Brownian Dynamics Simulation Method Research Articles

Brownian dynamics simulation of rotational correlation functions for a three-body macromolecular model

A former investigation [R. Ying and M. H. Peters, J. Chem. Phys. 91, 1287 (1989)] on the rotational dynamics of rigid and partially flexible macromolecules in solution by means of Brownian dynamics simulation methods is extended to a trimer or three-body macromolecular model. We present expressions for the torque constraints in rigid and semirigid trimer systems that allows for a comprehensive simulation of the translational, rotational, and coupled translational–rotational motions of the three interacting spherical Brownian particles comprising the trimer (trumbell). The torque constraint expressions are verified by comparisons of the Brownian dynamics simulation results to exact analytical results for a rigid trimer system (Appendix). Computer simulations and analytical solutions for the rigid trimer system indicate that the inclusions of rotational motions of the model’s elements can have an appreciable effect on macromolecular dynamics. Macromolecular flexibility can also be easily introduced into the model through varying the parameters of the torque and force constraint expressions. Extensions to an N-body macromolecular model are also outlined based on the trimer system studied here.

Brownian simulation of protein association and reaction

The Brownian dynamics simulation method has been developed as an alternative to conventional molecular dynamics or simple analytical diffusion theories in order to study the diffusive dynamics and interaction between two whole proteins. Highly detailed and realistic models of protein structures and their electrostatic interactions were used based on an atomic-level spatial description. The Coulombic and excluded volume torques and forces between the molecules are computed at each Brownian time step and rotational and translational diffusional trajectories are generated between interacting proteins. For the first time the rotation of both proteins is included. This method has been applied to study the association and electron transfer between horse heart ferrocytochrome c and yeast cytochrome c peroxidase, horse heart ferricytochrome c and bovine ferrocytochrome b5 and the electron self-exchange of P. aeruginosa cytochrome c551. Accurate residue charge assignments at the appropriate pH and ionic strength are computed by the Tanford-Kirkwood theory with surface accessibility modification. Accurate interaction potentials are computed by iterating solutions of the Poisson-Boltzmann equation on a grid. The low dielectric constant inside proteins, electrolyte screening effects, and irregular protein surface topography are taken into account. Realistic criteria for determining the successful docking of the cytochromes are based on a combination of mutual orientation of heme planes and heme edge-to-edge distance. We examine the role of electrostatic charge distribution and solvent mediation in the facilitation of protein-protein docking prior to the electron transfer step. We expect that, with improvements, the Brownian dynamics method will be capable of predicting the effects of site-directed mutagenesis on protein-protein and protein-ligand interactions.

Structure factor of charged colloidal suspensions using Brownian-dynamics simulation: Comparison of Yukawa and Sogami pair potentials

Static structure factorsS(Q) are obtained for dilute charged colloidal systems using Brownian dynamics simulation method for the widely used screened Coulomb repulsive Yukawa potential and the recently proposed Sogami pair potential. The latter potential has, in addition to the usual repulsive part, an attractive term which is necessary to understand the reentrant phase transition reported in these colloids. It is shown for the first time thatS(Q) obtained using the Sogami potential for parameters favourable for liquid-like order agrees well with that measured experimentally. Thus it appears that the Sogami potential explains features of a homogeneous liquid as well as phase separated states, whereas Yukawa potential does not.

The distribution and dynamics of small ions in simulations of ordered polyelectrolyte solutions

The diffusion limit brownian dynamics simulation method has been used to investigate some properties of the counterions in infinite arrays of hexagonally packed cylindrical polyelectrolytes. The level of description is that of the primitive model, and the hard cylinders representing the macroions have been given characteristics appropriate for B-DNA molecules. The simulations were carried out in a semi-infinite model system of the ordered macroion phase. The minimum image convention was used in all directions, and the long-range electrostatic interactions were described using the Ewald summation method. The results are compared with simulations in the corresponding cell model representations of the systems, and with the predictions of mean field theory. Some aspects of the static distribution of mono- and divalent counterions in ordered systems of different polyelectrolyte concentrations are presented. The dynamic behaviour of the counterions is characterized in terms of average residence times, and macroscopic diffusion coefficients for the motion in the infinite ordered array of macroions are calculated. The interactions of the nuclear quadrupole moments of the counterions with the electric field gradients of the systems are discussed, and estimates of the quadrupolar splitting for 23Na+ counterions in systems of hexagonally packed B-DNA are given.

Simulation of the diffusion-controlled reaction between superoxide and superoxide dismutase. II. Detailed models.

AbstractA two‐stage Brownian dynamics simulation method is used to study the diffusion‐influenced bimolecular reaction between superoxide and superoxide dismutase (SOD). The crystal structure of the dimeric enzyme is used in constructing detailed topographical and electrostatic models. Several electrostatic models are considered. In the most realistic, the excluded volume of the protein, which is impermeable to penetration by mobile ions, is assigned a dielectric constant of 2 and the surrounding “solvent” is assigned a value of 78. A finite difference method is used to solve the linearized Poisson–Boltzmann equation. For native SOD, the simulations reproduce the pronounced salt dependence of the rate constant observed experimentally. This salt dependence is attributed to electrostatic interactions between enzyme and substrate that are inherently attractive and amplified by the low dielectric constant of the protein interior. The simulation method is also applied to a modified enzyme, acylated SOD.

Extended Brownian dynamics of diffusion controlled reactions

The Brownian dynamics simulation method of Northrup et al. is extended so that dynamical trajectories can be initiated with the reactants in close proximity to one another. A more general analysis is presented which shows that this procedure is exact in cases where the first-time encounter flux to the more proximal starting surface is isotropic, such as cases where interparticle forces are centrosymmetric, but is approximate otherwise. Diffusion controlled rate constants for three model systems obtained by this procedure are compared with analytic results or with exact rate constants derived from simulations following the original Northrup procedure. Agreement is good to excellent in all cases considered. The extended method is expected to be of considerable practical importance in systems with highly anisotropic reactivity where it is computationally inefficient to obtain rate constants by the original method.

Simulation of the diffusion-controlled reaction between superoxide and superoxide dismutase. I. Simple models.

AbstractA Brownian dynamics simulation method is used to study the diffusion‐influenced bimolecular reaction between superoxide and superoxide dismutase (SOD). Using simple models, the details of which are based on the crystallographic structure of SOD, it is found that the electrostatic charge distribution of SOD serves to guide superoxide into the active site and enhance the diffusion‐controlled rate constant by about 40%.