• Increases if the degree of reduction of the carbon source (the parameter y in equation 3a) is smaller or larger than about 3.8
Equation 3a further shows that for heterotrophic growth 1/Ygx ranges between about 200 and 1,000 kJ/C-mol biomass, for the C sources explored, for which:
• The number of carbon atoms in the carbon source ranges between C = 1 (e.g., CO2, formate, methane) and C = 6 (e.g., glucose, citrate).
• The degree of reduction of the C source y ranges between 0 (for CO2) and 8 (for CH4).
The effect of the number of C atoms (C) and degree of reduction (y) of the C source can be simply understood as follows:
• Biomass contains many polymers that contain monomers of four to six C atoms. If the C source contains fewer than four to six C atoms, the microorganism must perform extra biochemical reactions to achieve C-C couplings. This requires extra Gibbs energy, compared to a C source that has six C-atoms, Hence 1/ YsX increases for C-sources with less carbon atoms.
• Biomass has y = 4.2. If the C source is more reduced (y > 4.2) or more oxidized (y < 4.2), there is a need for additional oxidation reactions or reduction reactions, respectively, as compared to a carbon source (like glucose) with y = 4. These additional reactions lead to extra Gibbs energy dissipation, leading to a higher value of 1/ YsX.
Simply stated, the more biochemical tinkering is needed to convert an organic C source into biomass, the more Gibbs energy is dissipated and the higher 1/ YsX becomes. Obviously glucose (C = 6, y = 4) is a nearly ideal C-source because it requires the least Gibbs energy dissipation for biomass production. According to equation 3a, for glucose
1/YGX = 200 + 0 + 36 = 236 kJ/C-mol biomass. In contrast, CO2 is a very poor C source, because it requires about four times as much Gibbs energy (1/YsX = 200 + 236 + 460 = 986 kJ/C-mol according to equation 3a). Equation (3b) shows that for autotrophic growth, in the situation where RET is needed (which occurs for many inorganic electron donors), 1/Ygx has a very high value of 3,500 kJ/ C-mol biomass. This value should be compared to auto-trophic growth without RET as occurs with, for example, H2 or CO as electron donor (for which 1/Y3X ^ 1,000 kJ/ C-mol according to equation 3a).
Obviously, the use of RET increases the Gibbs energy dissipation needed for biomass production tremendously. The explanation is that, using the RET process, the electrons of the electron donor are increased in energy level, up to the energy level of electrons in NADH in order to make CO2 reduction to biomass thermodynamically feasible. This "energy-pumping" process (RET) apparently requires a large amount of Gibbs energy, of about 3,500 — 1,000 = 2,500 kJ/C-mol biomass produced.
The effect that the type of the available C source has on the Gibbs energy needed for biomass synthesis is well known in biochemistry. Biochemists express the energy need in ATP. Figure 6 compares the calculated Gibbs energy dissipation needed for biomass synthesis (1/ YSX, in kJ/C-molX) with the theoretically calculated amount of ATP expenditure for biomass synthesis in mol ATP/C-mol X. The points shown are for different C sources, ranging from glucose (28.8) to CO2 (2.5). The parenthetical numbers are the published (10) biomass yields on ATP in gram-X/mol ATP. It is clear that there is a close correspondence, which is logical. Equations 3a and 3b provide the energy needed for biomass synthesis in kilojoules, whereas the biochemists use mol ATP as the energy measure.
In conclusion, it should be realized that equations 2, 3a and 3b are completely sufficient to estimate a biomass yield and the full macrochemical equation for any arbitrary chemotrophic growth system (Example 4).
The predictive accuracy of this correlation for chemo-trophic growth has been shown (2,4) to be ± 10 to 20% rela-
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