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Diffusive motion of regulatory enzymes on biopolymers with eventual captureat a reaction site is a common feature in cell biology. Using a lattice gasmodel we study the impact of diffusion and capture for a microtubule polymeraseand a depolymerase. Our results show that the capture mechanism localizes theproteins and creates large-scale spatial correlations. We develop an analyticapproximation that globally accounts for relevant correlations and yieldsresults that are in excellent agreement with experimental data. Our resultsshow that diffusion and capture operates most efficiently at cellular enzymeconcentrations which points to in vivo relevance.

A nonequilibrium diffusion and capture mechanism ensures tip-localization of regulating proteins on dynamic filaments