A systematic comparison of mathematical models for inherent measurement of ciliary length: how a cell can measure length and volume.

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.

Quantitative analysis and modeling of katanin function in flagellar length control.

Flagellar length control in Chlamydomonas reinhardtii provides a simple model system in which to investigate the general question of how cells regulate organelle size. Previous work demonstrated that Chlamydomonas cytoplasm contains a pool of flagellar precursor proteins sufficient to assemble a half-length flagellum and that assembly of full-length flagella requires synthesis of additional precursors to augment the preexisting pool. The regulatory systems that control the synthesis and regeneration of this pool are not known, although transcriptional regulation clearly plays a role. We used quantitative analysis of length distributions to identify candidate genes controlling pool regeneration and found that a mutation in the p80 regulatory subunit of katanin, encoded by the PF15 gene in Chlamydomonas, alters flagellar length by changing the kinetics of precursor pool utilization. This finding suggests a model in which flagella compete with cytoplasmic microtubules for a fixed pool of tubulin, with katanin-mediated severing allowing easier access to this pool during flagellar assembly. We tested this model using a stochastic simulation that confirms that cytoplasmic microtubules can compete with flagella for a limited tubulin pool, showing that alteration of cytoplasmic microtubule severing could be sufficient to explain the effect of the pf15 mutations on flagellar length.

A principal role for the proteasome in endoplasmic reticulum-associated degradation of misfolded intracellular cystic fibrosis transmembrane conductance regulator.

Endoplasmic reticulum-associated degradation of misfolded cystic fibrosis transmembrane conductance regulator (CFTR) protein is known to involve the ubiquitin-proteasome system. In addition, an ATP-independent proteolytic system has been suggested to operate in parallel with this pathway and become up-regulated when proteasomes are inhibited (Jensen, T. J., Loo, M. A., Pind, S., Williams, D. B., Goldberg, A. L., and Riordan, J. R. (1995) Cell 83, 129-135). In this study, we use two independent techniques, pulse-chase labeling and a noninvasive fluorescence cell-based assay, to investigate the proteolytic pathways underlying the degradation of misfolded CFTR. Here we report that only inhibitors of the proteasome have a significant effect on preventing the degradation of CFTR, whereas cell-permeable inhibitors of lysosomal degradation, autophagy, and several classes of protease had no measurable effect on CFTR degradation, when used either alone or in combination with the specific proteasome inhibitor carbobenzoxy-l-leucyl-leucyl-l-leucinal (MG132). Our results suggest that ubiquitin-proteasome-mediated degradation is the dominant pathway for disposal of misfolded CFTR in mammalian cells and provide new mechanistic insight into endoplasmic reticulum-associated degradation.