Fig 1. Schematic of a depolymerizing gradient.

A. Depolymerizing proteins (red) accumulate at the tip of filament by directed transport from - to + end, and diffusion from the tip (+ end), where they are released. The resulting length dependent concentration of depolymerizing proteins at the filament tip leads to a length dependent depolymerization rate γ(L). Assembly also occurs at the tip at rate (r), which is determined by the monomer (tubulin) pool in the cell body. Flagella draw all protein components from a common pool. B. A linear concentration gradient forms when the depolymerizing proteins can only attach to the motors (not shown) at the base (–end) of the filaments. C. An exponential concentration gradient forms when the depolymerizers can bind to motors anywhere along the filament. C₀ is the concentration of depolymerizers in the cytoplasm, and λ is the characteristic length scale of the gradient.