Role of ryanodine receptor cooperativity in Ca²⁺-wave-mediated triggered activity in cardiomyocytes

Ca²⁺ waves are known to trigger delayed after-depolarizations that can cause malignant cardiac arrhythmias. However, modelling Ca²⁺ waves using physiologically realistic models has remained a major challenge. Existing models with low Ca²⁺ sensitivity of ryanodine receptors (RyRs) necessitate large release currents, leading to an unrealistically large Ca²⁺ transient amplitude incompatible with the experimental observations. Consequently, current physiologically detailed models of delayed after-depolarizations resort to unrealistic cell architectures to produce Ca²⁺ waves with a normal Ca²⁺ transient amplitude. Here, we address these challenges by incorporating RyR cooperativity into a physiologically detailed model with a realistic cell architecture. We represent RyR cooperativity phenomenologically through a Hill coefficient within the sigmoid function of RyR open probability. Simulations in permeabilized myocytes with high Ca²⁺ sensitivity reveal that a sufficiently large Hill coefficient is required for Ca²⁺ wave propagation via the fire-diffuse-fire mechanism. In intact myocytes, propagating Ca²⁺ waves can occur only within an intermediate Hill coefficient range. Within this range, the spark rate is neither too low, enabling Ca²⁺ wave propagation, nor too high, allowing for the maintenance of a high sarcoplasmic reticulum load during diastole of the action potential. Moreover, this model successfully replicates other experimentally observed manifestations of Ca²⁺-wave-mediated triggered activity, including phase 2 and phase 3 early after-depolarizations and high-frequency voltage-Ca²⁺ oscillations. These oscillations feature an elevated take-off potential with depolarization mediated by the L-type Ca²⁺ current. The model also sheds light on the roles of luminal gating of RyRs and the mobile buffer ATP in the genesis of these arrhythmogenic phenomena. KEY POINTS: Existing mathematical models of Ca²⁺ waves use an excessively large Ca²⁺-release current or unrealistic diffusive coupling between release units. Our physiologically realistic model, using a Hill coefficient in the ryanodine receptor (RyR) gating function to represent RyR cooperativity, addresses these limitations and generates organized Ca²⁺ waves at Hill coefficients ranging from ∼5 to 10, as opposed to the traditional value of 2. This range of Hill coefficients gives a spark rate neither too low, thereby enabling Ca²⁺ wave propagation, nor too high, allowing for the maintenance of a high sarcoplasmic reticulum load during the plateau phase of the action potential. Additionally, the model generates Ca²⁺-wave-mediated phase 2 and phase 3 early after-depolarizations, and coupled membrane voltage with Ca²⁺ oscillations mediated by the L-type Ca²⁺ current. This study suggests that pharmacologically targeting RyR cooperativity could be a promising strategy for treating cardiac arrhythmias linked to Ca²⁺-wave-mediated triggered activity.