A single NaK ATPase pump is present in the plasma membrane o

A single Na⁺/K⁺ ATPase pump is present in the plasma membrane of an artificial cell with an initial cellular environment of 500 molecules of Na⁺ and 1000 molecules of ATP inside the cell, 500 molecules of K⁺ outside the cell, and a net charge differential across the plasma membrane of 0. Assuming the only changes in the cellular environment are a result of the pump\'s actions, what would be the number of Na⁺, K⁺ and ATP molecules inside the cell after 10 cycles of the pump and what would be the net charge differential (inside - outside) across the plasma membrane?

300 Na⁺; 200 K⁺; 100 ATP and -100 charge differential (inside - outside)

470 Na⁺; 20 K⁺; 990 ATP and -20 charge differential (inside - outside)

30 Na⁺; 20 K⁺; 900 ATP and -10 charge differential (inside - outside)

470 Na⁺; 480 K⁺; 10 ATP and +100 charge differential (inside - outside)

30 Na⁺; 480 K⁺; 10 ATP and +20 charge differential (inside - outside)

Solution

Answer: (b) 470 Na+; 20 K+; 990 ATP and -20 charge differential (inside - outside)

In each cycle of the pumping action, 3 sodium ions exits while 2 potassium ions enter the cell, at the cost of 1 ATP molecule.

So, after 10 cycles of pumping, 30 sodium ions goes out and 20 potassium ions enters the cell at the cost of 10 ATP molecules.

Therefore, the net balance of the pumping action:

Inside the cell: (500-30) sodium ions, (1000-10) ATP and 20 potassium ions

= 470 sodium ions, 990 ATP, 20 potassium. Total charge = 490

Outside the cell: (500-20) potassium ions, 30 sodium ions

= 480 potassium ions, 30 sodium ions. Total charge = 510

So, charge difference (inside-outside) = 490-510 = -20