More free energy! The isomerization of dihydroxy-acetone phosphate (DHAP) to gly

Question

More free energy! The isomerization of dihydroxy-acetone phosphate (DHAP) to glyceroldehyde 3-phosphate (GAP) has an equilibrium constant of 0.0475 under standard conditions (298 K, pH 7). Calculate Delta G degree' for the isomerization. Next, calculate Delta G for this reaction when the initial concentration of DHAP is 2 times 10^-4 M and the initial concentration of GAP is 3 times 10^-6 M. What do these values tell you about the importance of Delta G compared with that of Delta G degree' in understanding the thermodynamics of intracellular reactions? A tenacious mutant. Suppose that a mutant enzyme binds a substrate 100 times as tightly as does the native enzyme. What is the effect of this mutation on catalytic rate if the binding of the transition state is unaffected? A question of stability. Pyridoxal phosphate (PLP) is a coenzyme for the enzyme ornithine aminotransferase. The enzyme was purified from cells grown in PLP-deficient medium as well as from cells grown in medium that contained pyridoxal phosphate. The stability of the enzyme was then measured by incubating the enzyme at 37 degree C and assaying for the amount of enzyme activity remaining. The following results were obtained: (a) Why does the amount of active enzyme decrease with the time of incubation? (b) Why does the amount of enzyme from the PLF deficient cells decline more rapidly?

Explanation / Answer

19) The equilibrium in question can be represented as

DHAP <=====> GAP

The equilibrium constant is given by

K = [GAP]/[DHAP] = 0.0475 under standard conditions (P = 1 atm, T = 298 K)

We know that the standard free energy of the conversion, G0’ = - R*T*ln K

Plug in values and obtain

G0’ = - (8.314 J/mol.K)*(298 K)*ln (0.0475) = 7549.225 J/mol (7549.225 J/mol)*(1 kJ/1000 J) = 7.549225 kJ/mol 7.55 kJ/mol (ans).

Since the standard free energy change for the reaction is positive, the reaction is non-spontaneous under standard conditions.

Next we are to find out G when the initial concentrations are given as [DHAP] = 2*10-4 M and [GAP] = 3*10-6 M. Find out the reaction quotient Q = [GAP]/[DHAP], both under non-standard conditions. Therefore, Q = (3*10-6 M)/(2*10-4 M) = 0.015

Find G = G0’ + R*T*ln Q = (7.55 kJ/mol) + (8.314 J/mol.K)*(298 K)*ln (0.015) = (7.55 kJ/mol) + (-10405.071 J/mol) = 7.55 kJ/mol – (10405.071 J/mol)*(1 kJ/1000 J) = 7.55 kJ/mol – 10.405 kJ/mol = -2.855 kJ/mol (ans).

Since G is negative, the reaction is spontaneous under these conditions. This therefore, indicates that the concentrations of the reactants and the products play an important role in determining the spontaneity and hence, feasibility of a reaction (ans).

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