Enzyme Kinetics and Metabolic Control Analysis
This fractional change in the rate of the
th reaction can also be accomplished by changing the level of the
ith enzyme, i.e.,
If we balance the change in the reaction rate due to the differential change of the intermediate by a change
in the enzyme level, we find from Eqs. (2) and (3)
and y' = l ,.
If we change the internal rates without changing the total flux
through the pathway, then by Eq. (4):
X' pJ dei
j ~ h
By combination of Eq. (5) with Eq. (4) we get
X C ,J^ ,= 0 ;
y = l ,.
..,/ - l
and since we imposed a fractional change on each of the
*= 0, we obtain the
flux-control connectivity theorem, Eq. (6.38).___________________________________________________
In addition to the flux-control connectivity theorem, Westerhoff and Chen (1984) introduced two
other connectivity theorems:
Z c , ^ , = - 1 ;
y = l,.
k * j
In matrix notation we can summarize all the theorems given in Eqs. (6.34), (6.36), and (6.38)-(6.40)