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

Abstract

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 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.

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

“…In this model, every individual parameter and state variable has an established electrophysiological meaning. Therefore, CBMs are broadly used to understand 'low-level' functions of neural systems (Eliasmith and Trujillo, 2014;O'Leary et al, 2015), such as monitoring the effects of specific conductance variations on neuronal dynamics (Giovannini et al, 2017;Poirazi and Papoutsi, 2020;Naudin et al, 2022c), or modeling gain-or loss-of-function mutations in genes encoding ion channels (Lemaire et al, 2021).…”

“…This type of neuron is found in a wide variety of nervous tissues (Davis and Stretton, 1989b;Goodman et al, 1998;Field and Chichilnisky, 2007), encodes neuronal information in an analog manner through graded responses (Lockery et al, 2009), and plays a crucial role in the functioning of many nervous systems (Roberts and Bush, 1981;Burrows et al, 1988;Laurent and Burrows, 1989;Davis and Stretton, 1989a;Bidaye et al, 2018). Further, three phenotypes of non-spiking neurons can be distinguished (Figure S2), each with its own computational properties (Naudin et al, 2022c): (i) near-linear, defined by smooth depolarizations or hyperpolarizations from the resting potential (phenotype 1), (ii) bistable, characterized by nonlinear transitions between the resting potential and a depolarized potential, with one resting potential (phenotype 2), and (iii) bistable with two resting potentials (phenotype 3). Naudin et al (2022c) described a general pattern of the phenotypic evolution of non-spiking neurons as a function of changes in calcium and potassium conductances.…”

“…Further, three phenotypes of non-spiking neurons can be distinguished (Figure S2), each with its own computational properties (Naudin et al, 2022c): (i) near-linear, defined by smooth depolarizations or hyperpolarizations from the resting potential (phenotype 1), (ii) bistable, characterized by nonlinear transitions between the resting potential and a depolarized potential, with one resting potential (phenotype 2), and (iii) bistable with two resting potentials (phenotype 3). Naudin et al (2022c) described a general pattern of the phenotypic evolution of non-spiking neurons as a function of changes in calcium and potassium conductances. As an example, Figure 1 illustrates the phenotypic transitions of non-spiking neurons as calcium conductance (g Ca ) decreases through a well-posed retinal cone non-spiking CBM (Kourennyi et al, 2004).…”

“…The remainder of the paper is organized as follows. Section 2 describes the evolution of the computational characteristics of the retinal cone CBM as g Ca decreases, that is representative of an ubiquitous and general pattern in non-spiking neurons (Naudin et al, 2022c). Section 3 proposes a numerical procedure to build a phenomenological model 3 that reproduces the computational characteristic evolution of the retinal cone CBM as g Ca reduces, as described in Section 2.…”

“…g Ca Figure 1: Phenotypic transitions of the voltage dynamics as g Ca decreases (Naudin et al, 2022c). A well-posed retinal cone model, with a wild-type phenotype 3, was used as an illustration.…”