Energy Considerations in a Model of Nematode Sperm Crawling

Abstract

In this paper we propose a mathematical model for nematode spermcell crawling. The model takes into account both force and energybalance in the process of lamellipodium protrusion and cellnucleus drag. It is shown that by specifying the (possiblyvariable) efficiency of the major sperm protein biomotor onecompletely determines a self-consistent problem of thelamellipodium-nucleus motion. The model thus obtained properlyaccounts for the feedback of the load on the lamellipodiumprotrusion, which in general should not be neglected. We study andanalyze the steady crawling state for a particular efficiencyfunction and find that all nonzero modes, up to a large magnitude,are linearly asymptotically stable, thus reproducing theexperimental observations of the long periods of steady crawlingexhibited by the nematode sperm cells.

Keywords

• crawling
• stability
• nematode sperm cell
• travelling wave solution.
• biomotor thermodynamics
• free bound-ary problem