# Living organisms and thermodynamics (Pentcho Valev)

Tue Oct 28 04:44:02 EST 1997

```Concerning the system

10 mM KCl                    M                     0 mM KCl

where M is a membrane permeable only to K+, Bill Tivol wrote:

Since the electrical potential is                                         <
assymtotically going to 0 as one goes away from the membrane, it is not   <
0 at any finite distance.  The [K+] will assymtotically approach a con-   <
stant value, but it will not be constant.  In order for the proposed      <
system to be at equilibrium, the electrochemical potential of K+ must be  <
the same far from one side of the membrane as it is far from the other.   <
Since [K+] approaches 0 far to the right, the electrical potential must   <
become more positive--this way, the electrical potential drives K+ to the <
left, and the diffusion potential balances this so there is no net move-  <
ment of K+.                                                               <

The assumtion that equilibrium can be achieved in the proposed           <
system is rather far removed from equilibrium systems of which we have    <
experience either in the lab or in living systems.  Thus it is difficult  <
to reconcile the resulting ion & potential profiles with one's intuition. <
This leads to thinking that the results are "absurd and contradictory",   <
when, in fact, they are consistant.  Clearly, all the K+ on the right     <
must see a very large negative electrical potential drop which attracts   <
the K+ to the space near the membrane, otherwise, diffusion would cause   <
[K+] to be >0 at the far right.  By imposing the condition that [K+]=0,   <
one must also impose the large electric field necessary to maintain       <
that condition, otherwise equilibrium will not have been established.     <

Both systems - this one and the more common one in which the initial KCl
concentration in the right-hand compartment is small but different from
zero, are extremely difficult for theoretical analysis. For instance, if
we use Poisson's equation and Boltzmann's statistical law, we can obtain for
the above system that, to the right from the membrane, the field decreases
in magnitude as 1/x (x is the distance from the membrane) and, accordingly,
the potential increases as ln(x). This is satisfactory for thermodynamics,
but unfortunately it is derived on the assumption that the membrane is
infinite so, in Poisson's equation, the partial derivatives along the
y and z axis are zero. In any real system the membrane is finite, but I
cannot deal with Poisson's equation in this case.
I think that the experimental verification is much easier - I still
believe that verification of both the second law and the central
bioenergetic scheme is worth doing.
By the way, these days I found that the possibility of ATP synthesis
at equilibrium can easily be derived from the simple fact that hydrophobic
and hydrophilic sectors of a membrane have quite different dielectric
constants. The average dielectric constant of hydrophobic materials is 2,
whereas one can expect the dielectric constant of a hydrated protein complex
to be close to that of water - 80. Therefore, the transmembrane electrical
force at hydrophobic sectors can be 40 times greater than that at hydrophilic
sectors. Accordingly, in the presence of electrical double layer, the
transmembrane CONCENTRATION gradient would cause a net ion flux in one
direction at hydrophilic sectors, whereas the transmembrane ELECTRICAL
gradient would cause an opposite and equal flux at hydrophobic sectors.
One of the two fluxes can do work, the other would restore the equilibrium
of the "working" system.
If somebody is interested, I could elaborate on this scheme - it could
tell us much about the early bioenergetic evolution.

Best regards,
Pentcho

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