Nernst equations - Can anyone help me with this?

alex taylor ataylor at superior.carleton.ca
Sun May 22 17:51:22 EST 1994


In article <Rq2Ndh9.gokelly at delphi.com>,
GREGORY C.O'KELLY  <gokelly at delphi.com> wrote:
>	Questions about Nernst equations and the offical view
>
>	The Nernst equation was derived by Walter Nernst in 1888 
>from thermodynamic principles.  He was attempting to find a way to 
>estimate potential difference due to ion gradients.  He expressed 
>this potential difference in volts.  Neuroscience has assumed that 
>these were the volts of electricity.  Electricity is the movement of 
>electrons across or along a conductor involving the valence shells of 
>the atoms of the conductor.

          This is an incorrect definition. An electrical current
results whenever any charged particle moves. Weather this is an
electron or not is totally irrelevant. Voltage is simply a measure of
a difference in potential energy-and by the way the Nernst potential
is equivalent to voltage in an electrical circuit.

>	The Nernst equation does not directly translate into the 
>potential difference of electricity.  In the case of the squid giant 
>axon we find that the Nernst equation results in for Na+, K+, and Cl- 
>simultaneously +55mV, -75mV, and -60mV.  If these values were 
>actually electrical values, then we would have -80mV for the 
>resting membrane potential, Vmr.

          Chloride equilibrates accross the membrane. It contributes
very little if anything the resting potential. P.S. electrochemical
gradients are a little more complicated than this. You must include
concentration of ion on both sides of the membrane as well as the
species of ion. This is usually covered in first year physics or
chemistry-try the relevant text.

>membrane to other ions.  It should be pointed out, however, that this 
>approach assumed that theoretical membrane potential was not only 
>a result exclusively of ion gradients of potassium, but that it 
>couldn't also simultaneously exist, as it did in the squid axon, with 
>an Ena of +55.  This approach equated E with V, Nernst membrane 
>potentials with electrical potentials, and insisted that Ek or Ena 
>must prevail, but that the two could not be simultaneous as they 
>were in the squid giant axon.  In other words, Vm would go from Ek 
>to Ena as the action potential passed and Na+ flowed across the 
>membrane.

          Actually, the Goldmann equation makes no such assumption,
nor are E and V treated as strictly equivalent. These equations are
derived in "Ionic Channels of Excitable Membranes" and in may other
sources. The real problem with the H and H model of the membrane has
to do with the time course of activation and inactivation of the
sodium and potassium currents. With the advent of patch-clamping it
was discovered that the timecourses of the currents were different in
the ensemble average (as modelled by H and H) than they were at the
single-channel level. 

>	Furthermore, because, with the passing of an action potential, 
>the Vm went from negative to positive, this was taken that Na+ 
>rushed in to the membrane, and K+ rushed out.  According to the 
>Nernst equations, if the concentration of Na+ intracellularly is 
>increased to more nearly what it is outside, then Ena is smaller than 
>+55mV.  Still it was thought that because Vm went from -60mV to 
>+45 or +50mV, and because, unlike in the giant axon of the squid, 
>these Ek and Ena could not exist simultaneously, and because Vm 
>was equated with Ex,  sodium was replacing potassium 
>intracellularly (in which case, according to the Nernst equations, 
>Ena should have been far smaller than +55mV).

          You have an incorrect concept, actually very little
charge moves. The membrane exists in a steady-state, not in
equilibrium. This is why H and H had to use the Goldmann equation to explain
what was going on. The voltage changes in a neuron because of the
capacitive discharge of the membrane, not because the intracellular
space is being filled up with sodium ion.

>	I suspect that the conflation between electrical potential 
>differences and Nernst potential differences, even though they are 
>expressed in the same terms, falsely equates ion gradients with 
>voltage.  I am told I don't know what I am talking about,
          
          You don't know what you are talking about. Voltage is
voltage. An intracellular recording rig is basically a glorified
voltmeter. The Nernst equation was simply one attempt to model a
phenomenon that was already known to exist-that is that there is a
potential difference accross the membrame of nerve cells of about -60
mV.

>all makes sense, that sodium pumps are legitimate ad hoc 
>stratagems to allow for ion currents which are purportedly 
>electrical. 

          Ion pumps are electrogenic if there is unequal charge
transfer eg the sodium-potassium pump. If they are blocked with a
toxin the membrane potential changes. The current that they generate
is as electrical as it gets.

>I am not denying membrane permeability, and ion 
>channels.  What I am questioning is the equating of Ex and Vm and 
>the insistence that Nernst equations tell us the latter too;  that Ek 
>and Ena cannot exist simultaneously across the same membrane wall 
>as they do in the squid, i.e., that Na+ displaces K+;  and that Em must 
>be one or the other.
>	Can anyone shed some light on this matter for my own 
>enlightenment without becoming ad hominem?  I will admit to being 
>a beginner in this area, so maybe there is something the textbook did 
>not cover.  If not, there could be some problems.

          I think that you would find some basic physical chemistry
more beneficial than a new textbook. The first few chapters of Kandel
and Schwartz would also be a good source of reading material.

















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