Many living creatures including human start their life when an egg cell is penetrated by a sperm. One of the events immediately following sperm entry is the occurrence of one or more waves of elevated Ca2+ concentration that travel from the site of sperm entry to the opposite end of the cell. These waves, called fertilization Ca2+ waves, are vital for the subsequent development of the fertilized egg. In egg cells of some species, the first few waves propagate further and further into the cellular space but fail to reach the opposite end. These waves are called ``incomplete'' waves. In this talk, I present a bidomain model of reaction-diffusion type that explains how such incomplete waves can occur. The model reveals that traveling fronts that propagate in an oscillatory manner, called tango waves, can occur in an excitable medium in the presence of spatial inhomogeneity. A preliminary theory is developed for studying stationary and traveling fronts and pulses in a more general model for excitable media. This study predicts a variety of experimental conditions under which tango waves can occur. Other areas of biology in which this theory may also apply will be discussed.
(A more technical talk closely related to this one will be presented at the Applied Math/Scientific Computing seminar on Oct 1.)