ABSTRACT
Figure 1 Typical enzyme-catalyzed reaction showing the
pre-steady-state (msec), the constant rate, and the declining
rate parts of the progress curve. (From Ref. 1)
lyzed reactions as a function of substrate concentration, ½A, resulted from an obligatory intermediate, the enzymesubstrate complex, ½EA, prior to product, P, formation [Eq. (1)]:
E þ A Ð k1
k1 EA Ð
k2 E þ P ð1Þ
Based on this premise, which has been shown now to be universal for all enzyme-catalyzed reactions, Michaelis and Menten in 1913 (4) developed an equation to numerically describe the observed relationship between velocity, v, and ½A. The derivation of the Michaelis-Menten equation is shown below, using the more modern concepts of initial velocity vo, and the steady-state assumption. The EA complex has a noncovalent bond. Let ½Eo ¼ total enzyme concentration
½Ao ¼ total substrate concentration, which is assumed to be much larger than ½Eo; therefore, ½A ¼ ½Ao during initial velocity, vo, measurements ð< 5% A converted to P during time of experiment)
½EA ¼ enzymesubstrate concentration, which is a noncovalent complex
½P ¼ product concentration (one product is formed in the general derivation; more than one product may be formed and released in a sequential manner in many examples)
½E ¼ free enzyme concentration The rate of formation of EA is [see Eq. (1)]:
dEA=dt ¼ k1½E½Ao ð2Þ While the rate of disappearance of EA is
dEA=dt ¼ k1½EA þ k2½EA ð3Þ When steady-state conditions are reached (within a few msec), dEA=dt ¼ dEA=dt so that
k1½EAo ¼ k1½EA þ k2½EA ¼ ðk1 þ k2Þ½EA ð4Þ Rearranging:
½E½Ao=½EA ¼ ðk1 þ k2Þ=k1 ¼ Km ð5Þ Km, the Michaelis constant, is given by either ½E½Ao= ½ES or ðk1 þ k2Þ=k1.
