Mathematical simulations of the effects of altered AMP-kinase activity on I and the action potential in rat ventricle

Alterations in the activity of a so-called "metabolic switch" enzyme, adenosine monophosphate-activated protein kinase (AMP kinase), in mammalian heart contribute to the conduction abnormalities and rhythm disturbances in the settings of Wolff-Parkinson-White syndrome and ventricular pre-excitation. A recent study by Light et al. has shown that augmented AMP kinase activity can alter the biophysical properties of mammalian cardiac sodium currents. These experiments involved an electrophysiological analysis following heterologous expression of human Na(v)1.5 in tsA201 cells. Constitutive activation of AMP kinase followed by co-transfection caused: (i) a hyperpolarizing shift in the activation curve for I(Na), (ii) a small change in the voltage dependence of steady-state inactivation, and (iii) a significant slowing in the rate of inactivation of I(Na). We have attempted to simulate these results using our mathematical model of the membrane action potential of the adult rat ventricular myocyte. The changes in I(Na) produced by AMP kinase activation and/or overexpression can be reconstructed mathematically by altering two rate constants in a Markovian model that governs the I(Na) kinetics. Simulated macroscopic I(Na) records in which a fraction (10-100%) of the Na(+) channels had the appropriate rate constants for two state-dependent transitions increased by a factor of 100-fold exhibited: (i) slowed inactivation, (ii) a shift in steady-state activation to more hyperpolarized membrane potentials, and (iii) a very small change in the voltage dependence of steady-state inactivation. Thus, straightforward modifications of a previously published kinetic scheme for the time and voltage dependence of mammalian heart I(Na), when incorporated into a mathematical model for the rat ventricular action potential can reproduce the main features of these AMP kinase-induced modifications in I(Na) in mammalian ventricle. Ongoing mathematical simulations are directed toward developing formulations that mimic the molecular mechanisms for the AMP kinase effects, e.g., changes in the kinetics of I(Na) resulting from selective phosphorylation/dephosphorylation of sites on the alpha or beta subunits which comprise human Na(v)1.5. Thereafter, incorporation of these changes into a mathematical model for the action potential of the human ventricular myocyte is planned.