Length regulation of multiple flagella that self-assemble from a shared pool of components

The single cell biflagellate Chlamydomonas reinhardtii has proven to be a very useful model organism for studies of size control. We consider a model of flagellar length control whose key assumption is that proteins responsible for the intraflagellar 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 flagellum grows and its length, which has been observed experimentally, and has been shown theoretically to provide a mechanism for length control. We extend our length-control model to two flagella by considering different mechanisms of their coupling. Within our theoretical framework we conclude that, if tubulin and IFT proteins are freely exchanged between flagella, 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 flagellum, simultaneous length control can be achieved.