text: The elasticities for a reversible uni-uni enzyme catalyzed reaction was previously given by:
  An interesting result can be obtained by evaluating the sum . This can be shown to equal:
  Two extremes can be considered. At high saturation (), the right-hand term tends to zero so that:
  That is the absolute magnitudes of the substrate and product elasticities tends to equal each other. However, it is unlikely that a given enzyme will have both substrate and product concentrations much greater than their respective Kms. A more plausible scenario is when the enzyme is working under sub-saturating conditions (). Under these conditions we obtain the simpler result:
  Expressed in a different way we can state:
  That is, the absolute value for the substrate elasticity will be greater than the absolute value for the product elasticity. This means that a substrate will have a great influence over the forward reaction rate than the corresponding product. 
  This result has important implications for the distribution of flux control in a pathway with sub-saturated reaction steps. In general, a perturbation near the start of a pathway will have more influence over the steady state flux than steps downstream. This is because a perturbation that travels downstream is determined by all the substrate elasticities, whereas a perturbation downstream that has to travel upstream if determined by the product elasticities. Since we have seen that the substrate elasticities tends to be larger than the product elasticities, it means that perturbations traveling downstream will be less attenuated than perturbations traveling upstream. The net effect is that flux control tends to be more concentrated at upstream steps compared to downstream steps.
  The table below summarizes the extreme values for the elasticities given a reversible Michaelis-Menten rate law. Following   Westerhoff et al. the table is split into four cases that include one reversible type, and three irreversible types.