Learning Cycle-Linear Hybrid Automata for Excitable Cells.*

R. Grosu, S. Mitra, P. Ye, E. Entcheva, IV Ramakrishnan and S.A. Smolka

We show how to automatically learn the class of Hybrid Automata called Cycle-Linear Hybrid Automata (CLHA) in order to model the behavior of excitable cells (ECs). Such cells, whose main purpose is to amplify and propagate an electrical signal called the action potential (AP), serve as the ``biologic transistors'' of living organisms. The learning algorithm we propose comprises the following three phases: (1) Geometric analysis of the APs in the training set is used to identify, for each AP, the modes and switching logic of the corresponding Linear Hybrid Automata (LHA). (2) For each mode, the modified Prony's method (MPM) is used to learn the coefficients of the associated linear flows. (3) MPM is once again applied to the parameters of the LHA obtained in the first two phases to learn a CLHA. Our results show that the learned CLHA is able to successfully capture AP morphology and other important EC properties, such as refractoriness and restitution, up to a prescribed approximation error. Our approach is fully implemented in MATLAB and, to the best of our knowledge, provides the most accurate approximate model for ECs to date.

Submitted to HSCC'06, the 10th International Conference on Hybrid Systems: Computation and Control, Pisa, Italy, 2007.

*This work was partially supported by the NSF Faculty Early Career Development Award CCR01-33583 and the NSF CCF05-23863 Award.