Calcium ATPase pumps are proteins that sit in the membrane of a cell and use energy in the form of molecules of adenosine triphosphate (ATP) to remove Ca2+

from the cell, against a steep concentration gradient. They are vital components of all cells; if cells cannot control their intracellular Ca2+

concentration, they die, and then so do you.

The rate, r, at which a calcium ATPase pumps Ca2+

ions is a function of (at least) two things; the concentration of Ca2+

inside the cell cytoplasm (call this concentration

c) and the concentration of Ca2+ outside the cell (call this external concentration co). Typically, r is well described by for some constants Ki , αi .

a. If co is held fixed, what is the maximum rate of the pump, i.e., what is limc→∞ r(c)?

b. What happens as co gets larger?

c. When does the pump reverse direction? What is the maximal reverse flux?

d. If both c and co get very large, but in such a way that co = kc, for some constant k, what does the rate do as c gets very large?