Ax

Typical values of Ykcai range between 0.096 and 0.126 g/kcal for many microorganisms.

When significant amount of product is present, based on the stoichiometric description of cell growth (Eq. 3.36), total heat evolved (Eq. 3.48)

should be modified to

where (~AHpt) and (—APi) represent the heats of combustion of products Pi and the amount of those products respectively.

Example

In this example, stoichiometric balances and calculation of yield coefficients will be illustrated for growth of Pénicillium chrysogenum and penicillin production. For growth, a simple stoichiometric model can be used that is based on the theoretical analysis of biosynthesis and polymerization by Nielsen [424] and is given by:

CHl.&lOa. 58,No.2OSO.004^0.010 + 0.139C02 + 0A58NADH 1.139CH20 + 0.207V #3 + 0.004ffSC>4 + 0M0H2PC)4 + Yx,atpATP + 0.243NADPH. (3.53)

The stoichiometry (Eq. 3.53) is based on a cell with the composition given in Table 3.9. C-source is glucose, N-source is ammonia, S-source is sulfate and P-source is phosphate. The stoichiometry is given on a C-mole basis and the elemental composition of the biomass is calculated from the content of the various building blocks [424], The required ATP and NADPH for biomass synthesis are supplied by the catabolic pathways, and excess NADH formed in the biosynthetic reactions is, together with NADH formed in the catabolic pathways, reoxidized to oxygen via the electron transport chain. Based on the above stoichiometry, the yield coefficient of biomass on glucose can be easily calculated as Yx/S = 1.139 C-mole glucose/C-mole biomass. In a similar manner, the yield coefficient of biomass on other nutrient SOUrceS such, as i^/ammonia) and ^x/phosphate• Câll also be calculated. The yield coefficient is usually given as g per g dry weight in the literature. To convert the literature data to a C-mole basis a molecular weight of 24 g/C-mole and an ash content of 5% can be assumed.

For the calculation of the theoretical yield of penicillin, a simple stoichiometric balance proposed by Cooney and Acevedo [112] can be used:

1.5C6Hi206 + 2NH3 + H2SOi + 2NADH2 + PAA + 5ATP -> penicillin G + 2FADH2 + C02 + 1H20. (3.54)

a-AAA (a-Aminoadipic acid) is the starting compound in the pathway for penicillin biosynthesis and acts as a carrier. If it is recycled, its net synthesis is of little concern in the overall material and energy requirements for formation of large quantities of penicillin. But if it is used once and then degraded, the net demand for energy will contribute to the energy demands of penicillin and cell synthesis. If the synthesis of a-AAA cannot be neglected and if a-AAA is used once and discarded, then the overall stoichiometry is obtained as:

3CeH1206 + 3NH3 + H2SOi + PAA + 3ATP penicillin G + 2FADH2 + 4 C02 + 7 H20 + 4NADH2 + a- AAA. (3.55)

Both penicillin G and a-AAA would accumulate. Prom the above stoichiometry (Eqs. 3.54 and 3.55), the theoretical yield of penicillin on either glucose, or ammonia or sulfate can be calculated based on the definition of yield coefficient for the two cases (in which a-AAA is either recycled or discarded) [112]. Theoretical yield coefficients are presented in Table 3.10, [112] where the stoichiometry of Eq. 3.54 is used in case 1 and the stoichiometry of Eq. 3.55 is used in case 2.

Table 3.9. Composition, ATP and NADPH requirements of a Pénicillium chrysogenum. Adapted from [424].

Macromolecule

Content0

ATP6

ATP"

NADPH6

NADPH"

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