Molecular Dynamics

Abstract

Molecular dynamics (MD) is a widely used technique for computer simulation of complex systems, modelled at the atomic or some coarse‐grained level. In this article, basic concepts pertaining to MD simulations are systematically introduced and related to the underlying models of physical systems. The principles of the atomic force fields, representation of the environment, the time evolution of the system, as well as the derivation of kinetic and thermodynamic properties of interest from MD trajectories are discussed. Applications of MD to biological systems are illustrated by examples of large scale studies on protein structure and dynamics, protein–protein interactions, and drug design. Limitations and several recent extensions of classical MD, including Replica Exchange and Steered MD, are discussed in the context of applications to biological systems as well. Related simulation protocols, including Monte Carlo and free energy methods, are summarized, highlighting complementarity and common principles of these molecular simulation approaches.

Key Concepts

  • Computer simulations can be used to facilitate and complement experimental studies of biomolecular systems.

  • Empirical force fields describe interatomic interactions in the system and enable efficient computation of forces in MD simulations.

  • MD is routinely used to study biological macromolecules and their environment.

  • A physical quantity can be measured using MD simulations by taking an arithmetic average over instantaneous values of that quantity obtained from MD trajectories.

  • Other simulation methods, such as Monte Carlo, enhanced sampling and free energy methods, are often being used in conjunction with MD and its extensions.

  • Slow processes can be studied computing the relative free energies of different states.

  • MD and related methods can be applied to systems comprising millions of atoms, providing unique insights into complex biological systems.

Keywords: molecular simulations; force field; Monte Carlo; protein dynamics; steered molecular dynamics; replica exchange molecular dynamics

Figure 1.

Conformational ensemble of ubiquitin (PDB code 2K39). Secondary structures and relative solvent accessibility (a), as well as 3D rendering of individual models (b), obtained using the POLYVIEW‐3D server (Porollo and Meller, ) are shown for randomly selected 50 models from the ensemble. The secondary structures are shown using the following colour coding :: red – helix, green – extended strand, dark green – beta‐bridge, blue – coil, violet – hydrogen bonded turn and light blue – bend. The relative solvent accessibility is shown using shaded boxes (black corresponds to fully buried, whereas white to fully exposed residues). Note also that these individual models could be interpreted as snapshots taken during MD simulations of ubiquitin in solution, effectively representing an MD trajectory of the system. Note also that the highly flexible C‐terminus of ubiquitin adopts a certain conformation upon binding to ubiquitin‐associated protein (PDB code 2JY6, (c)).

Figure 2.

Simulation model of the satellite tobacco mosaic (STM) virus (based on the PDB code 1A34) in aqueous solution. The virion is placed into a box with water molecules and periodic boundary conditions are employed to define the implicit lattice copies of the simulation box. MD simulations of fully solvated large systems such as STM virus, comprising capsid proteins (shown in yellow), RNA molecules (shown in red in panel b), counter‐ions and explicit water molecules are becoming feasible, as illustrated by this and other studies.

Figure 3.

Schematic representation of the replica exchange method using five copies of the system (replicas) simulated at different temperatures. Colour coding indicates temperatures used for individual copies, with blue and red corresponding to the lowest and highest temperature, respectively.

Figure 4.

Example of an application of the SMD method to study the properties of an elastomeric protein from insects, called resilin. Three models with different extensions obtained as a result of applying harmonic pulling force, as indicated in (b), are shown (Petrenko R, Dickerson M, Naik R et al. (2009) Entropic force in Drosophila resilin: molecular dynamics study. BIOCOMP, pp. 598–603).

Figure 5.

The ATP‐hydrolysed state of GroEL–GroES complex (PDB code 1AON, Xu et al., ), with GroEL shown in blue and green, and GroES in red. A four helical bundle, representing the folding substrate from the study by Stan et al., is shown inside the GroEL cavity, which is capped by a dome‐shaped subunit of GroES. Picture generated using POLYVIEW‐3D.

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References

Adcock SA and McCammon JA (2006) Molecular dynamics: survey of methods for simulating the activity of proteins. Chemistry Review 106: 1589–1615.

Bond PJ, Holyoake J, Ivetac A, Khalid S and Sansom MSP (2007) Coarse‐grained molecular dynamics simulations of membrane proteins and peptides. Journal of Structural Biology 157: 593–605.

Brooks BR, Bruccoleri RE, Olafson BD et al. (1983) CHARMM: a program for macromolecular energy, minimization, and dynamics calculations. Journal of Computational Chemistry 4: 187–217.

Brooks CL Jr (1998) Simulations of protein folding and unfolding. Current Opinion in Structural Biology 8: 222–226.

Chennubhotla C, Yang Z and Bahar I (2008) Coupling between global dynamics and signal transduction pathways: a mechanism of allostery for chaperonin GroEL. Molecular BioSystems 4: 287–292.

Chipot C and Pohorille A (eds) (2007) Free energy calculations: theory and applications in chemistry and biology series. In: Springer Series in Chemical Physics, vol. 86. Berlin and Heidelberg: Springer.

Cornell WD, Cieplak P, Bayly CI et al. (1995) A second generation force field for the simulation of proteins and nucleic acids. Journal of American Chemical Society 117: 5179–5197.

Cuendet MA and Michielin O (2008) Protein–protein interaction investigated by steered molecular dynamics: the TCR‐pMHC complex. Biophysics Journal 95: 3575–3590.

Deng Y and Roux B (2009) Computations of standard binding free energies with molecular dynamics simulations. Journal of Physical Chemistry. B 113: 2234–2246.

Duan Y and Kollman PA (1998) Pathways to a protein folding intermediate observed in a 1‐microsecond simulation in aqueous solution. Science 282: 740–744.

Ellis RJ (2006) Inside the cage. Nature 442: 360–362.

Ewing TJ, Makino S, Skillman AG and Kuntz ID (2001) DOCK 4.0: search strategies for automated molecular docking of flexible molecular databases. Journal of Computer‐Aided Molecular Design 15: 411–428.

Freddolino PL, Arkhipov AS, Larson SB, McPherson A and Schulten K (2006) Molecular dynamics simulations of the complete satellite tobacco mosaic virus. Structure 14: 437–449.

Freddolino PL, Liu F, Gruebele M and Schulten K (2008) Ten‐microsecond MD simulation of a fast‐folding WW domain. Biophysical Journal 94: L75–L77.

Grossfield A, Feller SE and Pitman MC (2007) Convergence of molecular dynamics simulations of membrane proteins. Proteins: Structure, Function, and Bioinformatics 67: 31–40.

Hornak V, Okur A, Rizzo RC and Simmerling C (2006) HIV‐1 protease flaps spontaneously open and reclose in molecular dynamics simulations. Proceedings of the National Academy of Sciences of the USA 103: 915–920.

Jarzynski C (1997) Nonequilibrium equality for free energy differences. Physical Review Letters 78: 2690.

Jayachandran G, Vishal V and Pande VS (2006) Using massively parallel simulation and Markovian models to study protein folding: examining the dynamics of the villin headpiece. Journal of Chemical Physics 124: 164902.

Jorgensen WL and Thomas LL (2008) Perspective on free‐energy perturbation calculations for chemical equilibria. Journal of Chemical Theory and Computation 4: 869–876.

Kubelka J, Hofrichter J and Eaton WA (2004) The protein folding ‘speed limit’. Current Opinion in Structural Biology 14: 76–88.

Kuczera K (1996) Dynamics and thermodynamics of globins. In: Elber R (ed.) Recent Developments in Theoretical Studies of Proteins, pp. 1–64. Singapore: World Scientific.

Laio A and Parrinello M (2002) Escaping free‐energy minima. Proceedings of the National Academy of Sciences of the USA 99: 12562–12566.

Lange OF, Lakomek N‐A, Fares C et al. (2008) Recognition dynamics up to microseconds revealed from an RDC‐derived ubiquitin ensemble in solution. Science 320: 1471–1475.

Lindahl E and Sansom SP (2008) Membrane proteins: molecular dynamics simulations. Current Opinion in Structural Biology 18: 425–431.

Liu F, Du DG, Fuller AA et al. (2008) An experimental survey of the transition between two‐state and downhill protein folding scenarios. Proceedings of the National Academy of Sciences of the USA 105: 2369–2374.

Lu H, Isralewitz B, Krammer A, Vogel V and Schulten K (1998) Unfolding of titin immunoglobulin domains by steered molecular dynamics simulation. Biophysical Journal 75: 662–671.

Morfill J, Neumann J, Blank K et al. (2008) Force‐based analysis of multidimensional energy landscapes: application of dynamic force spectroscopy and steered molecular dynamics simulations to an antibody fragment‐peptide complex. Journal of Molecular Biology 381: 1253–1266.

Morris GM, Goodsell DS, Halliday RS et al. (1998) Automated docking using a Lamarckian genetic algorithm and empirical binding free energy function. Journal of Computational Chemistry 19: 1639–1662.

Perryman AL, Lin J‐H and McCammon JA (2006) Restrained molecular dynamics simulations of HIV‐1 protease: the first step in validating a new target for drug design. Biopolymers 82: 272–284.

Phillips JC, Braun R, Wang W et al. (2005) Scalable molecular dynamics with NAMD. Journal of Computational Chemistry 26: 1781–1802.

Porollo A and Meller J (2007) Versatile annotation and publication quality visualization of protein complexes using POLYVIEW‐3D. BMC Bioinformatics 8: 316.

Sagui C and Darden TA (1999) Molecular dynamics simulations of biomolecules: longe‐range electrostatic effects. Annual Review of Biophysics and Biomolecular Structure 28: 155–179.

Shirts MR and Pande VS (2000) Screen savers of the World unite! Science 290: 1903–1904.

Snow CD, Zagrovic B and Pande VS (2002) The Trp cage: folding kinetics and unfolded state topology via molecular dynamics simulations. Journal of American Chemical Society 124: 14548–14549.

Sotomayor M and Schulten K (2007) Single‐molecule experiments in vitro and in silico. Science 316: 1144–1148.

Stan G, Lorimer GH, Thirumalai D and Brooks BR (2007) Coupling between allosteric transitions in GroEL and assisted folding of a substrate protein. Proceedings of the National Academy of Sciences of the USA 44: 8803–8808.

Sugita Y (2009) Free‐energy landscapes of proteins in solution by generalized‐ensemble simulations. Frontiers in Biosciences 14: 1292–1303.

Sugita Y and Okamoto Y (1999) Replica‐exchange molecular dynamics method for protein folding. Chemical Physics Letters 314: 141–151.

Taylor RD, Jewsbury PJ and Essex JW (2002) A review of protein‐small molecule docking methods. Journal of Computer‐Aided Molecular Design 16(3): 151–166.

Trebst S, Troyer M and Hansmann UHE (2006) Optimized parallel tempering simulations of proteins. Journal of Chemical Physics 124: 174903.

van Gunsteren WF, Billeter SR, Eising AA et al. (1996) Biomolecular Simulation: The GROMOS96 Manual and User Guide. Zürich: Vdf Hochschulverlag.

Wang M, Tang Y, Sato S et al. (2003) Dynamic NMR line‐shape analysis demonstrates that the villin headpiece subdomain folds on the microsecond time scale. Journal of American Chemical Society 125: 6032–6033.

White SH (2009) Biophysical dissection of membrane proteins. Nature 459: 344–346.

Xu Z, Horwich AL and Sigler PB (1997) The crystal structure of the asymmetric GroEL‐GroES‐(ADP)7 chaperonin complex. Nature 388(6644): 741–750.

Zavodszky MI, Sanschagrin PC, Korde RS and Kuhn LA (2002) Distilling the essential features of a protein surface for improving protein–ligand docking, scoring, and virtual screening. Journal of Computer‐Aided Molecular Design 16: 883–902.

Zhang D, Raasi S and Fushman D (2008) Affinity makes the difference: nonselective interaction of the UBA domain of ubiquilin‐1 with monomeric ubiquitin and polyubiquitin chains. Journal of Molecular Biology 377: 162–180.

Zheng W, Brooks BR and Thirumalai D (2006) Low‐frequency normal modes that describe allosteric transitions in biological nanomachines are robust to sequence variations. Proceedings of the National Academy of Sciences of the USA 103: 7664–7669.

Zheng W, Brooks BR and Thirumalai D (2007) Allosteric transitions in the chaperonin GroEL are captured by a dominant normal mode that is most robust to sequence variations. Biophysical Journal 93: 2289–2299.

Further Reading

Gao M, Sotomayor M, Villa E, Lee EH and Schulten K (2006) Molecular mechanisms of cellular mechanics. Physical Chemistry Chemical Physics 8: 3692–3706.

Glen RC and Allen SC (2003) Ligand–protein docking: cancer research at the interface between biology and chemistry. Current Medicinal Chemistry 10(9): 763–767.

Karplus M and McCammon JA (2002) Molecular dynamics simulations of biomolecules. Nature Structural Biology 9: 646–652.

Schneidman‐Duhovny D, Nussinov R and Wolfson HJ (2004) Predicting molecular interactions in silico: II. Protein–protein and protein–drug docking. Current Medicinal Chemistry 11(1): 91–107.

Totrov M and Abagyan R (2001) Protein–ligand docking as an energy optimization problem. In: Raffa RB (ed.) Drug‐Receptor Thermodynamics: Introduction and Applications, pp. 603. New York: Wiley.

Yang Z, Majek P and Bahar I (2009) Allosteric transitions of supramolecular systems explored by network models: application to chaperonin GroEL. PLoS Computational Biology 5: e1000360.

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Petrenko, Roman, and Meller, Jarosław(Mar 2010) Molecular Dynamics. In: eLS. John Wiley & Sons Ltd, Chichester. http://www.els.net [doi: 10.1002/9780470015902.a0003048.pub2]