46
RICE UNIVERSITY STUDIES
amount of enzyme being fixed; 4) the dependence of enzyme catalytjc
activity on concentrations of “foreign” bodies, i. e., substances not
involved in the step catalyzed by the enzyme; and 5) the relative reversi-
bility of most elementary steps, as opposed to the energetic irreversibility
of the overall reactions.
I will proceed confidently, assuming that 1 know or can guess the
detailed mechanisms of the reactions which will follow. This implies a
knowledge of all the enzymes and their idiosyncracies, which is certainly
not true even in the well-studied case I have chosen. What I will do in
fact is propose a scheme which is sufficiently complex to reproduce the
known behavior of the system at steady state. This involves writing
kinetic expressions, imposing mass conservation conditions on enzymes
and intermediates, and doing some elementary algebra.
The Example Reaction Set
My example set is the group of reactions by which many organisms
regenerate the indispensible and ubiquitous phosphate compound ATP.
The source of biochemical energy is the breakdown of a substrate, e. g.,
glucose, to CO2 and H2O, a process which involves many enzyme
catalyzed steps. I am not going to worry about how the cell reduces
glucose to the three-carbon residues which are used by the extended
Krebs cycle; this was discussed in an earlier paper, and is not difficult
to separate in principle (and in fact) from the reaction system I will be
concerned with.
The example reaction set is found in organisms ranging from E. Coli
to man. Geometrically, the various steps take place in a subregion of a
particular cell which is quite small. From here on, we are concerned only
with this microcosm, which takes in oxygen, phosphate, ADP, and
pyruvic acid (the three-carbon fuel), and returns CO2, H2O, and ATPto
the surroundings.
There are two major reaction pathways involved in the set. These are
1) the expanded tricarboxylic acid (Krebs) cycle, which converts pyru-
vate to CO2 and produces a number of equivalents of reduced coenzyme
intermediates, and 2) the electron transport path, which reoxidizes the
coenzymes so that they can be used again in the first cycle, and in the
process converts phosphate and ADP to ATP. A detailed description
of these reaction paths can be found in any modern biochemistry text.
I have attempted to abstract the essential features of these systems in
Figures 1 and 2. I have let Ii be a typical intermediate in the Krebs cycle,
with I0 being pyruvate. Oj and ri are oxidized and reduced forms of
intermediate ɪ in the electron transport pathway. In both cases, the
equations shown are the overall stoichiometric ones, and do not include
the details of the actual fundamental steps. ATP formation is apparently