Title:  Analysis of traveling waves in a non-local model of cell surface mechanics

Abstract: We analyze a model of the surface of eukaryotic cells that includes mechanics and assembly/disassembly dynamics. This model is expressed as a system of partial differential equations, one of which is integrated over the spatial coordinate at each time and is therefore equivalent to a non-local equation. The model was previously studied numerically, where evidence was found for excitability and traveling waves, depending on parameter values. Here we demonstrate that excitability emerges via a Canard explosion. In the excitable regime, we derive a necessary condition for traveling waves and provide numerical evidence that it is also a sufficient condition. Thus, we demonstrate the analogue of a Maxwell condition for traveling waves applied to this non-local system.