Calculate how much energy it takes to pump substances across membrane. Since active transport is usually driven directly or indirectly by ATP hydrolysis, understand how steep a gradient ATP hydrolysis can maintain for a particular solute across membrane is important. For the questions below, assume that hydrolysis of ATP to ADP and Pi proceeds with a G of -12 kcal/mole; that is, ATP hydrolysis can drive active transport with a G of +12 kcal/mole. Assume that V is -60 mV. The gas constant, R, is 1.98 x 10 ^-3 kcal/oK mole and Faraday’s constant, F, is 23 kcal/V mole. 

A. What is the maximum concentration gradient that can be achieved by the ATP-driven active transport into the cell of an uncharged molecule such as glucose, assuming that 1 ATP is hydrolyzed for each solute molecule that is transported?  

B. What is the maximum concentration gradient that can be achieved by active transport of Ca ²⁺ from the inside to the outside of the cell? How does this maximum compare with the actual concentration gradient observed in mammalian cells which have 10 ^-4 mM inside of the cells and 1-2 mM outside of the cells?  

C. Calculate how much energy it takes to drive the Na ⁺ -K* pump. This remark- able molecular device transports five ions for every molecule of ATP that is hydrolyzed: 3 Na ⁺ out of the cell and 2 K ⁺ into the cell. The pump typically maintains internal Na+ at 10 mM, external Na ⁺ at 145 mM, internal K ⁺ at 140 mM, and external K ⁺ at 5 mM. We know that Na ⁺ is transported against the membrane potential, whereas K ⁺ is transported with it. (The G for the overall reaction is equal to the sum of the G values for transport of the individual ions.)  

D. How efficient is the Na+-K+ pump? That is, what fraction of the energy available from ATP hydrolysis is used to drive transport?