Molecular Dynamics

Abstract

Molecular dynamics (MD) is a handy computer simulation method which unveils principles of a large variety of fundamental processes by mimicking the real life perpetual motion of atoms triggered by interatomic forces. In MD, these forces are expressed through analytical functions and associated parameters, which are commonly referred to as the force field. The forces' effect on the movement of atoms is determined by Newton's second law. Most importantly, MD simulations are able to retrace the exact trajectories of interacting atoms by following their spatial evolution in time from a defined initial configuration. The resulting integrated trajectory of the system can be visualised and analysed with rigorous mathematical expressions of statistical mechanics, which relate averaged microscopic states to macroscopic properties relevant to the problem at hand.

Key Concepts

  • Molecular dynamics is a computation tool successfully used to unveil principles of a large variety of fundamental processes down to the atomic resolution.
  • Thanks to recent advances in computer simulations, atomistic MD can reach millisecond timescales, thus emerging as a powerful alternative method that successfully complements experimental measurements in biology.
  • Computational efficiency of molecular dynamics algorithms continues to pose challenges.
  • The collective efforts of many groups of researchers have enabled a great deal of force fields applied to many problems in biology.
  • Biomolecular simulations require the presence of solvent; hence, a reliable representation of water is crucial for achieving realistic results.
  • Several specialised methods stemming from MD allow to investigate various processes of biomolecules: REMD, SMD and TMD.

Keywords: molecular simulations; force field; biomolecular models; water models; structural biology; enhanced sampling methods

Figure 1. (a) Spatial and temporal scales of different processes occurring in biological molecules. (b) Characteristics of different resolution levels of computer simulations. More detailed theories offer higher accuracy and allow to describe more complex phenomena. Less detailed theories offer longer timescales and allow to simulate larger systems. Parallel or sequential modelling at different levels of theory (e.g. quantum/atomistic or atomistic/coarse grained) is known as multiscaling.
Figure 10. Beginning (a) and end (b) points of the SMD simulation of the paraoxonase enzyme (in the light blue ‘cartoon’ representation) and the paraoxon molecule (in liquorice representation in the transparent magenta surface). The catalytic calcium is represented as yellow ball in the centre (active site) of the enzyme. The green arrow on the left panel represents the direction of the drag force used in SMD. Amino acids of paraoxonase shown as liquorice are coordinating the water molecule (glutamic acid 53 and aspartic acid 269).
Figure 11. The paraoxon molecule (in the transparent magenta surface) docked in the active site of paraoxonase (in the transparent light blue). The yellow ball is the catalytic calcium. Key amino acids for the catalysis shown as liquorice. Glutamic acid 53 (GLU53) and aspartic acid 269 (ASP269) coordinate the water molecule (hydrogen bonds shown as black lines). Asparagine 168 (ASN168) stabilises the paraoxon. The green arrow represents the direction of the nucleophilic attack of hydroxyl produced by the dissociation of the water molecule.
Figure 12. The superposition of the starting (blue, based on 2YAT) and final (red, based on PDB ID: 3ERT) structures of the TMD simulation of human ER protein. The transparent parts of the protein are almost identical. The glossy part underwent the TMD pulling.
Figure 2. An experiment is usually made on a macroscopic sample that contains an extremely large number of atoms or molecules sampling an enormous number of conformations. In statistical mechanics, averages corresponding to experimental observables are defined in terms of ensemble averages. According to ergodic hypothesis (ensemble average = time average), if one allows the system to evolve in time indefinitely, that system will eventually pass through all possible states. Hence, long enough molecular dynamics simulation of a system at the equilibrium state can sample all relevant states of the statistical ensemble. Then, ensemble averages of microstates are used to determine macroscopic properties of the system via statistical mechanics.
Figure 3. Essential steps for the execution of a molecular dynamics simulation.
Figure 4. Available simulation ensembles (from left): grand canonical (μVT), canonical (NVT), microcanonical (NVE), isoenthalpic isobaric (NPH) and isothermal isobaric (NPT). The letters of the acronyms denote the macroscopic observable that is kept constant in the ensemble: μ, chemical potential; V, volume; T, temperature; N, number of particles; P, pressure; E, energy; H, enthalpy.
Figure 5. Five basic models of atomic interactions and their classical potentials used in the force‐field equations; a and b are the force constants of the bond and angle deformation based on Hooke's law; c is also a force constant which influences the height of the energy barrier to overcome during a torsional angle rotation (i.e. c ∼ barrier height). More complex torsional profiles can be produced by Fourier series of torsional terms with different periodicities of the cosine function; ke is the Coulomb constant; d0 and θ0 correspond to the equilibrium values of bond and angle, respectively; σim and ϵim are related to the range and strength of the van der Waals interaction, respectively. The parameters for the energy functions of the force field may be derived empirically (i.e. from physics or chemistry experiments), numerically (i.e. from quantum‐mechanics calculations) or both.
Figure 6. Step‐by‐step process of force‐field parameterisation for reliable molecular dynamics simulations, with iterative reparameterisation (red) in reference to quantum‐mechanical calculations and/or experimental measurements (blue).
Figure 7. Explicit water models. (a) SPC water molecule. Shown distances between centres of oxygen (red ball) and hydrogen (white), angle hydrogen–oxygen–hydrogen, partial charges on atoms (q1 and q2) and σ – parameter used in calculation of Lennard‐Jones potential, modelling vdW interactions with other atoms and thus used in the estimation of radius of the molecule. Only oxygen has vdW parameters in the SPC water; (b) TIP4P water molecule. The yellow ball, at a distance of 0.15 Å from the oxygen, is a pseudo atom (midpoint site); (c) TIP5P water molecule. Lone‐pairs pseudoatoms, shown as yellow balls at a distance of 0.7 Å from the central oxygen, keep all the negative charge in this molecule, leaving the oxygen without a partial charge.
Figure 8. Implicit water models. (a) Schematic representation of solvent‐accessible surface estimation with a sphere representing a solvent molecule (yellow) rolling over the vdW molecular surface created by atoms of a macromolecule (blue). The solvent‐accessible surface is estimated by positions of the centre of the solvent molecule (dotted line). (b) The contribution to solvent‐accessible surface (SAS) coming from this particular atom (in green) is estimated as the ratio of number of highlighted points (green points, not buried inside spheres of neighbouring atoms) times the area of the dotted sphere.
Figure 9. Exploration of the energy landscape by the system during an MD simulation at room (a) and high (b) temperature. Molecular dynamics simulation generates a sequence of points in the phase space as a function of time (i.e. trajectory) that belong to the same ensemble. Each point in phase space represents a microscopic state with different configuration and a particular potential energy based on the interactions between constituent atomic particles. The blue/red line and circles with consecutive numbers represent trajectory and visited minima, respectively. In this example, only two degrees of freedom and the potential energy hypersurface are illustrated for the sake of clarity. (c) Trajectory of MD simulation of a murein molecule (i.e. a building block of peptidoglycan wall in bacteria) depicted as a film strip (Mitkowski et al., ). Atoms can be coloured according to their atom types (as presented: C, grey; O, red; N, blue; H, white) or other properties (e.g. charge). Using molecular visualisation programs (e.g. visual molecular dynamics (VMD) (Humphrey et al., ) and PyMOL (DeLano, )), it is possible to display a trajectory from MD simulation as a movie, where images recorded on the ‘film frames’ are snapshots of the evolving system taken at consecutive time steps (Δt). Animating the MD trajectory is essential for in‐depth analysis of dynamics processes in biomolecular systems and an initial inspection of the behaviour of a system, while all properties can be calculated from the time sequence of the stored molecular coordinates and atom velocities.
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Wieczorek, Grzegorz, and Niedzialek, Dorota(May 2020) Molecular Dynamics. In: eLS. John Wiley & Sons Ltd, Chichester. http://www.els.net [doi: 10.1002/9780470015902.a0003048.pub3]