Propagation - Quantitative Neurophysiology - page 43

CHAPTER 4

Propagation

Experimental studies have shown that a neuron does not fire all at once. Rather, there is a wave of electrical
activity that is passed from one small patch of membrane to the next, and so on, around the cell. Likewise,
electrical impulses spread down dendrites to the soma by moving from one patch to the next. A similar
process is involved in the spread of electrical impulses from the axon hillock down the axon. These waves
of electrical activity are called propagation . Not all propagation, however, is the same. As the dendrites
are composed of passive patches of membrane, they will leak charge out of each patch as propagation
moves forward. Therefore, the strength of the impulse will be decreased or attenuated down the dendrite.
Attenuated propagation is often called passive propagation . The axon, on the other hand, is composed of
active patches of membrane that can generate their own currents (e.g., an action potential). Therefore,
an impulse that enters the axon hillock will propagate unattenuated to the end of the axon. Furthermore,
because of the refractory period, propagation can proceed in only one direction. Unattenuated propagation
is often called active propagation .
In this chapter, we will develop models to describe propagation. As passive propagation is consid-
erable more simple than active propagation, we will begin by considering propagation in the dendrites.
Active propagation in an axon will be explained as a special case of passive propagation.

4.1 PASSIVE PROPAGATION INDENDRITES

4.1.1 The Core Conductor Model
The dendrites of a neuron may be thought of as being composed of many small cylindrical patches
of passive membrane connected together into a thin one-dimensional cable (Fig. 4.1). In fact, these
assumptions are the same as those used by the pioneers of cable theory to describe propagation of electricity
down a wire. Since the theory of propagation down a wire was developed before propagation in neurons
was considered, the terms cable theory and core conductor theory have been adopted by electrophysiologists.
Consider the discrete cable in Fig. 4.2 where the passive elements are separated by dx and
connected together in the intracellular and extracellular space by resistance per unit length, r i and r e
( /cm ). From Fig. 4.2, we can choose a node in the center of this cable in Fig. 4.3 and write down intra
and extracellular currents at nodes 1, 2, and 3 using Kirchhoff 's Current Law.

At Node 2,

φ i φ i φ i φ i

− −

dx − dx −

dx · i m = 0 (4.1)

r i · r i ·

φ e − φ e φ e − φ e

dx − dx +

dx · i m = 0 (4.2)

r e · r e ·