Hybrid automata as a unifying framework for modeling excitable cells

We propose Hybrid Automata (HA) as a unifying framework for computational models of excitable cells. HA, which combine discrete transition graphs with continuous dynamics, can be naturally used to obtain a piecewise, possibly linear, approximation of a nonlinear excitable-cell model. We first show how HA can be used to efficiently capture the action-potential morphology - as well as reproduce typical excitable-cell characteristics such as refractoriness and restitution - of the dynamic Luo-Rudy model of a guinea-pig ventricular myocyte. We then recast two well-known computational models, Biktashev's and Fenton-Karma, as HA without any loss of expressiveness. Given that HA possess an intuitive graphical representation and are supported by a rich mathematical theory and numerous analysis tools, we argue that they are well positioned as a computational model for biological processes.