Chemoreceptor diffusion and reaction: first-order kinetics

Size effects in reactive circular site interactions

The complete series solution for the reactant diffusion and reaction at two diffusion-controlled chemically reactive surface sites of radii a(1) and a(2), located in an inert plane an arbitrary center-to-center distance d apart, is presented. Rigorous, analytical forms are developed to calculate the site reaction rates in terms of the dimensionless intersite distance σ[=d/(a(1) + a(2))] and the site radius ratio γ(=a(1)∕/a(2)). Numerical simulation and approximate theoretical results from the recent literature are compared to the exact site reaction rates. While general agreement was noted over the ranges of γ and σ, significant errors in the Wilemski-Fixman-Weiss site rates were found at small γ and σ < 3.

Interaction between two nearby diffusion-controlled reactive sites in a plane

The complete series solution for two diffusion-controlled chemically reactive sites, each of radius a, located on an inert plane an arbitrary center-to-center distance d apart, is presented. Simple analytical forms are developed to calculate the site reaction rates in terms of da. The impact of these results on a number of important problems in chemical physics is discussed.

Patch size effect on diffusion and incorporation in dilute suspension of partially active spheres

The normalized overall rate constant kp/kf for diffuse-and-incorporate processes in dilute suspension of spheres partially covered with randomly distributed nonoverlapping active patches is studied with a sped-up Brownian dynamic simulation scheme. The normalized overall rate constant is found to increase with decreasing characteristic size of the active patch under the condition of fixed fcover, the surface area fraction covered by the active patches. A scaling relation is proposed as (kp/kf)NDL/[(1 + P) - (1 + P/fcover)(kp/kf)NDL] approximately Np(1/2) with Np being the number of active patches on the sphere, P a parameter characterizing the relative dominance of surface incorporation over diffusion, and NDL signifying the nondiffusion-limited condition. This scaling relation is verified with rate constant data from the sped-up Brownian dynamic simulation. From this scaling relation, the maximum achievable kp/kf is derived to be (1 + P)/(1 + P/fcover). This result implies that kp/kf can approach unity under the diffusion-limited situation even for a partially active sphere by reducing the size of active patch, while it is not possible to achieve unit kp/kf for nondiffusion-limited systems.

Patch-distribution effect on diffusion-limited process in dilute suspension of partially active spheres

The normalized overall rate constant, kp/kf for diffusion-limited processes in a dilute suspension of spheres, partially covered with active patches of varying distribution states, is studied with sped-up Brownian dynamic simulations. A dimensionless separation index Is is defined to quantify the characteristics of patch distribution on the sphere surfaces, with values of 0 and 1 corresponding to the states of the most compact and loosest patch distributions, respectively. Remarkably, the normalized overall rate constant is found to strongly correlate with the dimensionless separation index at fixed patch coverage fcover exhibiting a positive, linear relationship. In addition, the slope of the kp/kf vs Is line, a measure of sensitivity of kp/kf to variation in the separation state of the distributed patches, is found to depend on patch coverage and patch size. This sensitivity exhibits a maximum value with respect to an increase in patch coverage, and the magnitude of the maximum sensitivity decreases with increasing patch size. The patch coverage, at which the maximum sensitivity occurs, increases with increasing patch size.