One-Substrate, Two-Product Enzyme Kinetics

Hydrolytic enzymes that release two products in a defined sequence require a slightly more complicated model for their kinetic behavior. These enzymes pass through two intermediate stages in the catalytic cycle, E S and E S, and the formation of products involves two steps with associated rate constants k2 and k3  

The rate-determining step is assumed to involve the release of the first product Pi and the conversion of E S into E S. Application of the steady-state approximation to both [E S] and [E S ] (i.e., assuming that d[E S]/df = 0 and d[E S ]/ df = 0) yields Eq. 2.25 for the reaction rate, after steps analogous to Eqs. 2.12-2.16  

While Eq. 2.25 looks much more complicated, it has the same form as Eq. 2.17. In fact, if the substitutions Vmax = cat[E]0 = k2k3/(k2 + fc3) [E]0, and Km (fc i +k2)/k2 k3/(k2 + k3) are made, Eq. 2.17 is obtained, and Michaelis-Menten kinetics are observed with these types of enzymes. 

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