Question

Intracellular concentrations of ATP, ADP, and inorganic phosphate in four cell types are given below. Which one of these cell types has the most negative \(\Delta G\) for ATP hydrolysis? 

Cell type	ATP (mM)	ADP (mM)	Inorganic phosphate (mM)
L	3.0	1.8	5.0
K	3.9	1.3	3.0
B	2.7	0.7	2.7
M	7.2	0.9	8.0

• A. L
• B. K
• C. B
• D. M

Hint:

When comparing $\Delta G$ of ATP hydrolysis across conditions, always calculate the ratio $\dfrac{[ATP]}{[ADP][P_i]}$. A larger ratio means ATP hydrolysis is more favorable (more negative $\Delta G$).

Answer 1

The Correct Option is C

Step 1: Free energy relation for ATP hydrolysis
The free energy change is given by:

ΔG = ΔG°' + RT ln(([ADP][Pi])/[ATP])

- More negative ΔG occurs when the ratio [ATP]/([ADP][Pi]) is higher.
Step 2: Calculate the ratio for each cell type
- For L: [ATP]/([ADP][Pi]) = 3.0 / (1.8 × 5.0) = 3.0 / 9.0 = 0.33
- For K: [ATP]/([ADP][Pi]) = 3.9 / (1.3 × 3.0) = 3.9 / 3.9 = 1.0
- For B: [ATP]/([ADP][Pi]) = 2.7 / (0.7 × 2.7) = 2.7 / 1.89 ≈ 1.43
- For M: [ATP]/([ADP][Pi]) = 7.2 / (0.9 × 8.0) = 7.2 / 7.2 = 1.0

Step 3: Compare the values
- Higher ratio [ATP]/([ADP][Pi]) ⇒ more negative ΔG.
- The highest ratio is for cell type B (≈ 1.43).
Final Answer: The most negative ΔG for ATP hydrolysis is in cell type B.