  Diffusive motion of regulatory enzymes on biopolymers with eventual capture
at a reaction site is a common feature in cell biology. Using a lattice gas
model we study the impact of diffusion and capture for a microtubule polymerase
and a depolymerase. Our results show that the capture mechanism localizes the
proteins and creates large-scale spatial correlations. We develop an analytic
approximation that globally accounts for relevant correlations and yields
results that are in excellent agreement with experimental data. Our results
show that diffusion and capture operates most efficiently at cellular enzyme
concentrations which points to in vivo relevance.
