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

Stoichiometry and Energetics of Metabolic Transformations
Stoichiometry of Cellular Growth and Product Formation
Elemental Mass Balances and Cellular Growth

Cell growth and its associated metabolic processes can be described by equations similar to those used to represent ordinary Chemical Reactions. To do this, one must first determine the "chemical formula" of dry cellular matter. If the Elemental Composition of a given strain growing under defined conditions is known (see, for example, the data in Table 5.10), it is straightforward to find the relative values of the coefficients in the empirical cell formula C_θH_aO_βN_δ. To assign a strictly defined formula and corresponding "molecular weight" to The Cell, it is convenient to set θ = 1 and then determine The values of a, β, and δ According to the elemental composition. The cell "formulas" given in Table 5.10 were obtained in precisely this manner. One C-mole of Cells is defined as The amount of cell mass containing one gram-atom (12.011 g) of carbon and corresponding to the empirical cell formula with θ = 1.

As a simple example of analyzing the stoichiometry of cell growth based on elemental mass balances, let us first consider cell growth under aerobic conditions, where no metabolic products other than new cells, CO₂, and H₂O are formed. If we denote the carbon and nitrogen sources by the formulas CH_хО_у and H_lO_mN_n, respectively, the cell growth equation can be written as follows:

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Here, the coefficient of the cell formula is set to unity, which does not affect the generality of the equation, since stoichiometric coefficients can be multiplied or divided by any same number.

It follows from equation (5.49) that the five unknown stoichiometric coefficients a', b', c', d', and e' are constrained by four equations:

An additional equation can be obtained by experimentally determining the respiratory quotient (RQ) of the cell growth reaction. The respiratory quotient is defined as the molar (or volumetric) ratio of respired CO₂

For the cell growth reaction expressed by equation (5.49),

RQ = e'/b'      (5.52)

Thus, the five equations (5.52) and (5.50) contain five unknown stoichiometric coefficients, and if the RQ is known, all these coefficients can be determined. Potential difficulties associated with very large fluctuations in stoichiometric coefficients resulting from relatively small errors in RQ measurement will be discussed in Exercise 5.16.

In the general case, the chemical formula representing the elemental COMPOSITION OF THE cell and the stoichiometric coefficients in equation (5.49) depend on the composition of the nutrient medium and the environmental conditions of the cells. It should be kept in mind that this dependence is descriptive in nature and, in the sense used here, reflects the net effect of numerous independent chemical reactions. To gain some insight into how the environment or growth conditions affect the stoichiometry of this process and to relate this influence to the metabolic pathways discussed above, one can, for example, divide the overall growth reaction into several reactions corresponding to different metabolic Functions (though not necessarily specific metabolic pathways).

We will now examine the growth stoichiometry of a chemoheterotrophic Organism under aerobic conditions in somewhat greater detail. We will associate each reaction with the generation and utilization of ATP. Below, the latter are written separately and are not included in the equations for the corresponding reactions involving carbon, hydrogen, oxygen, and nitrogen compounds due to certain practical difficulties associated with ATP stoichiometry; we will briefly discuss these difficulties as well.

Dissimilation of the energy source:

Oxidative Phosphorylation:

Biosynthesis:

Maintenance and energy dissipation:

с(АТР + Н₂О) → c(ADP + P_і)      (5.56)

The interrelationship between these reactions can be established by assuming that under the conditions considered here, neither ATP nor NADH accumulates, and consequently, the synthesis of these compounds must be balanced by their consumption.

The more complex, yet more realistic system of chemical equations describing cell growth presented above is obtained at the cost of a sharp increase in the number of stoichiometric parameters. Note that in equations (5.53) through (5.56), first, the stoichiometric coefficients reflect the elemental balance in each individual reaction and, second, the stoichiometric coefficient for the biomass CH_аО_βN_δ is assumed to be unity. Therefore, the coefficients a, b, and c in the other reactions essentially reflect the extent to which these reactions occur relative to the cell growth (biosynthesis) reaction. The stoichiometric coefficients for Water in two cases are denoted simply by the word "coefficient" rather than by a special symbol, since the uptake or release of water As a result of the reaction generally does not practically alter its total amount within the cell. The symbol ε_s denotes the number of phosphorylation events per carbon atom participating in catabolic processes.

The parameters y_В, y_S, and y_N denote the degrees of reduction of the biomass, the carbon source, and the nitrogen source, respectively. The degree of reduction y of a compound with the empirical formula CH_rO_sN_v is defined as y = 4 + r – 2s – 3v. It is easy to see that the degrees of reduction of CO₂, H₂O, and NH₃ are equal to zero.

The coefficient Y_АTP^mах denotes the mass of cells produced per mole of ATP consumed, provided that ATP is utilized exclusively for biosynthetic purposes. Attempts have been made to estimate the value of Y_ATP^mах from the known elemental composition of cells and biosynthetic pathways [13]. These estimates have shown that, for example, during the growth of E. coli on glucose and inorganic salts, Y_АTP^mах is 28.8 g of cells per gram-mole of ATP. To convert from mass units to molar units, the Molecular Weight of the cells, designated by the symbol MWB, is included in equation (5.556).

As noted above, P/O denotes The ratio of phosphorylated ADP molecules per atom of oxygen consumed. This parameter characterizes the efficiency of OXIDATIVE PHOSPHORYLATION AND generally depends on cell cultivation conditions. Calculations based on the average elemental composition of microorganisms show that the theoretical maximum P/O values are 2.25, 2.50, and 3.00 when using acetate, malate, and glucose as the primary nutrient, respectively.

Direct experimental Determination of the P/O parameter is complicated by the fact that it is extremely difficult to empirically study synthesis and utilization pathways of ATP separately; moreover, the relative amounts of ATP produced and consumed in each pathway depend on cell cultivation conditions. The primary difficulty here stems from the partial consumption of ATP in processes such as membrane transport, The biosynthesis of compounds subsequently degraded by intracellular Hydrolases, and other poorly understood processes (sometimes referred to as futile cycles). All of these ATP consumption sources, grouped together here into a single "reaction" (5.56) under the general heading of "maintenance and energy dissipation," naturally affect other ATP generation and utilization processes.

Since the amount of newly synthesized ATP must equal the amount of utilized ATP, any Changes in the relative amount of ATP participating in "reaction" (5.56) (which is reflected by the coefficient $c$) will inevitably lead to changes in the amounts of ATP involved in other reactions. Experimental data show that the ATP requirement for cell maintenance is determined not by stoichiometric factors, but by the rates of metabolic processes; therefore, we will postpone the Quantitative evaluation of these costs until we examine The kinetics of cell growth in Chapter 7.

It is worth noting here that experimentally determined biomass yields per mole of ATP utilized under anaerobic conditions typically show very little dependence on the substrate type and microorganism species, with the average Y_ATP value being 10.7 g of cell mass per mole of ATP. In chemoheterotrophic organisms, as a rule, significantly more substrate is used for energy production than for biomass growth. For example, one study demonstrated that during the growth of baker's Yeast Saccharomyces cerevisiae under anaerobic conditions in a glucose-rich medium (with glucose serving as the carbon source), 98% of the assimilated carbon was expended on energy production and only 2% on cell mass growth. Determining the amount of synthesized ATP with sufficient accuracy under aerobic growth conditions has proven extremely difficult. Available data indicate that the P/O ratio ranges from 0.5 to 1.8, which is significantly below the theoretical value. Studies of the bacterium Aerobacter cloacae showed that when grown in an aerobic minimal medium, 55% of the glucose is assimilated into newly synthesized biomass, while 45% is expended on energy production. These findings indicate that under aerobic conditions, the cell mass yield per unit of substrate utilized is generally higher than during anaerobic growth. For instance, the Y_x/s coefficient (mass of cells in grams produced per 1 mol of glucose) for Streptococcus faecalis in a glucose medium is 21.5 under anaerobic conditions and 58.2 during aerobic growth. In the next section, we will examine The Effect of such substrate distribution on the stoichiometry of metabolic processes.