Back to Departmental Colloquium: Fall 2016
Departmental Colloquium
Date: Tuesday, Dec 13, 2016
Time: 4:00PM
Location: JWB 335
Jun Allard
UC Irvine
Title |
A non-local Maxwell condition for mechano-chemical traveling waves in cells |
Abstract |
Traveling waves appear throughout biology and are often driven by local spatial coupling, e.g., diffusion. The past ten years have revealed traveling waves in cells. These waves can be pulses of biochemical factors (diffusing proteins or metabolites) and also mechanical factors (such as the cell cortex). One example of mechanical traveling wave is offered by cellular blebs, pressure-driven bubbles on the cell surface implicated in cell division, apoptosis and cell motility. Blebs exhibit a range of behaviors including contracting in place, travel around the cell’s periphery, or repeated blebbing, making them biophysically interesting. Mechanical traveling waves are naturally modeled using non-local integro-PDEs, which lack the theoretical tools available for reaction-diffusion waves, obfuscating simple questions such as what determines if a bleb will travel or not, and, if it travels, what determines its velocity? We present results in two parts: First, we develop a simple model of the cell surface describing the membrane, cortex, and adhesions, including the slow timescale cortical healing (treating implicitly the fast timescale of fluid motion). We find traveling and stationary blebs, which we characterize through numerical simulation. In the second part, we review the so-called Maxwell condition for reaction-diffusion systems that determines whether an excitation will travel or recover in place. We present our progress in deriving an analogue of the Maxwell condition for non-local integro-PDEs suitable for our cell surface model. This condition allows the theoretical (simulation-free) elucidation of this dynamic biological phenomenon. Spring 2017 |
Mathematical Biology
Differential Equations