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Controllability of Excitable Systems

Controllability of Excitable Systems

**Mark Pernarowski **

Department of Mathematical Sciences

Montana State University

pernarow@sparx.math.montana.edu

Mathematical models of cell electrical activity typically consist of a current balance equation, channel activation (or inactivation) variables and concentrations of regulatory agents. These models can be thought of as nonlinear filters whose input is some applied current I (possibly zero) and output is a membrane potential V. A natural question to ask is if the applied current I can be deduced from the potential V. For a class of quasilinear models the answer to this question is shown to be yes. A procedure for determining the inverse of the nonlinear filter is described and then demonstrated on two models. First, the procedure is demonstrated on the FitzHugh-Nagumo model. Next, the procedure is used to deduce model parameters from real experimental data in a model of bursting electrical activity in the pancreatic beta cell. The main advantage of this correlation technique is that only derivative information of the measured potential is needed to find parameter estimates.