Models for Cell Shape and Actin Filament Distributions

In this lecture I describe a model by Grimm et al (2003) Eur Biophys J 32: 563-577. The authors ask what processes might account for a parabolic density profile of actin seen across the front edge of a keratocyte. In an elegant coupled PDE model, they show that right and left growing actin filaments, competing for the actin branching complex Arp2/3 have solutions with the appropriate profile. I here
consider one of the cases, that of local competition and slow capping of filaments, where the equations are fully analytically solvable in closed form.