Question

The $\mathrm{\Delta }{G}^{\circ \prime }$ of the glycogen phosphorylase reaction is $+3.1\mathrm{kJ}/\mathrm{mol},$ whereas the $\mathrm{\Delta }G$ under physiologic conditions is $-6\mathrm{kJ}/\mathrm{mol}.$ What is likely to account for this difference of $\sim 9\mathrm{kJ}/\mathrm{mol}$ between the $\mathrm{\Delta }{G}^{\circ \prime }$ and $\mathrm{\Delta }G$ values?

Short answer

Answer: The difference between ΔG°' and ΔG is likely due to differences in the concentration of reactants and products under physiological conditions compared to standard conditions, as well as cellular regulation mechanisms that affect these concentrations and the overall reaction favorability.

Step-by-step solution

Understand the meaning of ΔG and ΔG°'

We are given the standard Gibbs free energy change (ΔG°') and the actual Gibbs free energy change (ΔG) for the glycogen phosphorylase reaction. The ΔG°' represents the change in energy under standard conditions (i.e., 1 M concentrations of all reactants and products, 298K, and 1 atm pressure), whereas ΔG represents the change in energy under actual physiological conditions, which are usually different from the standard conditions.

Relationship between ΔG, ΔG°', and concentrations

The difference between ΔG and ΔG°' can be mainly attributed to the difference in the actual concentration of the reactants and products compared to their concentrations under standard conditions. According to the Gibbs free energy equation, we have: ΔG = ΔG°' + RT ln(Q) where R is the universal gas constant (8.314 J/mol K), T is the temperature in Kelvin, and Q is the reaction quotient (ratio of products to reactants concentrations). If the concentrations of the reactants and products under physiological conditions are different from the standard conditions, ΔG and ΔG°' will also be different.

Analyze the given ΔG values

We are given that the ΔG°' for the glycogen phosphorylase reaction is +3.1 kJ/mol, indicating that the reaction is unfavorable under standard conditions. However, the actual ΔG under physiological conditions is -6 kJ/mol, which means the reaction is favorable under these conditions. This shows that the concentrations of reactants and products under physiological conditions have shifted to make the reaction favorable compared to the standard conditions.

Identify the likely cause of the difference

The difference of around 9 kJ/mol between the ΔG°' and ΔG values can likely be explained by the effects of cellular regulation mechanisms, such as allosteric regulation and enzyme activity control, and the concentration of reactants and products under physiological conditions. These cellular mechanisms may result in the alterations of the substrate and product concentrations, thus affecting the reaction quotient (Q), which in turn alters the actual ΔG from the ΔG°' value. In summary, the difference of approximately 9 kJ/mol between the standard Gibbs free energy change (ΔG°') and the actual Gibbs free energy change (ΔG) for the glycogen phosphorylase reaction is likely due to differences in the concentration of reactants and products under physiological conditions compared to the standard conditions, as well as cellular regulation mechanisms that affect these concentrations and the overall reaction favorability.