Becker's World of the Cell 9th Edition by Lewis Kleinsmith, Jeff Hardin, Gregory Paul Bertoni

Exercise 12

Derivation of the Michaelis-Menten Equation. For the enzyme-catalyzed reaction in which a substrate S is converted into a product P (see Reaction 6-5), velocity can be defined as the disappearance of substrate or the appearance of product per unit time:
(1)
Beginning with this definition and restricting your consideration to the initial stage of the reaction when [P] is essentially zero, derive the Michaelis-Menten equation (see Equation 6-7). The following points may help you in your derivation:
(a)Begin by expressing the rate equations for d[S]/dt, d\P]/dt, and d[ES]/dt in terms of concentrations and rate constants.
(b)Assume a steady state at which the enzyme-substrate complex of Reaction 6-6 is being broken down at the same rate as it is being formed such that the net rate of change, d[ES]/dt, is zero.
(c)Note that the total amount of enzyme present, E t , is the sum of the free form, E f , plus the amount of complexed enzyme ES1: E t = E f + ES.
(d)When you get that far, note that V max and K m can be defined as follows:
(1)