Simulation of the Fertilization Ca2+ Wave in Xenopus laevis Eggs

Abstract

In the preceding paper Fontanilla and Nuccitelli (Biophysical Journal 75:2079-2087 (1998)) present detailed measurements of the shape and speed of the fertilization Ca2+ wave in Xenopus laevis eggs. In order to help interpret their results, we develop here a computational technique based on the finite element method that allows us to carry out realistic simulations of the fertilization wave. Our simulations support the hypothesis that the physiological state of the mature egg is bistable, i.e., that its cytoplasm can accommodate two alternative physiological Ca2+ concentrations: a low concentration characteristic of the prefertilization state and a greatly elevated concentration characteristic of the state following the passage of the wave. We explore this hypothesis by assuming that the bistability is due to the release and re-uptake properties of the endoplasmic reticulum (ER) as determined by inositol trisphosphate (IP3) receptor/Ca2+ channels and sarcoendoplasmic reticulum calcium ATPase (SERCA) pumps. When combined with buffered diffusion of Ca2+ in the cytoplasm, our simulations show that inhomogeneities in the Ca2+ release properties near the plasma membrane are required to explain the temporal and spatial dependences of the shape and speed of these waves. Our results are consistent with an elevated IP3 concentration near the plasma membrane in the unfertilized egg that is augmented significantly near the site of fertilization. These gradients are essential in determining the concave shape of the Ca2+ fertilization wave front.

Simulation of calcium waves in ascidian eggs: insights into the origin of the pacemaker sites and the possible nature of the sperm factor

“…It was shown that the correct shape of the fertilization wave in Xenopus oocyte can be reproduced by assuming that Ins(1,4,5)P3 is locally generated at the fertilization site (Bugrim et al, 2003). Moreover, these studies emphasize the role of the spatial inhomogeneities in the ER distribution (Bugrim et al, 2003;Hunding and Ipsen, 2003), in the Ins(1,4,5)P3Rs distribution (Bugrim et al, 2003) or in Ins(1,4,5)P3 production (Wagner et al, 1998) to reproduce the experimentally observed spatial profiles. None of these studies, however, deals with repetitive Ca 2+ waves, as those observed at fertilization of many species, including ascidians and mammals.…”

“…Some theoretical models have already investigated the spatial characteristics of the Ca 2+ increase occuring at fertilization (Wagner et al, 1998;Bugrim et al, 2003;Hunding and Ipsen, 2003). It was shown that the correct shape of the fertilization wave in Xenopus oocyte can be reproduced by assuming that Ins(1,4,5)P3 is locally generated at the fertilization site (Bugrim et al, 2003).…”

A bidomain threshold model of propagating calcium waves

“…The stability of solutions is then determined by equation (31). More specifically, we now consider perturbations of the firing times of the form g(x) = e λx to obtain the characteristic equation where…”

A Tridimensional Model of Proangiogenic Calcium Signals in Endothelial Cells

“…Several authors have discussed the role of 3D cell structure experimentally and theoretically: however, the interest is usually focused on calcium release from intracellular stores rather than on calcium entry from extracellular medium [5,20]. Secondly, the distribution and properties of calcium 'buffers' (proteins, mitochondria) changes from cell to cell and may contribute to the spatial restriction [21,22]. Finally, several evidences suggest the existence of lipidic rafts or caveolae and supermolecular complexes called signalplexes (or signallsomes) in virtually all cell types including ECs: interestingly, many molecules involved in calcium homeostasis and signaling are included in caveolae [23][24][25][26].…”