Conductance-Based Phenomenological Nonspiking Model: A Dimensionless and Simple Model That Reliably Predicts the Effects of Conductance Variations on Nonspiking Neuronal Dynamics.

The modeling of single neurons has proven to be an indispensable tool in deciphering the mechanisms underlying neural dynamics and signal processing. In that sense, two types of single-neuron models are extensively used: the conductance-based models (CBMs) and the so-called phenomenological models, which are often opposed in their objectives and their use. Indeed, the first type aims to describe the biophysical properties of the neuron cell membrane that underlie the evolution of its potential, while the second one describes the macroscopic behavior of the neuron without taking into account all of its underlying physiological processes. Therefore, CBMs are often used to study "low-level" functions of neural systems, while phenomenological models are limited to the description of "high-level" functions. In this letter, we develop a numerical procedure to endow a dimensionless and simple phenomenological nonspiking model with the capability to describe the effect of conductance variations on nonspiking neuronal dynamics with high accuracy. The procedure allows determining a relationship between the dimensionless parameters of the phenomenological model and the maximal conductances of CBMs. In this way, the simple model combines the biological plausibility of CBMs with the high computational efficiency of phenomenological models, and thus may serve as a building block for studying both high-level and low-level functions of nonspiking neural networks. We also demonstrate this capability in an abstract neural network inspired by the retina and C. elegans networks, two important nonspiking nervous tissues.

A general pattern of non-spiking neuron dynamics under the effect of potassium and calcium channel modifications.

Electrical activity of excitable cells results from ion exchanges through cell membranes, so that genetic or epigenetic changes in genes encoding ion channels are likely to affect neuronal electrical signaling throughout the brain. There is a large literature on the effect of variations in ion channels on the dynamics of spiking neurons that represent the main type of neurons found in the vertebrate nervous systems. Nevertheless, non-spiking neurons are also ubiquitous in many nervous tissues and play a critical role in the processing of some sensory systems. To our knowledge, however, how conductance variations affect the dynamics of non-spiking neurons has never been assessed. Based on experimental observations reported in the biological literature and on mathematical considerations, we first propose a phenotypic classification of non-spiking neurons. Then, we determine a general pattern of the phenotypic evolution of non-spiking neurons as a function of changes in calcium and potassium conductances. Furthermore, we study the homeostatic compensatory mechanisms of ion channels in a well-posed non-spiking retinal cone model. We show that there is a restricted range of ion conductance values for which the behavior and phenotype of the neuron are maintained. Finally, we discuss the implications of the phenotypic changes of individual cells at the level of neuronal network functioning of the C. elegans worm and the retina, which are two non-spiking nervous tissues composed of neurons with various phenotypes.