In the case of the indicator reaction of the coupled auxiliary enzyme reaction mechanism, we have shown that if the indicator reaction has adequate speed, then the mass action equations can be approximated by the intersection of the nullclines, x * . Thus, the QSSA is a natural consequence of the phase-plane geometry, and the requirement that the initial substrate concentration (s 0 1 ) be in excess of the initial auxiliary enzyme concentration (e 0 2 ) is not necessary for the validity of the QSSA, provided the indicator reaction has sufficient speed. Moreover, for extremely fast indicator reactions, the rate expression for product formation reduces to