Living organisms and thermodynamics (Pentcho Valev)

Fri Oct 17 03:42:21 EST 1997

I wrote:
>   The only contradictory point is whether or not the electrical potential<
>extends far from the semipermeable membrane. This can be verified for     <
>another, even more simplified, system:                                    <
>     10 mM  KCl                  M                        1 mM KCl        <
>where M is a membrane permeable only to K+.                               <
>   For this system thermodynamics says that, at equilibrium, the          <
>electrical potential difference between points symmetrical with respect   <
>to but far from the membrane remains constant - 60 mV. However there is   <
>serious reason to believe that the potential approaches zero with         <
>distance, in both directions. There has been a discussion in the biophysics<
>group on this problem but to no avail.                                     <

Lukasz Salwinski replied:
what about consulting any standard electrochemistry textbook ?            <
AFAIK concentration cells (and that's what you describe above)            <
do work. In fact, if I remember correctly (it was a few years ago) we     <
were actually measuring potentials generated in such systems during       <
our freshmen biophysics lab. the potentials were measured between bulk    <
solutions and were as high as expected.                                   <

It is not as simple as that. You can find contradictory descriptions in
the literature. Generally, the following two types of curves showing how
the potential varies with distance can be found:

                       -membrane +

                       -       ox+xo o o o o o o o o o o o o o o

                       -     ox  +       x

x x x x x x            -    xo   +             x x x x x x x x x

                x      -  xo     +

o o o o o o o o o o o x-xo       +

                       -         +

    The curve x x x  demonstrates that the potential is different from zero
in some region around the membrane, but goes to zero far from it. This curve
is consistent with the Guy-Chapman model describing an analogous system,
and also with the ditribution of the potential with distance for a
finite-sized capacitor (the electrical structure around the membrane is
capacitor-like). Recently Bill Tivol cited, in the biophysics group, a book
where the same Donnan system is characterized by the same curve.
   The curve o o o is predicted by thermodynamics. It demonstrates that
the potential is constant and different from zero no matter how far from
the membrane.
   There is a simple thought experiment allowing quickly to find which curve
is correct. Those who support the thermodynamic prediction usually add that
only the potential is different from zero far from the membrane, whereas
both the charge density and the field aprroach zero with distance. If so, we
can take a positive test charge and move it from infinity up to one end of
the system. As the test charge enters the system, no electrical work is done
since the field there is zero, i.e. the test charge crosses no field.
Therefore, the potential at the end of the system is equal to that of the
infinity reference point, i.e. zero.
   Of course, it would be better to measure the potential difference between
the two ends experimentally. If, for instance, two microelectrodes reversible
for K+ are placed at the two ends of the system, thermodynamics predicts
zero voltage whereas I expect 60 mV, i.e. I expect the only factor "pushing"
the electrons in the electrodes to be the K+ concentration difference,
since it is universally accepted that the field at both ends is zero.

Best regards,
Pentcho Valev

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