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Motility of animal cells is fundamentally important and is the most striking process underlying the phenomena of wound healing, morphogenesis and cancerogenesis. Despite recent radical advances in cell biology and the biophysics of the motile cell, we still do not have a complete picture of how animal cells move across surfaces. One reason for this is that a huge variety of molecular mechanisms are involved in locomotion, which leads to a multiplicity and redundancy in force generation machineries and regulatory pathways. Theoretical modeling helps to search for truth in this situation.

Amoeboid motility, in all its forms save one, is associated with the actin cytoskeleton. The crawling sperm of nematodes are the exception. An intriguing aspect of nematode sperm motility is that these cells discard their actin-based cytoskeleton and deploy an entirely new motility machinery based on a major sperm protein. Nematode sperm offer at least one advantage for investigating principles of cell crawling: these cells are remarkably simple and dedicated entirely to locomotion, yet their migrating behavior is essentially indistinguishable from that of actin-based cells.

I will present some preliminary results of quantitative modeling of the sperm cells. Two approaches will be discussed: one is based on Monte Carlo simulations of ensembles of cytoskeletal polymers. Another one incorporates what is known about relevant molecular mechanisms into partial integro-differential equations for the essential spatio-angular cytoskeletal densities. These equations are solved on a domain with a moving boundary of the cell. I will demonstrate how these models produce sperm-like shapes, movement and forces and advance our understanding of the dynamic principles of cell locomotion.