The filament-based lamellipodium model: where mathematical cell motility begins We paraphrase Vic Small’s seminal work to motivate the derivation of a mathematical model that accounts for a range of biomechanical processes at the level of actin filaments, with active cell migration emerging as a macroscopic outcome. The model incorporates polymerisation, nucleation, capping, branching, and fragmentation of actin filaments; myosin-induced lamellipodial contractility; integrin-mediated cell–matrix adhesion; and cadherin-mediated cell–cell adhesion. We describe the mathematical formulation of these processes and present a series of specialised numerical experiments demonstrating that the model reproduces key cell migration phenomena, including chemo- and haptotaxis, cell–cell collisions and adhesion events, and early-stage cell cluster formation. This article was published on 2025-11-29
