Dynamics in Cortical Neurons: Regulation of cAMP-induced MMOs

Recent experimental findings (Lezmy et al. 2021) demonstrated that increases in cAMP intracellular concentration lead to alteration of the electrical activity of cortical neurons with the generation of mixed-mode oscillations (MMOs). Researchers justified the emergence of these complex temporal evolutions through the sole cAMP-activation of HCN channels. We propose a five-dimensional model, based on a previous model of cortical neurons presented by Lezmy and colleagues, which replicates the patch-clamp recordings faithfully and extends the experimental hypothesis by supporting that it is the cooperation of HCN and M channels to promote the generation of MMOs. Thanks to its multiple-time scale structure, we studied the generation mechanism of MMO via three- and four-dimensional reductions. The former provides insights regarding the source of MMO, which is folded node- or singular Hopf bifurcation-based, depending on the activation levels of HCN and M channels. However, the geometrical properties of the three-dimensional reduction cannot explain the sequences of small and large amplitude oscillations of the five-dimensional model temporal series. For this reason, we studied a four-dimensional model reduction, which reconstructs the MMO organisation perfectly and helps to prove that the discrepancies observed in the lower-dimensional case are associated with the perturbation of the singular strong canard surface.