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Alternans of cardiac calcium cycling in a cluster of ryanodine receptors: a simulation study

¹Biological Physics Group, School of Physics and Astronomy, and ²Unit of Cardiac Physiology, School of Medicine, the University of Manchester, Manchester, United Kingdom

Submitted 19 September 2007 ; accepted in final form 23 May 2008

Mechanical alternans in cardiac muscle is associated with intracellular Ca²⁺ alternans. Mechanisms underlying intracellular Ca²⁺ alternans are unclear. In previous experimental studies, we produced alternans of systolic Ca²⁺ under voltage clamp, either by partially inhibiting the Ca²⁺ release mechanism, or by applying small depolarizing pulses. In each case, alternans relied on propagating waves of Ca²⁺ release. The aim of this study is to investigate by computer modeling how alternans of systolic Ca²⁺ is produced. A mathematical model of a cardiac cell with 75 coupled elements is developed, with each element contains L-type Ca²⁺ current, a subspace into which Ca release takes place, a cytoplasmic space, sarcoplasmic reticulum (SR) release channels [ryanodine receptor (RyR)], and uptake sites (SERCA). Interelement coupling is via Ca²⁺ diffusion between neighboring subspaces via cytoplasmic spaces and network SR spaces. Small depolarizing pulses were simulated by step changes of cell membrane potential (20 mV) with random block of L-type channels. Partial inhibition of the release mechanism is mimicked by applying a reduction of RyR open probability in response to full stimulation by L-type channels. In both cases, systolic alternans follow, consistent with our experimental observations, being generated by propagating waves of Ca²⁺ release and sustained through alternation of SR Ca²⁺ content. This study provides novel and fundamental insights to understand mechanisms that may underlie intracellular Ca²⁺ alternans without the need for refractoriness of L-type Ca or RyR channels under rapid pacing.

sarcoplasmic reticulum; computer modeling; diffusion; computer model

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