Brownian dynamics applications

Madura J D, Davis M E, Gilson, M K, Wade R C, Luty B A and McCammon J A 1994 Biological applications of electrostatic calculations and Brownian dynamics simulations Rev. Comput. Chem. 5 229-67... 

Jeffry D. Madura, Malcolm E. Davis, Michael K. Gilson, Rebecca C. Wade, Brock A. Luty, and J. Andrew McCammon, Biological Applications of Electrostatic Calculations and Brownian Dynamics Simulations. 

In order to determine a system thermodynamically, one has to specify some independent parameters (e.g. N, T, P or V) besides the composition of the system. The most common choice in MC simulation is to specify N, V and T resulting in the canonical ensemble, where the Helmholtz free energy A is the natural thermodynamical potential. However, MC calculations can be performed in any ensemble, where the suitable choice depends on the application. It is straightforward to apply the Metropolis MC algorithm to a simple electric double layer in the iVFT ensemble. It is however, not so efficient for polymers composed of more than a few tens of monomers. For long polymers other algorithms should be considered and the Pivot algorithm [21] offers an efficient alternative. MC simulations provide thermodynamic and structural information, but time-dependent properties are not accessible. If kinetic or time-dependent properties are of interest one has to use molecular dynamic or brownian dynamic simulations. 

Similar to the role that DNS and discrete particle models (see Section IV,B,3) might play in the development of improved turbulence models, which can be used in engineering applications, and closure laws for gas-solid continuum models. Brownian dynamics (BD) should be mentioned as a powerful tool to develop closure models for non-Newtonian fluids (Brady and Bossis, 1988). 

An interesting application of the molecular dynamics technique on single chains is found in the work of Mattice et al. One paper by these authors is cited here because it is relevant to both RIS and DRIS studies and deals with the isomerization kinetics of alkane chains. The authors have computed the trajectories for linear polyethylene chains of sizes C,o to Cioo- The simulation was fully atomistic, with bond lengths, bond angles, and rotational states all being variable. Analysis of the results shows that for very short times, correlations between rotational isomeric transitions at bonds i and i 2 exist, which is something a Brownian dynamics simulation had shown earlier. 

Chapter 19 addresses another important technological application, the polymerization of rod-like molecules results of Brownian dynamics simulations are compared to those obtained from approximate theories and experimental studies. 

Pairwise Brownian dynamics has been primarily used for the analysis of diffusion controlled reactions involving the reaction between isotropic molecules with complex reactive sites. Since its introduction by Northrup et al. [58], the pairwise Brownian dynamics method has been considerably refined and modified. Some of the developments include the use of variable time steps to reduce computational times [61], efficient calculation methods for charge effects [63], and incorporation of finite rates of reaction [58,61,62]. We review in the following sections, application of the method to two example problems involving isotropic translational diffusion reaction of isotropic molecules with a spherical reaction surface containing reactive patches and the reaction between rodlike molecules in dilute solution. 

A computer simulation approach has been derived that allows detailed bimolecular reaction rate constant calculations in the presence of these and other complicating factors. In this approach, diffusional trajectories of reactants are computed by a Brownian dynamics procedure the rate constant is then obtained by a formal branching anaylsis that corrects for the truncation of certain long trajectories. The calculations also provide mechanistic information, e.g., on the steering of reactants into favorable configurations by electrostatic fields. The application of this approach to simple models of enzyme-substrate systems is described. 

Brownian dynamics algorithms have been used to explore a number of slow processes in systems containing biopolymers. They include numerical simulations of local folding and unfolding,150 151 large-amplitude fluctuations in multilobed proteins,152-153 and the calculation of rate constants for the association of biopolymers these applications are described in Chapts. VII-IX.154155... 

Biological Applications of Electrostatic Calculations and Brownian Dynamics Simulations... 

The next two chapters have the theme of molecular simulations of biomolecules. In Chapter 4, Jeffry D. Madura, Malcolm E. Davis, Michael K. Gilson, Rebecca C. Wade, Brock A. Luty, and J. Andrew McCammon, many of whom have been or are associated with the Institute of Molecular Design at the University of Houston, describe biological applications of electrostatic calculations and Brownian dynamics. Many of the readers of this review series are fully aware of molecular dynamics in general but are less certain about Brownian dynamics what it is, how to use it, and pitfalls to avoid. The authors discussion of molecular simulations in environments consisting of solvent and ions ties in with the Mackinac Island recommendation mentioned above, namely, the need for theoretical and computational chemists to continue to develop more reliable and realistic descriptions of molecular systems. Treating ion atmospheres found in real systems is a complex issue that is covered in this chapter. 

Steinhoff HJ, Hubbell WL (1996) Calculation of electron paramagnetic resonance spectra from Brownian dynamics trajectories application to nitroxide side chains in proteins. Biophys J 71(4) 2201-2212... 

The illustrative applications in Sects. 14-16 to the momenum, mass, and energy fluxes are given for the Hookean dumbbell and Rouse models. These models are known to be very inadequate because of their mfinite extensibility. They have been used solely to show how to apply the general formulas of Tables 1 and 2. The next phase of study should emphasize calculations using beadspring chain models with finitely extensible springs, using molecular or Brownian dynamics [23, 33d, 33e, 33f]. 

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