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[QUESTION] How determine or define single channel conductances ?

Matt Jones jonesmat at ohsu.edu
Sat Apr 24 13:25:58 EST 1999

In article <7fsjj2$mik$1 at denws02.mw.mediaone.net> Richard Norman,
rsnorman at mw.mediaone.net writes:
>Think of the conductance as the conductance of a thin cylinder of salt
>solution, whose length is the thickness of the membrane and whose
>diameter is the width of the ion channel.  (Biophysically, things are
>a little more complex, but this is close enough).  The conductance
>depends on the geometry of the channel (length and width).  But it
>also depends on the bulk resistivity (conductivity) of the salt
>which, in turn, depends on concentration.
>The measurement of conductance is a tool to learn something about
>the properties of the ion channel -- the length is constant, so it is
>width (the "open-ness") that is of interest.  However, that
>is confounded by the ion concentration.  If you measure conductance
>under one concentration condition and I measure it under another,
>our measurements will differ, even though the channel is the same.

Another way of thinking of the concentration dependence of conductance is
to realize that ions have _binding sites_ within most channels. This is
actually important for several reasons:

Ions are normally very comfortable in water (which is why NaCl salt
dissolves into Na+ and Cl-). This means that ions are "solvated" while
free in solution. They have a cloud of water molecules srrounding them,
with the electronegative portions (the oxygen) forming hydrogen and van
der Waals bonds with positively charged ions, or the hydrogens forming
similar bonds with negatively charged ions. All these bonds have energy
associated with them, and thus provide a stable environment for the ion.
The lipid membrane, on the other hand, is a very "hostile" environment
for an ion (which simply means that it provides far less opportunities
for formation of favorable hydrogen bonds).  Therefore, membrane are
quite impermeable to ions. An ion channel tricks the ion into passing
across the membrane by providing an environment that the ion can't easily
distinguish from water. That is, the pore is lined partly with residues
that form hydrogen bonds and van der Waals bonds with the ion as it
passes through. This is what I meant by saying that ions have binding
sites within the channel.

The selective permeability, which determines the reversal potential in
the Nernst and Goldmann-Hodgkin_Katz equations, is a measure of how much
time an ion spends _within_ the channel, compared to another reference
ion.  In general, ions that bind more tightly will be more selectively
permeable than those which bind weakly. This is a large part of the basis
of ionic selectivity in channels. Another important part is the size of
the pore, as Richard Norman mentioned above, and yet another is the ease
with which the ion loses its waters of hydration in order to enter the

The conductance, however, is the total rate of transport of an ion from
one side to the other. In order for an ion to enter a pore and be
comfortable passing through it, it must be able to exchange some of its
waters of hydration for hydrogen bonds with residues inside the pore.
However, if it is too comfortable with the environment in the pore (that
is, if it forms very strong bonds there), then it will spend a lot of
time just sitting in the pore, and not as much time actually being
conducted from one side to the other. Such an ion will show a low
conductance, and will actually act as a channel blocker for other ions
trying to permeate. An excellent example of this is the block of calcium
channels by calcium. Normally, these channels pass calcium with a small
conductance, but basically don't pass any sodium at all. However, if you
remove all the calcium, then sodium actually passes with a higher
conductance than calcium would in isolation. Calcium is too happy in the
pore to give a large conductance, and blocks the passage of other ions.
You can easily guess from this that if you measured the conductance of
these channels for either calcium or sodium in isolation, you would find
that they both had a saturable Michaelis-Menten type
concentration-dependence, but that calcium would have a much lower EC50
than sodium. Calcium has a higher "affinity" for its binding sites within
the pore than sodium.

Chapter 14 of Hille gives some additional examples of the
concentration-dependence of conductance for some Na+, K+ and Cl-
channels. It is worth noting that these EC50 values range from about 10mM
to 200mM. That might seem like a big range, but in terms of the
structures of binding sites and whatnot, that range probably corresponds
to tiny, tiny differences in the structure of the binding sites. In many
systems, a difference of an Angstrom in interaction distance can lead to
several orders of magnitude differences in EC50.


Matt Jones

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