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For a compact set K⊂ℝ1 and a family {Cλ}λϵJ of dynamically defined Cantor sets sufficiently close to affine with dimH K + dimH Cλ > 1 for all λ ϵ J, under natural technical conditions we prove that the sum K+C\ has positive Lebesgue measure for almost all values of the parameter λ. As a corollary, we show that generically the sum of two affine Cantor sets has positive Lebesgue measure provided the sum of their Hausdorff dimensions is greater than 1.

The bimolecular kinetics of the mechanism of reduction of wild-type yeast iso-1-ferricytochrome C(ycytc) by ferrocytochrome b5 (cytb5) soluble in trypsin is influenced by the electrostatic charge modifications and steric changes involving factors such as electron transfer rates of yctc mutants K79A, K'72A, K79A/ K'72A and R38A: K' signifies the presence of trimethyllysine (Tml). The structural and functional properties associated with the rate of electron transfer under second-order reaction conditions are analyzed by evaluating this reduction reaction as a variable of pH, temperature and ionic strength.

Researchers used a structurally sound BD Brownian dynamics technique to simulate the kinetics of electron-transfer self-exchange reactions of trypsin-solubilized bovine liver cytochrome b5 (cytb5) and horse heart cytochrome c (cytc). The simulation of diffusional docking and electron transfer helped in calculating bimolecular rate constants, which were analyzed with respect to experimental findings.

Calculation of diffusion controlled bimolecular reaction rates for complicated macromolecular systems is made possible by a computer simulation approach based on the Brownian dynamics (BD) trajectory method. This is applied to the calculation of the diffusion controlled reaction rate between two charged spherical molecules, one of which represents a protein which possesses a strong dipole moment and asymmetric chemical reactivity. The role of the position of the dipole moment relative to reactive surfaces having various extents in media of varying ionic strength is assessed. No dipolar electrostatic effect on the diffusional rate constant of an isotropically reactive dipolar protein is observed. When the dipolar protein has a small axially symmetric reactive surface (e.g., of 10° extent), the dipole exerts a fivefold enhancement on the rate when the dipole vector is along the reactive patch axis, and retards the rate by a factor of 10 when oppositely disposed. A significant electrostatic effect persists through the physiological ionic strength regime. The positioning of dipolar charges relative to the protein surface at fixed dipole strength has an important effect on the electrostatic influence of the dipole. The variation of the protein dipole relative to its reactive surface can in fact be achieved in practice by chemical modification or site-directed mutagenesis. [ABSTRACT FROM AUTHOR]

One-dimensional Brownian dynamics algorithms for reaction and reflection recently developed by Lamm and Schulten are adapted into the special boundary topology necessary to compute diffusion-influenced rate constants of arbitrarily complicated bimolecular reactions in three dimensions. Performance of these relative to the primitive free diffusion algorithm commonly employed is discussed. Remaining sources of error arising from boundaries are (1) boundary curvature effects and (2) reactive discontinuity effects in cases where orientational criteria for reaction exist. The magnitudes of these errors are calculated as a function of simulation time step size. In addition, a special statistical sampling procedure is developed which allows the simultaneous treatment of a large class of reactive boundary problems in one simulation. This procedure is illustrated by the treatment of reactive patch size effects on the rate constant in the model of Solc and Stockmayer. [ABSTRACT FROM AUTHOR]

Brownian Dynamics of Cytochrome c and Cytochrome c Peroxidase Association BIOLOGICAL PROCESSES ON A MOLECULAR level require the transport of reactants through space by a diffusional mechanism leading to a [...]