## Thermodynamically Based Method To Estimate Growth Stoichiometry

In the previous paragraphs the methods for accurate measurement of a growth stoichiometric coefficient, as, for example, the biomass yield on electron donor FDX and the subsequent calculation of all the nonmeasured stoichio-metric coefficients of the macrochemical equation (using the conservation principles) have been provided. In past decades, the value of FDX for many different microorganisms, different electron donors, C sources, and electron acceptors has been measured under C- and energy-limited growth conditions. Many methods have been proposed to predict FDX because of its obvious importance. Recently, a critical evaluation of these methods has been performed (2). The following criteria were used for the evaluation:

• The method should be generally applicable to all chemotrophic growth systems.

• The method should relate directly to the second law of thermodynamics.

• No detailed knowledge of metabolism is required; only the identity of the electron donor, C source, and electron acceptor is known.

• Methodological problems are absent.

The conclusion of this evaluation was that none of the published methods satisfied these simple criteria. Therefore, an alternative method that satisfies the mentioned criteria has been proposed (2). This method is based on 1/FGX, which is the amount of Gibbs energy (in kilojoules) that must be dissipated for the production of 1 C-mol biomass.

The Gibbs energy stoichiometric parameter 1/FGX has already been introduced as one of the stoichiometric coefficients in the macrochemical reaction equation (Fig. 2b). Therefore, it is obvious that this energetic parameter can be calculated directly if only one of the chemical stoichio-

metric coefficients has been measured and if the electron donor, electron acceptor, and C source are known (see Example 1b, where 1/YGX = 1,052 kJ/C-mol biomass).

Furthermore it is well known that the value of growth yields depends on the growth rate (m) due to the Gibbs energy that must be used for maintenance (see earlier section). This means that the Gibbs energy needed to produce biomass should be divided into two parts:

1. A growth-related part

2. A maintenance-related part

Mathematically this can be expressed as

1/Ygx

Total needed Gibbs energy kJ/C-mol biomass i vm 1 GX

Gibbs energy for new biomass mG l

Maintenance Gibbs energy for existing biomass

where l/F^X is the Gibbs energy needed to make 1 C-mol of biomass (kJ/C-mol X) and mG is the Gibbs energy needed for biomass maintenance (kJ/C-mol biomass h). The biomass specific growth rate (h-1) is p.

Clearly, at high growth rate p, the mG/p term becomes negligible and 1/YGX becomes practically equal to Y^. At low growth rates YGX becomes much lower than YsX.

Equation 1c shows that in order to calculate YGX as a function of growth rate p we need information about YsX and mG. In the past years two simple correlations have been found with which to estimate YsX and mG (2,4). These correlations were established using a very large body of experimental growth yields, which covered carbon- and energy-limited growth for the following:

• Many different microorganisms (bacteria, fungi, plant cells)

• Many different C sources, including CO2 and a wide variety of organic substrates

• Different electron acceptors (aerobic, anaerobic, denitrifying)

• Electron donors that need reversed electron transport (RET)

The resulting correlations are given in equations 2 and 3. Figure 4 shows the mG data used to establish equation 2; Figure 5 shows the 1/YGmX data used to establish the correlations 3a and 3b.

Maintenance Gibbs Energy Need mG

The data for mG as a function of temperature shown in Figure 4 can be correlated with an Arrhenius type of relation:

donors, for aerobic and anaerobic conditions, and for a temperature range of 5-75 °C (4). Obviously, the main influencing factor is the temperature, which behaves as an Ar-rhenius function with an activation energy of 69,000 J/mol. The type of electron donor (organic or inorganic), the microorganism, and the electron acceptor are of minor importance. This seems logical, because maintenance is a biomass-linked Gibbs-energy-requiring process that counteracts the biomass-deteriorating processes (protein degradation, leakage over cell membranes, etc.).

### Gibbs Energy for Growth

The data for YjX shown in Figure 5a (heterotrophic growth) and Figure 5b (autotrophic growth) can be correlated by equations 3a and 3b as shown in Ref. 2. For au-totrophic growth it was found to be important to distinguish electron donors for which reversed electron transport (RET) was necessary. Such electron donors (e.g., Fe2 + / Fe3 + , NH+/NO-) provide electrons that have insufficient Gibbs energy to reduce the C source CO2 to biomass. Microorganisms using such electron donors first have to increase the Gibbs energy level of the donor electrons by the biochemical process RET.

Heterotrophic growth/autotrophic growth (-RET)

Autotrophic growth ( + RET)

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