SOS...please help, Na+/H+ pump problem

[aerez]

This problem is a the lone problem in a practice test in which majority of the problems are pretty simple, but this seems to stick out like a sore thumb. Its probably pretty simple, but I dont have a clue as to how to go about it.

here it is:

Animal cells often use Na+ as a cotransport ion to regulate the internal concentration of H+. How many H+ can be transported for each Na+ that moves across the membrane? Use the following data:

[H+]in =6.3 *10^-8 M [H+]out=4*10^-8 M
[Na+]in=12mM [Na+]out=145mM

T=37C or 310 Kelvin
R=1.987 cal/mol-deg K
Vm=-70mV or -0.07V
Faraday=23063 cal/mol-volt

I assume you use one of the following equations though I not 100 percent sure:

change Free energy=RTln[Xout]/[Xin], this is for H+ since its pumped out

change Free energy=RTln[Xin]/[Xout], this is for Na+ since it would be pumped in to the cell.

nernst: Ev=(RTln[Xout]/[Xin])/F


~Dan

[rui_benfeitas]

Well then, you know that the Na+/H+ pump works by coupling the Na+ transportation into the cell to the transportation of H+ to the extracellular fluid, and that for each atom of Na+ that it is transported across the cell, there is one H+ transported the other way.
Further more, you should aknolwedge that that pump has an alosteric regulation - that is, when the intracellular pH rises to the value of 7.2, the pump is disabled.
So, what i think you need to find out first is wheter the pHi is larger than 7.2. If it isnt, then you should calculate the transport potential of each of the ions. When the V(Na+)= Vm, the pump is disabled. So, what you need to know is:

Since Vm = -70mV
[H+]in =6.3 *10^-8 M [H+]out=4*10^-8 M
[Na+]in=12mM [Na+]out=145mM

T=37C or 310 Kelvin
R=1.987 cal/mol-deg K
Vm=-70mV or -0.07V
Faraday=23063 cal/mol-volt

using nernst equation Ev=(RTln[Xout]/[Xin])/F you have:

-70=(1.987*310*ln(145/[Nain])/23063 and with proper basic calculus, you will find out the value of [Na]in. That value should be larger than the one you allready have (i mean [Na+]in=12mM). The difference between the value you calculated and the one i just refered is the amount of sodium ions that travel through the cell.

Do the same for H+, but find out the amount of [H+] out.

That should give you the ion amount that travels. Furthermore, as you allready know, if 1 molecule of H+ travels outwards for each Na+ that is pumped in, the amount of H+ you should use would be the same of Na+ (though im not really sure about this here).

I hope i helped. If you have any doubt, leave a message here or send me one.