S. putrefaciens strain CN32 (CN32) was maintained aerobically and anaerobically in a defined growth medium based on Myers and Nealson (1988) and Belli et al. (2015) at 30°C (additional details in Supplementary material). Aerobic cultures were grown with approximately 10 mM sodium lactate in 15 ml borosilicate glass tubes with aerobic cap closures on an orbital shaker. Anaerobic cultures were grown with approximately 15 mM sodium lactate and 30 mM ferric citrate, in borosilicate glass tubes sealed with butyl rubber septum-type stoppers and aluminum seal rings. The anaerobic chamber was maintained with an N₂:H₂ atmosphere (98:2). Cultures were maintained with an initial cell density of 8 × 10⁵ (±2 × 10⁵) cells per mL, and were grown to late exponential phase. Cell count slides were prepared using polycarbonate 0.2 μm filter membranes with SYBR Green I dye following the procedure of Lunau et al. (2005) and with appropriate filters on a Zeiss Axiostar Plus microscope.

Calorimetric measurements were made on a TAM III nanocalorimeter measuring heat flux between a reaction and the reference vessel as a function of time (Johansson and Wadsö, 1999; Goldberg and Wadsö, 2001). The calorimetric response was calibrated by electrical heating and verified by measuring the protonation of TRIS at 25°C (Grenthe et al., 1970). Three milliliters of experimental cultures were grown in 4.22 mL glass vials, sealed with butyl rubber septa and aluminum sealing rings without agitation. Experiments were performed from 25 to 36°C with 2 replicates at each temperature.

To maintain media compositions similar to the maintenance cultures, aerobic and anaerobic cultures were prepared with the same base medium with an initial cell density of 5 × 10⁵ (±1 × 10⁵) cells per mL. Initial sodium lactate concentrations were kept the same as in the maintenance cultures, and the electron acceptor was limited for aerobic and anaerobic growth. Aerobic cultures were sealed under atmospheric conditions, yielding an initial headspace of approximately 10 μmol O₂. For the anaerobic cultures, the initial concentration of ferric citrate was approximately 7 mM, and the vials were sealed in the anaerobic chamber.

The total heat evolved during growth was measured by monitoring the heat flux in the calorimeter throughout the growth period and integrating under the resulting curve (see Supplementary material). Calculation of microbial growth rate was based on total heat evolution using an exponential model. The duration of lag phase was determined using miLag (Opalek et al., 2022).

The systems investigated in this work relate to the growth of CN32 under controlled conditions in reaction vials. From this point on, we refer to changes in the reaction vials as a result of microbial growth as “incubation” to recognize that abiotic or biotically influenced abiotic reactions will also occur. Simplified macrochemical equations were used to represent the growth of one carbon-mole (C-mol) of generic biomass, according to the formula CH_1.8O_0.5N_0.2 (Heijnen and Kleerebezem, 2010; Calabrese et al., 2021; Hunt et al., 2022). Microbial biomass formulas are known to have very similar elemental compositions (Popovic, 2019), and a 10% error in the biomass formula weight was propagated through calculations to take into account variations. The anabolic and catabolic components of the growth reaction are represented according to Equations (2) and (3). The coefficients for the anabolic and catabolic reactions were determined by solving a series of linear equations to satisfy balances of mass and charge.

To produce sufficient energy to drive anabolism, the catabolic reaction must be performed multiple times. This relationship defines the catabolic multiplicative factor necessary to produce one C-mol of biomass, f_cat, as described in Equation (4)

where Y_X/D is the C-mol of biomass produced per mol of the e⁻ donor consumed and YDan is the anabolic coefficient of the e⁻ donor.

From Equations (2)–(4), we can calculate the coefficients for the overall growth reaction (OGR) with Equation (5):

The Gibbs energy change during incubation was calculated for each experiment before and after growth on the basis of the activities of all the chemical species in the overall growth reaction. Measurements of pH and O₂ were made with an Orion 8103BN Ross semi-micro combination pH electrode and a Clark-type OX-NP-006340 oxygen microelectrode from Unisense, respectively. Fe(III) was measured with the ferrozine method (Viollier et al., 2000) under anaerobic conditions. Lactate was measured with a spectrophotometric assay according to Borshchevskaya et al. (2016). Biomass produced during incubation was determined by difference between final cell counts and initial cell counts. Standard states for this work at all temperatures and pressures are the unit activity of the pure solvent, the unit activity of aqueous species in a hypothetical 1 molal solution referenced to infinite dilution, the unit activity of pure minerals or other crystalline solids, and the unit fugacity of a pure gas at 1 bar. The standard state Gibbs energies of formation (ΔGf°) for the chemical species in the growth reaction were calculated at experiment temperature with the revised Helgeson-Kirkham-Flowers equations of state (HKF) (Helgeson et al., 1978, 1981; Tanger and Helgeson, 1988) using SUPCRT92 (Shock et al., 1989; Johnson et al., 1992). For biomass, ΔGf°=-67 kJ/mol was used for all growth experiments (Heijnen and van Dijken, 1992). The standard-state Gibbs energies of reactions (ΔGr°) of the overall growth reaction determined for each experiment were calculated using Equation (6), where ΔGf,products° and Gf,reactants° are the standard-state Gibbs energies of formation for the products and reactants of the growth reaction, respectively, and Yiogr is the stoichiometric coefficient of the ith chemical species in the overall growth reaction.

The change in Gibbs energy of a given chemical reaction (ΔG_r) represents the Gibbs energy potentially available for microbial growth. This is defined by Equation (8), where ΔGr° is modified with the concentration-dependent reaction quotient (Q), the universal gas constant (R), and absolute temperature (T).

Q was calculated according to Equation (9), where a_i is the thermodynamic activity of the i^th chemical species in the overall growth reaction (r) and v_{i, r} is the stoichiometric coefficient for that species.

Activities of the aqueous species were calculated using PHREEQC (Parkhurst and Appelo, 2013). Activity of biomass in solution was converted from molality (C-mol/kg solvent) assuming an activity coefficient of 1 (Tebes-Stevens et al., 1998; Xu et al., 1998; Parkhurst and Appelo, 1999; Hunt et al., 2022). The overall change in Gibbs energy during incubation, ΔG_inc, for each experiment was calculated with Equation (10) as the difference between the initial ΔG_r available (ΔG_{r, initial}), calculated from the initial chemical composition of the medium solution and biomass, and the final ΔG_r available (ΔG_{r, final}), calculated from the final chemical composition of the medium solution and biomass (see Supplementary material for chemical compositions of the media).

Hunt et al. (2022) provides a detailed description of the energy partitioning model used in this work. Here, we present a brief description of this approach. An Arrhenius relationship is applied to the specific energy consumption rate (q_J, kJ C-mol⁻¹ h⁻¹) of a cell that is corrected for temperature (T) relative to the reference temperature at 298 K (qJ ′). This relationship is shown in Equation (11), where E_J is the specific activation energy for energy consumption and R is the gas constant. The underlying assumption for this Arrhenius dependence is that a cell obtaining energy is the growth rate limiting step.

The specific lactate consumption (q_L) and specific heat evolution rate (q_H) are used as proxies to infer the specific energy consumption rate. These relationships are shown in Equations (11) and (12), where YJL is the energy consumed per mole of lactate and YHJ is the heat evolved per unit of energy consumed.

The heat evolved normalized to C-mol of biomass formed (ΔH_inc) is linearly related to the biomass yield (Y_X/D), YJL, and YHJ as shown in Equation (13).

The model of Pirt (1982) as amended by Tijhuis et al. (1993) is used to determine the division of the energy consumed into the growth-associated biomass yield [defined as growth-associated costs (GAC)] and costs to maintain viability [defined as maintenance without growth (NGAM)], as shown in Equation (14). Specific energy consumption is the product of the growth rate (μ hour⁻¹) and the GAC. NGAM is the temperature-dependent maintenance. Specific lactate consumption rates, specific heat evolution rates, heat evolved per biomass, biomass yield on lactate, and specific growth rate for each experimental replicate were simultaneously fitted to Equations (11)–(14) for parameter estimation. A Jackknife cross-validation approach was used to assess the error of the parameters. This approach estimated parameters from a subset of the data by removing one data point and repeating this process until each data point had been removed. The observations were randomly ordered, and this process was repeated 1,000 times.

Microbial growth calorimetry aggregates all biotic and abiotic processes that contribute to Gibbs energy dissipation (Gustafsson, 1991). Systematic bias may be introduced in heat flow measurements for reactions and processes that are not associated with cell growth. Some reactions such as protonation and complexation reactions can be corrected based on the change in the chemical speciation of the media (von Stockar et al., 1993a). We calculated this speciation change in the medium with PHREEQC (Parkhurst and Appelo, 2013) and estimated that the influence of these reactions was less than 8% of the heat evolved in Fe(III)-based incubation and less than 1% of the heat evolved in O₂-based incubation. Other processes that have the potential to influence the heat flow signal cannot be corrected for, such as cells settling out of solution, cells adhering to the reaction vessel. These processes may introduce additional errors in the calorimetric measurements.

In the aerobic system, calorimetric data were successfully obtained at 27, 30, and 35°C. At 25 and 36°C, no clear calorimetric signal was consistently observed within 60 h of incubation. For each condition where calorimetric data was obtained, the total heat evolved was normalized to C-mol biomass produced (Figure 1). For aerobic growth, ΔH_inc was significantly more exothermic (p = 0.03) at 27°C than at 35°, but not 30°C. Anaerobic growth was also significantly affected by temperature. At 25, 27, and 30°C, ΔH_inc values for anaerobic growth were not different with 95% confidence. ΔH_inc significantly increased (p < 0.001) at 33 and 35°C compared to 30°C.

The total amount of Gibbs energy consumed during incubation was also normalized to C-mol biomass produced. ΔG_inc, illustrated in Figure 1, shows trends similar to ΔH_inc. ΔG_inc for the aerobic data was indistinguishable (p > 0.1) at different temperatures. In the anaerobic system, ΔG_inc exhibited an identical statistical trend to ΔH_inc. At 25, 27, and 30°C ΔG_inc values were not different (p > 0.9). ΔG_inc significantly increased (p < 0.005) at 33 and 35°C compared to lower temperatures.

Figure 2 illustrates the f_cat values, which describe the catabolic cycles needed to generate the observed biomass. The anaerobic system had higher f_cat values than the aerobic systems at all temperatures. The aerobic f_cat values ranged from approximately 0.8 to 2 with no significant differences between temperatures (p >0.1). Anaerobic f_cat values at 30°C and below were approximately 3 and indistinguishable with temperature (p >0.5). Above 30°C, f_cat values increased to approximately 8 and 15 at 33°C and 35°C, respectively. This increase was significant enough to distinguish these f_cat values (p < 0.05) from lower temperatures.

We determined the catabolic reactions for each growth strategy based on Equation (3) and the constraints provided by the changes in the growth medium. As shown in Equations (15) and (16), the stoichiometric ratios of the electron donor and acceptor differed between growth with O₂ and Fe(III). For aerobic growth, one mole of O₂ is reduced per mole of oxidized lactate. In Fe(III) growth, 1.33 moles of Fe(III) are reduced per mole of lactate. For both growth systems, lactate was partially oxidized and acetate/acetic acid was produced along with CO₂. The anabolic reaction, solved according to Equation (2), is the same for aerobic and anaerobic growth, as the electron acceptor is not involved in the reaction, as shown in Equation (17). The reaction involved the conversion of lactate, ammonium, and protons into biomass. The overall growth reactions, as determined with Equations (4) and (5), for aerobic and anaerobic growth are shown in Equations (18) and (19), respectively. Those reactions predict that 0.74 moles of O₂ will be reduced per mole of lactate in the aerobic system and 0.99 moles of Fe(III) per mole of lactate in the anaerobic system. The observed ratio of O₂:lactate in the experiments was 1.20 ± 0.23. The Fe(III): lactate ratio in the experiments was 1.46 ± 0.15. These results are more consistent with the stoichiometry for the catabolic reaction than overall growth reaction.

For both growth strategies, an upper limit of the growth temperature was established. Consistent O₂ growth was not observed above 36°C, and 35°C was the maximum temperature for growth on Fe(III). It is noteworthy that the growth strategies yielded different temperature limits, and this likely reflects differences in the physiological underpinnings of those metabolism. Specifically, the temperature limits for these growth strategies may differ because different enzymes are required for growth on O₂ and Fe(III) (Myers and Myers, 1993; Blakeney et al., 2000). However, due in large part to the complex nature of electron transfer through the cell envelope and the multiple cytochromes that are thought to be involved in CN32 growth (Blakeney et al., 2000), few details regarding the exact enzymes involved in O₂ and Fe(III) growth have been quantified. Since the growth temperature limits often depend on the limits of the enzymatic activity (Daniel, 1996), we can infer a similar effect for CN32.

Another factor that may influence the growth temperature limits is the growth medium. Furthermore, since the growth medium was different for aerobic and Fe-based growth (in lactate concentration and Fe(III) vs. O₂ presence) those differences must be considered when comparing the data. For both media, the ionic strength was approximately 0.04 M. There is some evidence that increasing ionic strength can yield a higher temperature limit for bacterial growth (Nichols et al., 2000). This suggests that if salt concentrations in the medium were increased, the temperature limit could also increase. Fe(III)-based experiments had slightly higher ionic strength (0.045 vs. 0.041 M for the O₂ experiments) due to the higher concentration of lactate and the ionic nature of the electron acceptor. That difference is much smaller than those that have been observed to incur temperature limit impacts. Therefore, the ionic strength difference between the two grow media was likely not large enough to influence the temperature limits for growth.

The clear relationship between temperature and f_cat for Fe(III)-based growth indicates that the allocation of the energy produced in catabolism also changes with temperature. This is in contrast to aerobic growth, where there was no clear relationship as a function of temperature. Because f_cat reflects the proportion of Gibbs energy used in anabolism, this allocation of energy reflects its relative use in the production of new biomass (anabolism) vs. other non-growth processes. At higher temperatures, the expenditure of energy to maintain sufficient cellular functioning, rather than to reproduce, may explain the statistically significant increase in f_cat above 30°. As has been previously shown, protein instability and aggregation, along with membrane fluidity, increase with temperature, thus affecting cellular homeostasis (de Mendoza and Cronan, 1983; Schramm et al., 2019). These changes require the cell to overcome that physiological stress to maintain its internal functions, which is likely to result in increased energy use.

The energy partitioning model corroborates the observed increase in f_cat for Fe(III)-based growth. Figure 3A illustrates the fit of the measured specific heat evolution rate to Equation (12). The model predicts an increase in the specific heat evolution rate with temperature, which is consistent with the data. As the temperature increases, the growth rate reaches a maximum at 27°C and then decreases (Figure 3B). The modeling estimates of heat dissipation per Gibbs energy consumed and Gibbs energy consumed per mol lactate from the model fit agreed with the thermodynamics-based calculations (Supplementary Figures 5, 6). Figure 3C illustrates the predicted partition of the specific energy consumption rate into GAC (G×μ) and NGAM (m_V). Below 30°C, more than 50% of the specific energy consumption rate is predicted to be divided into GAC. This is consistent with the observed biomass yield, which is shown as a function of temperature in Figure 4. The biomass yield above 30°C showed a distinct decrease compared to lower temperatures. Data suggest that between 30 and 33°C is a tipping point where temperature stress diverts a substantial amount of energy away from GAC to NGAM. The energy partitioning model predicts this “tipping point” temperature to be ≈31°C where GAC is equal to NGAM.

It is important to note that the modeling in this work based biomass yield on cell counts. Energetic resources diverted to the production of organic carbon exudates were not measurable given the small sample volumes (3 ml), multiple analyses performed (cell counts, substrate consumption, and metabolite production), the dilution needed for the measurement, and the presence of organic carbon from the electron donor and waste products. Consequently, if exudate or biofilm production is not measured and taken into account when calculating the total C-mol biomass produced, the biomass yield and f_cat values will be impacted. Macroscopic instances of biofilm were not observed, however, biofilm is typically observed by scanning electron microscopy (Alhede et al., 2012). Smaller biofilms may have been missed with the fluorescence microscopy used in this study. Two of the variables that influence exudate/biofilm production were included in these experiments: O₂ and elevated temperatures.

For Shewanella strains in particular, the presence of O₂ has been shown to dramatically increase exudate/biofilm production (Wu et al., 2013). In contrast, Yan et al. (2020) and Pinel et al. (2021) have shown that elevated temperature reduces exudate/biofilm formation in other taxa. In Fe(III) growth experiments, we expect a lesser, if any, amount of exudate/biofilm production. In aerobic experiments, these impacts could be substantial. The aerobic data showed only a slight influence of the temperature. Biomass yield at 30°C was significantly (p < 0.05) higher than at 25°C, and ΔH_inc at 27°C was more exothermic than higher temperatures (see above). The lack of a clear influence of temperature and lack of calorimetric data at temperature extremes precludes energy partitioning modeling and any maintenance energy insights for aerobic growth. The lack of consistent temperature influence may be due to undetectable exudate/biomass that would alter biomass yield. This impact would be expected to occur more frequently at lower temperatures, where oxygen solubility is also higher. Consequently, aerobic incubation may be affected by temperature more strongly than was detected in this work.

Considering growth efficiency across conditions can be helpful in understanding the physiological limits of microbial life and the potential for geochemical impacts of metabolism. Microbial growth efficiency is often interpreted from parameters such as biomass yield (del Giorgio and Cole, 1998). However, from a thermodynamic perspective, efficiency is an output/input ratio in energy units (Gnaiger, 1990). This can be applied to microbial growth when energy consumption is modeled in terms of catabolic and anabolic reactions (e.g., Calabrese et al., 2021). The ratio of ΔG_inc used by the anabolic reaction (ΔGincAn) relative to the Gibbs energy released by the catabolic reaction (ΔGincCat) scaled with f_cat is used here to consider the thermodynamic efficiency of microbial growth (η, Equation 20) under experimental conditions.

Figure 5 illustrates the thermodynamic efficiency of growth experiments in this study relative to the compilation of Smeaton and Van Cappellen (2018). Calabrese et al. (2021) identified a power-law scaling relationship between the thermodynamic efficiency of microbial growth and the electron donor uptake rate (μ_ED). A major geochemical implication of this relationship is that estimations of thermodynamic efficiency can be made from commonly measured parameters in microbial growth investigations (specific growth rate and biomass yield). This provides the means to improve biogeochemical modeling.

The data collected in this study that do not exhibit significant temperature stress generally agree with the power-law scaling relationship of Calabrese et al. (2021). Aerobic data generally cluster with the majority of data. The anaerobic data at 30°C and below cluster tightly along the scaling relationship. Fitting a new power-law scaling relationship to the data of Smeaton and Van Cappellen (2018) including the aerobic data and anaerobic data at 30°C and below from this work produces slope and intercept values of −0.506 ± 0.202 and −1.469 ± 0.118, respectively. These parameters are statistically indistinguishable from the slope [−0.476 with 2σ confidence interval (−0.719, −0.271)], and intercept [−1.443 with 2σ confidence interval (−1.579, −1.306)] values from Calabrese et al. (2021). Experiments with thermodynamic efficiencies less than 10⁻² are poorly predicted by the power-law scaling relationship. This result is not surprising in the context of the various lines of evidence showing the impact of temperature stress on iron incubations at 33 and 35°C: ΔH_inc and ΔG_inc increase, catabolic cycles increase, NGAM increases, and biomass yield decreases. The thermodynamic efficiency of microbial growth may generally deviate from this power-law scaling relationship when under extreme stress, such as nearing the maximum growth temperature. This is an area for future work to better understand potential geochemical impacts when catabolic cycles are high and biomass production is limited.

Making biogeochemical predictions based on thermodynamic modeling of microbial growth is predicated on the ability to describe growth with chemical reactions that reasonably reflect chemical consumption and/or metabolite production. For example, Equation (21) illustrates the established stoichiometry for Fe(III) growth by S. putrefaciens as described in Lovley (1993). This stoichiometry has been applied without verification (Tran et al., 2020).

The measurements made in this work, however, are consistent with a very different reaction stoichiometry (see Equation 16). Geochemical predictions of Fe(II) production based on Equation (21) would over-predict production approximately 3 times according to the present work. These differences are substantial and could alter geochemical predictions of mineral phase stability, redox conditions, ionic strength, and similar variables. Consequently, verification of reasonable chemical equations of microbial growth is critical to accurate geochemical modeling.

Another approach to predicting microbial biomass yield or chemical changes in the absence of microbial growth data is based solely on standard state parameters that describe an overall growth equation. Standard state values for both O₂ and Fe(III)-based growth, for 1 C-mol of biomass, are illustrated in Figure 6 together with measured values of ΔG_inc and ΔH_inc. The thickness of curves spans the variation in standard state predictions from 25 to 36°C. For O₂ growth, ΔGr° is slightly more negative than ΔHr°. This predicts that the entropic component of growth (ΔSr°) is minimal, which agrees with the data (ΔG_inc≈ΔH_inc). At the highest biomass yield (≈0.84 C-mol/mol lactate at 30°C), the aerobic data are the closest to predictions, which are ≈6 times more exergonic/exothermic. Standard state predictions of growth on Fe(III) show the same general trend as O₂ (ΔGr° more negative than ΔHr°), but the magnitude of that difference is much greater. Consequently, the entropic component of growth is predicted to be more significant. This can be conceptualized by considering the metabolite stream during growth. Production of small metabolites would increase entropy during growth, thus helping drive ΔGr° negative (von Stockar and Liu, 1999). The data do not show a significant entropic component during incubation; that is, ΔH_inc is very similar to ΔG_inc. Similarly to the aerobic system, Fe(III) growth is closest to standard state predictions at the highest biomass yields (≈0.33 C-mol/mol lactate at ≥30°C). This suggests that when f_cat is minimized or η is maximized, we observe experimental data that come closest to standard state predictions. Consequently, predictions based on standard state parameters may be most useful under ideal conditions for growth when maximum coupling between the catabolic and anabolic cycles are achieved.