What is the maximum ratio of [I – ] in to [I – ] out that could be maintained at

Question

What is the maximum ratio of [I–]in to [I–]out that could be maintained at equilibrium if the Na+ gradient is kept constant (by other transport processes) such that transport of Na+ into the cell has a ?G of –30 kJ/mol. Assume the membrane potential is –155 mV (inside negative) and that transport of iodide does not affect the size of the Na+ gradient. Perform your calculation at body temperature (37°C).

Hint: You will need to balance unfavorable the iodide ion transport against this favorable energy for Na+ transport.

Explanation / Answer

We know that ions move under influence of driving force deltaG and and membrane potential created by distribution of ions across the membrane. The governing equation is -

deltaG =ZFVm + RT*ln(Cin/Cout) or deltaG = ZFVm + 2.303RT*log (Cin/Cout)

Here Z is the charge on ion, Ris gas constant (8.135 J/K*mol), F is Faraday's contant (9.65 x 10^4 C/mol), T is temperature (given as 37C or 310 k), Vm is membrane potential (given as -155mV or -0.155V)

Now since I- transport has to be balance by Na+, therefore, Cin/Cout will be I-in/I-out and Z = -1. Putting all the values in the equation, we have-

-30x 10^3 J/mol = (-1)*(9.65x 10^4 C/mol)*(-0.155V) + 2.303*(8.135J/K*mol)*310K*log[I-]in/[I-]out

This gives log[I-]in/[I-]out = 7.75 or [I-]in/[I-]out = 10^7.75 = 5.6 x 10^7

Thanks!

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