The Filament Based Lamellipodium Model (FBLM) describes actin-driven cell motility but is analytically intractable in its full form. We investigate a strongly simplified filament ensemble model that isolates the mechanical effect of Coulomb-type repulsion between neighboring actin filaments. Filaments are modeled as rigid rods sliding on a flat substrate under friction, inward confining forces, and an auxiliary tension that counteracts longitudinal destabilization caused by repulsion.\\

Starting from a microscopic description, we derive a nonlinear continuum model in the form of a coupled system of parabolic partial differential equations for filament orientations and centers of mass. The system is rotationally symmetric and admits a one-parameter family of trivial steady states. A linear stability analysis identifies a critical value of a dimensionless parameter at which these steady states lose stability.\\

A formal bifurcation analysis shows that the instability leads to a pitchfork bifurcation, which can be either supercritical or subcritical depending on parameter values. The bifurcating solutions correspond to deformed filament configurations that generate collective motion with constant velocity. Numerical simulations of the time-dependent problem support the analytical results and reveal additional nonlinear dynamics.\\

\medskip
\noindent
Ref: A. Manhart, D. Oelz, C. Schmeiser, and N. Sfakianakis,
\textit{An extended Filament Based Lamellipodium Model produces various moving cell shapes in the presence of chemotactic signals},
Journal of Theoretical Biology, 382 (2015), 244--258.