Final answer:
The actual free energy change (ΔG') for the conversion of glucose-6-phosphate to fructose-6-phosphate can be calculated using the standard free energy change, concentrations of the reactants and products, and the temperature. This requires a formula that incorporates these factors to assess the spontaneity of the reaction under cellular conditions.
Step-by-step explanation:
The conversion of glucose-6-phosphate (G6P) to fructose-6-phosphate (F6P) involves an enzyme called phosphogluco-isomerase, which facilitates this reaction in the glycolysis pathway. The standard free energy change (ΔG°') for this reaction has been given as 410 cal/mol. To calculate the actual free energy change (ΔG') in the cell, we need to use the following formula that relates ΔG' with ΔG°' and the reactant and product concentrations:
ΔG' = ΔG°' + RTln(Q)
Where ΔG' is the actual free energy change, ΔG°' is the standard free energy change, R is the gas constant (1.987 cal/mol·K), T is the absolute temperature in Kelvin (310K for 37°C), and Q is the reaction quotient, which is the ratio of the product concentration to the reactant concentration.
Substituting the given values, we get:
ΔG' = 410 cal/mol + (1.987 cal/mol·K)(310K)ln(14 µM / 83 µM)
To solve, first, we convert the µM to M by dividing by 10^6 and then plug in the values:
ΔG' = 410 cal/mol + (1.987 cal/mol·K)(310K)ln(14e-6M / 83e-6M)
After calculating the natural logarithm and then multiplying by RT, we add the result to the ΔG°' to get the actual ΔG' in calories per mole.
This calculation will determine if the reaction will favor the formation of F6P or G6P under the actual cellular conditions, which is crucial for metabolic regulation and understanding how energy is produced and consumed during glycolysis.