4.6 Article

Biological emergent properties in non-spiking neural networks

Journal

AIMS MATHEMATICS
Volume 7, Issue 10, Pages 19415-19439

Publisher

AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/math.20221066

Keywords

complex network; neural network; neuron model; non-spiking neurons; bifurcation dynamics; Caenorhabditis elegans; retina

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The goal of this paper is to better understand the emergence of non-spiking neuron behavior through the analysis of mathematical models. The study suggests that the up-and down-states in non-spiking neurons may be driven by bistable presynaptic neurons, rather than the intrinsic properties of the neurons themselves.
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.

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