Diffusion controlled reaction rates in spheroidal geometry. Application to repressor--operator association and membrane bound enzymes

The von Smoluchowski-Debye formulae for diffusion controlled reaction rates are extended to the more general case of spheroidal geometry. Their application to the association of represser and operator is thoroughly discussed in the light of recent experiments on the lac system by Riggs et al. The conclusions suggest that the surprisingly high association rate is not essentially due to electrostatic attraction but rather to unspecific binding of represser to nonoperator DNA with subsequent diffusion along the chain.