VAGAL CONTROL OF SINOATRIAL RHYTHM - A MATHEMATICAL-MODEL

The ionic mechanisms underlying vagal control of the cardiac pacemaker were investigated using a new single cell mathematical model of sinoa trial node electrical activity. The model was formulated from a wide r ange of electrophysiological data available in the literature, with pa rticular reference to whole cell recordings from enzymatically isolate d sinoatrial node cells. Development of the model was prompted by the lack of an existing physiologically accurate formulation of sinoatrial node activity that could reproduce the known complex chronotropic res ponse of the pacemaker to brief-burst vagal stimulation, as observed i n whole animal and isolated sinus node preparations. Features of the m odel include the dynamic modulation of the hyperpolarisation-activated current (i(f)) and the L-type calcium current (i(Ca,L)) by acetylchol ine, the improved characterisation of the muscarinic potassium current (i(K,ACh)), assigning the entire background potassium current (i(b,K) ) to spontaneous openings of its channels, and the utilisation of seco nd order kinetics for acetylcholine within the neuroeffector junction. Simulations performed using brief vagal stimuli elicited a strong hyp erpolarisation of the membrane which prolonged the cycle in which it w as delivered in a phase-dependent manner. This phase-dependency was pr esented in the form of a standard phase response curve which was chara cterised by a positive linear slope region, a breakpoint characteristi c and a ''no effect'' zone in which the vagal pulse could no longer pr olong the cycle. The breakpoint was manifested as a discontinuity in t he curve which was examined by bracketing this point at the limit of t he double precision arithmetic employed. At these boundary points on e ither side of the breakpoint, the vagal stimulus was able to activate outward i(K,ACh) in such a manner as to finely balance the increasing inward i(Ca,L) trying to generate phase 0 upstroke. On decay of i(K,AC h), the membrane either subsequently repolarised or fired to produce a n action potential depending on the precise phase of the stimulus. The positive linear slope portion of the PRC was characterised by a stron g resetting type behaviour in which the membrane hyperpolarised to app roximately the same value, irrespective of the phase of stimulus deliv ery. For vagal stimulus bursts applied throughout the ''no effect'' zo ne, outward i(K,Ach) was not sufficiently activated in order to overco me the strong inward drive of i(Ca,L) and could not prevent upstroke o ccurring. For these vagal stimuli, the subsequent cycle was hyperpolar ised and prolonged. The size of the ''no effect'' zone was directly re lated to the inherent latency incorporated in the activation character istic of i(K,ACh). In contrast to previous models of vagal pacemaker c ontrol, our new model was able to reproduce the classical triphasic ch ronotropic response to brief vagal stimulation characterised by a prim ary inhibition response, a postinhibitory rebound and a secondary inhi bition response. In particular, the postinhibitory rebound was due to activation of the inward hyperpolarisation-activated current by the va gally-induced membrane hyperpolarisation, whilst the secondary inhibit ion phase resulted from the inhibition of the hyperpolarisation-activa ted current by acetylcholine. The model suggests that the complex chro notropic responses of the cardiac pacemaker to brief vagal stimulation arises from inherent ionic mechanisms operating within the sinoatrial node. (C) 1996 Academic Press Limited