KINETICS ON THE MICROBIAL SCALE
45
proxι∏1*ty (ɪθ-ʒ or IO-6 cm) to one another. Even though very large
complicated intermediates are involved, their diffusivities are probably
large enough so that they can get from one enzyme to the next without
producing serious diffusional limitation.1
The question of time scales is important, since I would like to employ
the “steady-state” hypothesis in dealing with the reaction set. This is
merely the assumption that the rate of accumulation of intermediates
can be neglected on the “reaction time scale.” We can use E. Coli again
to give us an idea of the order of magnitude of this time scale.
E. Coli uses glucose at an average rate of 5 x 10^6 moles∕cm3-sec.If we
suddenly shut off the glucose supply from outside, the bacterium would
use up its internally stored glucose in approximately one second. This
is, then, the “reaction time scale,” and it is about a thousand times shorter
than the “half-life.” We can probably get away with the steady-state
hypothesis in an environment where changes occur on the order of
minutes or longer, i. e., on the cell-division time scale rather than on the
reaction time scale.
In summary, we will focus on a neighborhood of order 10"5cm in
diameter in which a large set of reactions is assumed to occur without
controlling diffusional rate limitation. A few reactants will pass in,
a few products will leave, and a large number of intermediates will
exist locally at stationary concentration, at least on the time scale of
interest. The only thing to consider then is kinetics.
Elementary Steps and Kinetic Expressions
One of the first things a good student learns in a modern kinetics course
is that a knowledge of stoichiometry is necessary but not sufficient. We
cannotjust look at the equation of an overall reaction and guess the form
of the kinetic expression which will describe the overall rate. Especially
in the case of heterogeneously catalyzed reactions, we must know or
guess the detailed mechanism by which the reaction proceeds. We then
write down the series of chemical equations which describe the mecha-
nism, make sure they add up to the overall reaction, and then we try to
write kinetic expressions to account for the steps.
This procedure is also appropriate in the case of biochemical reaction
schemes. The prospect is frightening at first glance because of the large
number of reactions and catalysts involved. However, complicated
relations are inevitable, since the behavior we wish to model is extremely
complex.
Some of the qualitative features which our kinetic equations must
include are 1) the effects of shared intermediates in two or more complex
reaction paths; 2) the limitation imposed by closed cycle reaction path-
ways; 3) the use of a specific enzyme to catalyze each step, the total