Experimental bifurcation analysis of neurons using control-based continuation

The behaviour of biological systems is governed by a wide range of complex phenomena that are intrinsically nonlinear and interact on different time and spatial scales. Mathematical modelling currently plays a central role in understanding the dynamic behaviour of these nonlinear systems. Take, for example, neuron models that are studied to unveil the bifurcations underlying the cell's bursting behaviour [1]. The major caveat with this approach is that discovered bifurcations and other nonlinear features critically depend on the model assumptions (i.e. captured physics) and the model parameter values identified experimentally. As of now, there exist no experimental method that can directly measure nonlinear dynamic features such as bifurcations directly in biological experiments.
Pioneered at Bristol, control-based continuation (CBC) is a non-parametric method that maps out the dynamic features of a nonlinear physical system directly during experimental tests, without relying on the estimation of the parameters of a mathematical model, or a particular model structure. Combining feedback control with numerical continuation algorithms, CBC modifies, on-line, the input applied to the system in order to isolate the nonlinear behaviour of interest. In this way, CBC offers the best conditions to analyse these dynamic features in detail, to follow them as experimentally-controllable parameters are changed, and to detect and track boundaries between qualitatively different types of behaviour (i.e. bifurcations). The fundamental principles of CBC are well established, and the method has been applied to a wide range of non-living (i.e. electro-mechanical) systems. For instance, the method was recently demonstrated by LR on a multi-degree-of-freedom structure exhibiting complex nonlinear phenomena such as mode interaction, quasi-periodic oscillations and isolated response curves [2-3]. CBC proved able to extract dynamic features of the system such as curves of limit-point bifurcations that are key to the understanding of its behaviour (hysteresis, multi-stability, etc.).
This PhD project aims to further develop CBC such that it can be applied to neurons and exploited to experimentally characterise their bursting dynamics.