We present an approach based on hybrid automata (HA), which combine discrete transition graphs with continuous dynamical systems, to modeling complex biological systems. Our goal is to efficiently capture the behavior of excitable cells previously modeled by systems of nonlinear differential equations. In particular, we derive HA models from the Hodgkin-Huxley model of the giant squid axon, the Luo-Rudy dynamic model of a guinea pig ventricular cell, and a model of a neonatal rat ventricular myocyte. Our much simpler HA models are able to successfully capture the action-potential morphology of the different cells, as well as reproduce typical excitable cell characteristics, such as refractoriness (period of non-responsiveness to external stimulation) and restitution (adaptation to pacing rates). To model electrical wave propagation in a cell network, the single-cell HA models are linked to a classical 2D spatial model. The resulting simulation framework exhibits significantly improved computational efficiency in modeling complex wave patterns, such as the spiral waves underlying pathological conditions in the heart.
In Proc. of CMSB'05, Computational Methods in Systems Biology Workshop, April 2005, Edinburgh, UK.
*R. Grosu and P. Ye were partially supported by the NSF Faculty Early Career
Development Award CCR01-33583.