Page 102 - Thermodynamics of Biochemical Reactions

5.3 Coupling of Biochemical Reactions 97

A basis for the null space v’ of conservation matrix 5.2-5 at specified pH
obtained with equation 5.1-19 or with a computer is

ATP -1
H20 -1
vf = ( 5.2- 1 0)
ADP 1
p, 1

which is referred to as an apparent stoichiometric matrix because it is made up of
the stoichiometric numbers for a reactants at specified pH, rather than species.
Matrix 5.2-10 corresponds with

ATP + H,O = ADP + P, (5.2-11)

which is referred to as a biochemical reaction to distinguish it from the underlying
chemical reactions. This equation does not balance hydrogen atoms because the
chemical potential of hydrogen ion is specified (see Problem 5.3). This conversion
of a set of chemical equations to a single biochemical equation is discussed by
Alberty (1992b).
The product of the apparent conservation matrix A’ and the column vector
n’ of amounts of reactants (pseudoisomer groups) gives the column vector n: of
the amounts of the apparent components:
A’n‘ = n: (5.2- 1 2)

This is like the product of the conservation matrix A and the amounts n of species,
which gives the amounts of components n, (equation 5.1-12). The apparent
components in equation 5.2-4 are ATP, H,O, and ADP.
In summary, the linear algebra of the hydrolysis of ATP at specified pH is
very much like the linear algebra of chemical reactions, even though hydrogen
atoms are not conserved in the biochemical reaction and the reactants are sums
of species.

5.3 COUPLING OF BIOCHEMICAL REACTIONS

Some enzyme-catalyzed reactions are sums of biochemical reactions that could in
principle occur separately. This is important in considering conservation equa-
tions because the mechanisms of such reactions may introduce additional conser-
vation equations, in other words, additional components. When two biochemical
reactions without a common reactant are coupled together by an enzymatic
mechanism, the number of biochemical reactions in the system is decreased by
one, but the number of reactants is unchanged: AC = AN’ - ARf
= 0 - (- 1) = 1. There is then one more apparent component. In discussing
enzyme-catalyzed reactions, it is convenient to use EC numbers (Webb, 1992).
Glutamate-ammonia ligase (EC 6.3.1.2) couples the following two reactions:
Glutamate + ammonia = glutamine + H,O (5.3-1)

ATP + H20 = ADP + Pi (5.3-2)
so that the reaction catalyzed is

Glutamate + ATP + ammonia = glutamine + ADP + Pi (5.3-3)
The transposed stoichiometric number matrix for this reaction is

Glutamate ATP Amm ADP Pi Glutamine
(,J‘)T = (5.3-4)
-1 -1 -1 1 1 1