12.2. Simplified mechanism of the action potential[[Student version, January 17, 2003]] 459
̃V(t)=V(0,t
)V^0̃v(t 2 ) ttA0234561Bjqa
b
Figure 12.8:(Sketch graphs.) (a)The time course an action potential (not drawn to scale). The sketch shows the
membrane potentialV ̃(t), measured at a fixed locationx=0. ̃v(t)refers to the difference between the membrane
potential and its resting valueV^0. The dashed lines are six particular moments of time discussed in the text.
(b)Reconstruction of the total membrane current from (a), using Equation 12.15. An Ohmic stage“A”gives way
to another stage“B.”In “B” the membrane potential continues to rise but the current falls and then reverses; this
is non-Ohmic behavior.
Wecan understand this result graphically, without any calculations. Note that the membrane cur-
rent is particularly simple at the inflection points of panel (a) (the dashed lines labeled 1, 3, and
5): Here the first term of Equation 12.15 equals zero, and the sign of the current is opposite to that
of the slope ofV ̃(t). Similarly, at the extrema of panel (a) (the dashed lines labeled 2 and 4) we
find that thesecondterm of Equation 12.15 vanishes: Here the sign of the current is that of the
curvatureofV ̃(t), as shown. With these hints we can work out the sign ofjq,rat the points 0–6;
joining the dots gives the curve sketched in panel (b).
Comparing the two panels of Figure 12.8 shows what is happening during the action potential.
Initially (stage “A”) the membrane conductance is indeed Ohmic: The cell’s interior potential
begins to rise above its resting value, driving an outward current flux, exactly as predicted from
your calculation of the potential of 3 resistor-battery pairs (Your Turn 12a on page 450). But when
the membrane has depolarized by about 10mV,something strange begins to happen (stage “B”):
The potential continues to rise, but the net current falls.
Idea 12.13 made the key point needed for understanding the current reversal, in terms of a switch