In this paper we introduce a novel cycle-linear hybrid-automata (CLHA) model for excitable cells that efficiently and accurately captures both action-potential morphology and typical excitable-cell characteristics such as refractoriness and restitution. To motivate the need for CLHA, we first show how to recast two well-known approximate models for excitable cells as hybrid automata (HA): the (piecewise) linear model of Biktashev and the nonlinear model of Fenton. We than show that our CLHA model combines the simplicity of the first with the expressiveness of the latter. CLHA are not restricted to excitable cells; they can be advantageously used to model any dynamic system that exhibits nonlinear, pseudo-periodic behavior. Moreover, HA in general, and CLHA in particular, are ideally suited as a computational model for any biological processes: (i) they possess a very intuitive graphical (and formal) representation, combining discrete transition graphs with continuous dynamics; (ii) they emerge in a natural way during the linearization (approximation) process of any nonlinear system; (iii) they posses a rich theory and a great variety of analysis tools.
IET Systems Biology (SYB), vol. 2(1), pp. 24-32, January, 2008.
*This work was supported by the NSF Faculty Early Career
Development Award CCR01-33583 and the NSF CCF05-23863 Award.