Fig. 5: Back flux under sulfate limitation or with variable starting butane concentrations.

A, D Temporal evolution of measured concentrations of butane (C₄H₁₀, circles) and sulfide (HS^–, diamonds), along with trend lines fitted using the first-order dynamic model. Gray shades indicate measurements from low-sulfate incubations (5 mmol/L sulfate) with three different starting ¹³C-bicarbonate concentrations (A; 1.12%, 50%, and 98%), or from incubations with two different initial butane concentrations (D; 3 mmol l⁻¹ vs. 6 mmol l⁻¹). B, E Development of isotope compositions of butane (\({{{\rm{\delta }}}}^{13}{{{\rm{C}}}}_{{{{\rm{C}}}}_{4}{{{\rm{H}}}}_{10}}\)). Color shades represent the same incubation conditions as in A; Error bars in B, E, are standard deviations of technical replicates (n = 3). C, F Ratio of back flux relative to the net AOB rate (f₋/f_net) and Gibbs free energy change of the overall AOB reaction (∆G) estimated from measured concentrations and/or isotope compositions. Black lines show calculated values for low-sulfate assays with 50% ¹³C-bicarbonate (C) and for low-butane assays (F). The f₋/f_net and ∆G calculated for the assay with 6 mmol l⁻¹ C₄H₁₀ 98% ¹³C-bicarbonate, and 28 mmol l⁻¹ sulfate are shown for comparison (grey lines in C, F). The shaded envelopes in (C, F) indicate the 95% confidence interval of estimated values. Source data are provided as a Source Data file.