Molecular Dynamics, Monte Carlo Simulations, and Langevin Dynamics: A Computational Review

Abstract

Macromolecular structures, such as neuraminidases, hemagglutinins, and monoclonal antibodies, are not rigid entities. Rather, they are characterised by their flexibility, which is the result of the interaction and collective motion of their constituent atoms. This conformational diversity has a significant impact on their physicochemical and biological properties. Among these are their structural stability, the transport of ions through the M2 channel, drug resistance, macromolecular docking, binding energy, and rational epitope design. To assess these properties and to calculate the associated thermodynamical observables, the conformational space must be efficiently sampled and the dynamic of the constituent atoms must be simulated. This paper presents algorithms and techniques that address the abovementioned issues. To this end, a computational review of molecular dynamics, Monte Carlo simulations, Langevin dynamics, and free energy calculation is presented. The exposition is made from first principles to promote a better understanding of the potentialities, limitations, applications, and interrelations of these computational methods.

Computational Methods for Ab Initio Molecular Dynamics

“…Molecular dynamics, which we recently reviewed in [30], is suitable for larger molecular system. A drawback is that it is not adapted for the simulation of chemical complexes, since it is not based on first principles as its quantum mechanics counterpart.…”

“…As we have recently explained in a computational review on molecular dynamics [30], an isothermal process cannot be obtained by adding an extra term to the Lagrangian. Rather, the equations of motions must be modified directly as a result of the non-Hamiltonian nature of the isothermal process [31].…”

“…One should notice that × fictitious momenta P ( ) =Ṙ ( ) have been formally introduced. These momenta are required in order to evaluate numerically the path integral with Monte Carlo techniques [30,43]. The reader should notice that the momenta affect neither the partition function (up to an irrelevant normalisation factor) nor the physical observables.…”

The G‐JF Thermostat for Accurate Configurational Sampling in Soft‐Matter Simulations

“…This is especially true for the relatively small systems that often are simulated as a proxy for thermodynamically large ensembles. A number of methods for constraining the temperature of a simulated system (thermostats) exists; two representative ones are the deterministic (e.g., Nosé-Hoover [5,6]) and stochastic (Langevin) thermostats [7]. Here we focus on integration methods for Langevin Dynamics (LD).…”

Determinants of Substrate Specificity in APOBEC3B

“…45 These simulations model dynamics of all the atoms of a chemical system, starting with an initial geometry and undergoing motion according to the laws of physics at physiologic temperature. MD simulation is now capable of handling not just proteins, but also solvents, ions, and nucleic acids accurately.…”