The geometry and motion of nematode sperm cells

The nematode sperm cell crawls by recycling major sperm protein (MSP) from dimers into subfilaments, filaments, and filament complexes, as a result of thermal writhing in the presence of hydrophobic patches. Polymerization near leading edges of the cell intercolates MSP dimers onto the tips of growing filament complexes, forcing them against the cell boundary, and extending the cytoskeleton in the direction of motion. Strong adhesive forces attach the cell to the substrate in the forward part of the lamellipod, while depolymerization in the rearward part of the cell breaks down the cytoskeleton, contracting the lamellipod and pulling the cell body forward. The movement of these cells, then, is caused by coordinated protrusive, adhesive and contractile forces, spatially separated across the lamellipod. This paper considers a phenomenological model that tracks discrete elements of the cytoskeleton in curvilinear coordinates. The pseudo-two dimensional model primarily considers protrusion and rotation of the cell, along with the evolution of the cell boundary. General assumptions are that pH levels within the lamellipod regulate protrusion, contraction and adhesion, and that growth of the cytoskeleton, over time, is perpendicular to the evolving cell boundary. The model follows the growth and contraction of a discrete number of MSP fiber complexes, since they appear to be the principle contributors for force generation in cell boundary protrusion and contraction, and the backbone for the dynamic geometry and motion.