## Decremental Conduction on Dendrites The Space Constant

Figure 1.2-1 illustrates the lumped-parameter, linear RC circuit that is used to model a cylindrical dendrite having a passive cell membrane. Ie(x) is a current sunk at a point x on the surface of the dendrite into an external electrode. Ie(x) has the units of amp/m. iL(x, t) is the net longitudinal current in the axoplasm or outside the dendrite's surface. Most generally, iL is a function of displacement x and time; it has the units of amp. im(x, t) is the net transverse current through the membrane

External (Ag I AgCl Electrode)

(Outside dendrite)

(Outside dendrite) (Inside dendrite)

FIGURE 1.2-1 Equivalent lumped-parameter model of a passive-membrane dendrite. The sections form a lossy RC transmission line.

(Inside dendrite)

FIGURE 1.2-1 Equivalent lumped-parameter model of a passive-membrane dendrite. The sections form a lossy RC transmission line.

capacitance and conductance; its units are amp/m. vm(x, t) is the transmembrane potential change (superimposed on the dc resting potential, Vm0). Use of Kirchoff's voltage law yields:

Vm(x + Ax) = Vm(x) - iL(x)(ro + ri) Ax V By rearranging terms and dividing by Ax, 