Effects of length-dependent positive feedback on length distributions of microtubules undergoing hydrolysis

Despite a rapid turnover of subunits, how cells control the lengths of cytoskeletal filaments (such as microtubules) is a fundamental question in cell biology. Here, we theoretically investigate how microscopic processes affect the length distributions of multiple microtubules growing stochastically in a shared subunit pool. In particular, we consider length-dependent positive feedback on filament growth and the chemical conversion from GTP-tubulin to GDP-tubulin (hydrolysis) inside a filament. We found different dynamical regimes for a single filament by simulating a model of microtubule kinetics, where both bimodal and unimodal (bell-shaped) length distributions emerge in the steady state. More significantly, the length distributions of multiple filaments were not unimodal, predicting a collective effect for more than one filament. Interestingly, when length distributions were bimodal, we also observed bistable toggling of individual lengths. Therefore, regulation of biophysical parameters (e.g., hydrolysis rate and feedback strength) can lead to length diversity in an ensemble of multiple microtubules.