Control of filament length by a depolymerizing gradient

Cells assemble microns-long filamentous structures from protein monomers that are nanometers in size. These structures are often highly dynamic, yet in order for them to function properly, cells maintain them at a precise length. Here we investigate length-dependent depolymerization as a mechanism of length control. This mechanism has been recently proposed for flagellar length control in the single cell organisms Chlamydomonas and Giardia. Length dependent depolymerization can arise from a concentration gradient of a depolymerizing protein, such as kinesin-13 in Giardia, along the length of the flagellum. Two possible scenarios are considered: a linear and an exponential gradient of depolymerizing proteins. We compute analytically the probability distributions of filament lengths for both scenarios and show how these distributions are controlled by key biochemical parameters through a dimensionless number that we identify. In Chlamydomonas cells, the assembly dynamics of its two flagella are coupled via a shared pool of molecular components that are in limited supply, and so we investigate the effect of a limiting monomer pool on the length distributions. Finally, we compare our calculations to experiments. While the computed mean lengths are consistent with observations, the noise is two orders of magnitude smaller than the observed length fluctuations.Author summary: A fundamental problem in cell biology is how molecules self-organize into functional structures. Flagella and cilia are filamentous structures made of hundreds of thousands of proteins, which undergo rapid turnover, and for them to function properly cells need to maintain them at a precise length. Based on experiments on flagellated single cell organisms, we consider a model of length control by a depolymerizing gradient. Such gradients form when depolymerizing proteins are transported to the tip of the filament by a combination of diffusion and directed transport. The result is an accumulation of depolymerizing proteins at the tip of the filament leading to length-dependent depolymerization of the filament. This negative feedback of length on filament assembly provides length control for multiple filaments even when all the molecular components are drawn from a shared cytoplasmic pool. Using a chemical master equation description of this model of length control, we compute the distribution of filament lengths, and analyze their dependence on model parameters. We find good agreement between our model and experiments, and suggest new experiments to test model predictions.