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 Source of Gibbs energy Source of electron donor C-source Light (phototrophic) Inorganic (lithotrophic) CO2 (autotrophic) Chemical (chemotrophic) organic (organotrophic) organic (heterotrophic)

metric coefficient, that is, YDX, which is the traditional biomass yield on substrate (equal to carbon source and electron donor). All the other stoichiometric coefficients then follow from the so-called conservation equations (elements, electric charge, and enthalpy) (Example 1a) and the Gibbs energy balance (Example 1b).

+ 1CH18O05N02 + 10.63HCO-

All the different biomass yields can be read from this reaction equation; thus, YAX = 1/1.857 = 0.538 C-mol biomass/mol O2 or YCX = 1/10.63 = 0.094 C-mol biomass per mol CO2.

EXAMPLE 1a

Calculation of stoichiometric coefficients in the macrochemical equation

Consider the aerobic growth of Pseudomonas oxalaticus on oxalate using NH+ as the N source. The relevant chemical compounds in this growth system are the five compounds [biomass (CH18O0.5N02), NH4+, HCO—, H+, H2O], the electron donor oxalate (C2O2~), and the electron acceptor O2. In total there are seven compounds and four elements (C, H, O, N). The conversion rates of these compounds are mathematically related by the conservation relations of C, H, O, N, and electric charge. In total there are five independent relations. This means that seven conversion rates are related by five conservation equations, and that the measurement of two rates (e.g., biomass production rx and consumption of the electron donor oxalate rD), which is equivalent to the measurement of YDX = rX/ —rD, allows the calculation of all other yields.

Suppose that from measurement the biomass yield YDX is found to be +0.086 C-mol biomass produced per C-mol oxalate consumed. The proper macrochemical reaction equation can be written in a general form, without knowing all the stoichiometric coefficients but one (+1 for biomass), as

The following conservation equations can now be written:

C conservation H conservation o conservation N conservation Charge conservation

Clearly there are six unknown stoichiometric coefficients (a-f) that are related by five conservation equations. (Biomass has been assigned a convenient, yet arbitrary coefficient + 1.) Having one measured coefficient allows the calculation of all other coefficients. Ydx was measured as 0.086. This means that 1/0.086 = 11.63 C-mol oxalate are consumed to produce 1 C-mol biomass. The previously defined macrochemical equation contains fmol of oxalate, which was two carbon atoms. The stoichiometric coefficient f therefore has the value -11,63/2 = -5.815 (remember the minus sign). Using this fvalue and the five conservation equations, one can calculate the whole chemical growth stoichiometry. The result is

In the Example 1a, only the chemical stoichiometry was calculated. However, there are two additional biomass yields of interest that relate the heat production and Gibbs energy dissipation occurring during the growth process to biomass production. These yields can be simply calculated if the full chemical stoichiometry is known by using tabulated DHf and DGf- values (at pH = 7 and standard conditions) and calculating the enthalpy and Gibbs energy of reaction (Example 1b).

Table 2 contains all the required thermodynamic information as taken from Thauer et al. (11). The values for biomass are taken from Roels (1). Although there is some discussion about the value of Df for biomass, its value is not very important in thermodynamic calculations, as shown by Heijnen (3).

EXAMPLE 1b

Calculation of the yield of biomass on enthalpy and Gibbs energy (Vqx and Vox)

The chemical stoichiometry from Example 1a and the appropriate DHf and DGf values from Table 2 can be used to obtain the heat (enthalpy) and Gibbs energy of reaction.

The enthalpy of reaction, using from Table 2, is calculated as

(10.63)(—692) + 1( —91) — (5.42)(—286) — (1.857)(0)

— (0.8)(0) — (0.2)(—133) — (5.815)(—824) = —1078.7 kJ

For the Gibbs energy of reaction using Df values there follows a value of — 1052.4 kJ. Because in the macrochemical reaction 1 C-mol of biomass is produced, this means that for each 1 C-mol biomass produced there is a heat production of 1078.7 kJ and a Gibbs energy dissipation of 1052.4 kJ, showing that Yqx = 1/ 1078.7 = 0.00093 C-mol biomass produced per kilojoule heat produced and that YGX = 1/1052.4 = 0.0095 C-mol biomass produced per kilojoule of Gibbs energy dissipated. The complete chemical and energetic stoichiometry now can be written as

— 5.815C2O2~ — 0.2NH4+ — 0.8H+ — 1.857O2 — 5.42H2O + 1CH18O0.5N0.2 + 10.63HCO— + 1078.7 kJ heat

+ 1052.4 kJ Gibbs energy

Example 1 shows that the complete chemical and energetic stoichiometry of microbial growth can be calculated from one measured yield using conservation equations and the Gibbs energy and enthalpy balance (elements, charge, 