A cell-free system is designed to synthesize dipeptides from free amino acids

CHEMISTRY · Multi-part · AP · Chemistry · Thermodynamics and Electrochemistry · Thermodynamics and Electrochemistry

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) 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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