Analytical Solution of a Tapering Cable Equation for Dendrites and Conformal Symmetry

Abstract

Progress towards detailed characterization of structural and biophysical properties of dendrites emphasizes the importance of finding analytical solutions for more realistic dendrite models with circular cross-section and varying diameter. In this regard, we employ symmetry methods and the passive cable theory to deduce a generalized analytical solution for electric propagation in a family of tapering dendrites. In particular, we study the effect of such tapering geometries on the obtained electric voltage. Simulations using the deduced analytical solution indicate that for a subfamily of tapering profiles neural integration is better than in the stereotypical profile given by a cylinder.