Modeling Vesicle Traffic Reveals Unexpected Consequences for Cdc42p-Mediated Polarity Establishment

Abstract

Summary Background Polarization in yeast has been proposed to involve a positive feedback loop whereby the polarity regulator Cdc42p orients actin cables, which deliver vesicles carrying Cdc42p to the polarization site. Previous mathematical models treating Cdc42p traffic as a membrane-free flux suggested that directed traffic would polarize Cdc42p, but it remained unclear whether Cdc42p would become polarized without the membrane-free simplifying assumption. Results We present mathematical models that explicitly consider stochastic vesicle traffic via exocytosis and endocytosis, providing several new insights. Our findings suggest that endocytic cargo influences the timing of vesicle internalization in yeast. Moreover, our models provide quantitative support for the view that integral membrane cargo proteins would become polarized by directed vesicle traffic given the experimentally determined rates of vesicle traffic and diffusion. However, such traffic cannot effectively polarize the more rapidly-diffusing Cdc42p in the model, without making additional assumptions that seem implausible and lack experimental support. Conclusions Our findings suggest that actin-directed vesicle traffic would perturb, rather than reinforce, polarization in yeast.

Morphogenesis and the Cell Cycle

“…At present, there is no evidence for active internalization of Cdc42p, and current estimates of the Cdc42p diffusion constant (Marco et al 2007) are an order of magnitude higher than the values required for the model to develop robust polarity (Layton et al 2011), so the viability of Cdc42p vesicular recycling as a way to concentrate Cdc42p at the prebud site remains unclear.…”

“…Mathematical modeling indicates that effective Cdc42p polarization by a vesicle recycling mechanism would require that the Cdc42p be actively endocytosed and that it diffuse very slowly in the plasma membrane (Layton et al 2011). At present, there is no evidence for active internalization of Cdc42p, and current estimates of the Cdc42p diffusion constant (Marco et al 2007) are an order of magnitude higher than the values required for the model to develop robust polarity (Layton et al 2011), so the viability of Cdc42p vesicular recycling as a way to concentrate Cdc42p at the prebud site remains unclear.…”

“…Actin patches represent sites of endocytosis at a late stage where the plasma membrane is in the process of invaginating (Kaksonen et al 2006). Markers of an earlier step of endocytosis (Ede1p or clathrin) are not as highly asymmetric (Newpher et al 2005;Stimpson et al 2009), and it was recently suggested that endocytic patches wait until they fill up with cargo before they initiate actin polymerization and invagination (Layton et al 2011). In buds, where directed secretion delivers many proteins (e.g., v-SNAREs) to the plasma membrane that subsequently become endocytic cargo, the clathrin patches fill with cargo rapidly and convert to actin patches; in mothers, where there is little secretion, the clathrin patches must wait much longer to collect sufficient cargo, so conversion to actin patches is rare (Layton et al 2011).…”

Stochastic models of intracellular transport

“…Various experimental studies suggest that there are at least two independent but coordinated positive feedback mechanisms that can establish cell polarity (WedlichSoldner et al, 2004). One involves the reinforcement of spatial asymmetries by the directed transport of signaling molecules along the cytoskeleton to specific locations on the plasma membrane (Altschuler et al, 2008;Layton et al, 2011;Marco et al, 2007), whereas the other involves the coupling of membrane diffusion with bistable enzymatic dynamics Mori et al, 2008;Semplice et al, 2012).…”

“…One limitation of the model, however, is that the packaging of signaling molecules into discrete vesicles is ignored, that is, the model treats transport as a continuous flux of proteins. As highlighted by Layton et al (2011), incorporating vesicular transport into the model makes cell polarization more difficult to sustain. A simple argument for this proceeds as follows.…”