A mathematical model of pacemaker activity recorded from mouse small intestine
This CellML version of the model runs in both COR and PCEnv. Although the model produces pacemaker potentials, there are discrepancies between the original and the CellML model - including a different behaviour at the resting membrane potential and a different frequency of generation of slow waves. The units have been checked and are consistent. We'd like to acknowledge Nandita Carvalho for providing us with access to her Matlab code, which played a critical role in the process of successfully translating the model into CellML. Also Alberto Corrias for his feedback on the CellML model
Phasic gastrointestinal (GI) muscle is able to autonomously generate rhythmic contractions independent of the enteric nervous system. The electrical activity that generates these rhythmic contractions are called slow waves, or pacemaker potentials (PP), and they are produced by a specialised group of pacemaker cells called Insterstitial Cells of Cajal (ICC). Pacemaker potentials pass via gap junctions from the ICC to smooth muscle cells (SMC), activating L-type Ca2+ channels, Ca2+ influx and the contraction of the SMC.
In the study described here, Jae Boum Youm et al. have developed a mathematical model which quantitatively describes the transmembrane ion flows and intracellular Ca2+ dynamics from a single ICC pacemaker unit. The model includes seven major currents that flow across the ICC membrane to transport three ions, Na+, Ca2+ and K+ (see the figure below). These currents include: the inward rectifier current (Ik1), L-type Ca2+ current (ICaL), voltage-dependent and dihydropyridine-resistant current (IVDDR), autonomous inward current. (IAI), Na+/Ca2+ exchanger current, (INaCa), Na+/K+ pump current (INaK), and the plasmalemmal Ca2+ pump current (IPMCA).
It should be noted that the model described here in CellML is not identical to the published model. Instead, it represents the working model written in Matlab by Nandita Carvalho, who carried out an extensive literature review and had personal correspondence with the author of the original model Jae Boum Youm. On comparison, the final model was able to replicate experimental results and hence it was used to make predictions of slow wave characteristics of the small intestine.
|A schematic diagram of the cell model. There are 7 membrane currents. IVDDR is known to be responsible for propagation and its influx into the cell causes a slight depolarisation which increases the probability of Ca2+release from th SR through IP3-gated channels. This further depolarises the cell causing an influx of ions into the cell (via the pacemaker current IAI), which the initiates the slow wave.|
The complete original paper reference is cited below:
A mathematical model of pacemaker activity recorded from mouse small intestine, Jae Boum Youm, Nari Kim, Jin Han, Euiyong Kim, Hyun Joo, Chae Hun Leem, Gazunori Goto, Akinori Noma, and Yung E. Earm, 2006, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences , 364, 1135-1154. (Full text and PDF versions of the article are available to journal subscribers on the Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences website.) PubMed ID: 16608700