A Systematic Comparison of Mathematical Models for Inherent Measurement of Ciliary Length: How a Cell Can Measure Length and Volume

Abstract

Cells control organelle size with great precision and accuracy to maintain optimal physiology, but the mechanisms by which they do so are largely unknown. Cilia and flagella are simple organelles in which a single measurement, length, can represent size. Maintenance of flagellar length requires an active transport process known as intraflagellar transport, and previous measurements suggest that a length-dependent feedback regulates intraflagellar transport. But the question remains: how is a length-dependent signal produced to regulate intraflagellar transport appropriately? Several conceptual models have been suggested, but testing these models quantitatively requires that they be cast in mathematical form. Here, we derive a set of mathematical models that represent the main broad classes of hypothetical size-control mechanisms currently under consideration. We use these models to predict the relation between length and intraflagellar transport, and then compare the predicted relations for each model with experimental data. We find that three models-an initial bolus formation model, an ion current model, and a diffusion-based model-show particularly good agreement with available experimental data. The initial bolus and ion current models give mathematically equivalent predictions for length control, but fluorescence recovery after photobleaching experiments rule out the initial bolus model, suggesting that either the ion current model or a diffusion-based model is more likely correct. The general biophysical principles of the ion current and diffusion-based models presented here to measure cilia and flagellar length can be generalized to measure any membrane-bound organelle volume, such as the nucleus and endoplasmic reticulum.

Screen-based identification and validation of four new ion channels as regulators of renal ciliogenesis

“…These findings not only suggest a possible role for primary cilia in the pathophysiology of conditions associated with LQTS, but they offer new insights into the general importance of ion channels and ion signaling in ciliopathies. Identification of four new ion channels that localize to primary cilia and are required for ciliogenesis, supports previously published data showing that the length of the ciliary structure is regulated by ion current, and ion channel stimulation can result in cilia-generated signaling (Ludington et al, 2015). Our data suggest that disturbance of ion balance by loss of the ion channel KCNQ1 results in ciliopathy phenotypes in vitro.…”

Protein transport in growing and steady‐state cilia

“…If the activation of such a freely diffusible factor occurs at the ciliary tip and its inactivation is time‐dependent, a tip‐to‐base gradient of active factor will be established which could adjust ciliary protein influx in response to changes in organelle length . Several alternative models of how cells could sense ciliary length have been described . Real‐time measurements of ciliary length fluctuations in steady‐state could help to pinpoint the length‐regulating pathway.…”

Intraflagellar transport: mechanisms of motor action, cooperation, and cargo delivery

“…It has long been recognized that IFT is required for ciliogenesis because it delivers cargo consisting of axonemal precursors such as tubulin subunits, preassembled radial‐spoke complexes and dynein arms to their site of assembly at the tip of the cilium . The delivery of these same cargo molecules is also relevant to the interesting topic of cilium length control, a topic that has been pioneered by Marshall and others . IFT is also thought to be involved in the delivery of specific molecules required for the compartmentalization of the cilium and, via cooperation with the BBSome, to contribute to the biogenesis of the ciliary membrane .…”