Abstract
In most neuronal models, ion concentrations are assumed to be constant, and effects of concentration variations on ionic reversal potentials, or of ionic diffusion on electrical potentials are not accounted for. Here, we present the electrodiffusive Pinsky-Rinzel (edPR) model, which we believe is 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 edPR model is an expanded version of the two-compartment Pinsky-Rinzel (PR) model of a hippocampal CA3 neuron. Unlike the PR model, the edPR model includes homeostatic mechanisms and ion-specific leakage currents, and keeps track of all ion concentrations (Na+, K+, Ca2+, and Cl-), electrical potentials, and electrical conductivities in the intra- and extracellular space. The edPR model reproduces the membrane potential dynamics of the PR model for moderate firing activity. For higher activity levels, or when homeostatic mechanisms are impaired, the homeostatic mechanisms fail in maintaining ion concentrations close to baseline, and the edPR model diverges from the PR model as it accounts for effects of concentration changes on neuronal firing. We envision that the edPR model will be useful for the field in three main ways. Firstly, as it relaxes 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 should supplement the PR model when simulating scenarios where ion concentrations are expected to vary over time. Thirdly, being applicable to conditions with failed homeostasis, the edPR model opens up for simulating a range of pathological conditions, such as spreading depression or epilepsy.
Highlights
The neuronal action potential (AP) is generated by a transmembrane influx of Na+, which depolarizes the neuron, followed by an efflux of K+, which repolarizes it
By running long-time simulations on both models, we identify the firing conditions under which the two models maintained a similar firing pattern, and under which conditions concentration effects became important so that dynamics of the electrodiffusive Pinsky-Rinzel (edPR) model diverged from the original PR model over time
The here proposed electrodiffusive Pinsky-Rinzel model is inspired by the original Pinsky-Rinzel (PR) model [3], which is a two-compartment version of a CA3 hippocampal cell model, initially developed by Traub et al [2]
Summary
The neuronal action potential (AP) is generated by a transmembrane influx of Na+, which depolarizes the neuron, followed by an efflux of K+, which repolarizes it. In Hodgkin-Huxley type models, the large number of ion pumps, cotransporters and passive ionic leakages that strive towards maintaining baseline conditions are not explicitly modeled. Instead, they are assumed to do their job and are grouped into a single passive and non-specific leakage current Ileak = gleak(φm−Eleak), which determines the cell’s resting potential (for a critical study of this approximation, see [9])
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