(Integrates with Chapter \(3 .)\) The standard free energy change \(\left(\Delta G^{\circ \prime}\right)\) for hydrolysis of fructose- 1,6 -bisphosphate (FBP) to fructose6-phosphate (F-6-P) and \(\mathrm{P}_{\mathrm{i}}\) is \(-16.7 \mathrm{kJ} / \mathrm{mol}\) \\[ \mathrm{FBP}+\mathrm{H}_{2} \mathrm{O} \longrightarrow \text { fructose- } 6-\mathrm{P}+\mathrm{P}_{\mathrm{i}} \\] The standard free energy change \(\left(\Delta G^{\circ \prime}\right)\) for ATP hydrolysis is \(-30.5 \mathrm{kJ} / \mathrm{mol}\) \\[ \mathrm{ATP}+\mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{ADP}+\mathrm{P}_{\mathrm{i}} \\] a. What is the standard free energy change for the phosphofructokinase reaction: \\[ \text { ATP + fructose- } 6 \text { -P } \longrightarrow \mathrm{ADP}+\mathrm{FBP} \\] b. What is the equilibrium constant for this reaction? c. Assuming the intracellular concentrations of [ATP] and [ADP] are maintained constant at \(4 \mathrm{m}\) Mand \(1.6 \mathrm{m} M\), respectively, in a rat liver cell, what will be the ratio of [FBP]/[fructose-6-P] when the phosphofructokinase reaction reaches equilibrium?

The concept of standard free energy change, \(\Delta G^{\circ \prime}\), is central to understanding the behavior of biochemical reactions. It's the amount of energy exchanged in a reaction under standard biochemical conditions (1 M concentration, pH 7, 25°C, and 1 atmosphere of pressure). This value can indicate the spontaneity of a reaction; a negative value, as in the case of ATP hydrolysis, which has a \(\Delta G^{\circ \prime}\) of -30.5 kJ/mol, implies that the reaction occurs spontaneously.

Bioenergetics is concerned with these energy changes, as they inform us about the cellular processes that can occur without the input of additional energy. When considering a reaction that is not under standard conditions, the actual change in free energy (\(\Delta G\)) will differ but can be related back to the standard free energy change through concentration and other factors affecting the reaction.

ATP hydrolysis is a critical reaction that releases energy by breaking the high-energy bond between the last two phosphates in ATP, resulting in ADP and an inorganic phosphate (\(P_i\)). The standard free energy change is approximately -30.5 kJ/mol, signifying that ATP hydrolysis is a highly exergonic process, which means it releases a significant amount of energy that cells harness for their metabolic functions.

In biologic systems, ATP is often referred to as the 'energy currency' because it provides the energy needed for many endergonic reactions (those that require an input of energy) to proceed. The phosphoryl group transfer potential of ATP is what makes it so central in metabolism.

Understanding ATP Hydrolysis in Metabolic Pathways

By coupling the favorable ATP hydrolysis with unfavorable reactions, cells effectively lower the overall energy demand, allowing complex biosynthetic and transport tasks to be performed. This coupling drives the transformation of reactants to products in various metabolic pathways.

The phosphofructokinase (PFK) reaction is a pivotal step in the glycolytic pathway, involving the conversion of fructose-6-phosphate (F-6-P) into fructose-1,6-bisphosphate (FBP) with the help of ATP. This specific reaction is controlled by the enzyme phosphofructokinase-1, which plays a significant role in regulating the rate of glycolysis.

The standard free energy change of the PFK reaction can be computed using the changes of ATP hydrolysis and FBP hydrolysis. Once we know these values, we can assess the direction in which the reaction will proceed and understand how the reaction is regulated in the context of cellular metabolism.

Calculating the Free Energy Change of PFK

We apply Hess's Law to find the standard free energy change for the PFK reaction by taking the difference between the energy changes of ATP hydrolysis and FBP hydrolysis. The calculation reflects how energy transductions within a single pathway are intricately connected.

The equilibrium constant (K') of a reaction is a value that offers deep insight into the reaction's dynamics at equilibrium. For reactions in biochemistry, K' is calculated using the relation between the standard free energy change and the concentrations of reactants and products. Specifically, the relationship is expressed mathematically by the equation \(K' = e^{(-\Delta G^{\circ \prime}/(RT))}\), where R is the gas constant and T is the temperature in Kelvin. A large K' implies that, at equilibrium, the concentration of products will be greater relative to the reactants.

Understanding the equilibrium constant is fundamental for biochemical analysis, allowing us to predict how changes in reactant or product concentrations, temperature, pH, or other factors might shift the position of equilibrium in a given reaction. This, in turn, helps in understanding how biological systems maintain homeostasis and regulate metabolic processes.

Applications in Cellular Metabolism

An example can be seen in the PFK reaction within glycolysis, where the equilibrium constant helps predict how the concentrations of fructose-1,6-bisphosphate and fructose-6-phosphate will change in response to cellular conditions.