Q.36 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 ΔG 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
Understanding how to determine the most negative ΔG for ATP hydrolysis is a high‑yield concept for biochemistry and competitive exams such as CSIR NET and GATE. This solved MCQ uses intracellular concentrations of ATP, ADP and inorganic phosphate to show how the mass‑action ratio controls the actual free‑energy change in cells. Mastering this approach helps you quickly identify which cellular conditions make ATP hydrolysis most thermodynamically favorable.
Question statement
Intracellular concentrations of ATP, ADP and inorganic phosphate (Pi) in four cell types are given below. Which one of these cell types has the most negative ΔG for ATP hydrolysis?
| Cell type | ATP (mM) | ADP (mM) | Inorganic phosphate, Pi (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 |
Correct answer: Cell type B (Option C)
Key concept: ΔG of ATP hydrolysis
For the reaction:
ATP + H2O ⇌ ADP + Pi
the actual free‑energy change in a cell is given by:
ΔG = ΔG°′ + RT ln ( [ADP][Pi] / [ATP] )
- ΔG°′ is the standard free‑energy change under biochemical standard conditions.
- R is the gas constant and T is the absolute temperature.
- The term [ADP][Pi] / [ATP] is the mass‑action ratio for this reaction.
A more negative ΔG occurs when the mass‑action ratio [ADP][Pi] / [ATP] is smaller. In simple terms, high ATP and low ADP and Pi make ATP hydrolysis more favorable.
Step-by-step solution
1. Use the expression for ΔG
For all four cell types, ΔG°′, R and T are the same, so differences in ΔG depend only on the term:
ln ( [ADP][Pi] / [ATP] )
Therefore, comparing ΔG reduces to comparing the values of the ratio [ADP][Pi] / [ATP]. The cell with the smallest ratio will have the most negative ΔG.
2. Identify what makes ΔG more negative
- If [ADP][Pi] / [ATP] decreases, the natural log becomes more negative.
- So smaller values of [ADP][Pi] / [ATP] correspond to more negative ΔG.
3. Calculate the mass‑action ratio for each cell
Compute [ADP][Pi] / [ATP] for each cell type (using mM values and ignoring units):
- Cell L: (1.8 × 5.0) / 3.0 = 9.0 / 3.0 = 3.0
- Cell K: (1.3 × 3.0) / 3.9 = 3.9 / 3.9 ≈ 1.0
- Cell B: (0.7 × 2.7) / 2.7 = 1.89 / 2.7 = 0.7
- Cell M: (0.9 × 8.0) / 7.2 = 7.2 / 7.2 ≈ 1.0
4. Compare the ratios
- Smallest ratio: Cell B (0.7)
- Intermediate ratios: Cells K and M (both ≈ 1.0)
- Largest ratio: Cell L (3.0)
Because cell B has the lowest [ADP][Pi] / [ATP] value, the logarithmic term RT ln( [ADP][Pi] / [ATP] ) is most negative in this cell. This makes ΔG for ATP hydrolysis most negative in cell type B.
Even though cell M has the highest ATP concentration, its product term ADP × Pi is also high, so its ratio is larger than that of cell B. Therefore, M does not have the most negative ΔG.
The order of negativity of ΔG (from most negative to least negative) is:
B > K ≈ M > L
Option-wise explanation
Option (A) L – Incorrect
- Cell L has high ADP and Pi relative to ATP, giving the largest mass‑action ratio (3.0).
- This makes the ln term least negative, so ΔG for ATP hydrolysis is the least negative among the four cell types.
Option (B) K – Incorrect
- Cell K has a better ATP:ADP ratio than L and a lower Pi level, producing a ratio of about 1.0.
- ΔG is more negative than in L but still less negative than in cell B, which has the smallest ratio.
Option (C) B – Correct
- Cell B has the lowest ADP and moderate ATP, leading to the smallest ratio (0.7).
- This minimizes [ADP][Pi] / [ATP], makes the ln term most negative and gives the most negative ΔG for ATP hydrolysis.
Option (D) M – Incorrect
- Cell M contains very high ATP, which by itself would favor a negative ΔG, but ADP and Pi together are also relatively high.
- The resulting ratio (about 1.0) is larger than in cell B, so ΔG for ATP hydrolysis is less negative than in B and comparable to K.
Key takeaway
By focusing on the mass‑action ratio [ADP][Pi] / [ATP] rather than on absolute concentrations alone, this MCQ clearly shows why cell type B yields the most negative ΔG for ATP hydrolysis. This method is broadly applicable to similar exam questions involving Gibbs free energy and reaction quotients.
