12.3. The full Hodgkin–Huxley mechanism and its molecular underpinnings[[Student version, January 17, 2003]] 471
-3-2-101234-150 -100 -50 0 50 100 150current,pANa+K+applied voltage, mVgNa+=25pS
gK+=3. 2 pSFigure 12.15: (Experimental data.) Current-voltage relation of single sodium channels reconstituted into an
artificial bilayer in solutions of NaCl and KCl. The vertical axis gives the current observed when the channel was in
its open state. The channels were kept open (that is, channel inactivation was suppressed) by adding batrachotoxin,
the neurotoxin found in the skin of the poison dart frog. The slopes give the channel conductances shown in the
legend; the unitpSequals 10−^12 Ω−^1 .The data show that this channel is highly selective for sodium. [Data from
Hartshorne et al., 1985.]
ten times as great as the conductance to other similar cations. The potassium channel is even more
precise, admitting potassium fifty times as readily as sodium.
It’s not hard to imagine how a channel can accept smaller ions, like sodium, while rejecting
larger ones, like potassium and rubidium: We can just suppose that the channel is too small for the
larger ions to pass. (More precisely, this geometrical constraint applies to the hydrated ions; see
Section 8.2.2 on page 265.) It’s also not hard to imagine how a channel can pass positive ions in
preference to neutral or negative objects: A negative charge somewhere in the middle can reduce
the activation barrier for a positive ion to pass, increasing the rate of passage (Section 3.2.4 on
page 79), while having the opposite effect on anions. Real sodium channels seem to employ both
of these mechanisms.
Whatishard to imagine is how a channel could specifically pass alargecation, rejecting smaller
ones, as the potassium channel must do! C. Armstrong and B. Hille proposed models explorin this
idea in the early 1970s. The idea is that the channel could contain a constriction so narrow that
ions, normally hydrated, would have to “undress” (lose some of their bound water molecules) in
order to pass through. The energy needed to break the corresponding hydration interactions will
in general create a large activation barrier, disfavoring ion passage, unless some other interaction
forms compensating (favorable) bonds at the same time. The first crystallographic reconstructions
of a potassium channel, obtained by R. Mackinnon and coauthors in 1998, indeed showed such a
constriction, exactly fitting the potassium ion (diameter 0.27nm)and lined with negatively charged
oxygen atoms from carbonyl groups in the protein making up the channel. Thus, just as the
potassium ion is divested of its companion water molecules, it picks up similar attractive interactions
to these oxygens, and hence can pass without a large activation barrier. The smaller sodium ion
(diameter 0. 19 nm), however, does not make a tight fit and so cannot interact as well with the
fixed carbonyl oxygens; nevertheless, it too must lose its hydration shell, giving a large net energy