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Nernst equations - Can anyone help me with this?

GREGORY C.O'KELLY gokelly at delphi.com
Mon May 23 00:22:55 EST 1994

	Thanks a bunch for the tips.  You referred me to Kandel, Jessel, 
and Schwartz's PRINCIPLES OF NEURAL SCIENCE, and that is the book 
I have before me, and the book about which I have questions.  You say 
that a lot of terms are used, but that E and V are the same for the 
biologist, that a bit of history is involved here, that one must go to 
the original historical context and papers to make sense of it all, 
but that E and V are the same for the biologist.  And that is just 
what I have questions about.  Is the assumption justified?  
Considering the historical context I can only conclude that the 
assumption is not justified.
	All through the nineteenth century and into the first part of 
the twentieth century electricity was thought of as a fluid, and it 
was figured that the laws of fluid dynamics were directly 
applicable.  The Nernst equations were developed by Walter Nernst 
two decades before a term, 'amperes', was even agreed upon for I as 
in V = IR;  a decade before the discovery of the electron;  more than 
two decades before the place of the electron was understood in the 
molecule.  Nernst included the term 'valence' in his equation, but for 
him valence was the tendency to be attracted to one pole or another 
in an electrolyitc solution based upon the sign of the ion.  Ions in the 
1880's and 90's were finally widely accepted, along with atoms and 
molecules, by chemists as things that really existed rather than 
theoretical postulates.  It would still be more than a quarter of a 
century before Mendeleev's 1865 periodic table of the elements 
could be understood in terms of electron 'shells', and longer still 
before Pauling's 1939 treatise on the nature of covalent and ionic 
bonds.  Submolecular chemistry was poorly understood by the 
chemist until then, and this ignorance was manifest in the 
chemotherapy of Paul Ehrlich who searched for a 'magic bullet' early 
in the twentieth century based upon the results of inductive, time-
consuming trial-and-error.  The valence of Nernst is not the valence 
of Pauling or that of electomagnetists speaking of the movement of 
electrons in a conductor involving the valence shells of the 
conductor's electrons traveling at near the speed of light.
	It was theorizing about the electron which lead in the 1930's 
and 1940's to the view that it was fundamentally different from any 
fluid, it exhibited wave/particle duality and field effects and 
traveled at near the speed of light on a wire.  This was unlike any 
ion, certainly.  The four fundamental forces of nature were defined 
as the strong force, the weak force, electromagnetism, and gravity.  
The first two dealt with atomic nuclei;  the third with light, 
magnetism, electricity, and particles exhibiting a wave/particle 
duality;  and the last, gravity, with everything else including fluid 
flow even of ions.  Gravity dealt with bodies extended in space, not 
point charges.   Nernst was heavily into thermodynamics which 
sought to explain heat in terms of atomic or molecular kinetics, a 
helpful explanation, but no way near the modern day view of heat as 
light or photons given off as electrons drop to lower energy levels in 
the atom.  So I must conclude, Tom, that history casts suspicion on 
the idea that Em = Vm even if the units of measure are the same.

	You write, "It's charge separation, baby.  It's all charge.  
Whether you're dealing with x mol of electrons separated by y 
distance, or x mol of Cl- separated by y distance, it's all charge.  
Remember, voltage is a measure of potential energy.  That's all it 
	I agree with this, but there is quite a difference between the 
potential difference of bodies extended in space and that of the 
electromagnetist who deals with electricity.  The first potential 
difference is that of the fundamental force of gravity, the second 
potential difference is that of electromagnetism.  I think the trouble 
I am having has its roots in the elision of these two different 
subject matters.

	You write, "A concentration gradient is potential energy.  
(letting a chem flow down its gradient can perform work) A charge 
separation is *also* potential energy."
	Sure, I can go along with this, but again they are two types of 
potential energy involving two different fundamental forces of 
nature even if the unit of measure, volts, is the same.  We're not 
talking about the same thing.  What I would like to know is what is 
the justification for equating Ex with Vm;  I am not content to take 
it on authority because there are some problems with reason and 
physics if this identity should be allowed.

 	You write, "If we have a membrane and we put different 
concentrations of an ion on both sides, that ion will want to move 
down its gradient.  So will any other ions involved in the system."
	Okay.  But what makes this happen is entropy, not the doing of 
work or the expenditure of energy,  but the loss of energy to the 
overall dissipation and 'disorderliness' of the universe.  If we see 
this Nernst potential as the amount of stored work in producing the 
gradient, that says nothing about our ability to take this work out of 
storage by letting the gradient run down.  It's entirely a statistical 
thing.  Someone is taking the potential difference idea too far.  If it 
were so then why isn't power also derived at hdydroelectric plants 
from the movement of the ions as the ion current goes by?  Because 
there is no stored difference in charge?  Check out the types of ions 
that coexist internally and externally in the squid giant axon.  
Negative ions coexist with positive.  So, the more polluted the water 
the more ion current, and therefore the bigger the resevoir of 
potential energy to be mined?  Sound absurd?  No?  Too bad.

	You write, "If we punch a perfectly selective hole in the 
membrane that *only* lets Na flow through, we see it flow down its 
gradient.  It also builds up charge on the side it's flowing into.  So, 
we are converting the potential energy of the concentration 
gradient into the potential energy of the electrical 
	Here I have to disagree.  You're saying that entropy, the running 
down of the ion gradient, is just a change of potential energy from 
chemical to electrical?  If the concentration seeks to balance 
through the hole we've punched, then the charge too is going to be 
the same per unit volume on either side.  There is no charge gradient 
unless there is a density difference per unit volume, and that is 
chemical concentration, not charge difference.  The Nernst equations 
are about ion concentrations, not electrical charge.  We can only be 
talking statistics here for the signs of the molecules of Na remain 
the same as they flow through the hole.

	You write, "The ion would tend to flow down the conc. gradient 
until it is exactly opposed by the charge it is building up.  This 
equilibrium is what is calculated by the Nernst potential."
	The Nernst equations say nothing about the buildup of charge.  
What they say is that there is a potential that is indicated by a 
difference of concentration across a membrane which acts to reduce 
the concentration difference such that ln [K+]outside/[K+] inside will 
approach 0 as that ration approaches 1.

	You write, "To prove this to yourself [what I am trying to 
deny], dig up the free-energy calcs for a charge separation and for a 
conc. gradient.  Set them equal and opposite to each other.  
Bingo, you get the Nernst potential
equations.  (textbook: Alberts et al, Mol Bio of the Cell, p 314)
   charge: ^G = zFV       (^=delta)
   conc:   ^G = -RTln(Cout/Cin)
      so you get zFV = RTln(Cout/Cin)"
	Here you are talking about 'free-energy calcs'.  Do you know 
why they call it free energy?  Not because there is so much of it 
around to be tapped, but because it can't be tapped.  It is the force of 
entropy.  No one has ever made an apparatus and ever will that runs 
on this as a source of energy.  There are no perpetual motion 
machines!  This kind of 'energy' is not like electrical or 
electrochemical energy which involves electrons and negative 
charge, and which is usable, and which also has the unit 'volts'.

	You write, "...to reach the Nernst potential, the ion has 
to be permeable.  It also would have to be the only ion 
	The Nernst equations say nothing about permeability, only ion 
concentration gradients.   Where does this requirement come from?  
The Goldman equation?  All that was was a device to explain 
experimental results with regard to the effects of K+, Na+, and Cl- 
on measured membrane potential in such a way that the results were 
those predicted by the Nernst equations.  It was believed the 
membrane had to be permeable to the select ion otherwise the 
Nernst equations wouldn't hold (you couldn't add Ek, Ena, and Ecl and 
come up with -65mV, but you could come close is you thought only 
Ek was pertinent, =Vm that is).  By assuming certain permeabilities 
to each of the three ions the Nernst potential could be made to agree 
with exprimental results.

	You write, "Example: Put two different conc of NaCl across a 
membrane.  Punch a *NON-SELECTIVE* hole.  What happens?  Both Na 
and Cl flow down conc gradients. Na would try to build a + 
charge, Cl a - charge.  Result?  They cancel."
	If this is so, then the Nernst potentials should cancel too 
shouldn't they?  But they don't.  So maybe we're again talking about 
two different kinds of potential.

	You respond to my :  >  If these values were 
>actually electrical values, then we would have -80mV for the 
>resting membrane potential, Vmr.
	"Again, *weighted* average.  The ions have to move to build 
	I'm not sure what you're talking about here.  Do you mean the 
ions must collect in a group;  certainly not that ionization itself 
depends upon movement?  If the ions collect in a group, the Nernst 
equations address the concentration gradient of two groups, not the 
electrical charge of one in relation to another.

	You write, "EK and ENa *do* exist simultaneously.  And, why 
not?  They are just the theoretical values for *how much charge 
could be separated ***if*** the ion were allowed to move 
***and*** it were the only one allowed to move.  Open Na 
channels, you move towards ENa.  Open K channels, you 
move towards EK."
	But the Nernst equations don't say this.  They say that if the 
ions are allowed to run across the gradient Ek or Ena goes to zero as 
the ratio of ions within and without approaches unity.  Ex is 
determined by gradients, and the running down of these gradients 
doesn't move us toward Ex, instead it runs Ex to 0.

	You write, "Why not equate ion gradients with voltage?  What's 
the difference between separating a charge composed of Cl- 
ions and separating a charge composed of electrons?  It's still 
potential energy, isn't it?"
	Here is the problem.

	You write, "You're just assuming that there's something 
magical about the units of charge that are normally used 
for electricity that means that they can't be used to talk 
about ionic charge."
	It looks like it's the other way around.  Tom, it appears that 
you and neural science are assuming that there is something magical 
that allows Nernst potentials to be equated with electrical 

	You write, "Also, remember that there are (for 
historical reasons) a lot of different terms being used.  E 
and V are identical to the biologist, so don't get screwed 
up by that.  We measure Vm and Ex now, but if you go back 
to original papers, it may be different.  (also, the origninal 
papers also measured outside voltage wrt inside, thus the signs 
were all backwards)"
	You then appreciate history and its effects on the formulations 
and theorizations and terminology of science.  I think neural science 
is also a victim of the distorting effect of unarticulated paradigms 
or metaphysical views, and that is what we are witnessing here.  I 
think that all the laboratory tests and measurements taken can be 
explained just as well using another approach to the nature of nerve 
impulse propagation, to it being semiconduction on an N type 
semiconductor, and this is why we have the organic anions of acid 
and protein which make up almost as much of a presence in the axon 
of the squid as the potassium ions.  I think its plain to see that Vm 
has nothing to do with ion gradients or the movement of ions, and 
this is the central fallacy of modern neural science.  I could be 
wrong.  I'm just a beginner at this, and have yet to complete a course 
in it.  I am trained in the philosophy and history of science, so I must 
profess ignorance.


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