General cable theory for cells of algae Characeae

Abstract

Cable theory is extended to objects of finite dimensions such as giant cells of the algae Characeae. The solution of the cable equation is obtained taking into account the definite resistance of cell nodes for the general case of an applied current, the strength of which alters with time by any f( t) law. Two important cases for the function f( t) are considered in detail, viz. f( t) = f(o) = constant and f( t) = kt. Practical formulae for determining the fundamental characteristics of the cell are obtained: membrane resistance and capacity (of plasmalemma), the nodal resistance and the characteristic length of the cell. It has been shown that a simplified method for measuring membrane resistance suggested first by Hogg et al. (J. Hogg, E. J. Williams and R. J. Johnston, J. Theor. Biol., 24 (1969) 317) can be used for the determination of the membrane time constant and hence the membrane capacity. Taking into account the nodal resistance of the cell gives an improved value for the electrode position in terms of the critical coordinate: x er = 0.38 l, where 2 l is the length of the cell. The current electrode has to be inserted in the middle of the cell.