A particularly useful and important feature of MCA is that it can relate the kinetic properties of the individual
reactions (local properties) with (global) properties of the whole intact pathway. This is done through the
connectivity theorems [
Kacser73] that relate the control
coefficients and the elasticity coefficients of steps with common intermediate species.
The connectivity theorem for flux-control coefficients [
Kacser73] states that, for a common
species $S$, the sum of the products of the flux-control coefficient of all ($i$) steps affected by
$S$ and its elasticity coefficients towards $S$, is zero:
$$\sum_{i} C_{v_{i}}^{J} \, \epsilon_{[S]}^{v_{i}} = 0$$
For the concentration-control coefficients, the following two equations apply [
Westerhoff84]:
$$\sum_{i} C_{v_{i}}^{[A]} \, \epsilon_{[S]}^{v_{i}} = 0$$,
where $A \ne S$
$$\sum_{i} C_{v_{i}}^{[A]} \, \epsilon_{[S]}^{v_{i}} = -1$$
The first equation applies to the case in which the reference species $A$ is different from the perturbed
species $S$. Whereas the second applies to the case in which the reference species is the same as the perturbed
species.
The connectivity theorems allow MCA to describe how perturbations on species of a pathway propagate through the
chain of enzymes. The local (kinetic) properties of each enzyme effectively propagate the perturbation to and from
its immediate neighbors.
