Abstract
Ventricular myocytes are excitable cells whose voltage threshold for action potential (AP) excitation is ∼-60 mV at which I(Na) is activated to give rise to a fast upstroke. Therefore, for a short stimulus pulse to elicit an AP, a stronger stimulus is needed if the resting potential lies further away from the I(Na) threshold, such as in hypokalemia. However, for an AP elicited by a long duration stimulus or a diastolic spontaneous calcium release, we observed that the stimulus needed was lower in hypokalemia than in normokalemia in both computer simulations and experiments of rabbit ventricular myocytes. This observation provides insight into why hypokalemia promotes calcium-mediated triggered activity, despite the resting potential lying further away from the I(Na) threshold. To understand the underlying mechanisms, we performed bifurcation analyses and demonstrated that there is a dynamical threshold, resulting from a saddle-node bifurcation mainly determined by I(K1) and I(NCX). This threshold is close to the voltage at which I(K1) is maximum, and lower than the I(Na) threshold. After exceeding this dynamical threshold, the membrane voltage will automatically depolarize above the I(Na) threshold due to the large negative slope of the I(K1)-V curve. This dynamical threshold becomes much lower in hypokalemia, especially with respect to calcium, as predicted by our theory. Because of the saddle-node bifurcation, the system can automatically depolarize even in the absence of I(Na) to voltages higher than the I(Ca,L) threshold, allowing for triggered APs in single myocytes with complete I(Na) block. However, because I(Na) is important for AP propagation in tissue, blocking I(Na) can still suppress premature ventricular excitations in cardiac tissue caused by calcium-mediated triggered activity. This suppression is more effective in normokalemia than in hypokalemia due to the difference in dynamical thresholds.