On the generation of force required for cell and bacteria motility

The fundamental quest of how forces are generated in a motile cell, a lamellipodium, and a comet tail is the subject this note. It is now well established that cellular motility is the result of the polymerization of actin, the most abundant protein in eukaryotic cells, into an interconnected set of filaments. We portray this process in a continuum mechanics framework, claiming that polymerization promotes a mechanical swelling in a narrow zone about the nucleation loci, which ultimately results in cellular or bacterial motility. To this aim, a new paradigm in continuum multi-physics has been designed departing the well-known theory of Larche-Cahn chemo-transport-mechanics. In this note, we set up the theory of network growth and compare the outcomes of numerical simulations with experimental evidence.