Paul Bressloff, University of Utah – Applied Mathematics Colloquium

Title: Coupling active motor transport with cytoskeletal structure and dynamics
Abstract:  There are a growing number of phenomena in cell biology that involve the coupling between active motor-driven transport and the dynamics of cytoskeletal structures. Two important application domains are cell polarization and cellular length control. In this talk I present some recent PDE models of transport-cytoskeletal interactions. First, I will consider a reaction-diffusion model of cell polarization in the neural growth cone. During neural development, the growth cone of an axon has to respond accurately to extracellular chemical gradients that direct its growth. Chemoattractants (repellants) are detected by receptors in the growth cone membrane, which trigger signaling cascades, subsequent restructuring of the cytoskeleton, and growth towards (away from) the stimulus. The steering mechanism is based on the regulation of microtubule (MT) lengths by a variety of signaling proteins including Rac1 and stathmin. Second, I consider a stochastic model of flagellar length control. A eukaryotic flagellum is a microtubule-based structure that protrudes from the cell membrane up to about 10 microns in length. Assembly of MTs is mediated by molecular motor complexes known as intraflagellar transport (IFT) particles, which carry tubulin to the tip of the flagellum, where length-dependent assembly and disassembly of microtubules take place. Recent experimental studies indicate that the injection rate of IFTs into a flagellum is also regulated in a length-dependent manner. We model this in terms of a doubly stochastic Poisson process. Finally, time permitting, I will discuss a model of cytoneme-based transport of morphogens during embryogenesis. (A cytoneme is a thin actin-rich filament that forms direct contacts between cells and is thought to provide an alternative to diffusion-based morphogen gradient formation.)