An outstanding question is how cells control the number and size of membrane organelles. The small GTPase Rab5 has been proposed to be a master regulator of endosome biogenesis. Here, to test this hypothesis, we developed a mathematical model of endosome dependency on Rab5 and validated it by titrating down all three Rab5 isoforms in adult mouse liver using state-of-the-art RNA interference technology. Unexpectedly, the endocytic system was resilient to depletion of Rab5 and collapsed only when Rab5 decreased to a critical level. Loss of Rab5 below this threshold caused a marked reduction in the number of early endosomes, late endosomes and lysosomes, associated with a block of low-density lipoprotein endocytosis. Loss of endosomes caused failure to deliver apical proteins to the bile canaliculi, suggesting a requirement for polarized cargo sorting. Our results demonstrate for the first time, to our knowledge, the role of Rab5 as an endosome organizer in vivo and reveal the resilience mechanisms of the endocytic system.

Key cellular functions and developmental processes rely on cascades of GTPases. GTPases of the Rab family provide a molecular ID code to the generation, maintenance and transport of intracellular compartments. Here, we addressed the molecular design principles of endocytosis by focusing on the conversion of early endosomes into late endosomes, which entails replacement of Rab5 by Rab7. We modelled this process as a cascade of functional modules of interacting Rab GTPases. We demonstrate that intermodule interactions share similarities with the toggle switch described for the cell cycle. However, Rab5-to-Rab7 conversion is rather based on a newly characterized 'cut-out switch' analogous to an electrical safety-breaker. Both designs require cooperativity of autoactivation loops when coupled to a large pool of cytoplasmic proteins. Live cell imaging and endosome tracking provide experimental support to the cut-out switch in cargo progression and conversion of endosome identity along the degradative pathway. We propose that, by reconciling module performance with progression of activity, the cut-out switch design could underlie the integration of modules in regulatory cascades from a broad range of biological processes.

An outstanding question is how receptor tyrosine kinases (RTKs) determine different cell-fate decisions despite sharing the same signalling cascades. Here, we uncovered an unexpected mechanism of RTK trafficking in this process. By quantitative high-resolution FRET microscopy, we found that phosphorylated epidermal growth factor receptor (p-EGFR) is not randomly distributed but packaged at constant mean amounts in endosomes. Cells respond to higher EGF concentrations by increasing the number of endosomes but keeping the mean p-EGFR content per endosome almost constant. By mathematical modelling, we found that this mechanism confers both robustness and regulation to signalling output. Different growth factors caused specific changes in endosome number and size in various cell systems and changing the distribution of p-EGFR between endosomes was sufficient to reprogram cell-fate decision upon EGF stimulation. We propose that the packaging of p-RTKs in endosomes is a general mechanism to ensure the fidelity and specificity of the signalling response.DOI: http://dx.doi.org/10.7554/eLife.06156.001

Let P be a probability distribution on q-dimensional space. The so-called Diaconis-Freedman effect means that for a fixed dimension d << q, most d-dimensional projections of P look like a scale mixture of spherically symmetric Gaussian distributions. The present paper provides necessary and sufficient conditions for this phenomenon in a suitable asymptotic framework with increasing dimension q. It turns out that the conditions formulated by Diaconis and Freedman (1984) are not only sufficient but necessary as well. Moreover, letting P be the empirical distribution of n independent random vectors with distribution P , we investigate the behavior of the empirical process √ n( P − P ) under random projections, conditional on P .

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