Spatiotemporal equations expressing microscopic two-dimensional membrane-potential dynamics

New technologies such as microelectrode arrays and high-resolution optical recording have been yielding microscopic, dynamic, and wide observation-area measurements of membrane-potential behavior. To analyze near-future experimental data, a new potential dynamics theory will inevitably be required. Microscopically speaking, the membrane extends two-dimensionally with various shapes in the three-dimensional world. This paper presents two-dimensional membrane-potential equations to analyze the microscopic spatiotemporal behavior of the membrane potential. The two-dimensional treatment is a good approximation when the curvature of the nonplanar membrane is not so large. Results of numerical calculations predict, as an example, that the signal velocity v on a soma has a dependence of upsilon proportional to D-0.77 on the conductive-layer thickness D, instead of upsilon proportional to D-1/2 in the case of cylinders used in the cable theory. We also present a virtual experimental result which suggests that the temporal coincidence of action-potential pulses has more significant effects when the conductive-layer thickness reduces. (C) 2002 Elsevier Science B.V. All rights reserved.