Calculation Details

How do environmental conditions shape metabolic feasibility?

Whether a microbial metabolism can support growth depends on whether the overall reaction releases free energy (ΔG < 0). Microorganisms couple an electron donor half-reaction (oxidation) to an electron acceptor half-reaction (reduction). Both the sign and magnitude of ΔG depend on the actual concentrations of substrates and products in the environment — which is why the redox tower shifts when conditions change.

Free energy from paired half-reactions

For a complete reaction combining an electron donor half-reaction (D) and an electron acceptor half-reaction (A), the Gibbs free energy change is:

ΔG = −n_e · F · ΔE where ΔE = E_acceptor − E_donor

A metabolism is exergonic (feasible) when ΔG < 0, i.e. when the acceptor reduction potential exceeds the donor's (ΔE > 0). On the tower, reduction potential increases downward, so a feasible pairing has the acceptor half-reaction sitting below the donor — electrons flow downward.

How does E change with conditions? — The Nernst equation

To consider how delta G (or delta E) change with conditions, we thus look at the potential of each half reaction. Each half-reaction has a standard reduction potential E°, measured relative to the Standard Hydrogen Electrode (SHE) — the universal electrochemical reference, defined to have E = 0 V by convention. E°(SHE) reflects the inherent tendency of a half-reaction to accept electrons when all species are at standard conditions (1 M or 1 bar, including H⁺ at 1 M, i.e. pH = 0).

At actual environmental concentrations the reduction potential shifts according to the Nernst equation:

E = E°(SHE) − (RT / n_eF) · ln(Q)

where Q = [products] / [reactants] is the reaction quotient of the reduction half-reaction (Ox + n_ee⁻ → Red), n_e = electrons transferred, R = 8.314 J mol⁻¹K⁻¹, F = 96 485 C mol⁻¹, T = 298 K, and RT/F ≈ 25.7 mV at 25 °C. When all species are at standard activities, Q = 1 and E = E°(SHE).

In microbiology the standard reference is pH = 7 rather than pH = 0. The corresponding standard potential E°′ is E°(SHE) with the pH = 7 correction already applied. In the calculations here we start from E°(SHE) and keep H⁺ explicit in Q, so all pH dependence is visible — E°′ is recovered by setting pH = 7 (as shown in the example below).

Example — aerobic respiration (Glucose + O₂)

To illustrate how this condition depenence is calculated in detail we consider aerobic respiration which couples glucose oxidation (donor) to oxygen reduction (acceptor). Both half-reactions are written in their reduction form as they appear on the tower. H₂O does not appear in Q (activity = 1 by convention).^†

Acceptor O₂ + 4H⁺ + 4e⁻ → 2H₂O    (n_e=4, E°(SHE)=+1229 mV)
   Q = [H₂O]² / (p_O₂·[H⁺]⁴) = 1 / (p_O₂·[H⁺]⁴)
   E = 1229 mV − (RT/4F)·ln(1/(p_O₂·[H⁺]⁴))
     = 1229 mV + (RT/4F)·ln(p_O₂) + (RT/4F)·4·ln([H⁺])
     = 1229 mV + (RT/4F)·ln(p_O₂) − (RT/F)·ln(10)·pH
  At pH=7, p_O₂=1: E = 1229 mV − 7×25.7 mV×ln(10) = 1229 mV − 414 mV = +816 mV = E°′

Donor 6CO₂ + 24H⁺ + 24e⁻ → Glucose + 6H₂O    (n_e=24, E°(SHE)=−16 mV)
   Q = [Glc] / (p_CO₂⁶·[H⁺]²⁴)
   E = −16 mV − (RT/24F)·ln([Glc]/(p_CO₂⁶·[H⁺]²⁴))
     = −16 mV + (RT/4F)·ln(p_CO₂) − (RT/F)·ln(10)·pH − (RT/24F)·ln([Glc])
  At pH=7, p_CO₂=1, [Glc]=1 M: E = −16 mV − 414 mV = −430 mV = E°′

At standard conditions (pH 7, all species at 1 M or 1 bar):

E(O₂/H₂O) = +816 mV | E(CO₂/Glc) = −430 mV
ΔE = (+816 mV) − (−430 mV) = +1246 mV
ΔG = −24 × 96.485 C mol⁻¹ × 1.246 V = −2885 kJ/mol

At trace oxygen (p_O₂ = 10⁻⁵ bar, typical of hypoxic habitats; pH 7, all else standard):

Q(O₂/H₂O) = 1 / (10⁻⁵·(10⁻⁷)⁴) = 10³³
E_acceptor(O₂/H₂O) = 1229 mV − (25.7 mV/4)·ln(10³³) = 1229 mV − 488 mV = +741 mV
ΔE = E_acceptor − E_donor = (+741 mV) − (−430 mV) = +1171 mV
ΔG ≈ −2712 kJ/mol (still strongly exergonic)

In this example, the concentration-driven shift in ΔG is modest relative to the large standard potential difference — aerobic respiration remains strongly exergonic across a wide range of conditions. For redox pairs with a small ΔE at standard conditions, however, concentration effects can be decisive, flipping a reaction from feasible to infeasible or vice versa.

Included reactions

The interactive tool currently includes 16 half-reactions and 15 complete metabolisms, spanning aerobic respiration, anaerobic respiration, fermentation, and syntrophic pathways. All reactions and their thermodynamic parameters are defined in CSV files available in the GitHub repository (cremerlab/redox-tower). Further details on the data format, how the Nernst equation is applied to each entry to generate the interactive redox tower, and how to extend the tool with additional half-reactions or environmental presets are explained in the repository README.

The tool also provides a set of reference environmental conditions (cow rumen, human colon, marine sediment, freshwater sediment, anaerobic digester, activated sludge) as starting points for exploration. These values are chosen to illustrate typical scenarios and should be treated as order-of-magnitude estimates; actual concentrations and partial pressures in any given environment can deviate substantially from these representative values.

Relation to the companion paper table

The supplementary table in Scarampi, Cremer, Soyer et al. lists the same set of metabolisms with their standard half-reaction potentials and ΔG°′ values. Two differences exist between that table and the values used here:

Fermentation reactions. The paper table uses the intracellular pyruvate/glucose couple (E°′ ≈ −700 mV) as the electron donor for ethanol, butyrate, lactate, and homoacetate fermentation, reflecting the actual intracellular electron carrier (NADH) in glycolysis. This tool instead uses the extracellular CO₂/glucose couple (E°′ = −430 mV) as donor, because environmental glucose concentration is the measurable quantity available on the sliders. The overall ΔG°′ for each fermentation is the same in both framings.

Acetoclastic methanogenesis. The paper table lists a lumped "Acetate/CH₄" couple (E°′ = −198 mV) as the acceptor half-reaction. This tool pairs CO₂/Ac⁻ (donor, −290 mV) with CO₂/CH₄ (acceptor, −245 mV) — standard half-reactions that are already present in the tower for other metabolisms. Both representations give ΔG°′ ≈ −31 to −35 kJ/mol, consistent with the accepted literature value.

^† E°(SHE) is defined with water as the solvent (activity = 1 by convention). In the dilute aqueous conditions considered here this does not change, so the water activity is the same in Q as in the standard state and cancels out of the Nernst equation.