(Integrates with Chapter 3 .) Fructose is present outside a cell at \(1 \mu M\)
concentration. An active transport system in the plasma membrane transports
fructose into this cell, using the free energy of ATP hydrolysis to drive
fructose uptake. What is the highest intracellular concentration of fructose
that this transport system can generate? Assume that one fructose is
transported per ATP hydrolyzed; that ATP is hydrolyzed on the intracellular
surface of the membrane; and that the concentrations of ATP, ADP, and \(P_{i}\)
are \(3 \mathrm{m} M, 1 \mathrm{m} M,\) and \(0.5 \mathrm{m} M,\) respectively.
\(T=298 \mathrm{K}\). (Hint: Refer to Chapter 3 to recall the effects of
concentration on free energy of ATP hydrolysis.)