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.

A Simple Model of Nonspiking Neurons.

Due to the ubiquity of spiking neurons in neuronal processes, various simple spiking neuron models have been proposed as an alternative to conductance-based models (a.k.a. Hodgkin-Huxley-type models), known to be computationally expensive and difficult to treat mathematically. However, to the best of our knowledge, there is no equivalent in the literature of a simple and lightweight model for describing the voltage behavior of nonspiking neurons, which also are ubiquitous in a large variety of nervous tissues in both vertebrate and invertebrate species and play a central role in information processing. This letter proposes a simple model that reproduces the experimental qualitative behavior of known types of nonspiking neurons. The proposed model, which differs fundamentally from classic simple spiking models unable to characterize nonspiking dynamics due to their intrinsic structure, is derived from the bifurcation study of conductance-based models of nonspiking neurons. Since such neurons display a high sensitivity to noise, the model aims at capturing the experimental distribution of single-neuron responses rather than perfectly replicating a single given experimental voltage trace. We show that such a model can be used as a building block for realistic simulations of large nonspiking neuronal networks and is endowed with generalization capabilities, granted by design.

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

Unlike spiking neurons which compress continuous inputs into digital signals for transmitting information via action potentials, non-spiking neurons modulate analog signals through graded potential responses. Such neurons have been found in a large variety of nervous tissues in both vertebrate and invertebrate species, and have been proven to play a central role in neuronal information processing. If general and vast efforts have been made for many years to model spiking neurons using conductance-based models (CBMs), very few methods have been developed for non-spiking neurons. When a CBM is built to characterize the neuron behavior, it should be endowed with generalization capabilities (i.e. the ability to predict acceptable neuronal responses to different novel stimuli not used during the model's building). Yet, since CBMs contain a large number of parameters, they may typically suffer from a lack of such a capability. In this paper, we propose a new systematic approach based on multi-objective optimization which builds general non-spiking models with generalization capabilities. The proposed approach only requires macroscopic experimental data from which all the model parameters are simultaneously determined without compromise. Such an approach is applied on three non-spiking neurons of the nematode Caenorhabditis elegans (C. elegans), a well-known model organism in neuroscience that predominantly transmits information through non-spiking signals. These three neurons, arbitrarily labeled by convention as RIM, AIY and AFD, represent, to date, the three possible forms of non-spiking neuronal responses of C. elegans.

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

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.