It should be pointed out that the condition λ max 1, which can be ensured by requiring an excess of the initial amount of substrate s 2 (i.e., requiring that s 0 2 be large enough so that s 0 1 s 0 2 ), is sufficient but not necessary for the validity of the reduced model presented in (61). In general, it is desirable that s 0 2 be much larger than the maximum of amount of e A 2 over the timescale of the indicator reaction. If the indicator reaction is fast, then the maximum amount of available enzyme will be small; thus, the requirement that s 0 Time has been mapped to the t∞ scale: t∞(t) = 1 -1/ ln(t + e).