Page 121 - Thermodynamics of Biochemical Reactions

6.7 Calculation of the Equilibrium Composition for Glycolysis 117

expression for the apparent equilibrium constant KY;Ly under these conditions can
be written

(6.6- 13)

where KkLY is a function of 7; P, pH, [ATP], [ADP], [NAD,,], [NAD,,,], [P,],
and ionic strength. Equilibrium constants are dimensionless, but the reference
concentration cn = 1 M is omitted in the denominator of equation 6.6-13 as a
simplification. This equilibrium expression provides the most global view of the
thermodynamics of glycolysis. The value of the apparent equilibrium constant
KkLy can be calculated when AfGIO values are known for the 16 reactants at the
desired 7; P, pH, and ionic strength. These values can be used in equations like
6.5-25 to calculate the A,GY0 values of the reactants at the desired concentrations
of the coenzymes.
Figure 6.2 shows the content of each of these reactants in terms of compo-
nents; in other words, the rows give the values of N,(i) for each of the components
held constant. Equation 6.5-26 can then be used to calculate the A, G”’(iso) values
of the C, and C, pseudoisomer groups. In order to calculate the numerical value
for KLLY using equation 6.5-28, the reaction between pseudoisomer groups should
be written C, = 2C,( +2H,O) because A,G”O(H,O) is involved in calculating
KkLy. Note that A, G”O(H,O) = A, G”(H,O) because H,O does not contain
coenzymes. The equilibrium concentrations of C, and C, can be calculated using
equation 6.6-13, and then the concentrations of C, and C, can be divided into
the equilibrium concentrations of each of the reactants (noncomponents) by use
of equation 6.5-27. Thus KkLc provides the means to calculate the equilibrium
concentrations of the 11 reactants for which concentrations have not been
specified.
This more global view of the thermodynamics of a system of biochemical
reactions provides different information than the net reaction (equation 6.6- 1 1) for
the system because it deals with the pseudoisomer groups C, and C,. The
expression for the apparent equilibrium constant for the net reaction for glycolysis
can be used to calculate the equilibrium value of [Pyr]2/[Clu] by setting the
concentrations of the coenzymes equal to their steady state values. The apparent
equilibrium constant for the net reaction at 298.15 K, pH 7, and 0.25 M ionic
strength calculated from A,G” values is 1.41 x When the steady state
concentrations of ATP and NAD,,, are 0.01 M and of ADP and NAD,, are lop5
M, and that of P, is 0.001 M, the equilibrium concentration of glucose will exceed
that of pyruvate. The advantage of the equilibrium expression in equation 6.5-13
is that it yields the equilibrium concentrations of pseudoisomer groups C, and
C,: that is, it accounts for all of the reactants in glycolysis.”The equilibrium
calculations given here show how calculations become simpler as the values of
more intensive variables are held constant.

6.7 CALCULATION OF THE EQUILIBRIUM
COMPOSITION FOR GLYCOLYSIS

The standard transformed Gibbs energies of formation of the reactants in the first
five reactions of glycolysis are known at pH 7 and 0.25 M ionic strength (see the
first column of Table 6.2), and so the equilibrium composition can be calculated
for specified steady state concentrations of ATP and ADP (Alberty, 2001g). The
standard further transformed Gibbs energies of formation at two different sets of
concentrations of ATP and ADP are given in the last two columns.
There is n3 adjustment for glucose, and the adjustment for G6P is given by
A, G”O(G6P) = A,G’O(G6P) - (A,G”(ATP) + RTlnCATP])

+ (A,G“(ADP) + RTln[ADP]] (6.7-1)