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Do small changes in permeability produce small changes in Vm for both Na+ and K+? Are...

Do small changes in permeability produce small changes in Vm for both Na+ and K+? Are large changes in permeability required to approach the E ion for Na+ and K+?
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Answer #1

Concepts

Formula Used: Goldman equation

where PK, PNa and PCl= permeabilities for K+, Na+ and Cl- ions, respectively. Vm is the membrane potential. z is the valence the ion. Since, Cl- ion is not included, hence,

Answer:

Increasing permeability of a membrane for ion shifts the membrane potential towards the equilibrium potential for that type of ion.

Now, we can assume Goldman equation to be a logarithmic equation of type y = log(x)

Differentiating this equation we get,

   

Assume to be Vm and to be the term containing permeability. This equation indicates that the magnitude of depends on the magnitude of and x.

  • if , increase in is much more than the increase in .
  • if increase in is less in comparison to increase in .

Living membranes are highly permeable to potassium but have limited permeability for sodium.

Hence, even a small change (increase) in the permeability of potassium shifts the Vm value towards the Eion (equilibrium potential) of potassium.

However, a large amount of change (increase) in the permeability of sodium is required to shift the Vm value to the Eion of sodium ion. This is because of the permeability of sodium ions. It is very less for biological membranes.

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