442 Chapter 12. Nerve impulses[[Student version, January 17, 2003]]
under such conditions, a signal would suffer serious degradation as a consequence of resistive losses—
aform of dissipation. In contrast, even your longest nerve cells faithfully transmit signals without
loss of amplitude or shape. We know the broad outlines of the resolution to this paradox from
Chapter 1: Living organisms constantly flush energy through themselves to combat dissipation.
We’d like to see how nerve cells implement this program.
This chapter contains somewhat more historical detail than most of the others in this book.
The aim is to show how careful biophysical measurements, aimed at answering the questions in the
previous paragraph, disclosed the existence of yet another remarkable class of molecular devices, the
voltage-gated channels, years before the specific proteins constituting those devices were identified.
The Focus Question for this chapter is:
Biological question:How can a leaky cable carry a sharp signal over long distances?
Physical idea:Nonlinearity in a cell membrane’s conductance turns the membrane into an excitable
medium, which can transmitwaves by continuously regenerating them.
12.1 The problem of nerve impulses
Roadmap Section 11.1 described active ion pumps as the origin of the “resting potential” across
the membranes of living cells. Section 12.1 attempts to use these ideas to understand nerve impulses,
arriving at the “linear cable equation” (Equation 12.9). Unfortunately, this equation doesnothave
solutions resembling traveling impulses: Some important physical ingredient, not visible in the
resting properties of cells, is missing. Section 12.2 will argue that voltage-gating is the missing
ingredient, and show how a slight modification to the linear cable equation (Equation 12.21) does
capture some of the key phenomena we seek. Section 12.3 will qualitatively sketch Hodgkin and
Huxley’s full analysis, and the subsequent discovery of the molecular devices it predicted: voltage-
gated ion channels. Finally, Section 12.4 sketches briefly how the ideas used so far to describe
transmission of information have begun to give an understanding of computation in the nervous
system, and its interface to the outside world.
Some nerve cells in higher animals are surrounded by a layer of electrical insulation called the
“myelin sheath.” Throughout this chapter we will consider only the case of “unmyelinated” axons,
those lacking this structure. With appropriate changes, however, the analysis given here can be
adapted to myelinated axons as well.
12.1.1 Phenomenology of the action potential
Section 2.1.2 on page 38 discussed anatomy, the shape and connectivity of neurons. The nerve cell’s
functioncan be summarized as three processes:
- Stimulation of the cell’s inputs (typically the dendrite) from the preceding cells’ outputs
(typically axon terminals); - Computation of the appropriate output signal; and
- Transmission of the output signal (nerve impulse) along the axon.
Sections 12.2–12.3 will discuss the last of these in some detail; Section 12.4 will discuss the other
twobriefly. (A fourth activity, theadjustmentof synaptic properties, will also be mentioned in
Section 12.4.3.)