Rate enhancement by guided diffusion. Chain length dependence of repressor-operator association rates.

Association rates are calculated for cases where one reaction partner belongs to a chain that has an unspecific affinity to the other. Provided that the unspecific attachment does not completely suppress diffusion along the chain, this channeling may considerably speed up the association. Explicit formulae are derived to show how this effect depends on the chain length and other parameters. The influence of electrostatic forces and reaction barriers is discussed. Time dependent solutions of the diffusion equations are analyzed in order to test the usual steady state assumptions. Experiments on the repressor-operator system seem to be in good agreement with our theory.