A mathematical model for simultaneous spatio-temporal dynamics of calcium and inositol 1,4,5-trisphosphate in Madin-Darby canine kidney epithelial cells

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 Ca(2+) levels in the flagellum must increase. The major mechanism for providing Ca(2+) 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 Ca(2+) channels in sperm, but their roles in hyperactivation have not been clearly established. Another Ca(2+) source for hyperactivation is the store in the redundant nuclear envelope of sperm. To stabilize levels of cytoplasmic Ca(2+), sperm contain Ca(2+) ATPase and exchangers. The interactions between channels, Ca(2+) ATPases, and exchangers are poorly understood; however, mathematical modeling can help to elucidate how they work together to produce the patterns of changes in Ca(2+) 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 Ca(2+) dynamics has been used to develop a model for Ca(2+) clearance and for CatSper-mediated Ca(2+) dynamics. Models may also be used to understand how Ca(2+) patterns produce flagellar bending patterns of sperm in fluids of low and high viscosity and elasticity.

A model of CatSper channel mediated calcium dynamics in mammalian spermatozoa

CatSpers are calcium (Ca(2+)) channels that are located along the principal piece of mammalian sperm flagella and are directly linked to sperm motility and hyperactivation. It has been observed that Ca(2+) entry through CatSper channels triggers a tail to head Ca(2+) propagation in mouse sperm, as well as a sustained increase of Ca(2+) in the head. Here, we develop a mathematical model to investigate this propagation and sustained increase in the head. A 1-d reaction-diffusion model tracking intracellular Ca(2+) with flux terms for the CatSper channels, a leak flux, and plasma membrane Ca(2+) clearance mechanism is studied. Results of this simple model exhibit tail to head Ca(2+) propagation, but no sustained increase in the head. Therefore, in this model, a simple plasma membrane pump-leak system with diffusion in the cytosol cannot account for these experimentally observed results. It has been proposed that Ca(2+) influx from the CatSper channels induce additional Ca(2+) release from an internal store. We test this hypothesis by examining the possible role of Ca(2+) release from the redundant nuclear envelope (RNE), an inositol 1,4,5-trisphosphate (IP(3)) gated Ca(2+) store in the neck. The simple model is extended to include an equation for IP(3) synthesis, degradation, and diffusion, as well as flux terms for Ca(2+) in the RNE. When IP(3) and the RNE are accounted for, the results of the model exhibit a tail to head Ca(2+) propagation as well as a sustained increase of Ca(2+) in the head.