Bindschadler, Sneyd, 2001

Model Status

This model is able to produce oscillating output similar to that shown in figures from the publication. ValidateCellML verifies this model as valid CellML, with fully consistent units.

Model Structure

Intracellular calcium waves occur in a range of different cell types, including epithelial cells, hepatocytes, and pancreatic acinar cells. They are an important means of communication between cells and they allow neighbouring cells to coordinate their behaviour. There are a number of different molecular mechanisms underlying the calcium waves, and these fall into two main categories:

• The first mechanism occurs in cells which are able to respond to an increase in intracellular calcium (which maybe released through the gap junctions of neighbouring cells) by the release of a large amount of additional calcium from the intracellular stores (such as the endoplasmic reticulum). These cells are able to form connections, becoming a single excitable medium, able to actively propagate a calcium wave. Given a pacemaker cell oscillating with sufficient amplitude, each oscillation of the pacemaker could send out a wave, resulting in a series of waves travelling across the cells. Such a mechanism is relatively easy to describe with a mathematical model.

• The second method arises if each cell has an autonomous oscillator but it is coupled to its neighbours by the diffusion of a signal molecule. This then allows the individual oscillations to be coordinated by the coupling into the period waves that traverse the field of cells. There is evidence to suggest that this is the mechanism which underlies the calcium waves in pancreatic acinar cells and hepatocytes.

In the Bindschadler and Sneyd 2001 publication described here, the authors use a mathematical model based on the intracellular calcium dynamics of pancreatic acinar cells to study the behaviour of two oscillating cells that are coupled by the diffusion of calcium through gap junctions. A schematic diagram of one cell in the mathematical model can be seen in the figure below. Using model simulation results, the authors find that several periodic behaviours arise, including in-phase oscillations, anti-phase oscillations, and oscillations of different amplitudes.

The complete original paper reference is cited below:

A bifurcation analysis of two coupled calcium oscillators, Michael Bindschadler and James Sneyd, 2001, CHAOS , 11, 237-246. (A PDF version of the article is available to subscribers on the CHAOS website.) PubMed ID: 12779457