A MULTIPLE TIMESCALE NETWORK MODEL OF INTRACELLULAR CALCIUM CONCENTRATIONS IN COUPLED NEURONS: INSIGHTS FROM ROM SIMULATIONS.

Abstract

In [16], the authors analyzed the synchronization features between two identical 3D slow-fast oscillators, symmetrically coupled, built as an extension of the FitzHugh–Nagumo dynamics generating Mixed-Mode Oscillations. The third variable, which is slow, represents the intracellular calcium concentration in neurons. Here, we consider an extension of this model in two directions. First, we consider heterogeneity among cells and analyze the coupling of two oscillators with different values for one parameter tuning the intrinsic frequency. We identify new patterns of antiphasic synchronization, with non-trivial signatures and that exhibit a Devil’s Staircase phenomenon in transitions. Second, we introduce a network of N cells divided into two clusters: the coupling between neurons in each cluster is excitatory, while between the two clusters is inhibitory. Such system models the interactions between neurons tending to synchronization in two subpopulations inhibiting each other, like ipsi- and contra-lateral motoneurons assemblies. To perform the numerical simulations when N is large, as an initial step towards the network analysis, we consider Reduced Order Models to save computational costs. We present the numerical reduction results in a network of 100 cells. To validate the numerical reduction method, we compare the outputs and CPU times obtained in different cases.