Uncorrelated changes of subunit stability can generate length-dependent disassembly of treadmilling filaments

Unregulated polymer assembly typically leads to exponential length distributions. In living cells, though, the length distribution of cytoskeletal filaments often shows a sharp maximum at a finite value. We discuss a simple mechanism for length regulation that is based on generating an effectively length-dependent disassembly rate by locally acting cytoskeletal proteins. We analyze steady-state distributions by stochastic simulations and develop a method to analytically characterize the typical filament length. We find three different types of behavior: (1) unbounded filament growth, (2) exponential distributions and (3) unimodal distributions, which can be very sharp with a standard deviation much smaller than the mean filament length. We discuss possible implications of our results for subcellular processes.