Vagal Control of Sinoatrial Rhythm: a Mathematical Model

Model Status

This is the original unchecked version of the model imported from the previous CellML model repository, 24-Jan-2006.

Model Structure

Sinoatrial (SA) node cells have an inherent ability to generate a depolarising, unstable resting potential leading to automaticity. The rhythmic, electrical activity of the sinoatrial cells set the rate at which the entire heart beats, hence the sinoatrial node myocytes are referred to as the pacemaker cells. This cardiac pacemaker activity is under vagal control. The ionic mechanisms underlying the vagal inhibition of the cardiac pacemaker are the subject of investigation in a mathematical model published by Socrates Dokos, Branko Celler and Nigel Lovell (1996).

In this paper, the authors review the existing knowledge surrounding the vagal control of sinoatrial rhythm. It is known that following vagal stimulation, acetylcholine (ACh) is released into the parasympathetic neuroeffector junction, and then binds to muscarinic receptors on the plasma membrane of the SA node cells. This receptor-binding triggers membrane hyperpolarisation, and/or decreases the rate of pacemaker depolarisation, in turn prolonging the spontaneous cycle duration, and decreasing the rate of autorhythmic firing. The principal mechanism underlying this ACh-mediated inhibition of the cardiac pacemaker is an increase in the membrane permeability to K⁺. However, it has been suggested that the influence of ACh on other ion currents may also have a significant effect on pacemaker activity.

The focus of the Dokos et al. 1996 model was to gain a better understanding of the mechanisms underlying vagal control of the cardiac pacemaker. Their model was based on a wide range of electrophysiological data, and their aim was to reproduce these experimental results with their mathematical model. This model is an extension of their previously published mathematical model of the SA node (see Dokos et al., 1996). In this new model, the background potassium current i_b,K has been replaced by an ACh-activated potassium current i_K,ACh . In addition, the new model incorporates the influence of ACh on the other ionic currents, such as the inhibition of the hyperpolarisation-activated current i_f , and the inhibition of the L-type calcium current i_Ca,L .

Vagal control of pacemaker activity is modelled using a three compartment model describing ACh release and uptake in the neuroeffector junction (see the figure below). Upon vagal stimulus, ACh is released into the neuroeffector junction, activating i_K,ACh and inhibiting i_f and i_Ca,L .

The complete original paper reference is cited below:

Vagal Control of Sinoatrial Rhythm: a Mathematical Model, Socrates Dokos, Branko Celler, and Nigel Lovell, 1996, Journal of Theoretical Biology , 182, 21-44. (A PDF version of the article is available to subscribers of the Theoretical Journal of Biology.) PubMed ID: 8917735

A schematic diagram of the Dokos et al. 1996 mathematical model of vagal control of cardiac pacemaker activity.