Chemistry

Chemistry

Problem

A cell-free system is designed to synthesize dipeptides from free amino acids. The direct condensation of two generic amino acids (AA) to form the dipeptide AA–AA has ΔG∘=+21 kJ mol−1\Delta G^{\circ}=+21\,\text{kJ mol}^{-1} at 298 K298\,\text{K}. Investigators can choose to couple this condensation to the hydrolysis of either ATP or GTP, whose standard free-energy changes depend on pHpH according to the empirical relations below: ΔGATP hydrolysis∘=−35 kJ mol−1+1.5(pH−7)ΔGGTP hydrolysis∘=−33 kJ mol−1+1.2(pH−7)\begin{aligned} \Delta G^{\circ}_{\text{ATP hydrolysis}} &= -35\,\text{kJ mol}^{-1} + 1.5(pH-7)\\ \Delta G^{\circ}_{\text{GTP hydrolysis}} &= -33\,\text{kJ mol}^{-1} + 1.2(pH-7) \end{aligned} (a) Derive an expression for the overall ΔGcond∘\Delta G^{\circ}_{\text{cond}} of the coupled dipeptide-forming reaction as a function of pHpH when ATP hydrolysis is used as the driving reaction. (b) Repeat the derivation for GTP hydrolysis. (c) Determine the range of pHpH values (to the nearest tenth) for which coupling to ATP hydrolysis renders the condensation thermodynamically favorable (ΔGcond∘<0\Delta G^{\circ}_{\text{cond}}<0). Perform the same determination for GTP. (d) At pH=8.0pH=8.0, which nucleotide triphosphate provides the smaller magnitude of negative ΔGcond∘\Delta G^{\circ}_{\text{cond}}? Explain why choosing the less exergonic option might be advantageous for conserving cellular energy stores. (a) Derivation for ATP-driven coupling (b) Derivation for GTP-driven coupling (c) Determination of favorable pHpH ranges (d) Comparison and energy-conservation rationale

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