Fundamentals of Biochemical Engineering Part 1 - Bailey J., Ollis D. 1989

Stoichiometry and Energetics of Metabolic Transformations
Stoichiometry of Cell Growth and Product Formation
Stoichiometry of Metabolite Production Processes

A multitude of final metabolic products are secreted by The Cell into the culture medium or accumulated intracellularly. Based on stoichiometric characteristics, metabolic product formation processes can be conveniently divided into the four types listed below; the first three types correspond to the Classification of anaerobic metabolic pathways originally proposed in 1955 by Heden Jr.

1. The primary metabolic product results from primary METABOLISM/26.html">Energy Metabolism. An example is ethanol production during the anaerobic growth of Yeast.

2. The formation of the main metabolic product is not directly coupled to energy metabolism, as seen, for instance, in The Biosynthesis of citric acid during aerobic mold cultivation.

3. The end product is a secondary metabolite. An example is the biosynthesis of penicillin produced in an aerated mold culture.

4. Biotransformation. Here, the final metabolic product is formed from a substrate through one or more Reactions Catalyzed by cellular Enzymes. Steroid hydroxylation serves as a good example.

Processes of the first type are characterized by relatively simple stoichiometry, which is associated with a relatively constant ratio between The amount of metabolite produced and the amounts of accumulated cell mass and utilized substrate. In this case, the processes of substrate utilization, biomass synthesis, and final product formation can be formally expressed by a single chemical reaction equation, provided that, for example, the metabolic product CH_vO_w is added to the right-hand side of equation (5.49):

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(The stoichiometry of nitrogen-containing metabolite synthesis can be expressed in a similar way.)

It is also straightforward to derive an expression for the corresponding yield coefficient, keeping in mind that the amounts of substances in this parameter must be expressed in moles. Thus, if the substrate is glucose, whose molecule contains six atoms of carbon, reaction (5.57) will involve a'/6 moles of glucose. Similarly, if the metabolite molecule contains n_p carbon atoms, reaction (5.57) will yield f'/n_p of its molecules. Consequently, the molar yield coefficient Y_P/S (the number of moles of metabolic product formed per 1 mole of utilized substrate) is given by

Here n_s is the number of carbon atoms in the substrate molecule.

The simple stoichiometry of equation (5.57) is not applicable to second-type metabolites, the amounts of which are not necessarily proportional to the utilized substrate or the cell mass increment. In this case, the process stoichiometry can only be expressed using a separate reaction equation for metabolite formation. It is instructive to trace the reaction stoichiometry obtained by incorporating the metabolite formation stage into the cell growth reaction equations (5.53) — (5.56) given above:

Formation of the metabolic product:

Here, the coefficient 2 denotes the fraction of substrate carbon used for metabolite formation, as experimentally determined in the latter. The number of ATP molecules generated during metabolite biosynthesis is designated by the coefficient e_p; this coefficient can also take negative values if ATP is consumed rather than synthesized during metabolite formation. Similarly, if the coefficient (-y_s—zy_p) is negative, it means that reducing equivalents of NADH (or NADPH; at the relatively low level of metabolic pathway detail adopted here, there is no need to distinguish between these two agents) are consumed during metabolite formation.

The method for describing the stoichiometry of type 3 and 4 metabolite formation depends on The Nature of the substrates and metabolic products. In these cases, the formation of the latter is usually independent of cell growth. The accumulation of secondary metabolites is governed by kinetic factors and cellular activity.

Studying the stoichiometry of metabolite formation yields A number of Conclusions that are highly important from a biochemical engineering perspective. For instance, stoichiometric calculations can be used to estimate the maximum possible yield of a metabolic product, which in turn can prove extremely useful in preliminary economic evaluations of a technological process (see Chapter 12). As a first example, let us consider the anaerobic conversion of glucose to ethanol. (The aerobic metabolism reactions given above can also be applied to study anaerobic processes if O₂ and Oxidative Phosphorylation stages are omitted from all reactions.) Obviously, the optimal scenario is the utilization of the entire substrate exclusively for product formation. Assuming negligible cell growth, equation (5.57) takes a very simple form in this case:

СН₂О → ¹/₃СO₂ + ²/₃СН₃СO_0,5 (5.60)

It follows that, ideally, the metabolic product will contain two-thirds of the carbon from the utilized substrate. According to equation (5.58), the upper limit of the molar yield coefficient will be: (Y_P/S)_max = (²/₃)(⁶/₂) = 2.

A similar approach can be applied to the formation of all other metabolite types, including the simultaneous biosynthesis of multiple metabolic products. The limiting yield value of a given metabolite can be determined by assuming that no new Cells or other metabolites are formed concurrently. For example, based on the biosynthesis reaction equation of penicillin from precursor compounds:

it is easy to determine the maximum possible yield of penicillin, which is 1.2 g per 1 g of glucose. In actual Industrial processes, the yields are much lower (about 0.1 g/g), indicating significant potential for further optimization of both the technological process and the producing microorganism. The low actual yield of the metabolic product compared to the maximum calculated value indicates that a substantial amount of substrate is expended on cell growth, maintenance, or the Synthesis of Other substances.

Examining the relationship between energy metabolism and metabolite biosynthesis as expressed by equations (5.53) — (5.56) and (5.59) can provide useful insights into The Effect of cell maintenance costs on product yields. Suppose that under anaerobic conditions, in a medium containing ammonia as a nitrogen source, glucose is converted into ethanol. The sole source of ATP here is substrate-level phosphorylation [equation (5.53b)]. Under such conditions, relatively high substrate maintenance costs will cause comparatively large quantities of glucose to be funneled into dissimilatory reactions. This, in turn, will lead to the regeneration of a larger amount of NADH, which is not utilized in any significant quantities in the biosynthetic reaction [equation (5.55a)], since the degrees of reduction of the substrate and biomass are approximately equal. Reducing equivalents will be channeled into metabolite formation according to reaction equation (5.59a), leading to its accumulation in the medium, given that the degree of reduction of ethanol exceeds that of the substrate (glucose). Conversely, under aerobic conditions, where the process objective is frequently the synthesis of third- or fourth-type metabolites, an increase in substrate expenditure for cell maintenance results in a reduced product yield due to intensified substrate utilization for energy generation.

Obviously, metabolic conversions can be described by more than just equations (5.53) — (5.56) and (5.59). These equations must be modified, for instance, when multiple carbon and/or nitrogen sources are utilized simultaneously, or when the metabolic product contains nitrogen. Stoichiometric equations can also describe transformations along a specific metabolic pathway. Indeed, the combination of stoichiometric analysis and the experimental quantification of utilized substrate and produced metabolite has been successfully applied to estimate flux distributions through parallel and branched metabolic pathways. Alternative stoichiometric equations are discussed in greater detail in the exercises, as the principles and Methods of their formulation are very similar to those presented in this section. We will continue our Structure/133.html">Discussion of stoichiometry in the next section, which is dedicated to heat generation in metabolic processes.