On the Modeling of the Three Types of Non-spiking Neurons of the Caenorhabditis elegans

Abstract

The nematode Caenorhabditis elegans (C. elegans) is a well-known model organism in neuroscience. The relative simplicity of its nervous system, made up of few hundred neurons, shares some essential features with more sophisticated nervous systems, including the human one. If we are able to fully characterize the nervous system of this organism, we will be one step closer to understanding the mechanisms underlying the behavior of living things. Following a recently conducted electrophysiological survey on different C. elegans neurons, this paper aims at modeling the three non-spiking RIM, AIY and AFD neurons (arbitrarily named with three upper case letters by convention). To date, they represent the three possible forms of non-spiking neuronal responses of the C. elegans. To achieve this objective, we propose a conductance-based neuron model adapted to the electrophysiological features of each neuron. These features are based on current biological research and a series of in-silico experiments which use differential evolution to fit the model to experimental data. From the obtained results, we formulate a series of biological hypotheses regarding currents involved in the neuron dynamics. These models reproduce experimental data with a high degree of accuracy while being biologically consistent with state-of-the-art research.

Systematic generation of biophysically detailed models with generalization capability for non-spiking neurons

“…this paper), it has not only been shown to be an effective method [16,34], but also superior to other optimization methods such as genetic algorithms, simulated annealing and particle swarm optimization algorithm in terms of convergence speed, simulation time, and minimization of the cost function [35].…”

“…For instance, a large number of ion channels have been identified in non-spiking retinal networks [26]. Regarding the C. elegans neurons, there is extensive biological evidence (refer to [16] and references therein) supporting the existence of calcium, inwardly rectifying potassium and potassium channels. In more detail, C. elegans genome sequencing [27], electrophysiological measurements [7], and calcium imaging [28,29], combined with a series of in-silico experiments, identified the most suitable models for electrophysiology of RIM, AIY and AFD neurons [16] that we use in this paper as base models.…”

“…CBMs have become one of the most powerful computational approaches for characterizing the behavior of neurons [16]. In simple terms, a CBM is a biophysical representation of a neuron in which the ion channels are represented by conductances and the polar membrane by a capacitor [17,18].…”

A Simple Model of Nonspiking Neurons

“…With respect to voltage dynamics, classic simple spiking models are unfortunately unable to produce adequate non-spiking dynamics due to the topology of their phase space. In this paper, we present a simple suitable model derived from the bifurcation study of non-spiking conductance-based models, extensively used to characterize such behaviors (Kamiyama et al, 2009;Kourennyi et al, 2004;Naudin et al, 2020;Naudin et al, 2022;Nicoletti et al, 2019;Publio et al, 2006), which is able to qualitatively reproduce the two standard voltage dynamics of non-spiking neurons: near-linear and bistable. The near-linear behavior is defined by a smooth depolarization or hyperpolarization from the resting potential, while the bistable one is characterized by nonlinear transitions between the resting potential and a depolarized potential.…”

“…Finally, we compare the computational efficiency of the proposed model with respect to conductance-based models developed in Naudin et al (2020) for the same RIM, AIY and AFD neurons, as well as many additional neuron models. In particular, we show that the computational efficiency of the proposed model is of the same order of magnitude as the integrate-and-fire and Izhikevich models that are the most computational efficient neuron models to date (Izhikevich, 2003).…”