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

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.