Theoretical Estimates of Equilibrium Carbon and Hydrogen Isotope Effects in Microbial Methane Production and Anaerobic Oxidation of Methane

Abstract

Microbial production and consumption of methane are widespread in natural and artificial environments, with important economic and climatic implications. Attempts to use the isotopic composition of methane to constrain its sources are complicated by incomplete understanding of the mechanisms of variation in methane's isotopic composition. Knowledge of the equilibrium isotope fractionations among the large organic intracellular intermediates in the microbial pathways of methane production and consumption must form the basis of any exploration of the mechanisms of isotopic variation, but estimates of these equilibrium isotope fractionations are currently unavailable. To address this gap, we calculated the equilibrium isotopic fractionation of carbon (<sup>13</sup>C/<sup>12</sup>C) and hydrogen (D/H) isotopes among compounds in anaerobic methane metabolisms, as well as the abundance of multiple isotope substitutions ("clumping," e.g., <sup>13</sup>C--D) in these compounds. The Density Functional Theory calculations employed the M06-L/def2-TZVP level of theory and the SMD implicit solvation model, which we have recently optimized for large organic molecules and tested against measured equilibrium isotope fractionations. The computed <sup>13</sup>beta and <sup>2</sup>beta values decrease with decreasing average oxidation state of the carbon atom in the molecules, resulting in a preference for enrichment of the molecules with more oxidized carbon in <sup>13</sup>C and D. Using the computed $\beta$ values, we calculated the equilibrium isotope fractionation factors in the prominent methanogenesis pathways (hydrogenotrophic, methylotrophic and acetoclastic) and in the pathway for anaerobic oxidation of methane (AOM) over a temperature range of 0-700 degrees Celsius. Our calculated equilibrium fractionation factors compare favorably with experimental constrains, where available, and we used them to investigate the relation between the apparent isotope fractionation during methanogenesis and AOM and the thermodynamic drive for these reactions. We show that a detailed map of the equilibrium fractionation factors along these metabolic pathways allows an evaluation of the contribution of equilibrium and kinetic isotope effects to apparent isotope fractionations observed in laboratory, natural and artificial settings. The comprehensive set of equilibrium isotope fractionation factors calculated in this study provides a firm basis for future explorations of isotope effects in methane metabolism.

Experimental and theoretical determinations of hydrogen isotopic equilibrium in the system CH4H2H2O from 3 to 200 °C

“…For temperatures lower than those accessed by experiments (i.e. below 200°C), Bottinga (1969), Richet et al (1977), Chen et al (2019), Thiagarajan et al (2020), and Gropp et al (2021) are in general agreement with maximum differences of 2.3‰ between calculations from 0-200°C. Over this temperature range, these studies yield similar temperature dependencies: calculated differences in 1000ln 13  CH4(g)-CO2(g) range from 44.1 to 45.2‰ at 0 vs. 200°C.…”

“…We are aware of six published theoretical estimates of 1000ln 13  CH4(g)-CO2(g) as a function of temperature at isotopic equilibrium that could be used for such an exercise: Craig (1953), Bottinga (1969), Richet et al (1977), Chen et al (2019), Thiagarajan et al (2020), and Gropp et al (2021). For temperatures lower than those accessed by experiments (i.e.…”

“…We are aware of seven distinct theoretical estimates from four studies for 1000ln D  CH4(g)-H2O(g) vs. temperature (at isotopic equilibrium): Bottinga (1969), Richet et al (1977), Liu and Liu (2016), and Gropp et al (2021). In all studies, calculations were done at a minimum temperature of 0°C and maximum temperatures equal to or greater than 500°C.…”

Sulfate-dependent reversibility of intracellular reactions explains the opposing isotope effects in the anaerobic oxidation of methane

“…In the beginning of the experiment, composite reaction 2 is out of equilibrium, and the net isotopic fractionation expressed during this reaction is close to its KIE (with a best-fit carbon KIE value of 20‰). As sulfate is used over the course of the experiment, the reversibility of this reaction increases up to 0.33, resulting in combined expression of the KIE and EIE (the EIE is −47‰ at 50°C) (44). After 30 days, the shift from the kinetic end-member toward greater expression of the equilibrium fractionation endmember yields a net carbon isotope fractionation of zero, which translates to a net zero rate of change in methane  13 C values (Fig.…”

“…We prescribe the equilibrium isotope fractionation factors between the intermediate metabolites of the AOM pathway (44). We also prescribe the KFFs of the reactions in the AOM pathway, three of which for the Mcr-catalyzed reaction were experimentally determined (table S4) (62) and six of which are unknown and were drawn from uniform prior distributions, as described below.…”