The geometrical factors determining the electrotonic properties of a molluscan neurone

Abstract

1. Light and electron micrographs of sections of the gastro-oesophageal giant neurone (G cell) of the nudibranch mollusc, Anisodoris nobilis, show that its somatic and axonal membranes are deeply infolded. The surface and volume of its soma and axon have been calculated from measurements taken at the light and electron microscope on sections of the G cell.2. The surface of the soma is approximately 7.5 times as large as that of a sphere having the same volume. For a typical cell the soma has a volume of 1.5 x 10(-5) cm(3) and a surface of 2 x 10(-2) cm(2); the axon has a volume of 5 x 10(-5) cm(3) and a surface of 5 x 10(-1) cm(2).3. Because the axon is star shaped in cross-section, its geometry cannot be described by a single parameter (diameter or radius). Furthermore, the axon is beaded, and both the area (A) and the perimeter (P) of its cross-section change from point to point.4. However, in spite of the apparent irregularity of their cross-sections, all axons examined could be characterized by a constant A/P ratio. This ratio also remains constant when the axons are stretched.5. According to the equations derived in the Appendix, the geometrical factor for the length constant in a folded fibre is H = radical(A/P); therefore, in the G cell the length constant (and hence the conduction velocity) should be independent of the stretch applied to the axon.6. The geometrical factor required to calculate the axonal input conductance is M = radical(A.P). M changes in adjacent segments of the same axon; in each segment its value depends on how much the axon is stretched.7. The input conductance of the whole axon can be calculated by applying a modified form of Rall's equations for dendritic trees. The results suggest that the input conductance of the G cell axon should vary with stretch and should be large in comparison to that of the soma.