Redox-informed models of global biogeochemical cycles

Microbial activity mediates the fluxes of greenhouse gases. However, in the global models of the marine and terrestrial biospheres used for climate change projections, typically only photosynthetic microbial activity is resolved mechanistically. To move forward, we argue that global biogeochemical models need a theoretically grounded framework with which to constrain parameterizations of diverse microbial metabolisms. Here, we explain how the key redox chemistry underlying metabolisms provides a path towards this goal. Using this first-principles approach, the presence or absence of metabolic functional types emerges dynamically from ecological interactions, expanding model applicability to unobserved environments. “Nothing is less real than realism. It is only by selection, by elimination, by emphasis, that we get at the real meaning of things.” –Georgia O’Keefe

(S1) where -. /01 is the maximum growth rate and L is the population loss rate. Supplementary  Fig. 1 illustrates the trade-off with two functional types -an "opportunist" and a "gleaner" -competing for substrate in a virtual chemostat. Though the yield y is the same, the opportunist has a higher maximum growth rate and a lower substrate affinity than the gleaner, which has a lower R*. When substrate is supplied intermittently, one or the other may be excluded over time, or both may be sustained if the variable conditions prevent competitive exclusion entirely (as in Supplementary Fig. 1). In reality, we can understand that these tradeoffs may represent characteristics among populations carrying out a similar metabolism, and that conditions may select temporarily the most optimized from the species pool so that dynamic change can be expected on short time scales.
The redox-informed biomass yield is useful even if models of substrate uptake are empirical. For a heterotroph, for example, the yield determines the amount of substrate that is transformed and excreted as a respiration product such as CO 2 . In our example of the nitrification ecosystem, the redox-informed differences in the yield between ammonia and nitrite oxidizers have provided useful explanations for the observed differences between ammonia and nitrite concentrations and the biomasses of the two clades, despite uncertainty in uptake kinetics.
We can demonstrate the utility of the yield alone using a simple system for substrate concentration S and consuming biomass B: where S in is the substrate supply rate, V(S) is the specific uptake rate function that depends on the substrate concentration, y is the yield, and L is the loss rate. At steady state, we can solve for the steady concentration of biomass B* as: The steady state biomass is proportional to the inverse of the yield, and the uptake rate falls out of the equation. Therefore, the model can be useful in relating quantities of biomass to substrate supply, independent of uptake kinetics. Differences in yield alone also result in differences in the subsistence concentrations (Eqn. S1).
Recent data suggests that nitrite-oxidizing bacteria are more efficient with their allotted energy supply than ammonia-oxidizing archaea 8 . However, the data still agree with the redox-informed biomass yields in terms of assimilation per amount of N oxidized, and thus that differences in yields and cell size can explain much of the difference in abundance.
To explain, Kitzinger et al. 2020 calculate per cell oxidation rates for ammonia-oxidizing archaea (AOA) and nitrite-oxidizing Nitrospinae bacteria (NOB) in the Gulf of Mexico 8 . They find that the per cell nitrite-oxidation rates were ~15-fold higher than the per cell ammonia-oxidation rates. Per cell N assimilation rates were 0.91 for NOB and 0.12 for AOA, thus 7.5-fold higher for the larger NOB. Comparing the per cell nitrification rates to the per cell N assimilation rates provides the best test of the redox-based theoretical model, which predicts a three-fold difference in biomass yield in terms of biomass assimilation per mol N oxidized 9 . Together, these observations suggest that the biomass yield of AOA is approximately two-fold higher than the biomass yield of NOB (mol N assimilated per mol N oxidized), and so observations are 33% lower than the theoretical three-fold prediction.
Kitzinger et al. evaluate an efficiency in different terms: moles of carbon fixed per Joule (and converting from N assimilation with a constant elemental ratio). Our theoretical model predicts that the efficiency in these terms (moles of carbon fixed per Joule) is relatively similar for the two nitrifying populations. Specifically, the model relates the bulk ammonia oxidation rate (R AO ; nmol NH 4 + L -1 d -1 ) and bulk nitrite oxidation rate (R NO ; nmol NO 2 -L -1 d -1 ) to cellular rates as: for yield y (mol biomass per mol N oxidized), growth rate µ (d -1 ), and biomass B (mol C or N L -1 ). This shows that deviations from the steady state where R AO = R NO can result from changes in the relative growth rates or biomasses between the two populations if yields remain relatively stable over time.
Kitzinger et al. calculate the efficiency in terms of moles of carbon fixed per Joule by multiplying the above per cell nitrification rates by the Gibbs free energies of reactions as: for assimilation A (mol C assimilated L -1 d -1 ) and free energy release DG (kJ per mol N oxidized). In the model framework, A = µB, and therefore: D @A@ = ΔF @A -@A@ ,?
(S11) Thus, if the difference in yield is relatively equal to the difference in free energies, as is predicted theoretically, this difference cancels out in Eqns. S10 and S11, and the efficiencies in terms of assimilation per Joule are predicted to be relatively equal for the two populations. However, in their calculation, Kitzinger et al. calculate efficiencies using Eqns. S8 and S9 using measurements from a dynamic environment where R AO is four-fold higher than R NO (a large departure from a steady state), and they calculate a four-fold higher efficiency. Their calculation also assumes that the 7.5-fold higher assimilation rate of NOB applies in situ.
The metabolic functional type approach can mechanistically represent microbial activity in dynamic steady-state or time-varying environments. This predictive power is of particular benefit for resolution of microbial processes in fine-grained ocean circulation models where flow can vary on the order of days, similar to the timescales of microbial growth. However, solutions become dependent on the partitioning of metabolism among the functional types as the timescales of physical change approach the timescales of microbial growth.
For example, Supplementary Fig. 3 illustrates a model simulating a zonal transect through the S. Pacific Ocean, which contains an anoxic oxygen minimum zone. The ecosystem model resolves emergent metabolic activity along a gradient in oxygen with (for simplicity of illustration) just two resolved microbial metabolisms: aerobic and anaerobic (denitrifying: NO 3 à N 2 ) heterotrophy. The equilibrium state solutions of two versions of this model -one with two obligate (aerobic and anaerobic) populations and the other with one facultatively anaerobic population -are nearly identical at steady state, but different in the transient. Supplementary Fig. 4 illustrates the differences in the time evolution of the oxygen concentration and the denitrification rate following a perturbation in which oxygen concentrations are increased. In the model with the two obligate types, anaerobic denitrification does not cease throughout the recovery period because a population of anaerobes remains after O 2 is supplied and competitive exclusion has not come to completion. In contrast, the facultative population switches to respiring O 2 when it is supplied, and so denitrification rates cease immediately. Real community dynamics likely reflect both solutions: current understanding is that heterotrophic microorganisms are generally facultatively anaerobic, while chemoautotrophic anaerobic ammonium oxidizing (anammox) bacteria, which accounts for roughly a third of the fixed N loss in pelagic zones, are understood to be obligate anaerobes [10][11][12][13] .
Thus, knowledge of how metabolisms are distributed among populations is required for interpreting transient states. Other species-specific time-varying phenomena such as the lag response of organisms to substrate availability also becomes relevant 14 . These are limitations on one hand, and so require further constraint. On the other hand, these differences may serve as a tool for parsing out how metabolisms are distributed by comparing models with observed time series. The different solution states in Supplementary Fig. 4, for example, can serve as testable hypotheses against which the response of natural assemblages can be compared. Figure 1: A model simulation of the competition between two functional types characterized by a tradeoff among traits, with A. resulting biomasses and B. substrate concentration. The "opportunist" has a higher maximum growth rate and a lower substrate affinity than the "gleaner," which has a lower subsistence concentration (R*). The two populations grow in a virtual chemostat with dilution rate 0.1 d -1 , with a continual incoming substrate concentration of 1 μM C and an additional 10 μM C pulse of substrate added every 30 days. Here, the "opportunist" is parameterized with a maximum uptake rate of V max = 2 mol substrate C per mol biomass C per day and a half-saturation concentration k S = 1 μM C. For the "gleaner," has V max = 1 mol substrate C (mol biomass C) -1 d -1 and k S = 0.1 μM C. For both, substrate yield y = 0.3 mol biomass C (mol substrate C) -1 .