# Living organisms and thermodynamics (Pentcho Valev)

Sat Oct 18 08:21:42 EST 1997

```In reply to Lukasz Salwinski and Bryant Fujimoto

I still claim that the problem how the potential is distributed in a
Donnan system is extremely difficult, despite the deceiving simplicity
of the system. I have discussed it many times, with rather competent
people, but the number of unsurmountable contradictions is indeed great.
Still there is a line of argument which, in my opinion, could lead to the
desired solution. Please tell me what you accept and what you don't.

1. The electrical double layer at a Donnan membrane is capacitor-like.

2. For an infinite-sized capacitor, the field outside the capacitor is
zero, whereas the potential on the two sides is constant and different.
(This is a standard result in electrostatics so please do not say that
you do not accept it). Except for points very close to the membrane,
thermodynamics predicts the same potential far from the membrane. This
coincidence is suspicious - any real membrane is of course finite.

3. For a finite-sized capacitor, along its central axis, the field is
very weak outside it, near the plates, and decreases in magnitude with
distance. Accordingly, the potential also decreases in magnitude with
distance, but very slowly. (This is relatively easy to calculate
for a finite-sized capacitor in a vacuum). If the situation in a Donnan
system is analogous, we can understand why bulk measurements seem to
support the thermodynamic prediction - the slow decrease of the potential
simply cannot be detected. If, however, the system is long enough and
if this analogy works, the potential at both ends of the system must be
zero.

4. If the analogy with the finite-sized capacitor is valid, another very
interesting implication follows. The potential is greater in magnitude
along the central axis, but quickly goes to zero in a perpendicular
direction, e.g. for points lying on the capacitor plane but ouside the
capacitor.
The biological implication is even more interesting: If, at equilibrium,
a double layer is formed at a semipermeable spot on the membrane, the
potential quickly goes to zero for adjacent impermeable spots, i.e.
there is no transmembrane potential difference at the impermeable spots
and the concentration difference there can be used, e.g. for ATP synthesis.

What I have written about a finite-sized capacitor in a vacuum cannot
be doubted. However I am not at all sure to what extent this analogy is
valid. Obviously a special experiment is needed, and I hope one day it will
be done.

Pentcho

```