Stochastic dynamics, molecular modelling

Another way is to reduce the magnitude of the problem by eliminating the explicit solvent degrees of freedom from the calculation and representing them in another way. Methods of this nature, which retain the framework of molecular dynamics but replace the solvent by a variety of simplified models, are discussed in Chapters 7 and 19 of this book. An alternative approach is to move away from Newtonian molecular dynamics toward stochastic dynamics. 

P. G. Seybold, L. B. Kier, and C.-K. Cheng, Stochastic cellular automata models of molecular excited-state dynamics. J. Phys. Chem. 1988, 102, 886-891. 

An excellent comparison of the methods employed in conformational searching of organic molecules has been published11061. In the vast majority of published inorganic molecular modeling studies no stochastic or molecular dynamics conformational searches have been conducted. There are three reasons for this. 

Ludovice, Jaffe, and Yoon have used the same approach to characterize the inter- and intramolecular energy surface of polyvinyl chloride (PVC) model compounds.2-Chloropropane and 1,3-dichloropropane were studied, and a classical force field was fitted to their quantum chemically derived energy surfaces. The ultimate goals were to obtain a new force field for molecular mechanics and stochastic dynamics simulations and to analyze the atomic level morphology of this particular polymer. 

Due to the changes in the dynamics, a general relationship for stochastic dynamics is not available like it is for deterministic dynamics. However, for mesoscopic systems, a mesoscopic FR is useful. Therefore, there has been much work on developing stochastic models with different conditions. Andrieux and Gaspard developed a stochastic fluctuation relation for nonequilibrium systems whose dynamics can be described by Schnakenberg s network theory (e.g. mesoscopic electron transport, biophysical models of ion transport and some chemical reactions). Due to early experimental work on protein unfolding and related molecular motors, and their ready treatment by stochastic dynamics, a number of papers have appeared that model these systems and test the or JE for these. FR... 

Other dynamic simulations commonly used are Brownian dynamics- " and stochastic boundary molecular dynamics." These techniques are suitable when interest is limited to a small portion of a large system and the molecular details of the rest of the system are not of concern. Under such situations, MD will be an inefficient choice. For example, if the effect of a solvent on the dynamics of a solute molecule can be obtained by a suitable choice of parameters in the potential function, one can study the dynamics in more detail for longer times. In Brownian dynamics, the forces acting on a solute molecule have a component from intramolecular interactions in the solute and/or any external field, a component arising from the solvent friction, and a third random component to model the thermal fluctuations of the solvent molecules ... 

These results show that simplified molecular dynamics simulations can qualitatively account for micellization quite well. However, the computation time necessary for even such simple models is too great to allow the model to be useful for the calculation of other micellar properties or phase behavior or for an in-depth study of solubilization. Stochastic dynamics simulations, in which the solvent effects are accounted for through a mean-field stochastic term in the equations of motion, can also be used to study surfactant self-assembly [22], but the most efficient approach to date is still the one based on lattice Monte Carlo simulations, which are discussed next. 

Once a stochastic molecular dynamics-based framework is developed it is possible to modify it or use it as a building block in order to enhance sampling efficiency. One can for example incorporate these methods into kinetic Monte-Carlo, other metropolized schemes, or various advanced path sampling techniques. Thus the design of good molecular SDE methods is the cornerstone of much of modern molecular modelling. 

To give this some specificity for molecular dynamics, we write the stochastic dynamical model as... 

Particle-based simulation techniques include atomistic MD and coarse-grained molecular dynamics (CG-MD). Accelerated dynamics methods, such as hyperdynamics and replica exchange molecular dynamics (REMD), are very promising for circumventing the timescale problem characteristic of atomistic simulations. Structure and dynamics at the mesoscale level can be described within the framework of coarse-grained particle-based models using such methods as stochastic dynamics (SD), dissipative particle dynamics (DPD), smoothed-particle hydrodynamics (SPH), lattice molecular dynamics (LMD), lattice Boltzmann method (IBM), multiparticle collision dynamics (MPCD), and event-driven molecular dynamics (EDMD), also referred to as collision-driven molecular dynamics or discrete molecular dynamics (DMD). 

---