On the Question of the Metabolic Costs of the Main Metabolic Precursors in Escherichia coli

Abstract

The term metabolic cost (MС) is often used for assessment of energy consumption in the biosynthesis of various substances under different growth conditions or by different cell types. The MC of the metabolite is calculated according to a specified algorithm in universal ~P units, multiples of ATP molecules hydrolyzed to ADP and inorganic phosphate. Our analysis of the published data showed that the interpretation of the MC concept and the algorithms for its calculation, proposed by different authors, differ significantly. Since the MС is often considered in connection with system-level tasks, such as the metabolic flux analysis and the natural selection mechanisms, it seems appropriate to characterize this concept in detail. In this work, the term MС was clearly defined and used to calculate the energy consumption for the synthesis of 13 metabolic precursors of Escherichia coli biomass based on the modern model of the central metabolism of this bacterium. It was found that the MC, expressed in units of stored or hydrolyzed ATP molecules (~P), depends on the characteristics of the metabolism of an individual organism, its culturing conditions, and the P/O ratio, which characterizes the number of ATP molecules formed during the transfer of one electron pair to one oxygen atom in oxidative phosphorylation.

SUPPLEMENTARY MATERIALS

Calculation of the Gibbs energy for metabolic reactions

For a random chemical reaction:

$${{v}_{1}}{{S}_{1}} + {{v}_{2}}{{S}_{2}} \to {{\mu }_{1}}{{P}_{1}} + {{\mu }_{2}}{{P}_{2}},$$

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where S_i and P_j are the substrates and products of the reaction, respectively, v_i and μ_j are their stoichiometric coefficients. The Gibbs energy of this reaction (Δ_rG') can be calculated using the following formula:

$${{\Delta }_{{\text{r}}}}G{\kern 1pt} ' = {{\Delta }_{{\text{r}}}}G{\kern 1pt} {{'}^{{\text{o}}}} + RT{\text{ln}}{{\left( {{{{\left[ {{{P}_{1}}} \right]}}^{\mu }}^{1}{{{\left[ {{{P}_{2}}} \right]}}^{\mu }}^{2}} \right)} \mathord{\left/ {\vphantom {{\left( {{{{\left[ {{{P}_{1}}} \right]}}^{\mu }}^{1}{{{\left[ {{{P}_{2}}} \right]}}^{\mu }}^{2}} \right)} {\left( {{{{\left[ {{{S}_{1}}} \right]}}^{v}}^{1}{{{\left[ {{{S}_{2}}} \right]}}^{v}}^{2}} \right)}}} \right. \kern-0em} {\left( {{{{\left[ {{{S}_{1}}} \right]}}^{v}}^{1}{{{\left[ {{{S}_{2}}} \right]}}^{v}}^{2}} \right)}},$$

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where [S_i] and [P_j] are the molar concentration of substrates and products of the reaction, respectively; Δ_rG'^o are the standard Gibbs energy of the reaction under 1 atm, 25°С and 1 М concentration of each reagent; T is the absolute temperature, K; R is the universal gas constant (≈ 8.3144598(48) J mol^–1 K^–1).

The value of Δ_rG'^o for metabolic reactions can be extracted from specialized literature (for example, [26, 78]). The values of Δ_rG'^m for reactions under standard pressure and temperature are also given, but at 1 mM concentration of each reagents, as well as the values of standard Gibbs free energy of metabolite formation at 1 M (Δ_fG'^o) or 1 mM (Δ_fG'^m) concentrations. The available parameters of Δ_fG'^o are usually the result of theoretical evaluation using the group contribution method developed by M. Mavrovouniotis [79, 80] and supplemented by M. Jankowski et al. [75] and B. Du et al. [78] on the basis of calculated and experimental data obtained by R. Alberty [81].

If the values of Δ_rG'^o are known, we can determine the Δ_rG ' value, for example, for the reaction at physiological reagent concentrations, i.e., specified for metabolites of E. coli cells exponentially growing under aerobic conditions on glucose. In these conditions, according to [82]: [ATP] = 9.6 × 10⁻³, [ADP] = 5.6 × 10⁻⁴, [P_i] = 2 × 10⁻², [NAD⁺] = 2.6 × 10⁻³, [NADPH] = 1.2 × 10⁻⁴, [NADPH] = 8.3 × 10⁻⁵, [NADP⁺] = 2.1 × 10⁻⁶. These are the concentrations we used to calculate Δ_rG'.

The energy released during the hydrolysis of ATP to ADP and P_i (ATP maintenance requirement) is called the phosphorylation potential, and its value is estimated for the reaction performed under standard conditions [82]:

$$\begin{gathered} {\text{ATP}} + {{{\text{H}}}_{{\text{2}}}}{\text{O}} \to {\text{ADP}} + {{{\text{P}}}_{{\text{i}}}} \\ + \,\,{\text{H}}({{\Delta }_{{\text{r}}}}G^{'{\text{o}}} = - 6.7{\text{ kcal/mol}}), \\ \end{gathered} $$

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and at physiological metabolite concentrations the equation is represented as:

$$\begin{gathered} {{\Delta }_{{\text{r}}}}G{\kern 1pt} ' = {\text{ }}{{\Delta }_{{\text{r}}}}G^{'{\text{o}}} + RT{\text{ln}}{{\left( {[{\text{ADP}}][{{{\text{P}}}_{{\text{i}}}}]} \right)} \mathord{\left/ {\vphantom {{\left( {[{\text{ADP}}][{{{\text{P}}}_{{\text{i}}}}]} \right)} {\left[ {{\text{ATP}}} \right]}}} \right. \kern-0em} {\left[ {{\text{ATP}}} \right]}} \\ = \,\, - 10.9{\text{ kcal/mol}} = {\text{[}}{{{\text{P}}}_{{\text{i}}}}{\text{]}}. \\ \end{gathered} $$

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