The geometrical factors determining the electrotonic properties of a molluscan neurone

Abstract

SUMMARY1. 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 cm3 and a surface of 2 x 10-2 cm2; the axon has a volume of 5 x 10-5 cm3 and a surface of 5 x 10-1 cm2.3. 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 crosssection 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 = V(AIP); 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 = 4(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

The passive electrical properties of the membrane of a molluscan neurone

“…Table 1 summarizes the average anatomical and electrical measurements taken from ten selected cells. Estimates of the surface of the soma, S, and of the geometrical factor for the axonal input conductance, M, were computed from the equivalent cell diameter, d, according to the procedures described by Mirolli & Talbott (1972). The specific membrane resistance, Rm, was calculated from the expression (see Appendix to the paper of Mirolli & Talbott, 1972) Rm = (M + V(M2 +4STRI) (4) where GT is the whole neurone conductance (1/RT); and R, is the specific resistance of the axoplasm.…”

“…Estimates of the surface of the soma, S, and of the geometrical factor for the axonal input conductance, M, were computed from the equivalent cell diameter, d, according to the procedures described by Mirolli & Talbott (1972). The specific membrane resistance, Rm, was calculated from the expression (see Appendix to the paper of Mirolli & Talbott, 1972) Rm = (M + V(M2 +4STRI) (4) where GT is the whole neurone conductance (1/RT); and R, is the specific resistance of the axoplasm. We have assumed R, to be 100 U. cm, a value which is similar to those found for axons of other marine animals (Cole & Hodgkin, 1939;Hodgkin & Rushton, 1946;Hodgkin, 1947).…”

“…The major and minor axes of the G cell soma were measured under a dissecting microscope with a micrometer eyepiece and from these the equivalent diameter, d = W/(a2b) was calculated as previously described (Mirolli & Talbott, 1972).…”

“…The giant cell (G cell) of the gastro-oesophageal nervous system of the mollusc, Anisodoris nobilis (MacFarland), provides a convenient model for studying this problem. Mirolli & Talbott (1972) have given a set of estimates for the surface area of the soma and for the geometrical factor which determines the axonal conductance of the G cell. In the present paper, these results have been used in combination with electrical measurements to compute a set of values for the specific resistance and capacitance of its membrane.…”

Calcium depletion in frog muscle tubules: the decline of calcium current under maintained depolarization.

“…External Ca2+ depletion in particular seems to be a fairly general possibility, since restricted extracellular spaces exist in most preparations where Ca2+ currents have been studied. Muscle cells generally have transverse tubules or clefts or form bundles of densely packed cells, and the cell membranes of many molluscan neurones are highly invaginated with the neurones themselves surrounded by Schwann cells (Coggeshall, 1967;Mirolli & Talbott, 1972). Even where depletion can be ruled out as a major cause for a decline of ICa (Tillotson, 1979), external [Ca2+] changes as a result of repetitive activity may still occur.…”