Chapter 9, Problem 9.5PS

QUANTITATIVE Glucose Phosphorylation. The direct phosphorylation of glucose by inorganic phosphate is a thermodynamically unfavorable reaction:

$\begin{array}{c}\text{glucose}+{\text{P}}_{\text{i}}\to \text{glucose-}6\text{-phosphate}+{\text{H}}_2\text{O}\\ \Delta G{°}^{\prime }=+3.3\text{ kcal/mol}\end{array}$    (9-21)

In the cell, glucose phosphorylation is accomplished by coupling the reaction to the hydrolysis of ATP, a highly exergonic reaction:

$\begin{array}{c}\text{ATP}+{\text{H}}_2\text{O}\to \text{ADP}+{\text{P}}_{\text{i}}\\ \Delta G{°}^{\prime }=-7.3\text{ kcal/mol}\end{array}$    (9-22)

Typical concentrations of these intermediates in yeast cells are

$\begin{array}{l}\text{[glucose-}6\text{-phosphate}]=0.08\text{ m}M\\ \text{[ATP}]=1.8\text{ m}M\left[{\text{P}}_{\text{i}}\right]=1.0\text{ m}M\\ \text{[ADP}]=0.15\text{ m}M\end{array}$

Assume a temperature of 25°C for all calculations.

1. (a) What minimum concentration of glucose would have to be maintained in a yeast cell for direct phosphorylation (Reaction 9-21) to be thermodynamically spontaneous? Is this physiologically reasonable? Explain your reasoning.
2. (b) What is the overall equation for the coupled (ATP-driven) phosphorylation of glucose? What is its ΔG°′ value?
3. (c) What minimum concentration of glucose would have to be maintained in a yeast cell for the coupled reaction to be thermodynamically spontaneous? Is this physiologically reasonable?
4. (d) By about how many orders of magnitude is the minimum required glucose concentration reduced when the phosphorylation of glucose is coupled to the hydrolysis of ATP?
5. (e) Assuming a yeast cell to have a glucose concentration of 5.0 mM, what is ΔG′ for the coupled phosphorylation reaction?