Kinetics of Multiple Enzyme Systems

If two or more enzymes are involved in coupled reactions, the influence of all substances present in the reaction mixture on the activity of all enzymes has to be studied and considered in the kinetic model. Knowing the kinetic behavior of the single enzymes, coupling can be done by writing mass balances. 

As an example, the reduction of dihydroxyphenylpyruvic acid (DHPP) to dihydrox-yphenyllacetic acid (DHPL), a precursor of rosmarinic acid, is presented in Eq. (49) [mi. 

The reaction is catalyzed by D-hydroxyisocaproate dehydrogenase (D-HicDH). The essential cofactor PEG-NADH is regenerated from PEG-NAD+ by a second enzyme, formate dehydrogenase (FDH). By coupling to water-soluble polyethyleneglycol with a molar mass of 20 000 g mol-1, the cofactor can be retained, together with the enzymes, by an ultrafiltration membrane, and the whole process may be performed continuously in an enzyme membrane reactor. 

In this case Michaelis-Menten double substrate kinetics is chosen (compare to Eq. (45)). The system involving D-HicDH with DHPP and PEG-NADH as substrates exhibits Michaelis-Menten kinetics for both substrates and competitive product inhibition by PEG-NAD+. FDH also shows Michaelis-Menten kinetics for both substrates formate and PEG-NAD+ and competitive product inhibition by PEG- 

Both inhibiting effects are taken into consideration by an additional term in the denominator. This formal procedure is valid as it allows a correct fit of all initial rate data (not shown). 

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In Sect. 7.4.3, the reduction of dihydroxyphenylpyruvic acid (DHPP) to dihydrox-yphenyllactic acid (DHPL) was used as an example for discussion of the kinetics of multiple enzyme systems (Eq. (49)). The rate equations for the reduction reaction of DHPP to DHPL (v>i) and the regeneration of PEG-NAD+ to PEG-NADH (v2) have been introduced (Eqs. (50) and (51)). 

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