An electrodiffusive, ion conserving Pinsky-Rinzel model with homeostatic mechanisms
Authors: Sætra Marte J. , Einevoll Gaute T. , Halnes Geir 
Published: January 2020

Most neuronal models are based on the assumption that ion concentrations remain constant during the simulated period, and do not account for possible effects of concentration variations on ionic reversal potentials, or of ionic diffusion on electrical potentials. Here, we present what is, to our knowledge, the first multicompartmental neuron model that accounts for electrodiffusive ion concentration dynamics in a way that ensures a biophysically consistent relationship between ion concentrations, electrical charge, and electrical potentials in both the intra- and extracellular space. The model, which we refer to as the electrodiffusive Pinsky-Rinzel (edPR) model, is an expanded version of the two-compartment Pinsky-Rinzel (PR) model of a hippocampal CA3 neuron, where we have included homeostatic mechanisms and ion-specific leakage currents. Whereas the main dynamical variable in the original PR model is the transmembrane potential, the edPR model in addition keeps track of all ion concentrations (Na+, K+, Ca2+, and Cl−), electrical potentials, and the electrical conductivities in the intra- as well as extracellular space. The edPR model reproduces the membrane potential dynamics of the PR model for moderate firing activity, when the homeostatic mechanisms succeed in maintaining ion concentrations close to baseline. For higher activity levels, homeostasis becomes incomplete, and the edPR model diverges from the PR model, as it accounts for changes in neuronal firing properties due to deviations from baseline ion concentrations. Whereas the focus of this work is to present and analyze the edPR model, we envision that it will become useful for the field in two main ways. Firstly, as it relaxes a set of commonly made modeling assumptions, the edPR model can be used to test the validity of these assumptions under various firing conditions, as we show here for a few selected cases. Secondly, the edPR model is a supplement to the PR model and should replace it in simulations of scenarios in which ion concentrations vary over time. As it is applicable to conditions with failed homeostasis, the edPR model opens up for simulating a range of pathological conditions, such as spreading depression or epilepsy.

Author summary

Neurons generate their electrical signals by letting ions pass through their membranes. Despite this fact, most models of neurons apply the simplifying assumption that ion concentrations remain effectively constant during neural activity. This assumption is often quite good, as neurons contain a set of homeostatic mechanisms that make sure that ion concentrations vary quite little under normal circumstances. However, under some conditions, these mechanisms can fail, and ion concentrations can vary quite dramatically. Standard models are thus not able to simulate such conditions. Here, we present what to our knowledge is the first multicompartmental neuron model that in a biophysically consistent way does account for the effects of ion concentration variations. We here use the model to explore under which activity conditions the ion concentration variations become important for predicting the neurodynamics. We expect the model to be of great use for simulating a range of pathological conditions, such as spreading depression or epilepsy, which are associated with large changes in extracellular ion concentrations.