Guy C Brown wrote:
> All the dyes that I know of that measure mitochondrial membrane potential
> within cells work by accumulating in response to the potential difference
> not directly responding to the field, thus none of them have response times
> anywhere fast enough to see a change on the 1 millisecond scale.
>
While neuronal action potential durations are on the order of a few milliseconds,
cardiac action potentials last a few hundred milliseconds.
>>> There is no point in argueing for reasons why the cytoplasm does not become
> more positive during an action potential when thousands of measurements of
> intracellular potential have shown that it does.
>>
No one is disputing that something becomes more positive during the action
potential.
Let me construct in another fashion.
Postulate 1:
The cytoplasm, extracellular solution and the
mitochondrial solutions are highly conductive - they approximate pure conductors.
In physics, the definition of a pure conductor is that there is no electric field
within
them. Specifically, any charge within a conductor will distribute itself such the
electric field within the conductor is zero, ie, they will line along the boundary
of
the conductor.
Postulate 2:
The mitochondria is placed within the cytoplasm with an insulating boundary.
Postulate 3:
Charge is moved from the mitochondria to the cytoplasm. So that -Q charge
remains
on the mitochondria and +Q is on the cytoplasm.
Question:
What is the electric field outside the cytoplasm. Zero. The net charge within
any
closed surface is zero; therefore by Gauss's Law, E = 0.
What is the electric field within the cytoplasm? Zero. Because both the
mitochondria
and cytoplasm are conductors, the charges line along the boundary between the two.
So again, the net charge within any closed surface not including the boundary is
zero.
Therefore, E = 0.
What is the electric field within the insulator (mitochondrial membrane)?
E = e*e0 * Q* A/d, where e0 is the dielectric constant of vacuum, e is the
dielectric factor
of the membrane, A is the area, d is the width
of the membrane.
Postulate 4:
Place a conductor (extracellular solution) with an insulating boundary (plasma
membrane)
around the cytoplasm.
Postulate 5:
Move charge, q from the cytoplasm to the extracellular solution.
The same arguments hold for the interface between the cytoplasm and the
extracellular solution.
Crucial question:
Did the movement of charge q have an effect on the charge distribution between
the
mitochondria and the cytoplasm.
No. Because the cytoplasm is a conductor, the electric field within is zero.
So, the
net charge within any surface enclosing the mitochondria must be zero. However,
moving
charge from the cytoplasm to the extracellular solution does not move charge from
the
mitochondria to the cytoplasm. Therefore, charge Q and -Q remains lining the
mitochondrial
membrane.
This argument relies heavily on the 'pure' conductivity of the cytoplasm. If this
is true,
then Gauss's law can be used to demonstrate that the electric field within the
cytoplasm
is zero.
So we have a situation with a closed capacitor within another closed capacitor.
So charge movement during an action potential causes a change in the charge
distribution across just the membrane.
Additional evidence regarding the location of the voltage potential are the voltage
dependent and independent mechanisms of membrane proteins. The binding of
charged particles (for example to block channels) to ion channels can be
voltage dependent or independent - if the binding site is within or without the
voltage field (terminology used in electrophysiology, though I think that it
should be written electric field).
