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Goldman-Hodgkin equation : origin ??

William Moody profbill at u.washington.edu
Thu Feb 22 12:29:55 EST 1996


     Permeability is related to the ease with which an ion goes through 
the membrane, either absolutely, or in the case of the GHK equation, ease 
relative to other ions.  So, yes, its ability to compete for channel 
binding sites with other ions.  Permeability can be measured by 
radioactive flux experiments, or relative permeability by reversal 
potential measurements.  This term applies to single ions, and hence 
permeability is not concentration-dependent, except in unusual 
circumstances (e.g., ion concentration affects number of open channels).  
Conductance measures how many ions per second cross the membrane, and 
hence is measured as a current at a certain voltage.  Conductance is 
concentration-dependent, hence the use of high concentration of permeant 
ions to measure single channels in patch clamp experiments.
     If a channel selects by size, such as the Na channel, the 
conductance and permeability of various ions through it fall in the same 
order: a small, selected ion moves fast throught the channel.  For 
channels, such as the L-type Ca channel, which select by binding, the two 
are inversely related.  An ion with high relative permeability, such as 
Ca over Na, moves slowly through the channel because it is bound by the 
selectivity site.  This is most easily seen with Na moving through the Ca 
channel: in mixtures of Ca and Na, the channel's permeability to Ca over 
Na is very high, and almost no Na moves through.  If you remove all Ca 
(and Mg), the Ca channel passes Na very rapidly, and Na currents through 
Ca channels are much larger than Ca currents.
    About 25 years ago, Alex Mauro wrote a beautiful article defining the 
relationship between circuit and diffusional models of the membrane, and 
if you are serioud about this, it is well worth wading through.  e-mail 
me if you want the citation, as I can't find it right now.



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