Exploring the bifurcations of excitable cells with control-based continuation #

Mark Blyth, Krasimira Tsaneva-Atanasova, Kyle Wedgwood, Lucia Marucci, Ludovic Renson

11:10 Tuesday in 2Q50/51.

Part of the Neurodynamics session.

Abstract #

Control-based continuation is a hybrid numerical and experimental method for performing a bifurcation analysis on a physical system. Feedback controllers are used to identify and stabilise intrinsic dynamics of a system, without the need for a model. Numerical continuation is applied to the located features to trace out solution families. Here we discuss experimental work, performed in conjunction with collaborators from Exeter, where equilibrium curves of an excitable cell are unveiled with CBC. The cells of interest show complex voltage dynamics, as a result of nonlinear ion conductances. As a parameter is varied, the membrane potentials can exhibit limit cycles and equilibria, separated by with bifurcations. The presence or absence of fold bifurcations in the solution manifold indicate the excitability class of the cell. We will describe work towards developing an experimental protocol whereby extracellular solutions and dynamic clamp are used to modify the excitability of a cell. The resulting change in cellular excitability will be demonstrated through control-based continuation. This explicitly links the bifurcation-theoretic approach of mathematical communities with standard electrophysiology tools from the biological communities. Future directions for CBC-electrophysiology will be discussed.