Sneyd, Tsaneva-Atanasova, Bruce, Straub, Giovannucci, Yule, 2003

Model Status

This model contains partial differentials and as such can not currently be solved by existing CellML tools.

Model Structure

Exocrine cells display morphological and functional polarity, which allows distinct physiological processes to occur in specific regions of the cell. Many of these processes are triggered by an increase in the concentration of cytosolic calcium ([Ca²⁺]_i). Calcium waves can spread across the whole cell, or remain isolated in the apical region, and calcium oscillations can take on several different shapes. Underlying the wide variety of observed responses, acinar cells possess a wide variety of calcium handling mechanisms, including inositol trisphosphate receptors (IPR), ryanodine receptors (RyR), and mitochondria. In addition, these mechanisms have well defined spatial distributions which correlate with the spatial characteristics of the observed calcium waves and oscillations.

Although there is a vast amount of experimental data, the exact mechanisms underlying Ca²⁺ wave propagation in an acinar cell remain unknown. In their 2003 paper described here, Sneyd et al. develop a mathematical model of Ca²⁺ wave propagation in pancreatic and parotid acinar cells. Their aim is to better understand the variety of Ca²⁺ waves and their underlying mechanisms.

Due to the complexity of acinar cells, their model is broken down into five detailed sub-models:

• The IPR model which is based on Sneyd and Dufour, A Dynamic Model of the Type-2 Inositol Triphosphate Receptor, 2002 (see below);

• The RyR model which is based on Keizer and Levine, RyR Adaptation and Ca²⁺ Oscillations, 1996 (see below);

• The two models combined in a whole-cell model (see below);

• The spatial model;

and

• Mitochondrial transport which is based on Colegrove et al., Quantitative Analysis of Mitochondrial Ca²⁺ Uptake and Release Pathways in Sympathetic Neurons, 2000.

The principal prediction from the model is that there are two different ways in which calcium waves propagate in acinar cells: at low agonist concentration the wave is propagated by the diffusion of Ca²⁺ between release sites; at higher agonist concentrations the basal region of the cell responds later than the apical region, creating a wave which is independent of Ca²⁺ diffusion.

The complete original paper reference is cited below:

A Model of Calcium Waves in Pancreatic and Parotid Acinar Cells, J. Sneyd, K. Tsaneva-Atanasova, J. I. E. Bruce, S. V. Straub, D. R. Giovannucci, and D. I. Yule, 2003, Biophysical Journal , 85, 1392-1405. (Full text (HTML) and PDF versions of the article are available on the Biophysical Journal website.) PubMed ID: 12944257

A simplified diagram of the IPR model, where R represents the free receptor, O is the open state of the channel, A is the activated state of the channel and I1, I2, and S are three inactive states.

Schematic diagram of transitions among the four states of the RyR used to describe adaptation. States C1 and C2 are closed states and O1 and O2 represent open states, assumed to have the same single-channel conductance. The k are rate constants: only steps a and b are Ca2+ dependent.

Schematic of the model indicating Ca2+ compartmentation in the extracellular matrix, cytosol and the ER and pathways for Ca2+ ion movement between the compartments.