Role of architecture in determining passive electrical properties in gap junction-connected cells
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The electrical properties of gap junction-connected cells were analysed in terms of their architectural organization. Two major architectural categories 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 (triangular) co-ordination. The Bethe lattice is solved analytically by the transfer constant method, which allows the introduction of several physiologically relevant effects in a very simple manner. The experimental data for the length constant and the input resistance were fitted by varying the coupling and membrane resistances for various morphologies. The large variations in the length constant observed experimentally in two systems (turtle retina horizontal cells with and without dopamine and pancreatic β-cells in the active and silent phases) could not be explained by means of the Bethe lattice, indicating that the cell arrangements form rings. Subsequent analysis by means of a linear chain and the square and triangular lattices showed the crucial relevance of architecture in deriving the electrical characteristics of gap junction-connected cells from experimental data.
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