Electrical transient laws in neuronal microdomains based on electro-diffusion

TL;DR

This paper derives new analytical electro-diffusion laws for neuronal microdomains, revealing deviations from Ohm's law and the influence of microdomain geometry and channel location on electrical properties.

Contribution

It introduces novel I-V relations for microdomains with multiple ionic species, accounting for complex geometries and transient effects, advancing understanding of neuronal electrical behavior.

Findings

Large deviation from Ohm's law in microdomains

Narrow passages significantly affect electrical conduction

Voltage modulation depends on channel location during transients

Abstract

The current-voltage (I-V) conversion characterizes the physiology of cellular microdomains and reflects cellular communication, excitability, and electrical transduction. Yet deriving such I-V laws remains a major challenge in most cellular microdomains due to their small sizes and the difficulty of accessing voltage with a high nanometer precision. We present here novel analytical relations derived for different numbers of ionic species inside a neuronal micro/nano-domains, such as dendritic spines. When a steady-state current is injected, we find a large deviation from the classical Ohm's law, showing that the spine neck resistance is insuficent to characterize electrical properties. For a constricted spine neck, modeled by a hyperboloid, we obtain a new I-V law that illustrates the consequences of narrow passages on electrical conduction. Finally, during a fast current transient, the local voltage is modulated by the distance between activated voltage-gated channels. To conclude, electro-diffusion laws can now be used to interpret voltage distribution in neuronal microdomains.