Fermentation Technologies
Kinetics Analysis of Microbial Metabolic Reactions

Reaction rate equation, descriptive of microbial metabolic reactions, is an essential information for the design or development of bioreactors including fermentation reactors as well as fermentor reactors. The evaluation of the impact of immobilization on the effectiveness of an enzyme or microbe also uses the reaction rate equation as a performance base reference. The derivation of the reaction rate equations, however, depends on the metabolic reaction mechanism. Hence the reaction mechanism of the metabolic reaction is required to be well-known for the purposes of constructing a truly descriptive metabolic reaction rate equation. The significance of this need underlie the need for the development of the Monod equation as part of the study of microbial cellular growth analysis.

However, since the development of the Monod equation, it has been known that microbial metabolic reactions consists of two parallel sets reactions: Catabolic Reactions and Anabolic Reactions with the latter also dependent on the former for reactants, such as ATP; and as such the  Monod equation in fact embodies both the catabolic reaction dynamics and the anabolic reaction dynamics. Further, the Monod equation also takes into account, the reactions involving cellular divisions involved in cellular growth. While for cellular growth and therefore for the design or analysis of fermentor bioreactors the equations is entirely applicable because for all virtually all the products of metabolic reactions are consumed by the anabolic reactions, this is not the case for the design or analysis of fermentation reactors in which only some of the catabolic reaction products are used for cellular functions maintenance, by operation and also by design specification. In this regard then, for the purposes of good design, the metabolic reaction needs be thoroughly analyzed such that the internal cytoplasmic allocation of the products of the catabolic reactions to the anabolic reactions are effectively captured in the reaction rate equations.

Microbial metabolic reactions, of course, are microbe-specific and therefore for each microbe and for each substrate a comprehensive specification of the reaction mechanism is required. In pursuit of this goal, the catabolic reaction mechanism are being catalogued for several sugars utilizing microbes. While for many microbes, the mechanisms are not known even  vaguely, for a several others the reaction mechanism, also known as Biochemical Pathway,  are known to be either of Emden Myerhoff Pathway or the Entner-Duodoroff Pathway preceded by a prepping process, which may entail just phosphorylation or non-phosphorylation. The prepping reactions are in some cases Biochemical Pathway onto themselves, as per by the Lehoir Pathway. Of course, the  Biochemical Pathway of glycolysis terminates with the production of pyruvate which is then usually converted into the end-products of fermentation in another reactions. In the context of this view of the

 microbial metabolic reaction, the reaction rate could be further represented as follows:

where 's' is the substrate and (s) means function of S, r₁ is the rate of consumption of the substrates consumed in pure catabolic reaction rate resulting in the production of pyruvate and r₂ is the rate equation descriptive of the portion of the substrate converted into catabolic reaction products that gets consumed in the anabolic reactions. Of course embedded within these two rate equations is the contribution of the prepping reactions.

The rate equation, r₂, however may or may be coincide with the Monod equation for a given bioreactor. The expectation is that for bioreactors in which cellular growth occurs the r₂ just might coincide with the Monod equation and the parameters may be evaluated with a pure cellular growth reaction kinetics data. in any event, the parameters can still for evaluated assuming a rate equation of the form of the Monod equation even for a reaction analysis system designed to support only cellular function maintenance. the use of this approach is to circumvent the difficulty with the analysis of the anabolic reactions for which much information is not generally available by research.

Deriving the rate equation r₁, on the other hand, while possible, is quite tasking is undertaken with the object of being as descriptive of the reaction mechanism as possible. Generally, the reaction mechanism is postulated and the reaction rate equation is derived from the mechanism, and the rate tested against experimental data. by this reasoning then for a given microbe for which the reaction mechanism is fully known, beginning with the prepping reaction, the substrate utilizing Biochemical Pathway, and the fermentation reaction, the reaction is written out in details. Naturally each reaction that is an enzymatic reaction must also be so documented. Then shifting focus from the reactants to the enzyme, and the specifics of the enzyme participation in the effecting the reaction, the reaction is depicted with an Ising Model. Each reaction within the Biochemical pathway that is enzymatic therefore is depicted with an Ising Model. Enzymes that have a single active binding site participating in the reaction is depicted with a one dimensional Ising Model, while a reaction with two active sites participation is depicted with a two dimensional Ising Model, and so forth. The analysis of the Ising Models while accounting for the interfaces of each model which are the common possibly intermediary reactants ordinarily, results in the reaction rate equations. The constants of the rate equation generated by the analysis are then evaluated by reconciliation with the experimental data available.

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In principle this technique is readily extended into three dimensional Ising Models in which two  2-dimensional but layered Ising Models could be developed for the full microbial metabolic reactions - in those situations in which the anabolic reaction mechanisms are also known. Of course, the analysis and the ultimate derivation of the equations also get very complex and complicated. nonetheless, such rate equations are effective better descriptive of he mechanisms than ordinary correlation analysis

A systematic approach is suggested here for the analysis of microbial metabolic reactions. While admittedly the approach is not relatively easier, it necessarily provides a more global analysis of interactions of the parallel reactions sets of the metabolic reactions, and invariably resulting in more realistic rate equations for such reactions, and that could be used for the design of bioreactors with better predictability.

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