  The functional relevance of regulating proteins is often limited to specific
binding sites such as the ends of microtubules or actin-filaments. A
localization of proteins on these functional sites is of great importance. We
present a quantitative theory for a diffusion and capture process, where
proteins diffuse on a filament and stop diffusing when reaching the filament's
end. It is found that end-association after one-dimensional diffusion is the
main source for tip-localization of such proteins. As a consequence, diffusion
and capture is highly efficient in enhancing the reaction velocity of enzymatic
reactions, where proteins and filament ends are to each other as enzyme and
substrate. We show that the reaction velocity can effectively be described
within a Michaelis-Menten framework. Together one-dimensional diffusion and
capture beats the (three-dimensional) Smoluchowski diffusion limit for the rate
of protein association to filament ends.
