Mathematical modeling of calcium signaling during sperm hyperactivation

Mammalian sperm must hyperactivate in order to fertilize oocytes. Hyperactivation is characterized by highly asymmetrical flagellar bending. It serves to move sperm out of the oviductal reservoir and to penetrate viscoelastic fluids, such as the cumulus matrix. It is absolutely required for sperm penetration of the oocyte zona pellucida. In order for sperm to hyperactivate, cytoplasmic Ca2+ levels in the flagellum must increase. The major mechanism for providing Ca2+ to the flagellum, at least in mice, are CatSper channels in the plasma membrane of the principal piece of the flagellum, because sperm from CatSper null males are unable to hyperactivate. There is some evidence for the existence of other types of Ca2+ channels in sperm, but their roles in hyperactivation have not been clearly established. Another Ca2+ source for hyperactivation is the store in the redundant nuclear envelope of sperm. To stabilize levels of cytoplasmic Ca2+, sperm contain Ca2+ ATPase and exchangers. The interactions between channels, Ca2+ ATPases, and exchangers are poorly understood; however, mathematical modeling can help to elucidate how they work together to produce the patterns of changes in Ca2+ levels that have been observed in sperm. Mathematical models can reveal interesting and unexpected relationships, suggesting experiments to be performed in the laboratory. Mathematical analysis of Ca2+ dynamics has been used to develop a model for Ca2+ clearance and for CatSper-mediated Ca2+ dynamics. Models may also be used to understand how Ca2+ patterns produce flagellar bending patterns of sperm in fluids of low and high viscosity and elasticity.