Abstract
Neural synchronization is a basic functioning principle of the nervous system resulting from the coupling between the activities of different neurons. Recent advances in optical imaging have provided evidence that calcium activities measured in-vivo, as in motoneurons of zebrafish embryos, exhibit characteristic synchronized behaviors in the spinal cord. The data reveal a very strong synchronization of the oscillations in intracellular calcium levels between motoneurons located on the left and right side of the spinal cord respectively, while the activity profiles of these two clusters feature ‘‘antiphasic’’ properties: no calcium peak occur simultaneously in both clusters. A natural interpretation of these data points out the existence of an excitatory intra-cluster coupling and an inhibitory inter-cluster coupling. To study theoretically the synchronization properties in oscillatory patterns of intracellular calcium concentrations (ICC) between peripheral neurons, we have first built a compact slow-fast model of ICC dynamics in one cell taking particular advantage of the Mixed-Mode Oscillations feature for reaching the quiescence/active phase duration ratio and peak amplitude. While considering two coupled oscillators for representing the activity of clusters of strongly synchronized neurons is an oversimplification of the real network phenomenon, its simplicity allows us to perform singular perturbation analysis and study, at an aggregated level, the fundamental properties of the system in a formal way, both for inhibitory and excitatory coupling. I will present the analysis of the underlying dynamical mechanisms of synchronization of this coupled model, emphasize the role of MMOs and heterogeneity in parameter values among cells in the variability of behaviours and discuss the transition mechanisms between behaviors. Therefore I will explain a protocol of parameter estimation to reproduce all the qualitative properties observed in the experimental data with a clustered network model with mixed (inhibitory and excitatory) coupling types.