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

Abstract

Control of organelle size is a problem that has intrigued cell biologists for at least a 9 century. The single-celled green algae Chlamydomonas reinhardtii with its two flagella has proved to 10 be a very useful model organism for studies of size control. Numerous experiments have identified 11 motor-driven transport of tubulin to the growing ends of microtubules at the tip of the flagella as 12 the key component of the machinery responsible for controlling their length. Here we consider a 13 model of flagellar length control whose key assumption is that proteins responsible for the 14 intraflagellar transport (IFT) of tubulin are present in limiting amounts. We show that this 15 limiting-pool assumption and simple reasoning based on the law of mass action leads to an inverse 16 relationship between the rate at which a flagellum grows and its length, which has been observed 17 experimentally, and has been shown theoretically to provide a mechanism for length control. 18 Experiments in which one of the two flagella are severed have revealed the coupled nature of the 19 growth dynamics of the two flagella, and we extend our length-control model to two flagella by 20 considering different mechanisms of their coupling. We describe which coupling mechanisms are 21 capable of reproducing the observed dynamics in severing experiments, and why some that have 22 been proposed previously are not. Within our theoretical framework we conclude that if tubulin 23 and IFT proteins are freely exchanged between flagella simultaneous length control is not possible 24 if the disassembly rate is constant. However, if disassembly depends on the concentration of IFT 25 proteins at the tip of the flagellum, simultaneous length control can be achieved. Finally, we make 26 quantitative predictions for experiments that could test this model. 27 28 55 Buisson et al. (2013). IFT particles containing tubulin are transported along the flagellum by two 56 different motor proteins: kinesin-2 transports IFT particles from the flagellar base to tip (the 57 anterograde direction) whereas dynein carries IFT particles from the tip to the base (the retrograde 58 direction). 59 These observations motivated the development of mathematical models of flagellar length 60 dynamics such as the balance point model Marshall and Rosenbaum (2001); Marshall et al. (2005). 61 In the balance point model, the steady-state flagellar length is achieved when the assembly and 62 disassembly processes, which are in continual competition, come into a balance set by the finite pool 63 of tubulin shared between the flagellum and basal body. The balance point model yields a length-64 dependent assembly rate by assuming a constant number of transport complexes moving along the 65 flagellum. This is consistent with experimental evidence that the flagellar assembly rate decreases 66 with length Rosenbaum and Child (1967); Marshall and Rosenbaum (2001). Notably, however, 67 the balance-point does not explain how the cell could maintain a constant number of transport 68 458 A...

Length-dependent disassembly maintains four different flagellar lengths in Giardia

“…In contrast, the disassembly rate is thought to be length-independent (Engel et al, 2009; Ludington et al, 2013). Length-dependent assembly is proposed to arise from the depletion of the assembly motor, kinesin-2, at the flagellar base and the diffusive return of this essential IFT component from the flagella tip (Chien et al, 2017; Fai, Mohapatra, Kondev, & Amir, 2019; Hendel et al, 2018). In this way, the amount of kinesin-2 available to be incorporated into IFT trains acts as a length-ruler of flagella.…”

Analysis of Biological Noise in an Organelle Size Control System

“…One study (Banerjee 2020) analyzed a model closely related to our balance point model, which assumes the 1/L dependence of IFT on length, while a second study (Patra 2020) analyzed a more elaborate model in which IFT injection is regulated by a time-of-flight mechanism. A third recent study describes a model for length regulation based on length-dependent transport of disassembly factors (Fai 2019), which is distinct from our current model. Stochastic simulations of this model, in which IFT entry and the random walk of returning IFT motors are explicitly modeled as random processes, allowed for prediction of fluctuations in length.…”

“…A more comprehensive approach would address the full nonlinear model. Several nonlinear stochastic models have recently been proposed for flagellar length dynamics (Fai 2019; Banerjee 2020; Patra 2020). Two of these studies analyzed models for flagellar length control using master equations to represent the inherently stochastic nature of biochemical reactions, which has the advantage of not requiring an extra “noise source” to be postulated.…”

“…However, previous experimental studies of flagellar length variation have not distinguished between sources of variation that take place within the flagella (intrinsic noise) versus source of variation that take place in the cell body (extrinsic noise). Theoretical models for flagellar length regulation make distinct predictions concerning the nature of flagellar length fluctuation and variation (Bressloff 2006; Hendel 2018; Fai 2019; Banerjee 2020; Patra 2020), hence a measurement of length fluctuation has the potential to test existing models and inform future modeling efforts.…”

Intraflagellar Transport Proteins as Regulators of Primary Cilia Length

“…Cilia length is determined by the balance of cilia assembly and disassembly ( Marshall and Rosenbaum, 2001 ; Marshall et al, 2005 ). In C. reinhardtii , live imaging has revealed that frequency of IFT train ciliary entry, IFT train size and speed, and cargo loading vary with cilia length, which has led to various models of cilia length control ( Marshall et al, 2005 ; Wren et al, 2013 ; Chien et al, 2017 ; Fai et al, 2019 ; Wemmer et al, 2020 ). However, primary cilia length regulation in mammalian cells has been much less studied.…”