Energy considerations in a model of nematode sperm crawling

In this paper we propose a mathematical model for nematode sperm cell crawling. The model takes into account both force and energy balance in the process of lamellipodium protrusion and cell nucleus drag. It is shown that by specifying the (possibly variable) efficiency of the major sperm protein biomotor one completely determines a self-consistent problem of the lamellipodium-nucleus motion. The model thus obtained properly accounts for the feedback of the load on the lamellipodium protrusion, which in general should not be neglected. We study and analyze the steady crawling state for a particular efficiency function and find that all nonzero modes, up to a large magnitude, are linearly asymptotically stable, thus reproducing the experimental observations of the long periods of steady crawling exhibited by the nematode sperm cells.