An exploration of how the thermodynamic efficiency of bioenergetic membrane systems varies with c-subunit stoichiometry of F₁F₀ ATP synthases

Abstract

Recently the F₀ portion of the bovine mitochondrial F₁F₀-ATP synthase was shown to contain eight ‘c’ subunits (n = 8). This surprised many in the field, as previously, the only other mitochondrial F₀ (for yeast) was shown to have ten ‘c’ subunits. The metabolic implications of ‘c’ subunit copy number explored in this paper lead to several surprising conclusions: (1) Aerobically respiring E. coli (n = 10) and animal mitochondria (n = 8) both have very high F₁F₀ thermodynamic efficiencies of ≈90 % under typical conditions, whereas efficiency is only ≈65 % for chloroplasts (n = 14). Reasons for this difference, including the importance of transmembrane potential (∆Ψ) as a rotational catalyst, as opposed to an energy source, are discussed. (2) Maximum theoretical P/O ratios in animal mitochondria (n = 8) are calculated to be 2.73 ATP/NADH and 1.64 ATP/FADH₂, yielding 34.5 ATP/glucose (assuming NADH import via the malate/aspartate shuttle). The experimentally measured values of 2.44 (±0.15), 1.47 (±0.13), and 31.3 (±1.5), respectively, are only about 10 % lower, suggesting very little energy depletion via transmembrane proton leakage. (3) Finally, the thermodynamic efficiency of oxidative phosphorylation is not lower than that of substrate level phosphorylation, as previously believed. The overall thermodynamic efficiencies of oxidative phosphorylation, glycolysis, and the citric acid cycle are ≈80 % in all three processes.

Appendices

Appendix 1: Error propagation in thermodynamic calculations in Table 1

Taking the high-potential E. coli as an example, the experimental measurements are: Δψ = − 220(±22)mV; ΔpH = + 0.9(±0.09); [P_i] = 1(±0.1)mM; [ATP]/[ADP] = 10(±0.14).

H⁺ flow

∆μ_H+ is calculated from Eq. 2: F(−0.22 V) − 2.3RT(0.9) = − 6.3 kcal/mol H⁺.

The uncertainty in ∆μ_H+ is then: SQRT[(F(0.022 V))² + (2.3RT(0.09))²] = ± 0.52kcal/mol.

∆G_H+ is calculated from Eq. 3: − 6.3 kcal/mol H⁺ × 10/3 = − 21 kcal.

The uncertainty in ∆G_H+ is then: 0.52 kcal/mol × 10/3 = ± 1.7 kcal

ATP synthesis

Q’ for ATP synthesis is calculated from Eq. 5: 10/0.001 = 10,000 M⁻¹.

The relative uncertainty in Q’ is then: SQRT[(0.14/10)² + (0.1/1)²] = ± 0.101, and the absolute uncertainty in Q ’ = 10, 000 × 0.101 = ± 1010 M^− 1.

∆G_{ATP synth.} is calculated from Eq. 6: 7.6 + RTln(10, 000) = + 13.056 kcal/mol.

The uncertainty in ∆G_{ATP synth.} is then: RT(1010/10000) = ± 0.06 kcal/mol.

Net reaction: thermodynamic efficiency

The thermodynamic efficiency is calculated from Eq. 7: 13.056/21 = 62.2 %.

The relative uncertainty in the thermodynamic efficiency is then:

SQRT[(0.06/13.056)² + (0.52/21)²] = 0.0830, and the absolute uncertainty in the efficiency = 0.0830 × 62.2 % = 5.2 %

Appendix 2: Calculations of Q’ and ∆G

For the reactions presented in Tables 4 and 5, the balanced equations are as follows:

• 1. glucose combustion: C₆H₁₂O₆ + 6 O₂ ➔ 6 CO₂ + 6 H₂O

$$ Q\hbox{'}=\frac{{\left[C{O}_2\right]}_{matrix}^6}{{\left[\mathrm{glucose}\right]}_{cyt}{\left[{O}_2\right]}_{matrix}^6} $$

The relevant local concentrations are cytoplasmic for glucose, but mitochondrial matrix for O₂ and CO₂: Glucose is catabolized by glycolytic enzymes in the cytoplasm, whereas the mitochondrial matrix is the site of O₂ consumption and CO₂ release.

• 2. pyruvate combustion: C₃H₄O₃ + 5/2 O₂ ➔ 3 CO₂ + 2 H₂O

$$ Q\hbox{'}=\frac{{\left[C{O}_2\right]}_{matrix}^3}{{\left[\mathrm{pyruvate}\right]}_{matrix}{\left[{O}_2\right]}_{matrix}^{5/2}} $$

• 3. ET chains, FADH₂ combustion: FADH₂ + ½ O₂ ➔ FAD + H₂O

$$ Q\hbox{'}=\frac{{\left[ FAD\right]}_{mito\kern0.5em i.m.}}{{\left[{\mathrm{FADH}}_2\right]}_{mito\kern0.5em i.m.}{\left[{O}_2\right]}_{matrix}^{1/2}} $$

• 4. ET chains, NADH combustion: NADH + H⁺ + ½ O₂ ➔ NAD⁺ + H₂O

$$ Q\hbox{'}=\frac{{\left[ NA{D}^{+}\right]}_{matrix}}{{\left[\mathrm{NADH}\right]}_{matrix}{\left[{O}_2\right]}_{matrix}^{1/2}} $$

• 5. ATP synthesis: ATP⁴⁻ + H₂O ➔ ADP³⁻ + HOPO₃ ²⁻ + H⁺

$$ Q\hbox{'}=\frac{\left[ AD{P}^{3-}\right]\left[ HOP{O}_3^{2-}\right]}{\left[{\mathrm{ATP}}^{4-}\right]} $$

Q’ for ATP synthesis is calculated with cytoplasmic concentrations for glycolytic ATP; for citric acid cycle and oxidative phosphorylation ATP, mitochondrial matrix concentrations are used. These concentrations are listed in Table 3. For glucose combustion, typical concentrations (from Table 3) are:

• cytoplasmic glucose: 5.0 mM; matrix O₂: 25 μM; matrix CO₂: 1.1 mM,

• so for glucose combustion, $Q\hbox{'}=\frac{{\left[0.0011\right]}^6}{\left[0.0050\right]{\left[25\left({10}^{-6}\right)\right]}^6}=1.77\left(1{0}^{-18}\right)/1.22\left(1{0}^{-30}\right)=1.45\left(1{0}^{12}\right)$

• At 37 °C, $\begin{array}{l}\mathrm{RTlnQ}'=0.001987\;\mathrm{kcal}/\mathrm{mol}\cdotp \mathrm{K}\times 310.15\;\mathrm{K}\times \ln \left(1.45\left(1{0}^{12}\right)\right)=\hfill \\ {}\kern.1em 0.616\times 28.0=17.(3)\;\mathrm{kcal}/\mathrm{mol}\hfill \end{array}$,

• so ΔG = ΔG° ’ + RTlnQ ’ = − 687 + 17. (3) = − 670 kcal/mol

Metabolite concentrations vary quite widely with the metabolic state of the cell, and also with tissue type. A reasonable range of variation would be five-fold above and below the typical steady state values cited in Table 3. From this, a range of Q’ can be calculated. For glucose combustion, the high-end Q’ would be

$$ Q\hbox{'}=\frac{{\left[0.0055\right]}^6}{\left[0.0010\right]{\left[5.0\left({10}^{-6}\right)\right]}^6}=2.77\left(1{0}^{-14}\right)/1.56\left(1{0}^{-35}\right)=1.8\left(1{0}^{21}\right) $$

$$ \mathrm{RTlnQ}\hbox{'}=0.616\;\mathrm{kcal}/\mathrm{mol}\times \ln \left(1.8\left(1{0}^{21}\right)\right)=30\;\mathrm{kcal}/\mathrm{mol},\mathrm{and}\;\varDelta \mathrm{G}=-657\;\mathrm{kcal}/\mathrm{mol} $$

Conversely, the low-end Q’ would be

$$ Q\hbox{'}=\frac{{\left[2.2\left({10}^{-4}\right)\right]}^6}{\left[0.025\right]{\left[125\left({10}^{-6}\right)\right]}^6}=1.13\left(1{0}^{-22}\right)/9.5\left(1{0}^{-26}\right)=1.18\left(1{0}^3\right) $$

$$ \mathrm{RTlnQ}\hbox{'}=0.616\;\mathrm{kcal}/\mathrm{mol}\times \ln \left(1.18\left(1{0}^3\right)\right)=4\;\mathrm{kcal}/\mathrm{mol},\mathrm{and}\;\varDelta \mathrm{G}=-683\;\mathrm{kcal}/\mathrm{mol}. $$

Thus, in different tissues and different physiological conditions, the value of ∆G for glucose combustion can be estimated to range ± 13 kcal/mol around the ‘normal’ value of −670 kcal/mol. Similar ranges of Q’ and ∆G can be calculated for most of the reactions in Table 4. For the ATP hydrolysis reaction, the phosphate concentration and [ATP]/[ADP] ratio vary somewhat less than other metabolites (Stitt et al. 1982; Metelkin et al. 2009; Minakami and Yoshikawa 1965; Soboll and Stucki 1985; Lemasters et al. 1984. Values five-fold above and below the steady state [ATP]/[ADP] ratio, and four times above and below the steady state phosphate concentration were used to calculate, for ATP hydrolysis, Q’ = [P_i] ÷ ([ATP]/[ADP]).

		[Pi] ÷ ([ATP]/[ADP])	Q’	∆G (kcal/mol)
Cytoplasm:	Q’ (avg.):	$\frac{0.0010}{10}$	1.0 × 10−4	−13.3
	Q’ (low):	$\frac{0.0010/4}{10\times 5}$	5.0 × 10−6	−15.1
	Q’ (high):	$\frac{0.0010\times 4}{10/5}$	2.0 × 10−3	−11.4
Matrix:	Q’ (avg.):	$\frac{0.010}{3}$	3.33 × 10−3	−11.1
	Q’ (low):	$\frac{0.010/4}{3\times 5}$	1.67 × 10−4	−13.0
	Q’ (high):	$\frac{0.010\times 4}{3/5}$	6.67 × 10−2	−9.3