Stochastic dynamics simulations

One of the main advantages of the stochastic dynamics methods is that dramatic tirn savings can he achieved, which enables much longer stimulations to he performed. Fc example, Widmalm and Pastor performed 1 ns molecular dynamics and stochastic dynamic simulations of an ethylene glycol molecule in aqueous solution of the solute and 259 vvatc jnolecules [Widmalm and Pastor 1992]. The molecular dynamics simulation require 300 hours whereas the stochastic dynamics simulation of the solute alone required ju 24 minutes. The dramatic reduction in time for the stochastic dynamics calculation is du not only to the very much smaller number of molecules present hut also to the fact the longer time steps can often he used in stochastic dynamics simulations. 

Yun-Yu S, W Lu and W F van Gunsteren 1988. On the Approximation of Solvent Effects on Conformation and Dynamics of Cyclosporin A by Stochastic Dynamics Simulation Teclmiqi Molecular Simulation 1 369-383. 

WF van Gunsteren. Molecular dynamics and stochastic dynamics simulations A primer. In WF van Gunsteren, PK Weiner, AJ Wilkinson, eds. Computer Simulations of Biomolecular Systems. Leiden ESCOM, 1993, pp 3-36. 

T. Matsuda, G. D. Smith, R. G. Winkler, D. Y. Yoon. Stochastic dynamics simulations of n-alkane melts confined between solid surfaces Influence of surface properties and comparison with Schetjens-Fleer theory. Macromolecules 28 65- 13, 1995. 

Bernard , A., Raimondi, L., and Zanferrari, D., Conformational analysis of saccharides with Monte Carlo stochastic dynamics simulations, Theochem, 395, 361, 1997. 

Fig. 2.81. Snapshots from a stochastic dynamics simulation of DNAsupetcoiling. (Reprinted from P. Ahlstrom, O. Tdeman, and B. Jocsom, J. Am. Chem. Soc. 110 4198, 1988.)...

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. 

M. R. Reddy, P. J. Rossky, and C. S. Murthy, Counterion Spin Relaxation in DNA Solutions A Stochastic Dynamics Simulation Study, J. Phys. Chem., 91 (1987), 4923-4933. 

Stochastic Dynamics Simulations of Barrier Crossing in Solution... 

Activated processes in solution, such as conformational transitions for biomolecules that are fully exposed to solvent, can be treated by stochastic dynamic simulation methods (see Chapt. I V.D). Their use requires a knowledge of the solvent contribution to the potential of mean force. Also, the system must be small enough so that the simulation times can be extended to the nanosecond or microsecond range required to adequately sample the statistically rare events involved in activated processes. Alternatively, activated dynamics techniques can be used with a stochastic dynamics simulation.307,335... 

A stochastic dynamics simulation requires a value to be assigned to the collision frequency friction coefficient 7. For simple particles such as spheres this can be related to the diffusion constant in the fluid. For the simulation of a rigid molecule it may be possible to derive 7 via the diffusion coefficient from a standard molecular dynamics situation. In the more general case we require the friction coefficient of each atom. For simple molecules such as butane the friction coefficient can be considered to be the same for all atoms. The optimal value for 7 can be determined by trial and error, performing a stochastic dynamics simulation for different values of 7 and comparing the results with those from experiment (where available) or from standard molecular dynamics simulations. For large molecules the atomic friction coefficient is considered to depend upon the degree to which each atom is in contact with the solvent and is usually taken to be proportional to the accessible surface area of the atom (as defined in Section 1.5). 

Beier C, Steinhoff H-J (2006) A stmcture-based simulation approach for electron paramagnetic resonance spectra using molecular and stochastic dynamics simulations. Biophys J 91... 

The transition path sampling techniques we have described assume that an initial reactive pathway is available. Generating such a pathway is therefore an important step in applying the method. In the simplest cases, a trajectory connecting A and B can be obtained by running a long molecular dynamics (or stochastic dynamics) simulation. For most applications, however, the... 

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. 

Encouragingly, the acceleration methods described by Luo et al. are appHcable to many software packages and could improve many PB solvers. Although many applications can benefit from faster PB methods, perhaps the most profound advantage will be in the realm of stochastic dynamics simulations by enabling the efficient implicit solvent simulations of protein dynamics at the PB level of electrostatics theory. 

To obtain an adequate description of the diffusion in mesopores, diffusion mechanisms in micropores need to be imderstood based on the local force field, as well as various diffusion mechanisms in macropores. Eiuthermore, ideal Eickian behavior, in which diffusivity is independent of adsorbate concentration (Eq. 2), is realized only when the system is thermodynamically ideal. The modification of pore diffusivity is effective in predicting the adsorption and desorption rates molecular and stochastic dynamic simulations are important means of accounting for the transport phenomena in mesopores and designing mesopores suitable for a specific engineering application. 

The stationary brushes are likely to interpenetrate each other. On similar PLL-g-PEG layers, a comparison of brush—brush and brush—hard-wall experiments revealed a significant overlap of the opposing brushes at the onset of measurable repulsion. On the basis of stochastic dynamics simulations, Neelov et al. predict that at low compressions the polymer brushes interpenetrate only in the outermost region next to the interface. At high compressions and zero shear rates, the polymer chains completely interpenetrate each other. However, a shear motion of the two brushes will result in a shear alignment of the chains and a reduced interpenetration of the brushes. 

---