A method is developed and tested for extracting diffusion-controlled rate constants for condensed phase bimolecular reactions from Brownian dynamics trajectory simulations. This method will be useful when highly detailed model systems are employed, such as those required to explore the complicated range of interactions between enzymes and their substrates. The method is verified by comparing with exact analytical results for simple cases of spheres with uniform reactivity subject to various centrosymmetric Coulombic and Oseen slip hydrodynamic interactions. The utility of the method is illustrated for more complicated cases involving anisotropic reactivity and rotational diffusion.

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A bead model to determine the electrophoretic mobilities and translational diffusion constants of weakly charged peptides is developed that is based on a approximate structural model of peptides and is also grounded in electrohydrodynamic theory. A peptide made up of X amino acids is modeled as N=2X beads with 2 beads representing each amino acid in the chain. For the two beads representing a particular amino acid in a peptide, the radius of one bead is set to one-half the nearest neighbor Calpha-Calpha distance, and the radius of the other bead is chosen on the basis of the diffusion constant of the free amino acid. Peptide conformations, which are defined by a set of psi-phi dihedral angles, are randomly generated by using the transformation matrix approach of Flory (Flory, P. Statistical Mechanics of Chain Molecules; John Wiley: New York, 1969) and rejecting conformations which result in bead overlap. The mobility and diffusion constants are computed for each conformation and at least 100 independent conformations are examined for each peptide. In general, the mobility is found to depend only weakly on peptide conformation. Model and experimental mobilities are compared by examining the data of Janini and co-workers (Janini, G.; et al. J. Chromatogr. 1999, 848, 417-433). A total of 58 peptides consisting of from 2 to 39 amino acids are considered. The average relative error between experimental and model mobilities is found to be 1.0% and the rms relative error 7.7%. In specific cases, the discrepancy can be substantial and possible reasons for this are discussed. It should be emphasized that the input parameters of the peptide model are totally independent of experimental mobilities. It is hoped that the peptide model developed here will be useful in the prediction of peptide mobility as well as in using peptide mobilities to extract information about peptide structure, conformation, and charge. Finally, we show how simultaneous measurements of translational diffusion and mobility can be used to estimate peptide charge.

A numerical algorithm is developed to calculate electrophoretic mobilities of rigid model polyions that includes the effect of ion relaxation. The Navier−Stokes, Poisson, and ion transport equations are cast into forms that are amenable to numerical solution by boundary element procedures. The three equations are solved simultaneously by an iterative procedure. It is applied first to a spherical polyion containing a centrosymmetric charge distribution and double layer that is not thin compared to the radius of the sphere. Resulting mobilities compare favorably (to within 10%) with independent theory. The algorithm is then applied to spherical polyions containing noncentrosymmetric charge distributions. Although the present calculations are restricted to spherical polyions, there is no formal difficulty in extending them to nonspherical polyions.

Brownian dynamics is used to simulate the decay anisotropy of short linear DNA fragments modeled as a string of beads. The model is sufficiently general to allow for static bends, anisotropic bending, and elastic constants for bending and twisting which can vary along the chain. In limiting cases, simulations are found to be in excellent agreement with analytic theory down to a correlation length of at least 500 Å. This model is then used to analyze the 0–2.5 μs triplet depletion anisotropy decay of a 209 base pair sea urchin DNA fragment. It is concluded that the conventional worm-like chain model, in which bending is isotropic and/or there are no static bends along the chain, is unable to account for the experimental results unless a correlation length of 1000 Å is assumed. A worm-like chain with anisotropic bending requires a similar but slightly larger correlation length.

A new Monte Carlo (MC) algorithm is proposed for simulating inextensible circular chains with finite twisting and bending rigidity. This new algorithm samples the relevant Riemann volume elements in a uniform manner, when the constraining potential vanishes. Simulations are performed for filaments comprising 170 subunits, each containing approximately 28 bp, which corresponds to a DNA length of 4770 bp. The bending rigidity is chosen to yield a persistence length, P = 500 A, and the intersubunit potential is taken to be a hard-cylinder potential with diameter d = 50 A. This value of d yields the same second virial coefficient as the electrostatic potential obtained by numerical solution of the Poisson-Boltzmann equation for 150 mM salt. Simulations are performed for unknotted circles and also for trefoil knotted circles using two different values of the torsional rigidity, C = (2.0 and 3.0) x 10(-19) dyne cm2. In the case of unknotted circles, the simulated supercoiling free energy varies practically quadratically with linking difference delta l. The simulated twist energy parameter ET, its slope dET/dT, and the mean reduced writhe /delta l for C = 3 x 10(-19) dyne cm2 all agree well with recent simulations for unknotted circles using the polygon-folding algorithm with identical P, d, and C. The simulated ET vs. delta l data for C = 2.0 x 10(-19) dyne cm2 agree rather well with recent experimental data for p30 delta DNA (4752 bp), for which the torsional rigidity, C = 2.07 x 10(-19) dyne cm2, was independently measured. The experimental data for p30 delta are enormously more likely to have arisen from C = 2.0 x 10(-19) than from C = 3.0 x 10(-19) dyne cm2. Serious problems with the reported experimental assessments of ET for pBR322 and their comparison with simulated data are noted. In the case of a trefoil knotted DNA, the simulated value, (ET)tre, exceeds that of the unknotted DNA, (ET)unk, by approximately equal to 1.40-fold at magnitude of delta l = 1.0, but declines to a plateau about 1.09-fold larger than (ET)unk when magnitude of delta l > or = 15. Although the predicted ratio, (ET)tre/(ET)unk approximately equal to 1.40, agrees fairly well with recent experimental measurements on a 5600-bp DNA, the individual measured ET values, like some of those reported for pBR322, are so large that they cannot be simulated using P = 500 A, d = 50 A, and any previous experimental estimate of C.

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