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Notes: 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.

Notes: A 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%.

Notes: The difference between the theories of Manning, on the one hand, and of Odijk and Skolnick and Fixman, on the other, for the polyelectrolyte contribution to the persistence length of DNA is shown to arise entirely from a subtle geometrical error in the theory of Manning. The corrected theory of Manning predicts a negligible polyelectrolyte contribution in 1.0M NaCl and only 33 Å in 0.01M NaCl, thus giving a change in total persistence length by a factor of only 1.07 over that range, in agreement with Odijk. Pertinent data in the literature indicate that the persistence length must change by a factor of ≤ 1.6 between 1.0 and 0.01M NaCl, and very likely by less than a factor of 1.4. Evidently, the intrinsic rigidity of the uncharged double-strand filament dominates the bending rigidity at NaCl concentrations above 0.01M.

Notes: A 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.

Notes: The pertinent correlation function for nmr dipolar relaxation of 31P by its neighboring protons in DNA is derived for a comparatively realistic model of the internal Brownian motions. These motions include the collective torsional deformation modes of the elastic filament, uncoupled local overdamped reorienting motions of the P-H vectors in harmonic potential wells within the nucleotide unit, and the compartively slow end-over-end rotations of the local helix axis. These latter slow axial tumbling motions essentially completely determine T2 but have virtually no effect on T1 or the nuclear Overhauser effect (NOE), which are governed almost exclusively by rapid torsional deformations and local reorientations on the nanosecond time scale. The essential behavior of the relevant correlation function for the collective torsional motions has recently been determined experimentally in this laboratory using the decay of fluorescence polarization anisotropy of bound ethidium dye [J. C. Thomas et al. (1980) Biophys. Chem. 12, 177-180]. By using that result to carry out nmr relaxation calculations for various amplitudes and time constants of the uncoupled local motions and comparing them with the experimental data, it can be demonstrated that (within this model of purely dipolar relaxation), only rather small rms amplitudes of local reorientations (〈7°) occur and that their relaxation times are near 1 ns. Contrary to previous conclusions in the literature, the collective torsional deformation modes actually make the dominant contribution to T1 and NOE. At t = 1 ns the total rms azimuthal displacement of the P-H vector in this model is 19.5°, which results from a superposition of torsional deformations with rms displacement 18.2° and uncoupled local motions with rms displacement 7°. The contribution of pure chemical shift anisotropy (CSA) to the 1/T1 relaxation rate is calculated for the first time for the case when torsional deformation modes predominate, and it is predicted to be 46% of the corresponding dipolar relaxation rate or 31% of the total relaxation rate. Unusual magnetic field strength dependence of the pure CSA and dipolar contributions is predicted to arise as a consequence of the collective torsional deformation modes. This seriously weakens empirical arguments in favor of a small (〈10%) CSA contribution. In any case, a detailed interpretation of T1 and NOE incorporating both dipolar and CSA relaxation must await the evaluation of the CSA:dipolar interference term, or crossterm, contribution to the relaxation rate. The contribution of pure CSA to 1/T2 relaxation is likewise calculated for the case when local reorienting motions are negligible; it is found to be ≲16% of the corresponding dipolar relaxation rate for the comparatively short (300-600-base-pair) DNA fragments of interest. For high-molecular-weight DNAs we predict that the slow Rouse-Zimm coil-deformation modes will dominate 1/T2 relaxation and the linewidth. Dynamic light-scattering and other evidence is presented that the remarkable loss of nmr signal from DNA on addition of ethidium bromide, as reported by Hogan and Jardetzky, is actually a consequence of phase separation in such concentrated solutions. A pronounced decrease in T2, due to greatly hindered axial tumbling in the more concentrated phase, is advanced as a plausible line-broadening explanation for the apparent loss of nmr signal from DNA in that phase.

Notes: The method of Ermak and McCammon [Ermak, D. L. & McCammon, J. A. (1978) J. Chem. Phys. 69, 1352-1360] is used to simulate the Brownian dynamics of a system of identical, interacting beads. In the present study, we use the method to obtain transport coefficients for a variety of rigid and flexible structures modeled as arrays of spherical subunits. Constraints are enforced using the SHAKE algorithm or a modification, SHAKE-HI, that is described for the first time. In SHAKE-HI, hydrodynamic interactions between subunits are taken into account when the constraints are enforced. Use of SHAKE-HI yields transport coefficients that are in perfect agreement with those obtained by other methods. The primary advantage of the present method is its generality. We also propose that multistep Brownian dynamics may be important in simulating actual experiments (such as fluorescence depolarization) on well-defined model systems that possess an arbitrary degree of internal flexibility.