Living organisms and thermodynamics (Pentcho Valev)

Lukasz Salwinski lukasz at wlheye.jsei.ucla.edu
Fri Oct 17 09:14:51 EST 1997

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>It is not as simple as that.

unfortunately it is...

>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:

the rule of thumb is - if there's no differences in the _bulk_ concentrations
across the membrane nor slective flow of the ions across the membrane is possible
there's going to be no potential differences between bulk phases (xxx curve).
there are concentration differences and the membrane have selective properties
there's going to be a bulk potential on top of Guoy-Chappman. all the components
of the potential can and were measured experimentally. the agreement between
theory and experiment is one of the best in the whole biophysics without pulling
out any fudge factors. Check articles from the group of Wayne Hubbell published in
the late '70 and early '80.

>   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.

both curves are predicted by thermo for different systems.

>   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

no need to add it separately. charges sit wherever they form the double layer,
field at infinity is zero 'cause it is by definition a gradient of a constant
function (of the potential, that is).

>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.

charge _within the system_. if the system is finite on the way from infinity
into the system (whatever large) one's got to cross the boundary between
the system and it's surrounding. the work is going to be done at this boundary.

>Therefore, the potential at the end of the system is equal to that of the
>infinity reference point, i.e. zero.

wrong, wrong, wrong. see above.

>   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.

thermo (or at least equilibrium thermo we are dealing with) does not deal with
any kind of changes in time (like electrons or ions flowing through the system).
if one wants to talk about flows one's got to apply an appropriate tool - nonequilibrium
thermo.

if you got problems with measuring potentials with electrodes, once more, check
publications of W. Hubbell on the methods based on the measurements of partition
coefficients of charged compounds between compartments separated by a semipermeable
membrane. whatever was observed was in perfect agreement with the predictions of the
thermo theory you claim is wrong.

lukasz

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