The validity of (17a) is well-established , and we will not go into the details of this here. Further reduction of ( ) is possible when the speeds of the nonobservable and indicator reaction significantly differ, and in the subsequent sections we will convey the geometric interpretation of the reduced models that arise from when the indicator reaction is very fast or, in contrast, very slow. ). The numerical solution of the mass action equations ( ) (thick black curve that is barely visible) moves up, then down, the c 2 -nullcline (dashed red curve) in the phase-plane for the coupled auxiliary enzyme reaction mechanism. Movement is illustrated dynamically in Movie 1 available in the Supplementary Material. The dimensionless units used in the numerical integration of 6) are: