Diffusion-controlled reactions on spherical surfaces. Application to bacteriophage tail fiber attachment

We have explored the kinetic implications of a model that may account for the acceleration of tail fiber (F) attachment to baseplates (B) by whiskers (W) on bacteriophage T4. The model assumes that a W-F complex is formed initially, and that the tethered fiber then undergoes rotational diffusion until a B-F encounter takes place. In the absence of whiskers, B-F complexes must form unassisted. Formation of a W-F intermediate will accelerate F attachment to B if (a) the bimolecular rate constant for W-F complex formation is larger than that for direct B-F interaction and (b) subsequent rotational diffusion of the tip of F to B is not much slower than the dissociation of W-F. Condition a was investigated by applying a recent theory of orientational effects on translational diffusion-controlled reactions. This theory suggests that substantial rate enhancement is expected if the reaction half-angle theta 0 is larger for W-F than for B-F complex formation. Condition b was investigated by calculating the mean and the variance of the time required for the diffusion of a molecule (the proximal tip of the fiber) on a spherical surface (whose radius is the distance from the tip to the whisker tethering point) into a circular sink (the baseplate site). The mean time is on the order of the inverse rotational diffusion coefficient, DR, of the fiber, but is sensitive to theta 0. Both conditions are satisfied for plausible choices of parameters. The solution to the diffusion equation we have obtained should have application to other physical situations, such as the rate of quenching of a fluorophore as it diffuses on the surface of a spherical membrane into proximity with a quencher.