Defining new insight into fatal human arrhythmia: a mathematical analysis

Background: Normal cardiac excitability depends upon the coordinated activity of ion channels and transporters. Mutations in genes encoding ion channels affecting their biophysical properties have been known for over twenty years as a root cause of potentially fatal human electrical rhythm disturbance (arrhythmias). More recently, defects in ion channel associated protein (e.g. adapter, regulatory, cytoskeletal proteins) have been shown to cause arrhythmia. Mathematical modeling is ideally suited to integrate large volumes of cellular and in vivo data from human patients and animal disease models with the over goal of determining cellular mechanisms for these atypical human cardiac diseases that involve complex defects in ion channel membrane targeting and/or regulation. Methods and Results: Computational models of ventricular, atrial, and sinoatrial cells were used to determine the mechanism for increased susceptibility to arrhythmias and sudden death in human patients with inherited defects in ankyrin-based targeting pathways. The loss of ankyrin-B was first incorporated into detailed models of the ventricular myocyte to identify the cellular mechanism for arrhythmias in human patients with loos-of-function mutations in ANK2 (encodes ankyrin-B). Mathematical modeling was used to identify the cellular pathway responsible for abnormal Ca2+ handling and cardiac arrhythmias in ventricular cells. A multi-scalar computational model of ankyrin-B deficiency in atrial and sinoatrial cells and tissue was then developed to determine the mechanism for the increased susceptibility to atrial fibrillation in these human patients. Finally, a state-based Markov model of the voltage-gated Na+ channel was incorporated into a ventricular cell model and parameter estimation was performed to determine the mechanism for a new class of human arrhythmia variants that confer susceptibility to arrhythmia by interfering with a regulatory complex comprised of a second member of the ankyrin family, ankyrin-G. Conclusions: Ca2+ accumulation was observed at baseline in the ankyrin-B deficient ventricular model, with pro-arrhythmic spontaneous release and afterdepolarizations in the presence of simulated â-adrenergic stimulation, consistent with the finding of catecholaminergic-induced arrhythmias in human patients. The simulations demonstrated that loss of membrane Na+/Ca2+ exchanger and Na+-K+-ATPase contributed to Ca2+ overload and afterdepolarizations, with loss of Na+/Ca2+ exchanger as the dominant mechanism. In the atrial model of ankyrin-B deficiency, the loss of the L-type Ca2+ channel targeting was identified as the dominant mechanism for the initiation of atrial fibrillation. Finally, the simulations showed that human variants affecting ankyrin-G dependent regulation of NaV1.5 results in arrhythmia by mimicking the phosphorylation of the channel. Most importantly, mathematical modeling has been used to the molecular mechanism underlying human arrhythmia syndromes.