Modeling the response to external stimuli of the zebrafish’s optic tectum neurons with avalanche-like spontaneous activity

Previous studies found that the zebrafish spontaneous whole-brain neuronal dynamics, obtained with Ca2+ imaging, is avalanche-like, i.e., it has alternating periods of silence and collective cascading activity bursts, where both the duration of the bursts and the number of neurons that spiked during those bursts follow power law distributions with exponents close to the random field Ising universality class, but which deviate from their critical values for avalanches occurring when there is an unbalance between excitatory (E) and inhibitory (I) activity. Here, we model the response of the zebrafish neurons in the optic tectum, displaying avalanche dynamics in spontaneous activity, to an external stimulus, aiming to see whether the power law exponents change or if the dynamics is no longer avalanche-like, and how this is related to E/I unbalances. For this, we simulated the avalanche dynamics of a network of excitatory and inhibitory stochastic neurons with the stochastic Wilson-Cowan model, taking the connectivity matrix as function of data of the position of neurons in the optic tectum, and we found values of the parameters of the model that reproduce the experimental power law exponents. Then, we varied the value of the parameter representing the external input to neurons, e.g., an optogenetic stimulus, for various proportions of stimulated E or I neurons. We found that as the stimulus to the E neurons grows, the inhibition maintains the E/I balance and that avalanches get longer, until reaching a Poissonian regime. On the other hand, an increasing stimulus to the I neurons shortens avalanches and the E/I ratio, until E neurons get totally inhibited. Surprisingly, for reasonably high but balanced stimulus to E and I neurons, avalanche dynamics remains unchanged