Extracellular enzymatic assays were performed for three enzymes, β-glucosidase (BG), leucine aminopeptidase (LAP), and phosphatase (PHOS) on seven soil isolates, each from a different genera—Acinetobacter, Bacillus, Citrobacter, Comamonas, Enterobacter, Flaviobacterium, and Pseudomonas. The isolates were derived either from soil or worm castings and kept at -80°C with 20% glycerol until use. The isolates were revived from storage and grown in nutrient broth over a 2–3 days period at 25°C. We added 3-(N-morpholino)propanesulfonic acid buffer to maintain a pH of 7.2, which is the same pH as the microbes were originally isolated at. Before we began the enzyme assays, the isolate solution was plated on nutrient broth agar and total incubation time was determined by when cultures reached between 10⁵–10⁷ colony-forming units per mL.

The isolates were incubated in 96-well microplates with substrates at six temperatures: 4, 11, 25, 35, 45, and 60°C. We chose a large initial temperature range in order to capture the most accurate temperature response curve. The enzyme assay was modified from Bell et al. (2013). Forty microliters of 200 mM fluorometric substrate—4-MUB-β-D-glucopyranoside for BG, L-leucine-7-amido-4-methylcoumarin hydrochloride for LAP, and 4-MUB phosphate for PHOS—was added to 160 μL of a 1 isolate mixture: 15 acetate buffer solution. For each isolate × substrate combination, there were eight replicates for each temperature (7 isolates × 3 enzymes × 6 temperatures × 8 replicates). Standards ranging from 2.5 to 100 μM were used to calibrate the enzyme activity from each enzyme. 4-methylumbelliferone (MUB) was used to calibrate BG and PHOS and 7-amino-4-methylcoumarin (MUC) was used to calibrate LAP. The plates were incubated between 1 and 23 h depending on the temperature and scanned on a Tecan Infinite M200 plate reader at optimal florescence as determined by the MUB and MUC standards. Reaction rates were linear regardless of incubation time, as determined by preliminary experiments. The MUB and MUC standard curves were used to calculate the raw florescence of the samples using the slope and y-intercept, as described in Bell et al. (2013) and converted into units of nmol activity L culture^-1 hour^-1, so that samples were comparable across temperatures with varying incubation times.

In order to quantitatively characterize temperature responses of each of the 21 isolate × enzyme combinations, we plotted the natural log of the reaction rate against temperature and fitted both the Arrhenius and MMRT equations using an analytic Gauss-Newton for Arrhenius and a numerical Gauss-Newton for MMRT in JMP Pro 11 (Schipper et al., 2014; Alster et al., 2016). Parameters E_A and ΔCp‡, along with their uncertainty, were reported by the software. The optimum temperature (T_opt) and point of maximum temperature sensitivity (TS_max) from the MMRT curve fits were calculated by taking the derivative of the MMRT equation with respect to temperature (Alster et al., 2016). We used a Monte Carlo Simulation to estimate the standard error for T_opt and TS_max.

Analysis of variances (ANOVA) were performed using the software R version 3.2.1 (R Core Team, 2015) to determine the relative importance of substrate type and species type in explaining variation in the parameters from each of the models (ΔCp‡, ΔST0‡, ΔHT0‡, E_A, and A) as well as for T_opt and TS_max. We also used R to run pairwise comparisons with a Holm multiple testing adjustment to examine differences between each of the model parameters and T_opt and TS_max from each of the isolate × enzyme combinations. Differences in ΔCp‡ were calculated using a two-sampled approximate Z-test.

We used adjusted R² and Akaike information criterion corrected for a finite sample size (AICc) to determine the most parsimonious model between the Arrhenius and MMRT model fits for the full temperature range (4–60°C). Additionally, we re-ran the Arrhenius model fit for each isolate × enzyme combination, but only using temperatures 4–25 and 4–35°C to evaluate if, under more biologically relevant temperatures, the Arrhenius model fits were accurate predictors of reaction rate. To assess this, we calculated the percentage that each of the three models (MMRT from 4 to 60°C, Arrhenius from 4 to 35°C, and Arrhenius from 4 to 25°C) over or underestimated the reaction rate as compared to the actual experimental values and conducted corresponding lack-of-fit (LOF) tests. The importance of each of these models for predicting the percent error was examined with a linear model and tested with an ANOVA using the lmerTest package in R (Kuznetsova et al., 2014).

Out of the 21 isolate × enzyme combinations we tested, we present here the results from the 19 that worked. BG activity in Bacillus and PHOS activity in Comamonas were below detection limits. Thus, these two combinations were eliminated from the analysis. We plotted the reactions rates of the remaining 19 isolate × enzyme combinations vs. temperature and fit both the MMRT and Arrhenius equations to the data (Figure 1). These model fits for MMRT give temperature sensitivity parameters ΔCp‡, T_opt and TS_max, while Arrhenius gives E_A as a parameter.

We found that ΔCp‡ differed for some, but not all of the isolate × enzyme combinations. The ΔCp‡ differed among microbial isolates in BG and LAP enzymes (P < 0.05; Figures 2A,B). However, in PHOS, the isolates did not differ in ΔCp‡ (P > 0.05; Figure 2C). When comparing if ΔCp‡ differed between the same isolate for different enzymes we found significant differences in ΔCp‡ for Acinetobacter, Citrobacter, and Enterobacter (P < 0.05), but not for Bacillus, Comamonas, Flaviobacterium, or Pseudomonas. Patterns in statistical differences were identical for ΔCp‡, ΔS^‡, and ΔH^‡. Overall 70.9% of variation in ΔCp‡ was explained by the microbial isolate type, compared with 29.1% of the variation explained by the enzyme type.

The temperature optima (T_opt) and point of maximum temperature sensitivity (TS_max) also varied with the isolate × enzyme combinations (Table 1). Despite the 25°C conditions used during initial culturing of the inoculum isolates, T_opt ranged from 33.5°C in BG for the Enterobacter isolate to 60.7°C in LAP for the Bacillus isolate and TS_max ranged from 18.2°C in BG for the Acinetobacter isolate to 40.3°C in LAP for the Bacillus isolate. Pooling the T_opt and TS_max values across the same microbial isolate and enzyme type, we found differences for some of the values across both microbial isolate and enzyme type (P < 0.05). While differences between these pooled values for T_opt and TS_max were similar, they were not identical. Furthermore, similar to ΔCp‡, variation in T_opt and TS_max are best explained by the microbial isolate type, with SS values of 86.7 and 80.0%, respectively.

The three metrics of temperature sensitivity, ΔCp‡, T_opt and TS_max, each have unique statistical patterns of similarity across inocula × enzyme combinations. In this paper, we do not deeply examine the basis for groupings but focus instead on identifying if patterns of similarity and difference exist or if all enzymes behave similarly. For conciseness, we illustrate only patterns of differences for ΔCp‡ in Figure 2, and provide T_opt and TS_max findings in Table 1. For PHOS we found no differences in ΔCp‡ among the different microbial isolates (Figure 2). For TS_max of PHOS there were no differences, but for T_opt we found several significant differences among isolates (Table 1). Likewise for BG, there were quite a few differences among isolates in ΔCp‡ (Figure 2). However, there were no significant differences between different microbial isolates in TS_max for BG, and while there are differences in T_opt, they are not the same as the differences identified for ΔCp‡. Interestingly, patterns in significant differences among isolates for LAP are the same for T_opt and TS_max, but show a different pattern for ΔCp‡. Some of these patterns likely emerge because T_opt and TS_max are positively correlated (R² = 0.84), while ΔCp‡ does not correlated with T_opt or TS_max (R² = 0.23 and R² = 0.01, respectively).

For the temperature range of 4–60°C, we found that MMRT gave vastly superior fits to the data as compared to Arrhenius according to both AICc and R² criteria (Supplementary Table S1). MMRT was also superior when the Arrhenius model was fit to the more linear part of the temperature range (4–35 and 4–25°C) for 13 of the 19 isolate × enzyme combinations (see example, Figure 3A; Supplementary Table S1). For the six combinations where MMRT was not superior, AICc analysis found MMRT and Arrhenius to have equivalent explanatory power; in no case was Arrhenius the superior model. Phosphatase was the only enzyme where MMRT was significantly better in all isolates tested.

Despite the statistically improved fit of MMRT as compared to Arrhenius, when comparing the overall error produced from each of the model predictions, the results were less striking. We found 3.8% of the total variation was explained by LOF from the model in MMRT compared with 6.2% for Arrhenius from 4 to 35°C and 10.3% for Arrhenius from 4 to 25°C. This means that by using Arrhenius instead of MMRT we are introducing 1.6 and 2.7 times more error into our predictions for the Arrhenius 4–35 and 4–25°C models, respectively. ANOVA results for the percent error of the models compared to the experimentally observed results at 4, 11, 25, and 35°C, revealed a significant difference between MMRT and the Arrhenius 4–25°C model (P ≤ 0.05) and between the two Arrhenius models (P = 0.02). However, there was no significant difference in percent error between MMRT and the Arrhenius 4–35°C model fits when compared to original activity values at 4, 11, 25, and 35°C.

To examine the value of using activation energy as a trait, we compared activation energies derived from different temperature ranges to see if they vary. In a 3-way ANOVA examining the E_A values from all three of the Arrhenius model temperature ranges tested, we found that the temperature range explained 68.5% of variation in the data, compared to 12.7% explained by enzyme type and 11.0% explained by isolate type. Overall, we found that as the temperature range increased E_A values decreased (Figures 3B–D). Not only did the absolute values of E_A vary based on temperature range, but the relative E_A values also differ (Figures 3B–D) leading to different groupings of similarity among assays. In comparisons of E_A values for the different inocula × enzyme combinations that shared either the same enzyme or same isolate, 25% of the relationships changed between the Arrhenius 4–25 and 4–35°C estimates, and 36.8% of the relationships changed between the Arrhenius 4–35 and 4–60°C estimates. A similar analysis capturing different temperature ranges was not needed for MMRT since MMRT captures the peak.

This study advances efforts to understand how temperature sensitivity of extracellular enzymes varies by substrate and isolate type. Such an effect has long been speculated, based on assays conducted at the community level with whole soils (e.g., Trasar-Cepeda et al., 2007; Steinweg et al., 2013). We found that ΔCp‡ differed significantly among isolates for the BG and LAP enzymes, across the different isolates measured (Figure 2). Furthermore, heat capacity of different enzymes varied within the same isolate for three out of the seven isolates measured. While this study was not designed to elucidate the mechanisms behind why heat capacity varied between some enzymes and isolates but not others, here we provide a few possible explanations. One broad explanation for why we see these differences is that microbes adapt to their environment and more efficient enzymes are selected for in accordance to the thermodynamic conditions in that environment (Bradford, 2013); thus, microbes will adapt to produce isoenzymes with varying degrees of flexibility and consequently different heat capacities values depending on what is most advantageous for the microbial cell’s survival. The idea that isoenzymes have distinct temperature sensitivities is not particularly groundbreaking if comparing enzymes derived from thermophilic, psychrophilic, and mesophilic conditions (Zavodszky et al., 1998; Lonhienne et al., 2000; Feller and Gerday, 2003) or even across the same soil microbial community throughout seasons (Koch et al., 2007; Trasar-Cepeda et al., 2007; Wallenstein et al., 2009). However, in this study all of the isolates measured were derived from a mesophilic environment and raised in culture at the same temperature (25°C). Thus, we found that temperature sensitivity varies even among organisms raised under the same temperature conditions.

In contrast to BG and LAP, the heat capacity of PHOS was invariant with isolate type, suggesting that perhaps this enzyme did not undergo a similar type of adaptation over evolutionary history or that there are simply fewer isoenzymes. Although the PHOS enzyme is ubiquitous across different types of organisms, the genomic region encoding for the active site is highly conserved and fairly homologous across plants, animals, and bacteria, at least for the acidic version of the enzyme (Anand and Srivastava, 2012). As opposed to aminopeptidases in which relatively few homologies have been observed despite their high abundance (Taylor, 1993), gene conservation of PHOS might explain the lack of variation in heat capacity. Thermodynamic constraints of the enzyme or active site may also limit adaptation if there is a fundamental evolutionary tradeoff between the structure and function of the enzyme that is specific to the catalytic properties of PHOS (Bradford, 2013).

It is also worth noting that because these estimates of heat capacity were not necessarily of individual enzymes, but of the all of the isoenzymes produced by the isolates under the incubation conditions of this experiment. While it is unclear if multiple enzymes acting on the substrate impacted the results, it is worth highlighting that these results might be the average of one or more isoenzymes. It is also possible that given our sample size (seven isolates and three enzymes), more differences in heat capacity may have been observed if we had increased the diversity and number of the isolates and enzymes in the experiment. Furthermore, specific experimental conditions, such as pH, could potentially alter the temperature-response curve. Determining how heat capacity varies phylogenetically for different enzymes is an important avenue for future research.

Despite clear evidence of MMRT’s statistical superiority to Arrhenius in this experiment, we found that at the lower temperature ranges (i.e., 4–25 and 4–35°C) Arrhenius estimations were not necessarily poor. However, we still recommend that future estimations of temperature sensitivity for soil microbial enzymes that apply the Arrhenius equation use caution for the following reasons. First, we found that E_A values varied significantly with the range in which they were evaluated, making them an unreliable metric to use for comparisons across studies. These results are corroborated by Pawar et al. (2016), who tested 1,085 temperature-response curves from a variety of organisms and systems and determined that the calculated E_A value is an artifact of the temperature range, spread of temperatures measured, and where the temperature range falls. In order for temperature sensitivity to be used as a common currency of discussion and incorporated as a microbial trait, relationships should not be a function of different measurement methods. Second, even if Arrhenius is comparable to MMRT in a narrow temperature range, E_A fails to capture key phenomenological features of temperature sensitivity in soil biological systems. Other non-linear models have also been shown to give suitable empirical fits to the temperature dependence of enzyme activity (Peterson et al., 2004; Del Grosso et al., 2005; Daniel and Danson, 2013; Corkrey et al., 2014), but MMRT not only fits well empirically, but is derived from thermodynamic theory and thus has an underlying theoretical basis. Thus, even if E_A continues to be used in the future, E_A values should not be taken as true indicators of temperature sensitivity, at least for soil extracellular enzymes.

For nearly a decade, scientists have recognized the importance of using microbial traits as a framework for predicting ecosystem response to climate change (Green et al., 2008; Wallenstein and Hall, 2012). Many of these studies make predictions about how microbial traits (e.g., nutrient use efficiency) respond across a gradient of temperatures (Rinnan et al., 2009; Dell et al., 2011; Wallenstein and Hall, 2012). In this study we argue that temperature sensitivity is not only a measure of how biological traits respond across a gradient of temperatures, which is how it is typically characterized, but also that temperature sensitivity is an inherent biological trait. In light of this interest and our results, we developed a new conceptual model that develops a more precise definition of temperature sensitivity and organizes the factors that can lead to variation in temperature sensitivity itself.

In our framework, we first consolidated the Arrhenius and MMRT definitions of temperature sensitivity. Under the Arrhenius equations, activation energy is the singular factor driving the apparent temperature response (Figure 4). But, this violates laws of thermodynamics with regards to biological systems because of the large molecular size of enzymes characterized by large heat capacities impacting the temperature response (Arcus et al., 2016). MMRT expands thermodynamic theory initiated with Arrhenius by incorporating heat capacity as part of the temperature response (Figure 4). Implicit within the MMRT theory is that the ΔCp‡ is a function of enzyme flexibility and thus ΔCp‡ varies among enzymes (Schulte, 2015; Arcus et al., 2016). Given existing evidence for substrate type influencing activation energy (Davidson and Janssens, 2006), our outline of temperature sensitivity includes potential for enzyme flexibility to be a product of the substrate upon which the enzyme acts as well as the genetic variation among different enzymes (Figure 4). In this experiment, we tested if these additional factors (i.e., substrate type and genetic variation) impacted the temperature sensitivity by measuring heat capacity as a proxy for enzyme flexibility and found strong evidence for heat capacity varying by both enzyme and isolate type.

Based on this expanded framework of temperature sensitivity, we propose that use of ΔCp‡ and TS_max will give a more comprehensive basis to describe “temperature sensitivity” than Q₁₀ or E_A. Q₁₀ gives a false sense that a single constant can characterize the temperature sensitivity of a system (Davidson and Janssens, 2006). In order to overcome this obvious discrepancy authors using Q₁₀ often present multiple temperature sensitivity values at different temperature ranges for a given system, leading to results that are often difficult to compare. Conceptually, we consider temperature sensitivity to be the change in velocity per change in temperature (dV/dT). Unlike Q₁₀, E_A can be used as a summary term to capture temperature sensitivity of a system; this is effective because Arrhenius predicts a monotonic increase in rate with temperature. Since MMRT captures the inherently non-monotonic response of enzyme-catalyzed reactions, a single variable cannot fully capture the temperature sensitivity from the MMRT curve as is done by E_A in the Arrhenius equation. Thus the use of TS_max and T_opt provide two practical metrics to characterize this non-linear response of temperature sensitivity to temperature, although for modeling purposes ΔCp‡ and other thermodynamic parameters (i.e., ΔST0‡ and ΔHT0‡) are sufficient to explicitly predict reaction rates with temperature. Temperature optimum values are also commonly reported in the literature for extracellular enzymes (Huston et al., 2000; Daniel et al., 2001; Peterson et al., 2004; Eijsink et al., 2005), but are typically quite high and perhaps not biologically relevant. We argue that TS_max is actually a more important term to consider than T_opt because TS_max describes where the greatest change in rate occurs and it typically falls within environmentally relevant temperature ranges (Table 1). Consequently, by focusing on TS_max we capture the area of the temperature-reaction curve that will have the greatest impact on rates of nutrient cycling and greenhouse gas production. Characterizing temperature sensitivity with these unifying parameters gives us an avenue to incorporate temperature sensitivity into traits-based microbial models.

Our new framework suggests a number of future lines of inquiry. One immediate question is: how broadly does temperature sensitivity vary under this new definition of temperature sensitivity? If temperature sensitivity of different enzymes, microbes, or communities exhibit vastly different ΔCp‡ and TS_max values then this might impact current calculations of soil C and N dynamics. As the climate warms, does this inherent temperature sensitivity adapt or acclimate? What are the evolutionary constraints on rate of evolution and how is the overall temperature sensitivity value impacting by different groups of organisms? What other factors besides enzyme type and the microbe from which it was produced might impact enzyme flexibility? We hope that future research will be conducted in many of these avenues to elucidate mechanisms controlling temperature sensitivity of enzymes and determine what impact this has on communities, ecosystems, and nutrient cycling in soils.