Enzyme Kinetics and Metabolic Control Analysis
the slope of J ’(x). This is where the flux control coefficients are introduced.
In (6.30) the enzyme concentrations
are used instead of the rate constants
would be more correct to use the enzyme activities determined through the rate constants than
the enzyme concentrations
(or enzyme “dosages”) since the activity o f an enzyme is not
necessarily proportional with the enzyme concentration. Here we will, however, assume that
there is proportionality between enzyme concentration and enzyme activity. Flux and enzyme
concentrations are measured in units that are not commensurable, and consequently the
sensitivity of the flux with respect to changes in
is scaled by
in order to give dimensionless
flux control coefficients.
In the example we assume that the rate constants are proportional to the enzyme concentrations
and we obtain the following for the two cases of r,.
is the independent variable while
is a constant.
To obtain the result for (6.23b) the following “chain-rule” for differentiation is used:
ÔJ' dy x
dy dx J'
which means that also in general CJ, +
= 1, just as in the simple case (6.23a).
y (c + y)
in (6.31) together with
and dv/dx from (6.27) one obtains
as an explicit function of