Length regulation of multiple flagella that self-assemble from a shared pool of components
Control of organelle size is a problem that has intrigued cell biologists for at least a century. The single-celled green algae Chlamydomonas reinhardtii with its two 2agella has proved to be a very useful model organism for studies of size control. Numerous experiments have identi1ed motor-driven transport of tubulin to the growing ends of microtubules at the tip of the 2agella as the key component of the machinery responsible for controlling their length. Here we consider a model of 2agellar length control whose key assumption is that proteins responsible for the intra2agellar transport (IFT) of tubulin are present in limiting amounts. We show that this limiting-pool assumption and simple reasoning based on the law of mass action leads to an inverse relationship between the rate at which a 2agellum grows and its length, which has been observed experimentally, and has been shown theoretically to provide a mechanism for length control. Experiments in which one of the two 2agella are severed have revealed the coupled nature of the growth dynamics of the two 2agella, and we extend our length-control model to two 2agella by considering different mechanisms of their coupling. We describe which coupling mechanisms are capable of reproducing the observed dynamics in severing experiments, and why some that have been proposed previously are not. Within our theoretical framework we conclude that if tubulin and IFT proteins are freely exchanged between 2agella simultaneous length control is not possible if the disassembly rate is constant. However, if disassembly depends on the concentration of IFT proteins at the tip of the 2agellum, simultaneous length control can be achieved. Finally, we make quantitative predictions for experiments that could test this model.