Effects of random hydrolysis on biofilament length distributions in a shared subunit pool

The sizes of filamentous structures in a cell are often regulated for many physiological processes. A key question in cell biology is how such size control is achieved. Here, we theoretically study the length distributions of multiple filaments, growing by stochastic assembly and disassembly of subunits from a limiting subunit pool. Importantly, we consider a chemical switching of subunits (hydrolysis) prevalent in many biofilaments like microtubules (MTs). We show by simulations of different models that hydrolysis leads to a skewed unimodal length distribution for a single MT. In contrast, hydrolysis can lead to bimodal distributions of individual lengths for two MTs, where individual filaments toggle stochastically between bigger and smaller sizes. For more than two MTs, length distributions are also bimodal, although the bimodality becomes less prominent. We further show that this collective phenomenon is connected with the nonequilibrium nature of hydrolysis, and the bimodality disappears for reversible dynamics. Consistent with earlier theoretical studies, a homogeneous subunit pool, without hydrolysis, cannot control filament lengths. We thus elucidate the role of hydrolysis as a control mechanism on MT length diversity.