Based on the scaled equations ( )-(59b), we observe that the accumulation of s * 2 will occur along a trajectory that essentially crawls up the c 2 -nullcline if λ * 1. Moreover, we see again from the scaling that as the Michaelis constant for the indicator reaction gets smaller, the phase-plane trajectory does not necessarily follow the c 2 -nullcline towards (s * 2 , c * 2 ). This is primarily because for a fixed e 0 2 , the Michaelis constant can eventually get small enough so that λ * ∝ 1. In this case, the approach to s * 2 deviates (slightly) from the c 2 -nullcline. However, the condition λ * 1 is not necessary in order to impose the QSSA on the t s1 timescale. To see why, we rescale the complete set of mass action equations with respect to T ε = t/t s1 with an eye towards t * s2 ; this yields