## Catabolism and Anabolism

The catabolic conversion of acetate into CH4 and CO2 (Eq. 8.4) is a very simple reaction. We will use the method realized by methanogenic Methanotrix bacteria as an example for the evaluation of the stoichiometric equation describing catabolism and anabolism.

Starting from a general form considering only carbon, hydrogen and oxygen as elements of bacterial mass, we do not need to add nutrients and we can write:

Note that the substrate molecule and the "bacteria molecule" are each standardized relative to one carbon atom, resulting in the yield coefficients, three of which can be measured:

C for growth

YXC/SC

Yo ych4-c/sc

YCO2-C/SC

C of total substrate removal

C for CH4 formation C of total substrate removal

### C for CO2 formation C of total substrate removal

According to these formulas, the content of hydrogen and oxygen in the substrate molecule and the "bacteria molecule" are given by SH and SO as well as BH and BO, respectively. Now, we already know that we will obtain three mass balances for the three elements C, H and O. Therefore, we can calculate only three of the four yield coefficients. In order to complete the stoichiometric equations describing catabolism and anabolism, one of the four yield coefficients must be measured (however, see Section 4.2.1).

Let us use acetate as the substrate with CH2O (CH3COOH, written as C2H4O2 and divided by two, gives CH2O) and CHl8O0 s as a mean composition for the bacterial mass. Instead of Eq. (8.33), we now write:

YCO2-C/SCCO2 + YH2O-H/SCH2O

The balances for each of the three elements are:

C balance: 1 = YXC/SC + YCH4-C/SC + YCO2-C/SC (8.35)

H balance: 2 = 1.8 YXc/sc + 4 YCh-c/sc + 2 Y^o-h/sc (8.36)

O balance: 1 = 0.5 YXc/sc + 2 YCo2-c/sc + YH2o-h/sc (8.37)

From these three balances, three of the four yield coefficients can be calculated. To find the stoichiometry of Eq. (8.34), one of these yields must be measurable. Let us assume that we measure YCH4-C/S-C and we obtain:

Remember that, for catabolism alone, we would write YCH4-C/SC = 0.5 and YCO2-C/SC = 0.5. The solution of the three balances gives:

1-2Yo

YCO2-C/SC = 0.167 + 0.67 YCh4-c/sc = 0.49 mol CO2 (mol S-C)-1

The reaction describing the elements used for anabolism and catabolism is obtained after multiplying by a factor of two, considering the 2 C atoms in one acetate molecule:

CH3COOH ^ 0.060 CH18O0 5 + 0.96 CH4 + 0.98 CO2 + 0.026 H2O (8.38)

Only 3% of the acetate carbon is used for growth!

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