Kinetics and Modeling of Bioreactions

The reactions considered here are those in which an organic feed is converted into a product by the catalytic action of an enzyme or a microbe. These reactions can be represented as follows  

The main distinction between them is that in an enzymatic reaction, the enzyme, a lifeless chemical entity, does not reproduce. On the other hand, in microbial transformation, the reaction occurs within a living cell where it is catalyzed by the enzyme produced by it (just as in an enzymatic reaction). However, the cell also reproduces itself, generating more enzyme in the process. Thus the modeling of microbial reactions must take this growth process into account. Further, these reactions can produce three possible results, as shown in Table 20.3. The reaction can be tailored specifically to produce any one of these results. Our concern in this chapter is with result 1, the production of a specific product R. 

Michaelis-Menten and Briggs-Haldane models Enzymatic reactions can typically be represented as 

Reaction C + A. C + (cell) (reactant, (more which is food cells) for cell growth) R (product) 

To develop a model for such a scheme, the first assumption we make is that a fraction of the enzyme remains attached to the substrate, that is, [AE 0. Following this, we can make either of two further assumptions a rate-determining step is present or the steady-state approximation holds for the intermediate. Depending on which set of assumptions is made, we have either of two celebrated models, the Michaelis-Menten (MM) model or the Briggs-Haldane (BH) model, although the latter appears to be favored (Chance, 1943). 

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