Page 118 - Thermodynamics of Biochemical Reactions

114 Chapter 6 Systems of Biochemical Reactions

pseudoisomer group can be calculated by using
N,W
A,G"'(iso) = - RTln C exp " G"o(i) = - 450.03 kJ mol- (6.5-26)
i= 1
where N,,, is the number of pseudoisomers in the group, which is 4. The
equilibrium mole fractions of glucose, glucose 6-phosphate, fructose 6-phosphate.
and fructose 1,6-biphosphate can be calculated by using
1 (6.5-27)
ri = exp rfG'''(iso;; A, G"'(i)

Thus the equilibrium concentrations of glucose, glucose 6-phosphate, fructose
6-phosphate, and fructose 1,6-biphosphate are 8.21 x 1.56 x
4.34 x lop5, and 9.8 x lop2 M. Note how much the specification of the equilib-
rium concentrations of ATP and ADP has simplified this equilibrium calculation.
The level 2 discussion of reactions 6.5-17 to 6.5-19 at specified pH involves 6
reactants and 3 apparent equilibrium constants. The level 3 discussion at specified
pH and specified concentrations of ATP and ADP involves 4 reactants, but since
these reactants are pseudoisomers under these conditions, the system consists of
a single pseudoisomer group, and so equations 6.5-26 and 6.5-27 can be used.
Apparent equilibrium constants K" at specified concentrations of coenzymes
for a systemlarger than 6.5-17 to 6.5-19 can be calculated using
A.,G"' = -RTln K" (6.5-28)

6.6 CONSIDERATION OF GLYCOLYSIS AT SPECIFIED
[ATP],[ADP] 3 [NAk I, "A%d 19 AND CR I

Glycolysis involves 10 biochemical reactions and 16 reactants. Water is not
counted as a reactant in writing the stoichiometric number matrix or the
conservation matrix for reasons described in Section 6.3. Thus there are six
components because C' = N' - R' = 16 - 10 = 6. From a chemical standpoint
this is a surprise because the reactants involve only C, H, 0, N, and P. Since H
and 0 are not conserved at specified pH in dilute aqueous solution, there are only
three conservation equations based on elements. Thus three additional conserva-
tion relations arise from the mechanisms of the enzyme-catalyzed reactions in
glycolysis. Some of these conservation relations are discussed in Alberty ( 1992a).
At specified pH in dilute aqueous solutions the reactions in glycolysis are
represented by
GIC + ATP = G6P + ADP (6.6- 1 )
G6P = F6P (6.6-2)

F6P + ATP = FBP + ADP (6.6-3)
FBP = DHAP + GAP (6.6-4)
DHAP = GAP (6.6-5)

GAP + Pi + NAD,, = BPG + NAD,,, (6.6-6)
BPG + ADP = PG3 + ATP (6.6-7)
PG3 = PG2 (6.6-8)

PG2 = PEP (+ H,O) (6.6-9)
PEP + ADP = Pyr + ATP (6.6- 10)
where the following abbreviations are used: glucose (Glc), adenosine triphosphate
(ATP). adenosine diphosphate (ADP), glucose 6-phosphate (G6P), fructose 6-