The malate dehydrogenase reaction, written in the direction as it occurs in the citric acid cycle is:
malate + NAD+ → oxaloacetate + NADH + H+ ΔG˚' = +7.1 kcal/mol
Calculate the Keq and ΔG (in kcal/mol) for this reaction at the physiologic mitochondrial concentrations listed below, at 25˚C:
[malate] = 2 x 10-4 M
[NAD+] = 1 x 10-5 M
[OAA] = 1 x 10-8 M
[NADH] = 1 x 10-6 M
To calculate the equilibrium constant (Keq) and the free energy change (ΔG) for the malate dehydrogenase reaction, we can use the equation:
ΔG = -RT * ln(Keq)
where ΔG is the free energy change, R is the gas constant (8.314 J/(mol⋅K) or 0.00199 kcal/(mol⋅K)), T is the temperature in Kelvin (25°C = 298 K), and ln is the natural logarithm.
First, we need to convert the concentrations from Molar (M) to Mole/Liter (mol/L).
[malate] = 2 x 10^-4 M = 2 x 10^-4 mol/L
[NAD+] = 1 x 10^-5 M = 1 x 10^-5 mol/L
[OAA] = 1 x 10^-8 M = 1 x 10^-8 mol/L
[NADH] = 1 x 10^-6 M = 1 x 10^-6 mol/L
Now, we can use these concentrations to calculate the equilibrium constant (Keq):
Keq = ([OAA] * [NADH] * [H+]) / ([malate] * [NAD+])
Keq = (1 x 10^-8) * (1 x 10^-6) * 1 / (2 x 10^-4) * (1 x 10^-5)
Keq = 0.005
The value of Keq for this reaction at the given concentrations is 0.005.
Now, let's calculate the free energy change (ΔG) using the equation mentioned earlier:
ΔG = -RT * ln(Keq)
ΔG = -(0.00199 kcal/(mol⋅K)) * (298 K) * ln(0.005)
ΔG = -0.00119 kcal/mol
Therefore, the free energy change (ΔG) for this reaction at 25°C is approximately -0.00119 kcal/mol.