Title:

Tango Waves in a Bidomain Model of Fertilization Calcium Waves


Author: Yue-Xian Li

Department of Mathematics, University of British Columbia, Vancouver, BC

Abstract:

Fertilization of an egg cell is marked by one or several
Ca2+  waves that travel across the intra-cellular space, called fertilization Ca2+  waves. Patterns of Ca2+ waves observed in mature or immature oocytes include traveling fronts and pulses as well as concentric and spiral waves. These patterns have been studied in other excitable media in physical, chemical, and biological systems. Here, we report the discovery of a new wave phenomenon in the numerical study of a bidomain model of fertilization Ca2+  waves. This wave is a front that propagates in a back-and-forth manner that resembles the movement of tango dancers, thus is called a tango wave. When the medium is excitable,
a forward moving tango wave can generate traveling pulses that propagate down the space without reversal. The study shows that the occurrence of tango waves is related to spatial inhomogeneity in the local dynamics.
This is tested and confirmed by simulating similar waves in a medium with
stationary spatial inhomogeneity. Similar waves are also obtained in
a FitzHugh-Nagumo system with a linear spatial ramp. In both the bidomain model of Ca2+ waves and the FitzHugh-Nagumo system, the front is stable when the slope of a linear ramp is large. As the slope decreases beyond a critical value, front oscillations occur. The study shows that tango waves facilitate the dispersion of localized Ca2+. Key features of the bidomain model underlying the occurrence of tango waves are revealed. These features are commonly found in egg cells of a variety of species. Thus, we predict that tango waves can occur in real egg cells provided that a slowly varying inhomogeneity does occur following the sperm entry. The observation of tango wave-like waves in nemertean worm and ascidian eggs seems to support such a prediction.