Exploring the notion of space constant under different geometric and physical conditions

TL;DR

This paper investigates how the space constant in neuronal dendrites varies under different geometric and physical conditions, including passive and active transmission, morphology changes, and calcium diffusion.

Contribution

It provides a comprehensive analysis of calculating the space constant across various neuronal geometries and physical states, extending traditional models.

Findings

Space constant varies with dendrite tapering and branching.

Relationship between input resistance and space constant is characterized.

Diffusion of calcium in dendrites is linked to the space constant.

Abstract

The cable equation is a second order, parabolic, partial differential equation that describes the evolution of voltage in the dendrite of a neuron. Here we look at the various ways in which lambda(space constant/ variable space constant/length parameter) is calculated in the cases of linear, passive transmission as well as nonlinear active transmission. Changes in morphology are taken into account by including the case of tapering dendrite, branched dendrites, branched dendrites with taper or flare. The case of variable membrane resistance and the relationship between input resistance and space constant is explored. Finally the reaction diffusion equation governing the diffusion of calcium in dendrites and space constant associated with that is described.