Stochastic boundary molecular dynamics

A. Briinger, C. L. Brooks, III, and M. Karpins. Stochastic boundary conditions for molecular dynamics simulations of ST2 water. Chem. Phys. Lett., 105 495-500, 1982. 

Inner slip, between the solid wall and an adsorbed film, will also influence the surface-liquid boundary conditions and have important effects on stress propagation from the liquid to the solid substrate. Linked to this concept, especially on a biomolecular level, is the concept of stochastic coupling. At the molecular level, small fluctuations about the ensemble average could affect the interfacial dynamics and lead to large shifts in the detectable boundary condition. One of our main interests in this area is to study the relaxation time of interfacial bonds using slip models. Stochastic boundary conditions could also prove to be all but necessary in modeling the behavior and interactions of biomolecules at surfaces, especially with the proliferation of microfluidic chemical devices and the importance of studying small scales. 

In an investigation of the role of water in enzymic catalysis. Brooks and Karplus (1989) chose lysozyme for their study. Stochastic boundary molecular dynamics methodology was applied, with which it was possible to focus on a small part of the overall system (i.e., the active site, substrate, and surrounding solvent). It was shown that both structure and dynamics are affected by solvent. These effects are mediated through solvation of polar residues, as well as stabilization of like-charged ion pairs. Conversely, the effects of the protein on solvent dynamics and... 

Brooks III, C.L. and Karplus, M. (1983) Deformable Stochastic Boundaries in Molecular Dynamics, J. Chem. Phys. 79, 6312-6325. 

Brooks, C. L. Ill Briinger, A. T. and Karplus, M. (1985) Active Site Dynamics in Protein Molecules A Stochastic Boundary Molecular-Dynamics Approach, Biopolymers 24, 843-865. 

C. MOLECULAR DYNAMICS WITH STOCHASTIC BOUNDARY CONDITIONS... 

The stochastic boundary approach in conjunction with molecular dynamics is an approximate technique for studying such localized events in many-body systems.99 The method was developed initially to study nonequilibrium phenomena98 (e.g., chemical reactions and atomic diffusion across thermal gradients) and hence is well suited for some of the problems of interest here. The approach has been used to treat simple fluids,100101 as well as more complex fluids, including water,102 and solvated biomolecules.103... 

This algorithm has been used in the integration of the Langevin equation applied to the buffer zone atoms in the stochastic boundary molecular dynamics method (Chapt. IV.C), as well as in other stochastic dynamics calculations.102... 

To illustrate the solvent effect on the average structure of a protein, we describe results obtained from conventional molecular dynamics simulations with periodic boundary conditions.92,193 This method is well suited for a study of the global features of the structure for which other approaches, such as stochastic boundary simulation methods, would not be appropriate. We consider the bovine pancreatic trypsin inhibitor (BPTI) in solution and in a crystalline environment. A simulation was carried out for a period of 25 ps in the presence of a bath of about 2500 van der Waals particles with a radius and well depth corresponding to that of the oxygen atom in ST2 water.193 The crystal simulation made use of a static crystal environment arising from the surrounding protein molecules in the absence of solvent. These studies, which were the first application of simulation methods to determine the effect of the environment on a protein, used simplified representations of the surround-... 

To explore these effects more thoroughly, results are presented from stochastic boundary molecular dynamics simulations of the active-site cleft of lysozyme in the presence of aqueous solvent and in vacuum.108 The simulation... 

The correlation function, <-P2[am(0) ( )]>. provides a measure of the internal motions of particular residues in the protein.324 333 Figure 46 shows the results obtained for Trp-62 and Trp-63 from the stochastic boundary molecular dynamics simulations of lysozyme used to analyze the displacement and velocity autocorrelation functions. The net influence of the solvent for both Trp-62 and Trp-63 is to cause a slower decay in the anisotropy than occurs in vacuum. In vacuum, the anisotropy decays to a plateau value of 0.36 to 0.37 (relative to the initial value of 0.4) for both residues within a picosecond. In solution there is an initial rapid decay, corresponding to that found in vacuum, followed by a slower decay (without reaching a plateau value) that continues beyond the period (10 ps) over which the correlation function is ex-... 

For an understanding of protein-solvent interactions it is necessary to explore the modifications of the dynamics and structure of the surrounding water induced by the presence of the biopolymer. The theoretical methods best suited for this purpose are conventional molecular dynamics with periodic boundary conditions and stochastic boundary molecular dynamics techniques, both of which treat the solvent explicitly (Chapt. IV.B and C). We focus on the results of simulations concerned with the dynamics and structure of water in the vicinity of a protein both on a global level (i.e., averages over all solvation sites) and on a local level (i.e., the solvent dynamics and structure in the neighborhood of specific protein atoms). The methods of analysis are analogous to those commonly employed in the determination of the structure and dynamics of water around small solute molecules.163 In particular, we make use of the conditional protein solute -water radial distribution function,... 

To characterize structural waters and to follow the dynamics of reactions involving waters, it is necessary to be able to treat in detail the motions of these molecules. A methodology which includes solvents explicitly is required. Both conventional molecular dynamics techniques and the stochastic boundary molecular dynamics approaches can be used. When the region of... 

In the following, we briefly describe the techniques commonly employed in computer simulation studies of lipid assemblies (and of other biomole-cules " ), namely, Monte Carlo (MC) and dynamic simulations such as molecular dynamics (MD), Brownian dynamics and stochastic boundary mo-... 

Brownian Dynamics and Stochastic Boundary Molecular Dynamics... 

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