Skip to main content

Classical Molecular Dynamics in a Nutshell

  • Protocol
  • First Online:
Biomolecular Simulations

Part of the book series: Methods in Molecular Biology ((MIMB,volume 924))

Abstract

This chapter provides an overview of the various techniques that are commonly used in classical molecular dynamics simulations. It describes suitable algorithms for the integration of Newton’s equation of motion over many time steps for systems containing a large number of particles, different choices of boundary conditions as well as available force fields for biological systems, that is, the mathematical description of the interactions of atoms and molecules with each other. It also illustrates algorithms used to simulate systems at constant temperature and/or pressure and discusses their advantages and disadvantages. It presents a few methods to save CPU time and a summary of popular software for biomolecular molecular dynamics simulations.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Protocol
USD 49.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Cramer CJ (2004) Essentials of computational chemistry: theories and models. Wiley, Chichester, England

    Google Scholar 

  2. Jackson SE (1998) How do small single-domain proteins fold? Fold Des 3:R81–R91

    Article  PubMed  CAS  Google Scholar 

  3. Allen MP, Tildesley DJ (2007) Computer simulation of liquids. Oxford University Press, Oxford

    Google Scholar 

  4. Frenkel D, Smit B (2002) Understanding molecular simulation: from algorithms to applications. Academic Press, San Diego, CA

    Google Scholar 

  5. Rapaport DC (2004) The art of molecular dynamics simulation. Cambridge University Press, Cambridge.

    Book  Google Scholar 

  6. Zhong G, Marsden JE (1988) Lie–Poisson Hamilton–Jacobi theory and Lie–Poisson integrators. Phys Lett A 133:134–139

    Article  Google Scholar 

  7. Miller RH (1991) A horror story about integration methods. J Comput Phys 93:469–476

    Article  Google Scholar 

  8. Lasagni FM (1988) Canonical Runge–Kutta methods. Z Angew Math Phys 39:952–953

    Article  Google Scholar 

  9. Candy J, Rozmus W (1991) A symplectic integration algorithm for separable Hamiltonian functions. J Comput Phys 92:230–256

    Article  Google Scholar 

  10. Verlet L (1967) Computer experiments on classical fluids. I. Thermodynamical properties of Lennard–Jones molecules. Phys Rev 159:98–103

    Google Scholar 

  11. Swope WC, Andersen HC, Berens PH, Wilson KR (1982) A computer-simulation method for the calculation of equilibrium-constants for the formation of physical clusters of molecules—application to small water clusters. J Chem Phys 76:637–649

    Article  CAS  Google Scholar 

  12. Hockney RW, Goel SP, Eastwood JW (1974) Quiet high-resolution computer models of a plasma. J Comput Phys 14:148–158

    Article  Google Scholar 

  13. Allen MP, Tildesley DJ (1987) Computer simulation of liquids. Oxford University Press, Oxford

    Google Scholar 

  14. Tuckerman ME, Martyna GJ (2000) Understanding modern molecular dynamics: techniques and applications. J Phys Chem B 104:159–178

    Article  CAS  Google Scholar 

  15. Tuckerman ME, Alejandre J, Lopez-Rendon R, Jochim AL, Martyna GJ (2006) A Liouville-operator derived measure-preserving integrator for molecular dynamics simulations in the isothermal–isobaric ensemble. J Phys A: Math Gen 39:5629–5651

    Article  CAS  Google Scholar 

  16. Tuckerman M, Berne BJ, Martyna GJ (1992) Reversible multiple time scale molecular-dynamics. J Chem Phys 97:1990–2001

    Article  CAS  Google Scholar 

  17. Han G, Deng Y, Glimm J, Martyna G (2007) Error and timing analysis of multiple time-step integration methods for molecular dynamics. Comput Phys Commun 176:271–291

    Article  CAS  Google Scholar 

  18. Trotter HF (1959) On the product of semi-groups of operators. Proc Amer Math Soc 10:545–551

    Article  Google Scholar 

  19. Creutz M, Gocksch A (1989) Higher-order hybrid Monte-Carlo algorithms. Phys Rev Lett 63:9–12

    Article  PubMed  Google Scholar 

  20. Strang G (1968) On construction and comparison of difference schemes. SIAM J Numer Anal 5:506–517

    Google Scholar 

  21. Barth E, Schlick T (1998) Overcoming stability limitations in biomolecular dynamics. I. Combining force splitting via extrapolation with Langevin dynamics in LN. J Chem Phys 109:1617–1632

    CAS  Google Scholar 

  22. Batcho P, Schlick T (2001) Special stability advantages of position-Verlet over velocity-Verlet in multiple-time step integration. J Chem Phys 115:4019–4029

    Article  CAS  Google Scholar 

  23. Leach AR (2001) Molecular modelling: principles and applications. Pearson Education Limited, Essex, England

    Google Scholar 

  24. Brooks BR, Bruccoleri RE, Olafson BD, States DJ, Swaminathan S, Karplus M (1983) CHARMM—a program for macromolecular energy, minimization, and dynamics calculations. J Comput Chem 4:187–217

    Article  CAS  Google Scholar 

  25. Nilsson L, Karplus M (1986) Empirical energy functions for energy minimization and dynamics of nucleic-acids. J Comput Chem 7:591–616

    Article  CAS  Google Scholar 

  26. Daura X, Mark A, van Gunsteren W (1998) Parametrization of aliphatic CHn united atoms of GROMOS96 force field. J Comput Chem 19:535–547

    Article  CAS  Google Scholar 

  27. Schuler LD, Daura X, van Gunsteren WF (2001) An improved GROMOS96 force field for aliphatic hydrocarbons in the condensed phase J Comput Chem 22:1205–1218

    Google Scholar 

  28. Weiner SJ, Kollman PA, Case DA, Singh UC, Ghio C, Alagona G, Profeta S, Weiner P (1984) A new force-field for molecular mechanical simulation of nucleic-acids and proteins. J Am Chem Soc 106:765–784

    Article  CAS  Google Scholar 

  29. Cornell WD, Cieplak P, Bayly CI, Gould IR, Merz KM, Ferguson DM, Spellmeyer DC, Fox T, Caldwell JW, Kollman PA (1995) A 2nd generation force-field for the simulation of proteins, nucleic-acids, and organic-molecules. J Am Chem Soc 117:5179–5197

    Article  CAS  Google Scholar 

  30. Jorgensen WL, Tiradorives J (1988) The OPLS potential functions for proteins—energy minimizations for crystals of cyclic-peptides and crambin. J Am Chem Soc 110:1657–1666

    Article  CAS  Google Scholar 

  31. Kaminski GA, Friesner RA, Tirado-Rives J, Jorgensen WL (2001) Evaluation and reparametrization of the OPLS-AA force field for proteins via comparison with accurate quantum chemical calculations on peptides. J Phys Chem B 105:6474–6487, Symposium on molecular dynamics—the next millennium, New York, June 02–03, 2000

    Google Scholar 

  32. Ren PY, Ponder JW (2002) Consistent treatment of inter- and intramolecular polarization in molecular mechanics calculations. J Comput Chem 23:1497–1506

    Article  PubMed  CAS  Google Scholar 

  33. Ren PY, Ponder JW (2003) Polarizable atomic multipole water model for molecular mechanics simulation. J Phys Chem B 107:5933–5947

    Article  CAS  Google Scholar 

  34. Morse PM (1929) Diatomic molecules according to the wave mechanics. ii. vibrational levels. Phys Rev 34:57–64

    Article  CAS  Google Scholar 

  35. Kremer K, Grest G (1990) Dynamics of entangled linear polymer melts—a molecular-dynamics simulation. J Chem Phys 92:5057–5086

    Article  CAS  Google Scholar 

  36. Stillinger FH, Weber TA (1985) Computer-simulation of local order in condensed phases of silicon. Phys Rev B 31:5262–5271

    Article  CAS  Google Scholar 

  37. Tersoff J (1988) New empirical-approach for the structure and energy of covalent systems. Phys Rev B 37:6991–7000

    Article  Google Scholar 

  38. Lowe C (1999) An alternative approach to dissipative particle dynamics. Europhys Lett 47:145–151

    Article  CAS  Google Scholar 

  39. Nosé S (1984) A molecular-dynamics method for simulations in the canonical ensemble. Mol Phys 52:255–268

    Article  Google Scholar 

  40. Hoover WG (1985) Canonical dynamics—equilibrium phase-space distributions. Phys Rev A 31:1695–1697

    Article  PubMed  Google Scholar 

  41. Berendsen HJC, Postma JPM, van Gunsteren WF, Dinola A, Haak JR (1984) Molecular-dynamics with coupling to an external bath. J Chem Phys 81:3684–3690

    Article  CAS  Google Scholar 

  42. Schneider T, Stoll E (1978) Molecular-Dynamics study of a 3-dimensional one-component model for distortive phase-transitions. Phys Rev B 17:1302–1322

    Article  CAS  Google Scholar 

  43. Andersen HC (1980) Molecular-dynamics simulations at constant pressure and/or temperature. J Chem Phys 72:2384–2393

    Article  CAS  Google Scholar 

  44. Soddemann T, Dünweg B, Kremer K (2003) Dissipative particle dynamics: a useful thermostat for equilibrium and nonequilibrium molecular dynamics simulations. Phys Rev E 68:046702

    Article  Google Scholar 

  45. Frenkel D, Smit B (1996) Understanding molecular simulations: from algorithms to applications. Academic Press, London, UK

    Google Scholar 

  46. Nosé S (1986) An extension of the canonical ensemble molecular-dynamics method. Mol Phys 57:187–191

    Article  Google Scholar 

  47. Ciccotti G, Kalibaeva G (2004) Molecular dynamics of complex systems: non-Hamiltonian, constrained, quantum-classical. In: Karttunen M, Vattulainen I, Lukkarinen A (ed) Novel methods in soft matter simulations. Lecture notes in physics, vol 640, pp. 150–189. International summer school on novel methods in soft matter simulations (SOFTSIMU 20020), Helsinki, Finland, May 31–June 06, 2002

    Google Scholar 

  48. Tuckerman ME, Mundy CJ, Martyna GJ (1999) On the classical statistical mechanics of non-Hamiltonian systems. Europhys Lett 45:149–155

    Article  CAS  Google Scholar 

  49. Tuckerman ME, Liu Y, Ciccotti G, Martyna GJ (2001) Non-Hamiltonian molecular dynamics: generalizing Hamiltonian phase space principles to non-Hamiltonian systems. J Chem Phys 115:1678–1702

    Article  CAS  Google Scholar 

  50. Martyna GJ, Klein ML, Tuckerman M (1992) Nosé-Hoover chains—the canonical ensemble via continuous dynamics. J Chem Phys 97:2635–2643

    Article  Google Scholar 

  51. Tuckerman ME, Berne BJ, Martyna GJ, Klein ML (1993) Efficient molecular-dynamics and hybrid Monte-Carlo algorithms for path-integrals. J Chem Phys 99:2796–2808

    Article  Google Scholar 

  52. Harvey SC, Tan RKZ, Cheatham T (1998) The flying ice cube: velocity rescaling in molecular dynamics leads to violation of energy equipartition. J Comput Chem 19:726–740

    Article  CAS  Google Scholar 

  53. Leyssale JM, Vignoles GL (2008) Molecular dynamics evidences of the full graphitization of a nanodiamond annealed at 1500 K. Chem Phys Lett 454:299–304

    Article  CAS  Google Scholar 

  54. Evans DJ, Morriss GP (1990) Statistical mechanics of nonequilibrium liquids. Academic Press, London, UK

    Google Scholar 

  55. Bussi G, Donadio D, Parrinello M (2007) Canonical sampling through velocity rescaling. J Chem Phys 126:014101

    Article  PubMed  Google Scholar 

  56. Kampen NGV (1981) Stochastic processes in physics and chemistry. North-Holland, Amsterdam

    Google Scholar 

  57. Nikunen P, Karttunen M, Vattulainen I (2003) How would you integrate the equations of motion in dissipative particle dynamics simulations? Comput Phys Commun 153:407–423

    Article  CAS  Google Scholar 

  58. Müller M, Katsov K, Schick M (2006) Biological and synthetic membranes: What can be learned from a coarse-grained description? Phys Rep 434:113–176

    Article  Google Scholar 

  59. Nosé S, Klein ML (1983) Constant pressure molecular-dynamics for molecular-systems. Mol Phys 50:1055–1076

    Article  Google Scholar 

  60. Parrinello M, Rahman A (1981) Polymorphic transitions in single-crystals—a new molecular-dynamics method. J Appl Phys 52:7182–7190

    Article  CAS  Google Scholar 

  61. Parrinello M, Rahman A, Vashishta P (1983) Structural transitions in superionic conductors. Phys Rev Lett 50:1073–1076

    Article  CAS  Google Scholar 

  62. Ispolatov I, Karttunen M (2003) Collapses and explosions in self-gravitating systems. Phys Rev E 68:036117

    Article  CAS  Google Scholar 

  63. Miettinen MS (2010) Computational modeling of cationic lipid bilayers in saline solutions. Ph.D. thesis, Aalto University School of Science and Technology, Finland

    Google Scholar 

  64. Wang SS, Krumhans JA (1972) Superposition assumption. II. High-density fluid argon. J Chem Phys 56:4287–4290

    Google Scholar 

  65. Adams DJ (1979) Computer-simulation of ionic systems—distorting effects of the boundary-conditions. Chem Phys Lett 62:329–332

    Article  CAS  Google Scholar 

  66. Adams, D. J. (1980) The problem of the long-range forces in the computer simulation of condensed media. In: Ceperley, D. M. (ed) NRCC Workshop Proc., Berkeley 9, p. 13

    Google Scholar 

  67. Mandell MJ (1976) Properties of a periodic fluid. J Stat Phys 15: 299–305

    Article  Google Scholar 

  68. Impey RW, Madden PA, Tildesley DJ (1981) On the calculation of the orientational correlation parameter G2. Mol Phys 44:1319–1334

    Article  CAS  Google Scholar 

  69. Luckhurst GR, Simpson P (1982) Computer-simulation studies of anisotropic systems. VIII. The Lebwohl–Lasher model of nematogens revisited. Mol Phys 47:251–265

    Article  CAS  Google Scholar 

  70. Mouritsen OG, Berlinsky AJ (1982) Fluctuation-induced 1st-order phase-transition in an anisotropic planar model of N2 on graphite. Phys Rev Lett 48:181–184

    Article  CAS  Google Scholar 

  71. Lenstra D, Mandel L (1982) Angular-momentum of the quantized electromagnetic-field with periodic boundary-conditions. Phys Rev A 26:3428–3437

    Article  Google Scholar 

  72. Lees AW, Edwards SF (1972) Computer study of transport processes under extreme conditions. J Phys Part C Solids 5:1921–1928

    Google Scholar 

  73. Miettinen MS (2004) From molten globule to swollen coil: simulations of a lone polymer chain in an explicit solvent. Master’s thesis, Helsinki University of Technology, Finland

    Google Scholar 

  74. Mattson W, Rice BM (1999) Near-neighbor calculations using a modified cell-linked list method. Comput Phys Commun 119:135–148

    Article  CAS  Google Scholar 

  75. Heinz TN, Hünenberger PH (2004) A fast pairlist-construction algorithm for molecular simulations under periodic boundary conditions J Comput Chem 25:1474–1486

    CAS  Google Scholar 

  76. Gonnet P (2007) A simple algorithm to accelerate the computation of non-bonded interactions in cell-based molecular dynamics simulations. J Comput Chem 28:570–573

    Article  PubMed  CAS  Google Scholar 

  77. Ryckaert JP, Ciccotti G, Berendsen HJC (1977) Numerical-integration of cartesian equations of motion of a system with constraints—molecular-dynamics of N-alkanes. J Comput Phys 23:327–341

    Article  CAS  Google Scholar 

  78. Andersen HC (1983) RATTLE—a velocity version of the SHAKE algorithm for molecular-dynamics calculations. J Comput Phys 52:24–34

    Article  CAS  Google Scholar 

  79. Miyamoto S, Kollman PA (1992) SETTLE—an analytical version of the SHAKE and RATTLE algorithm for rigid water models. J Comput Chem 13: 952–962

    Article  CAS  Google Scholar 

  80. Hess B, Bekker H, Berendsen HJC, Fraaije JGEM (1997) LINCS: a linear constraint solver for molecular simulations. J Comput Chem 18:1463–1472

    Article  CAS  Google Scholar 

  81. Edberg R, Evans DJ, Morriss GP (1986) Constrained molecular-dynamics-simulations of liquid alkanes with a new algorithm. J Chem Phys 84:6933–6939

    Article  CAS  Google Scholar 

  82. Baranyai A, Evans DJ (1990) New algorithm for constrained molecular-dynamics simulation of liquid benzene and naphthalene. Mol Phys 70:53–63

    Article  CAS  Google Scholar 

  83. Plimpton S (1995) Fast parallel algorithms for short-range molecular-dynamics. J Comput Phys 117:1–19

    Article  CAS  Google Scholar 

  84. Phillips JC, Braun R, Wang W, Gumbart J, Tajkhorshid E, Villa E, Chipot C, Skeel RD, Kale L, Schulten K (2005) Scalable molecular dynamics with NAMD. J Comput Chem 26:1781–1802

    Article  PubMed  CAS  Google Scholar 

  85. Berendsen HJC, van der Spoel D, van Drunen R (1995) GROMACS—a message-passing parallel molecular-dynamics implementation. Comput Phys Commun 91:43–56

    Article  CAS  Google Scholar 

  86. Lindahl E, Hess B, van der Spoel D (2001) GROMACS 3.0: a package for molecular simulation and trajectory analysis. J Mol Model 7:306–317

    CAS  Google Scholar 

  87. Van der Spoel D, Lindahl E, Hess B, Groenhof G, Mark AE, Berendsen HJC (2005) GROMACS: fast, flexible, and free. J Comput Chem 26:1701–1718

    Article  Google Scholar 

  88. Hess B, Kutzner C, van der Spoel D, Lindahl E (2008) GROMACS 4: algorithms for highly efficient, load-balanced, and scalable molecular simulation. J Chem Theory Comput 4:435–447

    Article  CAS  Google Scholar 

  89. Pearlman DA, Case DA, Caldwell JW, Ross WS, Cheatham TE, Debolt S, Ferguson D, Seibel G, Kollman P (1995) Amber, a package of computer-programs for applying molecular mechanics, normal-mode analysis, molecular-dynamics and free-energy calculations to simulate the structural and energetic properties of molecules. Comput Phys Commun 91:1–41

    Article  CAS  Google Scholar 

  90. Case DA, Cheatham TE, Darden T, Gohlke H, Luo R, Merz KM, Onufriev A, Simmerling C, Wang B, Woods RJ (2005) The amber biomolecular simulation programs. J Comput Chem 26:1668–1688

    Article  PubMed  CAS  Google Scholar 

  91. Brooks BR, Brooks III CL, Mackerell Jr. AD, Nilsson L, Petrella RJ, Roux B, Won Y, Archontis G, Bartels C, Boresch S, Caflisch A, Caves L, Cui Q, Dinner AR, Feig M, Fischer S, Gao J, Hodoscek M, Im W, Kuczera K, Lazaridis T, Ma J, Ovchinnikov V, Paci E, Pastor RW, Post CB, Pu JZ, Schaefer M, Tidor B, Venable RM, Woodcock HL, Wu X, Yang W, York DM, Karplus M (2009) CHARMM: the biomolecular simulation program. J Comput Chem 30:1545–1614

    Article  PubMed  CAS  Google Scholar 

  92. Hein JI, Reid F, Smith L, Bush I, Guest M, Sherwood P (2005) On the performance of molecular dynamics applications on current high-end systems. Philos Trans Roy Soc A 363:1987–1998

    Article  Google Scholar 

  93. Limbach HJ, Arnold A, Mann BA, Holm C (2006) ESPResSo—an extensible simulation package for research on soft matter systems. Comput Phys Comp 174:704–727

    Article  CAS  Google Scholar 

  94. Stone JE, Phillips JC, Freddolino PL, Hardy DJ, Trabuco LG, Schulten K (2007) Accelerating molecular modeling applications with graphics processors. J Comput Chem 28:2618–2640

    Article  PubMed  CAS  Google Scholar 

  95. Van Meel JA, Arnold A, Frenkel D, Zwart SFP, Belleman RG (2008) Harvesting graphics power for MD simulations. Mol Simulat 34:259–266

    Article  Google Scholar 

  96. Hardy DJ, Stone JE, Schulten K (2009) Multilevel summation of electrostatic potentials using graphics processing units. Parallel Comput 35:164–177

    Article  PubMed  Google Scholar 

  97. Anderson JA, Lorenz CD, Travesset A (2008) General purpose molecular dynamics simulations fully implemented on graphics processing units. J Comput Phys 227:5342–5359

    Article  Google Scholar 

Download references

Acknowledgments

I would like to thank Markus Miettinen for providing some of the figures and Mikko Karttunen for reading the manuscript.

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer Science+Business Media New York

About this protocol

Cite this protocol

Hug, S. (2013). Classical Molecular Dynamics in a Nutshell. In: Monticelli, L., Salonen, E. (eds) Biomolecular Simulations. Methods in Molecular Biology, vol 924. Humana Press, Totowa, NJ. https://doi.org/10.1007/978-1-62703-017-5_6

Download citation

  • DOI: https://doi.org/10.1007/978-1-62703-017-5_6

  • Published:

  • Publisher Name: Humana Press, Totowa, NJ

  • Print ISBN: 978-1-62703-016-8

  • Online ISBN: 978-1-62703-017-5

  • eBook Packages: Springer Protocols

Publish with us

Policies and ethics