Role of architecture in determining passive electrical properties in gap junction-connected cells

The electrical properties of gap junction-connected cells were analysed in terms of their architectural organization. Two major architectural categori es were considered: trees and rings. Trees are described by means of Bethe lattices (lattices with no rings) with arbitrary co-ordination and rings by two-dimensional periodic lattices with fourfold (square) or sixfold (trian gular) co-ordination. The Bethe lattice is solved analytically by the trans fer constant method, which allows the introduction of several physiological ly relevant effects in a very simple manner. The experimental data for the length constant and the input resistance were fitted by varying the couplin g and membrane resistances for various morphologies. The large variations i n the length constant observed experimentally in two systems (turtle retina horizontal cells with and without dopamine and pancreatic beta-cells in th e active and silent phases) could not be explained by means of the Bethe la ttice, indicating that the cell arrangements form rings. Subsequent analysi s by means of a linear chain and the square and triangular lattices showed the crucial relevance of architecture in deriving the electrical characteri stics of gap junction-connected cells from experimental data.