Fundamentals of Biochemical Engineering Part 1 - Bailey J., Ollis D. 1989

Stoichiometry and Energetics of Metabolic Conversions
Stoichiometry of Cell Growth and Product Formation
Stoichiometry of Energy Metabolism; Estimation of Heat Generation and Associated Yield Coefficients

Chemical energy is utilized very efficiently within Cells, but, as in any real-world process, a portion of the substrate's energy is released as heat. This, in particular, necessitates the cooling of biological reactors containing Cell cultures. Cells generate heat primarily through METABOLISM and Energy Exchange associated with cell growth. Consequently, it can be assumed that There is a roughly proportional relationship between The amount of heat released and the amount of high-energy substrate utilized. In this regard, a specific parameter was introduced—the coefficient Y_∆ (The ratio of the mass of cells formed in grams to the amount of heat released in kilocalories), which is analogous to the other yield coefficients discussed above. If we denote the mass of cells (in grams) produced per gram of utilized substrate as Y_s, and the heats of combustion of the substrate and cellular mass (in kilocalories per gram) as ∆H_s and ∆H_c, respectively, the relationship between these quantities can be expressed by the following equation:

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FIG. 5.30. Approximate thermal balance of substrate utilization.

This equation stems from the approximate Energy balance between the two pathways of complete substrate oxidation during aerobic growth, which is schematically depicted in Fig. 5.30.

If oxygen is the primary oxidizing agent, the difference between the heat released during the Complete oxidation of one gram of substrate (∆H_S) and the Heat of Combustion of the cells (and the dry residue of the extracellular fluid) grown on the same amount of substrate (Y_s∆H_c) will be approximately equal to the amount of heat released per gram of utilized substrate during cell growth (as well as the release of Н₂О and СO₂).

The accuracy of the assumptions underlying equation (5.62) and the diagram in Fig. 5.30 can be evaluated using data related to the growth of Yeast on unbranched paraffinic Hydrocarbons. The experimentally determined values of ∆H_S and ∆H_c are 11.4 and 4.7 kcal/g, respectively; hence, using equation (5.62), we find that

Direct measurement of Y_S and Y_∆ yielded the following results [16]:

In the absence of experimental data, the heat of combustion of cells (as with any other Materials) can be determined based on the following empirical fact: when electrons are transferred from a compound with a degree of reduction y_s to compounds with a zero degree of reduction (such as СO₂ or Н₂O), an amount of energy equal to K'∙y_s is released, where K is a coefficient ranging from 26 to 31 kcal per chemical equivalent of the oxidized substance. Since molecular oxygen O₂ accepts four electrons during Respiration, the uptake of one mole of oxygen should be accompanied by the release of 104–124 kcal of heat. Figure 5.31 presents experimental data for two Bacteria, yeast, and Molds grown on various media. Although the scatter of results is quite large, the dependence of the heat generation rate on the Oxygen Uptake Rate is clearly discernible.

FIG. 5.31. Experimentally determined rates of heat generation and oxygen uptake during the growth of various microorganisms on different media (Glu — glucose medium, Mol — molasses medium, Sbm — soybean medium). The slope of the regression line is 124±3 kcal/mol O₂. [Reprinted with permission from: Cooney С. L, Wang D. I. С., Mateles R. I., Measurement of Heat Evolution and Correlation with Oxygen Consumption during Microbial growth, Biotech. Bioeng., 11, 269 (1968)].

As an example, let us estimate the heat of combustion of Pseudomonas fluorescens cells grown on a glucose medium. To do this, we first write the combustion reaction equation for the cells based on the experimentally determined gross formula, assuming that the combustion products are СO₂, Н₂O, and N₂:

Next, we determine the heat released during the combustion of the bacteria using equation (5.63), assuming the heat of combustion per mole of O₂ is 104 kcal:

However, in doing so¹, we did not account for the fact that the dry cell matter also contains ash. If the dry cellular matter contains 10% ash, the heat of combustion of the cells will be

Table 5.12. Yield coefficients for bacteria grown on media with various sources

^a From: Abbott В., Clamen A., The Relationship of Substrate, Growth Rate, and Maintenance Coefficient to SINGLE CELL PROTEIN Production, Biotech. Bioeng., 15, 117 (1973).

The value of Y_∆ depends on The Nature of both the microorganism (affecting ∆H_c) and the utilized substrate (affecting ∆H_s). Table 5.12 lists a series of calculated Y_∆ values as a function of the substrate nature. Note that, in general, hydrocarbons provide greater heat evolution than partially oxidized compounds [Y_∆(CH₄) < Y_∆(CH₃OH); Y_∆(n-alkanes) < Y_∆(glucose)]. Consequently, more reduced substrates place a greater demand on the bioreactor for heat removal. The Influence of energetic stoichiometry on process economics is discussed in Chapter 12.

In Fermentation or wastewater Treatment processes, substrates are frequently mixtures of numerous substances with varying heats of combustion. Servizi and Bogan [18] noted that the stoichiometric ratio m₀ (the number of moles of O₂ required for the complete oxidation of 1 mole of substrate) for A number of compounds is proportional to the Standard Free energy of combustion ∆G°. For example, for CARBOHYDRATES, TCA cycle intermediates, and certain Glycolysis products

∆G°= - 116m₀ kcal/mol substrate      (5.66)

and for Aromatic Compounds, alcohols, and aliphatic acids

∆G°= - 104m₀ kcal/mol of substrate      (5.67)

[Hattori (ref. [4] in Ch. 13) noted that if the chemical oxygen demand (COD) expressed in grams of oxygen per mole is known, COD/32 can be used instead of m₀ in these equations.] The average Free energy of complete oxidation for a mixture of substrates can be determined by summing the free energies of oxidation of all individual substrates:

where i represents the substrates; M_i is the number of moles of the i-th substrate; and ∆G_i° is the free energy of complete oxidation of the i-th substrate.

It has also been found that the growth yield Y of a process involving multiple species of unicellular organisms can be determined in the same way as for the single-species microbial processes (bacteria or Yeasts) described above. Servizi and Bogan [18] determined the average growth yields (expressed in grams of cells per mole of substrate) for activated sludge (see Ch. 14), which contains a multitude of microorganisms and a large variety of substrates, and found (Fig. 5.32) that

Given Y_s, all other quantities entering into equation (5.62) are readily determined experimentally; consequently, Y_∆ can also be calculated in this case.

FIG. 5.32. Dependence of the average activated sludge growth yield on the average free energy of substrate oxidation. [Reprinted from: Servizi J. A., Bogan R. H., Thermodynamic Aspects of Biological Oxidation and Synthesis, J. Water Pollut. Control Fed., 36, 607 (1961).]

It is to be expected that the value of the coefficient in equation (5.69) depends on the microbial species; therefore, experimental determination of this coefficient for the specific Organism(s) participating in the process is once again desirable. At the same time, assuming a proportional relationship between

Servizi and Bogan based their approach on a linear relationship between the average growth yield and the number N_ATP of ATP molecules synthesized during the utilization of 1 mole of substrate. Since is simply the amount of biomass (in grams) synthesized per gram of substrate, the proportionality constant between and ATP represents the mass of cells (in grams) synthesized per mole of ATP utilized. It is well known that the latter value is approximately constant for a wide range of anaerobes, but varies over much broader limits in the case of aerobes (Section 5.9.2). In the absence of more reliable data, equation (5.69) can generally serve as a basis for estimating systems consisting of multiple substrates and microorganisms. The accuracy of such an estimation is apparently within ±20–30%, as clearly evidenced by the correlation data presented in Fig. 5.32.

The aforementioned relationship between the number of electrons participating in a process and the internal energy of a substance can be used to estimate the maximum possible yield of organic matter from an organic substrate. The fraction of electrons transferred from the substrate to metabolic products during the reaction, ζ_p, can be determined from the equation

The last term on the right-hand side of equation (5.70) represents the yield coefficient Y_P/S. The number of electrons participating in the process per gram of organic matter can be expressed as σγ/12, where σ is the mass fraction of carbon in the compound and γ is the degree of reduction of that carbon. Substituting this expression into equation (5.70), we obtain

Since the energies of the substrate and the metabolic product are roughly proportional to the content of reactive electrons in them, the parameter ζ_p can also be interpreted as the energetic yield coefficient of the metabolic product from the substrate. In this case, obviously, the coefficient must not exceed unity. Consequently, the upper limit of the product yield Y_p/s^max can be determined from equation (5.71) at ζ_p = 1:

Values of Y_p/s^max for several substrates and metabolic products are listed in Table 5.13.