Ca2+ spiral waves in a spatially discrete and random medium

Long-range paracrine coupling-induced Ca^{2+} patterns in two-dimensional cell networks under inositol 1,4,5-triphosphate-cytosolic Ca^{2+} interaction

A two-dimensional model is designed for intercellular calcium (Ca^{2+}) waves in the presence of long-range (LR) paracrine coupling due to the action of extracellular messengers and Ca^{2+}-activated degradation of inositol 1,4,5-triphosphate (IP_{3}) by a 3-kinase. Using mean-field theory, a statistical variable is defined to detect the emergence of intercellular spiral waves of Ca^{2+}. The latter are generated by the local heterogeneity caused by asymmetrical stimulation of the network. It is confirmed that spiral waves may develop when the synchronization degree is low. It is found that balanced LR coupling and IP_{3} degradation, under appropriate external hormonal stimulation, can effectively control the creation and propagation of spiral waves. A higher LR degree disrupts network synchronization, and only specific ranges of stimulation factor support spiral waves. Weak IP_{3} degradation and stronger LR degree disintegrate spiral symmetry with increased hormonal stimulation. Strong IP_{3} degradation has the opposite effect.

Extending the IP3 receptor model to include competition with partial agonists

The inositol 1,4,5-trisphosphate (IP(3)) receptor is a Ca(2+) channel located in the endoplasmic reticulum and is regulated by IP(3) and Ca(2+). This channel is critical to calcium signaling in cell types as varied as neurons and pancreatic beta cells to mast cells. De Young and Keizer (1992) created an eight-state, nine-variable model of the IP(3) receptor. In their model, they accounted for three binding sites, a site for IP(3), activating Ca(2+), and deactivating Ca(2+). The receptor is only open if IP(3) and activating Ca(2+) is bound. Li and Rinzel followed up this paper in 1994 by introducing a reduction that made it into a two variable system. A recent publication by Rossi et al. (2009) studied the effect of introducing IP(3)-like molecules, referred to as partial agonists (PA), into the cell to determine the structure-function relationship between IP(3) and its receptor. Initial results suggest a competitive model, where IP(3) and PA fight for the same binding site. We extend the original eight-state model to a 12-state model in order to illustrate this competition, and perform a similar reduction to that of Li and Rinzel in the first modeling study we are aware of considering PA effect on an IP(3) receptor. Using this reduction we solve for the equilibrium open probability for calcium release in the model. We replicate graphs provided by the Rossi paper, and find that optimizing the subunit affinities for IP(3) and PA yields a good fit to the data. We plug our extended reduced model into a full cell model, in order to analyze the effects PA have on whole cell properties specifically the propagation of calcium waves in two dimensions. We conclude that PA creates qualitatively different calcium dynamics than would simply reducing IP(3), but that effectively PA can act as an IP(3) knockdown.