In the hydrolysis of ATP to ADP and Pi, the equilibrium...

In the hydrolysis of ATP to ADP and $P_{i}$, the equilibrium concentration of ATP is too small to be measured accurately. A better way of determining $K_{\mathrm{eq}^{\prime}}^{\prime},$ and hence $\Delta G^{\circ \prime}$ of this reaction, is to break it up into two steps whose values of $\Delta G^{\circ \prime}$ can be accurately determined. This has been done using the following pair of reactions (the first being catalyzed by glutamine synthetase): (1) $\mathrm{ATP}+$ glutamate $+\mathrm{NH}_{4}^{+} \rightleftharpoons \mathrm{ADP}+\mathrm{P}_{i}+$ glutamine $+\mathrm{H}^{+}$ \[\Delta G_{1}^{\circ \prime}=-16.3 \mathrm{kJ} \cdot \mathrm{mol}^{-1}\] (2) Glutamate $+\mathrm{NH}_{4}^{+} \rightleftharpoons$ glutamine $+\mathrm{H}_{2} \mathrm{O}+\mathrm{H}^{+}$ \[\Delta G_{2}^{\circ \prime}=-14.2 \mathrm{kJ} \cdot \mathrm{mol}^{-1}\] What is the $\Delta G^{\circ \prime}$ of ATP hydrolysis according to these data?

In the hydrolysis of ATP to ADP and $P_{i}$, the equilibrium concentration of ATP is too small to be measured accurately. A better way of determining $K_{\mathrm{eq}^{\prime}}^{\prime},$ and hence $\Delta G^{\circ \prime}$ of this reaction, is to break it up into two steps whose values of $\Delta G^{\circ \prime}$ can be accurately determined. This has been done using the following pair of reactions (the first being catalyzed by glutamine synthetase):
(1) $\mathrm{ATP}+$ glutamate $+\mathrm{NH}_{4}^{+} \rightleftharpoons \mathrm{ADP}+\mathrm{P}_{i}+$ glutamine $+\mathrm{H}^{+}$
\[\Delta G_{1}^{\circ \prime}=-16.3 \mathrm{kJ} \cdot \mathrm{mol}^{-1}\]
(2) Glutamate $+\mathrm{NH}_{4}^{+} \rightleftharpoons$ glutamine $+\mathrm{H}_{2} \mathrm{O}+\mathrm{H}^{+}$
\[\Delta G_{2}^{\circ \prime}=-14.2 \mathrm{kJ} \cdot \mathrm{mol}^{-1}\]
What is the $\Delta G^{\circ \prime}$ of ATP hydrolysis according to these data?

Key Concepts

Gibbs Free Energy

Gibbs free energy is a thermodynamic function that measures the maximum amount of work that can be extracted from a chemical reaction at constant temperature and pressure. In biology, the standard Gibbs free energy change (?G°') is used to quantify the energy change under defined conditions (pH 7, 1 M concentrations, 25°C), providing insight into the spontaneity of reactions such as ATP hydrolysis.

Hess's Law

Hess's Law states that the total enthalpy change for a reaction is the same regardless of the reaction pathway, meaning that the overall free energy change (?G°') can be obtained by summing the free energy changes of individual steps. This principle allows complex reactions to be analyzed through simpler, measurable sub-reactions, aiding in the indirect determination of difficult-to-measure reaction energetics.

Reaction Coupling

Reaction coupling involves linking a non-spontaneous reaction to a spontaneous one, so that the overall process becomes thermodynamically favorable. In biochemical systems, ATP hydrolysis is commonly used to drive unfavorable reactions forward. By splitting ATP hydrolysis into measurable steps, the overall energy change can be deduced using the principle of reaction coupling.

Standard Biochemical Conditions

Standard biochemical conditions are a set of defined parameters (such as pH 7, 25°C, and 1 M concentrations) used to measure and compare the energetics of biochemical reactions consistently. The notation ?G°' is used to indicate free energy changes measured under these standard conditions, which are especially useful in the context of enzyme-catalyzed reactions and cellular metabolism.

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