Page 117 - Thermodynamics of Biochemical Reactions

6.5 Three Levels of Calculation of Compositions for Systems of Biochemical Reactions 113

for spontaneous change and equilibrium is dG” d 0 at specified 7: P, pH, [ATP],
[ADPI, and amounts of remaining components.
To see the effects of specifying [ATP] and [ADP], consider the first three
reactions of glycolysis:
Glucose + ATP = glucose 6-phosphate + ADP (6.5- 17)
Glucose 6-phosphate = fructose 6-phosphate (6.5-1 8)
Fructose 6-phosphate + ATP = fructose 1,6-biphosphate + ADP (6.5-19)
These three biochemical reactions are catalyzed by hexokinase (EC 2.7.1.1),
glucose-6-phosphate isomerase (EC 5.3.1.9), and 6-phosphofructokinase (EC
2.7.1.11), respectively. The EC numbers are from Enzyme Nomenclature (Webb,
1992). The first step is to write the conservation matrix for this reaction system
at specified pH because that will show how to calculate the further transformed
Gibbs energies of formation at specified [ATP] and [ADP].
At specified pH the apparent conservation matrix for this system is

ATP ADP Glu G6P F6P F16BP
Aden 1 1 0 0 0 0
A‘ = (6.5-20)
P 3 2 0 1 1 2
Glu 0 0 1 1 1 1
where the C‘ components are the adenine group, phosphorus atoms, and the
glucose framework. Other components can be chosen, but the number of
components is 3 because C’ = N‘ - R‘ = 6 - 3 = 3. Row reduction yields
ATP ADP Glu G6P F6P F16BP
ATP 1 0 0 1 1 2
A’ = (6.5-21)
ADP 0 1 0 -1 -1 -2
Glu 0 0 1 1 1 1
Note that the C‘ components are now ATP, ADP, and glucose. Matrix 6.5-21
shows the amounts of ATP and ADP in the four pseudoisomers Glu, G6P, F6P,
and F16BP (see last row). G6P and F6P can each be considered to contain lATP
and - 1ADP. F16BP can be considered to contain 2ATP and - 2ADP. When the
rows and columns for ATP and ADP are deleted, this conservation matrix shows
that the remaining four reactants are pseudoisomers. The reactions between these
four pseudoisomer groups can be represented by
Glucose = glucose 6-phosphate (6.5-22)

Glucose 6-phosphate = fructose 6-phosphate (6.5-23)
Fructose 6-phosphate = fructose 1,6-biphosphate (6.5-24)
The standard further transformed Gibbs energies of formation of the
pseudoisomers can be calculated using equation 6.5-2 and can be written in the
form
A,G”’(i) = AfG’’(i) - N,,,(i)A,G’(ATP) - NADP(i)AfG’(ADP) (6.5-25)

where AfG’(i) = A,G”(i) + RTln[i]. The numbers of ATP molecules and ADP
molecules involved in these four reactions are shown in the row-reduced conser-
vation matrix (equation 6.5-21). When the equilibrium concentration of ATP is
0.0001 M and the equilibrium concentration of ADP is 0.01 M, the standard
further transformed Gibbs energies of formation in kJ mol-’ of the remaining
four reactants at 298.15 K and I = 0 are as follows: glucose, -426.71 (note that
this value is not changed); glucose 6-phosphate, - 439.73; fructose 6-phosphate,
- 436.55; fructose 1,6-biphosphate, - 449.98. Since these reactants are pseudo-
isomers, the standard further transformed Gibbs energy of formation of the