Mathematical modelling of gastrointestinal tract celluar pacemaker activity

Abstract

This thesis presents research that was conducted to develop a biophysically-based mathematical modelling framework representing the biophysical activity produced by the pacemaker cell for the gastrointestinal tract; the Interstitial Cells of Cajal (ICC). The model framework was based upon the physiological mechanisms proposed by the leading hypothesis of ICC pacemaker activity, which is termed in this work as the Sanders' Hypothesis. The ICC model introduced in this thesis is split up into two separate frameworks; 1) the pacemaker unit model, and 2) the slow wave model. The pacemaker unit model is representative of the complex sub-cellular Ca2+ handling mechanisms that are responsible for the activation of the pacemaker conductance; a Ca2+-inhibited non-selective cation conductance. Solutions of the pacemaker unit model produces spontaneously rhythmic unitary potential depolarisations with an amplitude of approximately 3 m V with a half-width of 0.21 s. The pacemaker unit model predicts that the pacemaker conductance is activated by depletion of sub-plasma membrane [Ca2+] caused by Sarco-Endoplasmic Reticulum Calcium ATPase Ca2+ sequestration. Furthermore, pacemaker activity predicted by the pacemaker unit model persists under simulated voltage clamp and is independent of [IP3] oscillations. The slow wave model extends the pacemaker unit modelling framework by including mechanisms necessary for coordinating unitary potential events, such as a T-type Ca2+ current, voltage-dependent K+ currents, and global Ca2+ diffusion. Solving the slow wave model equations produce spontaneously rhythmic membrane potential depolarisations with an amplitude of 65 m V at a frequency of 17.4 cycles min-1. Analysis of the whole cell 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 synchronisation of pacemaker unit discharge. Moreover, numerical investigations show that the whole cell model is capable of qualitatively replicating a wide range of experimental observations, such as voltage clamp, conductance block and dose-response simulations.