Biophysically based mathematical modeling of interstitial cells of Cajal slow wave activity generated from a discrete unitary potential basis

Model Status

This CellML model is known to run PCEnv. Because the model is in a CellML 1.1 format (as opposed to CellML 1.0) COR is unable to run the model. The units have been checked and they are consistent. Please note that the CellML model has been updated since the 2009 publication accccording the the first author's changes.

Model Structure

ABSTRACT: Spontaneously rhythmic pacemaker activity produced by interstitial cells of Cajal (ICC) is the result of the entrainment of unitary potential depolarizations generated at intracellular sites termed pacemaker units. In this study, we present a mathematical modeling framework that quantitatively represents the transmembrane ion flows and intracellular Ca2+ dynamics from a single ICC operating over the physiological membrane potential range. The mathematical model presented here extends our recently developed biophysically based pacemaker unit modeling framework by including mechanisms necessary for coordinating unitary potential events, such as a T-Type Ca2+ current, Vm-dependent K+ currents, and global Ca2+ diffusion. Model simulations produce spontaneously rhythmic slow wave depolarizations with an amplitude of 65 mV at a frequency of 17.4 cpm. Our model predicts that activity at the spatial scale of the pacemaker unit is fundamental for ICC slow wave generation, and Ca2+ influx from activation of the T-Type Ca2+ current is required for unitary potential entrainment. These results suggest that intracellular Ca2+ levels, particularly in the region local to the mitochondria and endoplasmic reticulum, significantly influence pacing frequency and synchronization of pacemaker unit discharge. Moreover, numerical investigations show that our ICC model is capable of qualitatively replicating a wide range of experimental observations.

In the study described here, Richard Faville et al. have developed a mathematical model of the ICC pacemaker potential. The model can be divided into two distinct components: the bulk cytoplasm and the pacemaker units. The later have been described previously (Faville et al., 2008, and the CellML description of this model can be found here). The pacemaker unit model quantitatively describes the transmembrane ion flows and intracellular Ca2+ dynamics from a single ICC pacemaker unit, and a schematic diagram of this model can be seen in the figure immediately below.

A schematic diagram of the pacemaker unit illustrating all the compartmental volumes and ionic conductances, together with their interactions.

The combined model is described here in CellML 1.1. The pacemaker unit is defined and is imported into the bulk cytoplasm 10 times (note that the number of pacemaker units that could be used within the modelling framework is completely arbitrary, however 10 appears to be the minimum number required to adequately describe the pacemaker potential depolarisation). In order to embed the pacemaker model within the bulk cytoplasm modelling framework the original pacemaker model had to be modified slightly. This is because the it was only representative of pacemaker activity near the resting membrane potential of -70mV. In its modified form and embedded within the bulk cytoplasm it is now capable of simulating pacemaker activity under conditions of membrane depolarisation (Vm > -60mV). A full schematic diagram of the combined model is illustrated in the figure below.

A full schematic diagram of the bulk cytoplasm model with the imported pacemaker units illustrating all the compartmental volumes and ionic conductances, together with their interactions.

The original paper reference is cited below:

Biophysically based mathematical modeling of interstitial cells of Cajal slow wave activity generated from a discrete unitary potential basis, R.A. Faville, A.J. Pullan, K.M. Sanders, S.D. Koh, C.M. Lloyd and N.P. Smith, 2009, Biophysical Journal, 96, 4834-4852. PubMed ID: 19527643