
    Templeton C, Elber R. 2018. Why does RNA collapse? The importance of water in a simulation study of helix–junction–helix systems. J. Am. Chem. Soc. 140:16948–51
    [Google Scholar]
  70. 70. 
    Ulitsky A, Elber R. 1990. A new technique to calculate steepest descent paths in flexible polyatomic systems. J. Chem. Phys. 92:21510–11
    [Google Scholar]
  71. 71. 
    van Erp TS, Moroni D, Bolhuis PG 2003. A novel path sampling method for the calculation of rate constants. J. Chem. Phys. 118:177762–74
    [Google Scholar]
  72. 72. 
    Vanden-Eijnden E, Venturoli M. 2009. Markovian milestoning with Voronoi tessellations. J. Chem. Phys. 130:19194101
    [Google Scholar]
  73. 73. 
    Venable RM, Ingolfsson HI, Lerner MG, Perrin BS, Camley BA et al. 2017. Lipid and peptide diffusion in bilayers: the Saffman-Delbruck model and periodic boundary conditions. J. Phys. Chem. B 121:153443–57
    [Google Scholar]
  74. 74. 
    Venable RM, Kramer A, Pastor RW 2019. Molecular dynamics simulations of membrane permeability. Chem. Rev. 119:95954–97
    [Google Scholar]
  75. 75. 
    Vives E, Schmidt J, Pelegrin A 2008. Cell-penetrating and cell-targeting peptides in drug delivery. Biochim. Biophys. Acta Rev. Cancer 1786 2:126–38
    [Google Scholar]
  76. 76. 
    Votapka LW, Amaro RE. 2015. Multiscale estimation of binding kinetics using Brownian dynamics, molecular dynamics and milestoning. PLOS Comput. Biol. 11:10e1004381
    [Google Scholar]
  77. 77. 
    Voth G. 2009. Coarse-Graining of Condensed Phase and Biomolecular Systems Boca Raton, FL: CRC Press
    [Google Scholar]
  78. 78. 
    Wilson MA, Pohorille A. 1996. Mechanism of unassisted ion transport across membrane bilayers. J. Am. Chem. Soc. 118:286580–87
    [Google Scholar]
  79. 79. 
    Young JAT, Collier RJ. 2017. Anthrax toxin: receptor binding, internalization, pore formation, and translocation. Annu. Rev. Biochem. 76:243–65
    [Google Scholar]
  80. 80. 
    Zhang BW, Jasnow D, Zuckerman DM 2010. The “weighted ensemble” path sampling method is statistically exact for a broad class of stochastic processes and binning procedures. J. Chem. Phys. 132:5054107
    [Google Scholar]
  81. 81. 
    Zhu YL, Pan D, Li ZW, Liu H, Qian HJ et al. 2018. Employing multi-GPU power for molecular dynamics simulation: an extension of GALAMOST. Mol. Phys. 116:7–81065–77
    [Google Scholar]
  82. 82. 
    Ziman JM. 1982. Models of Disorder: The Theoretical Physics of Homogeneously Disordered Systems Cambridge, UK: Cambridge Univ. Press
    [Google Scholar]
  83. 83. 
    Zwanzig R. 2001. Nonequilibrium Statistical Mechanics Oxford, UK: Oxford Univ. Press
    [Google Scholar]
/content/journals/10.1146/annurev-biophys-121219-081528
Loading
/content/journals/10.1146/annurev-biophys-121219-081528
Loading

Data & Media loading...

  • Article Type: Review Article
This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error