Biological emergent properties in non-spiking neural networks

A central goal of neuroscience is to understand the way nervous systems work to produce behavior. Experimental measurements in freely moving animals (e.g. in the C. elegans worm) suggest that ON- and OFF-states in non-spiking nervous tissues underlie many physiological behaviors. Such states are defined by the collective activity of non-spiking neurons with correlated up- and down-states of their membrane potentials. How these network states emerge from the intrinsic neuron dynamics and their couplings remains unclear. In this paper, we develop a rigorous mathematical framework for better understanding their emergence. To that end, we use a recent simple phenomenological model capable of reproducing the experimental behavior of non-spiking neurons. The analysis of the stationary points and the bifurcation dynamics of this model are performed. Then, we give mathematical conditions to monitor the impact of network activity on intrinsic neuron properties. From then on, we highlight that ON- and OFF-states in non-spiking coupled neurons could be a consequence of bistable synaptic inputs, and not of intrinsic neuron dynamics. In other words, the apparent up- and down-states in the neuron's bimodal voltage distribution do not necessarily result from an intrinsic bistability of the cell. Rather, these states could be driven by bistable presynaptic neurons, ubiquitous in non-spiking nervous tissues, which dictate their behaviors to their postsynaptic ones.