Soil samples were collected at the University of California Blodgett Experimental Forest, Sierra Nevada, CA, United States (120°39′40″ W; 38°54′43″ N), described by Hicks Pries et al. (2018). Briefly, Blodgett forest is located in a Mediterranean climate with mean annual precipitation of 1,660 mm and a mean annual air temperature of 12.5°C. The soil was classified as Alfisol of granitic origin, and has a developed O horizon. The site is a mixed coniferous forest with ponderosa pine (Pinus ponderosa), sugar pine (Pinus lambertiana), incense cedar (Calodefrus decurrens), white fir (Abies concolor) and douglas fir (Pseudotsuga menziesii) as dominant tree species. The mean annual soil temperature ranges between 11.5 and 10.4°C at 5 and 100 cm depths, respectively, although soil temperatures vary annually between 0–29°C, 1–19°C and 2–16°C at 5, 30, and 100 cm depth, respectively. Three soil cores were collected in July 2019 using a 4.78 cm diameter soil corer with a 10 kg hand-held slide-hammer. The surface litter layer of the O horizon was removed prior to sampling, and mineral soil samples were recovered sequentially in 10 cm increments down to 90 cm depth. Samples were kept cold during transportation to the laboratory, where they were sieved to 2 mm and stored at 4°C. Samples were analyzed within approximately a week of collection. To ensure the accessibility and discoverability of the samples generated here, and to align with the National Science Foundation’s guidelines of effective data practices, all samples have been registered with IGSN Global Sample Numbers through the System for Earth Sample Registration (SESAR). SESAR is maintained by the GeoInformatics Research Group of the Lamont-Doherty Earth Observatory at https://www.geosamples.org/. Sample IGSNs are shown in Supplementary Table 1.

Extracellular hydrolytic enzyme activities were determined fluorometrically according to standard assays (German et al., 2011b) at six depth intervals, following the experimental design in Table 1. Briefly, we used the methylumbelliferone (MUF)-linked substrates MUF-β-D-glucopyranoside and MUF-phosphate for determination of β-glucosidase (BG) and acid phosphatase (AP) activities, respectively. Leucine aminopeptidase (LAP) activity was determined using the substrate L-leucine-7-amido-4methylcoumarin (AMC). Assays were performed for each of six soil depths from each of three replicate soil cores, by combining 200 μL of soil homogenate with 50 μL of fluorogenic substrate solution in each microplate well. Soil homogenates were prepared with 1 g of fresh soil in 100 mL 50 mM acetate buffer with pH 5.5, by mixing with a regular blender. The same buffer was used to prepare all substrate solutions, soil homogenates, serial dilutions of standards in the absence or presence of soil homogenate (quenching controls), blank quenching controls without standards, and blank controls in the absence or presence of each of the eight substrate concentrations. Standards in the presence or absence of soil homogenates (quenched standards) were prepared over six 1:10 serial dilutions, from 0.625 to 20 μM for MUF, and 0.3125 to 10 μM for AMC. MUF and AMC standards without soil homogenates, blank controls with only substrates, and blank quenching controls with soil homogenates, but no MUF or AMC standards, were performed in duplicate. Each enzyme was assayed individually over a range of eight substrate concentrations, as follows: 10, 30, 60, 100, 150, 250, 450, and 800 μM for BG; 10, 20, 40, 70, 110, 190, 350, and 600 μM for LAP; and 10, 40, 80, 130, 200, 350, 700, and 1200 μM for AP (Table 1). Parallel assays for each sample, enzyme and substrate concentration were performed in black microplates individually covered with lids to avoid evaporation, and incubated in the dark at 4, 10, 16, 25, 35, or 50°C. Fluorescence was recorded (excitation: 365 nm, and emission: 450 nm) after approximately 1, 4, and 24 h to determine the optimal incubation time. Four analytical replicates were measured per sample for each combination of enzyme, substrate concentration and temperature. A set of standards, and blank, substrate and quenching controls was incubated together with each batch of assays at each temperature, to correct fluorescence measurements for temperature-specific effects in the assays. Incubation temperatures were selected in order to capture the unimodal response predicted by MMRT with T_opt-values well above native temperatures, as observed by previous studies of exoenzymes from temperate environments (Alster et al., 2016b), while including the temperature range and approximate seasonal averages at our experimental site.

Microbial biomass C (MBC), dissolved organic C (DOC) and total dissolved N (TDN) were determined at every 10 cm depth interval between 0–90 cm depth. MBC was estimated using the chloroform-fumigation extraction method (Brookes et al., 1985). Five-gram soil samples were fumigated in 50 mL closed vials containing a jumbo cotton ball soaked with ethanol-free chloroform over, but not touching, the soil, for 7 days, with chloroform replenished on day 4. Fumigated and a non-fumigated soil samples were extracted with 25 mL of 0.5 M K₂SO₄ on an orbital shaker table for 60 min, then gravity filtered through pre-leached #42 Whatman filter paper, and frozen until further analysis. DOC and TDN in fumigated and non-fumigated samples were quantified using a Lotix Combustion TOC/TN Analyzer (Teledyne Tekmar, Mason, OH, United States). No correction factor (k_EC) was applied to account for incomplete microbial biomass lysis during the fumigation.

All data manipulations and analyses were performed in R versions 3.6.1-4.0.4 (R Core Team, 2020). All enzyme trait abbreviations and definitions are indicated in Table 2. Net fluorescence in the enzyme assays, including quenching corrections, were calculated following German et al. (2011b). Negative values due to analytical error were excluded from the dataset (0.8%); analytical outliers were further identified based on the Interquartile Range method, and a maximum of one value was excluded out of the four analytical replicates per sample. In total, these procedures excluded 1917 out of 26784 data-points (7.2%). Enzyme maximal velocity (V_max) and Michaelis constants (K_m) were computed by fitting a 2-parameter Michaelis-Menten (MM) model over all analytical replicates of each of eight substrate concentrations using the drm function in the drc package (Ritz et al., 2015), with a data-driven self-starter function specific to the model. Following preliminary analyses, and when necessary, we excluded data points corresponding to one of the eight individual substrate concentrations for which all analytical replicates consistently did not fit the distribution of the remaining data (i.e., due to inhibition at high concentrations or technical errors during assay preparation). In order to alleviate variance heterogeneity of analytical replicates between substrate concentrations, we applied a Box-Cox transformation to all models using the boxcox function in the drc package (Ritz et al., 2015). Comparison between the parameters V_max and K_m estimated based on transformed and non-transformed models showed that Box-Cox transformation improved the fit of models with substantial analytical variance, but had a marginal or no effect on parameters estimated by models with initial good fit. Individual models yielding nonsignificant V_max or K_m estimates (p > 0.05) after Box-Cox transformation were considered to have bad fit and were thus excluded from further analyses (excluded 11 out of 324 models). To determine the optimal assay incubation time at each temperature, we compared MM models fit to data collected after each of three sequential incubation periods (1, 4, and 24 h). We selected the minimum incubation period necessary to reach the highest V_max-value, under the assumptions that lower V_max-values reflected either insufficient incubation time for reactions to reach saturation, decrease in activity, or loss of fluorescence due to prolonged incubation after saturation had been reached. The same incubation period was consistently selected for each batch of assays performed at the same temperature. V_max was expressed per mass of dry soil as V_max/ds (nmol g^–1 h^–1) and per unit of microbial biomass C (MBC) as V_max/MBC (nmol μg MBC^–1 h^–1). The apparent catalytic efficiency (CE_ds) was calculated as:

and the biomass-specific catalytic efficiency (CE_MBC) as:

Q₁₀ coefficients were calculated over the full experimental temperature range (six temperatures from 4 to 50°C) and over a realistic field range (five temperatures from 4 to 35°C) following the approach by Allison et al. (2018). Briefly, the degree of change in V_max, K_m or CE per °C was inferred based on linear regressions between the natural logarithm of each parameter and temperature, and converted to Q₁₀-values based on the relationship:

The Arrhenius activation energy (E_a) was calculated based on the slope of the linear regression between ln(V_max) and 1/T, and the relationship:

where T is the temperature in kelvin and R is the universal gas constant. Linear regression models were calculated using the lm function in the stats package native to R (R Core Team, 2020). The change in heat capacity (ΔC_p^‡), temperature optimum (T_opt) and point of maximum temperature sensitivity (TS_max) were calculated by fitting ln(V_max) over the six incubation temperatures between 4–50°C using the Macromolecular Rate Theory (MMRT) model, according to the equations and definitions described by Alster et al. (2020). The reference temperature T₀ was set to 315 K to best match the measured data, following the recommendations by Alster et al. (2020). Model fit comparisons were based on the Akaike Information Criterion (AIC) and respective relative likelihoods, corrected AIC (AICc), and Bayesian Information Criterion (BIC), following the guidelines by Burnham and Anderson (2004). AIC, BIC, and adjusted R²-values of the linear models were extracted from the linear regression model computed with the lm function in the stats package (R Core Team, 2020). AICc of all models, and AIC and BIC of the nonlinear models were calculated using the R package AICcmodavg (Mazerolle, 2020). One-way and two-way Analyses of Variance (ANOVA) were performed with the aov function, followed by post hoc Tukey’s tests using the function TukeyHSD with p-values adjusted for multiple comparisons, using the stats package (R Core Team, 2020). Compact letter displays for the Tukey’s tests were computed with the function HSD.test in the package agricolae (de Mendiburu and Yaseen, 2020). Assumptions of ANOVA were tested based on Levene’s tests with the leveneTest function in the package car (Fox and Weisberg, 2019), Shapiro-Wilk tests with the shapiro.test function in the package stats (R Core Team, 2020), skewness of residuals with the skewness function in the package agricolae (de Mendiburu and Yaseen, 2020), and plots of homogeneity of residuals’ variance and normality of residuals (Q-Q plots). Data was ln-transformed as necessary, and all tests reported as significant were based on a p-value < 0.05. Figure displays were prepared with the package cowplot (Wilke, 2020). The maximum percentage of variation (i.e., decline) in kinetic parameters with depth, per temperature, was calculated as the percentage of difference between the highest and lowest values within the upper and lower depth intervals mentioned in the text, for example:

As the ANOVA showed that variation in kinetic parameters with depth was not dependent on temperature, the percentages of variation with depth are reported as the average decline among all temperatures, per enzyme and kinetic parameter. The inconsistently high mean K_m-values only at 16°C was excluded from those calculations. All raw and processed data, as well as the code used to parse and analyze them are available as Supplementary Material (see “Supplementary_Materials_File_Descriptions.pdf”).

We determined the MM kinetics of the enzymes acid phosphatase (AP), β-glucosidase (BG), and leucine aminopeptidase (LAP) in soils collected at six depth intervals from triplicate soil cores down to 90 cm (0–10, 10–20, 30–40, 50–60, 60–70, and 80–90 cm), at six temperatures between 4 and 50°C (4, 10, 16, 25, 35, or 50°C) (Table 1). The activity of all enzymes showed typical MM behavior. Enzyme kinetic traits analyzed here and their definitions are indicated in Table 2.

The V_max of all three enzymes, estimated on a dry soil mass basis (V_max/ds), declined significantly with soil depth over all temperatures (p < 0.001), and differences among depths were not dependent on temperature (i.e., no significant depth × temperature interaction) (Figure 1A and Table 3). Mean V_max/ds declined almost continuously from the soil surface (0–20 cm) down to 60–90 cm by up to 96.4 ± 0.4% (mean ± standard error; see Materials and Methods for details) across all enzymes and temperatures. This variation was only significant between three to four depth ranges, which differed between enzymes (Figure 1A, Supplementary Table 2): V_max/ds of BG declined progressively down to 60 cm, but not below that depth; V_max/ds of AP declined only over the mid-depth range, from 20 to 30 cm and from 40 to 60 cm; V_max/ds of LAP also did not vary within the upper 20 cm, but declined gradually down to a lower depth than that of AP, namely from 20 to 30 cm, from 40 to 50 cm and from 60 to 80 cm.

Since the concentration of microbial biomass carbon (MBC) declined strongly with soil depth, especially over the upper 30 cm (Supplementary Figure 1), much of the decline in V_max/ds with depth may have been driven by lower microbial abundance. Therefore, we computed a biomass-specific V_max, by expressing it per unit MBC (V_max/MBC), under the assumption that cell lysis efficiency by chloroform fumigation was similar across samples, thus yielding comparable MBC estimates. V_max/MBC of all enzymes declined significantly down the soil profile over all temperatures, following the same trends as those of V_max/ds (p < 0.001) (Table 3, Supplementary Table 2, and Figure 1B). The overall decline in V_max/MBC between 10–20 and 60–90 cm was only 8% lower (88.4 ± 1.7%) than that of V_max/ds, indicating that variation in V_max/ds did not depend primarily on microbial biomass concentration. Like V_max/ds, V_max/MBC did not show a significant interaction between depth and temperature. Also similar to V_max/ds, V_max/MBC of AP and LAP did not vary within the upper 20 cm and declined mostly from 20 to 30 cm (Figure 1B). V_max/MBC did not decline significantly over the mid-depth range for either AP or LAP, but it was significantly lower at 80–90 cm than at 30–40 cm for AP, and lower between 60 and 90 cm than at 30–40 cm for LAP. V_max/MBC of BG declined more consistently down to 70 cm over all temperatures, but did not vary further.

K_m also declined (i.e., enzyme affinity increased) significantly with depth for all enzymes across temperatures (p < 0.001) with no significant interaction between depth and temperature (Table 3, Supplementary Table 2). However, K_m declined less with depth than V_max/ds or V_max/MBC, and mainly between the upper 20 cm and lower depths, by up to 85.6 ± 1.3%, with some differences between enzymes. K_m of AP and BG declined with depth following trends similar to those of their V_max (Figure 2): K_m of AP declined mainly from 20 to 30 cm and remained relatively constant down to 80 cm, although it was significantly lower at 80–90 cm than at 30–40 cm; K_m of BG declined consistently down to 40 cm, without further variation (despite a spuriously high mean K_m at 80–90 cm only at 16°C). Unlike its V_max, the K_m of LAP only declined from 20 to 30 cm, and did not vary significantly below that depth.

The apparent (i.e., observed) catalytic efficiency (CE_ds), estimated as the ratio between V_max/ds and K_m, reflects the catalytic efficiency of the enzyme pool present per mass of soil, regardless of microbial abundance or enzyme demand. CE_ds declined significantly across temperatures for all enzymes (p < 0.001), also without a significant interaction between depth and temperature (Table 3, Supplementary Table 2). The CE_ds of BG and LAP followed similar trends and declined mainly over the mid-depth range by up to 90.5 ± 1.1% over all temperatures, without significant variation in the upper 20 cm, or below 60 cm (Figure 3A). CE_ds of AP declined much less through the soil profile (58.1 ± 3.0%), and it was only significantly lower at 60–90 cm than in the upper 10 cm. Biomass-specific catalytic efficiency (CE_MBC), estimated as the ratio between V_max/MBC and K_m, represents the inherent catalytic efficiency of the enzyme pool produced by the local microbiome, as a function of its specific enzyme production capacity and demand. CE_MBC declined significantly with depth for BG and LAP (p < 0.001) across temperatures, but not for AP (Table 3, Supplementary Table 2, and Figure 3B). CE_MBC of BG and LAP varied less with depth than other kinetic properties, and declined significant mainly below 60 cm by up to 71.8 ± 2.5% (Figure 3B). These declines in CE_MBC reflected the decline in V_max/MBC at lower depths, where K_m remained relatively constant. Like for all other kinetic parameters, depth-dependent differences in CE_MBC were not dependent on temperature (Table 3).

As there was no significant interaction between depth and temperature for any kinetic parameter (Table 3), we performed a random effects ANOVA with depth as independent variable and temperature as block variable, to control for possible confounding effects of the latter on depth-dependent differences. This analysis yielded the same results as the fixed effects ANOVA reported above, with the single exception that V_max/ds of AP declined significantly also between 50–60 cm and 80–90 cm (data not shown).

All kinetic properties varied significantly among enzymes at all depths and across temperatures (p < 0.001), but there was only a significant interaction between enzyme and temperature in the upper 10 cm for K_m, CE_ds and CE_MBC (p < 0.001) (Supplementary Table 3). V_max differed significantly among all enzymes at all depths, with AP having consistently the highest values, followed by BG and then LAP (p < 0.05) (Supplementary Table 4 and Figures 1A,B). K_m differed significantly among all enzymes between 10 and 60 cm (p < 0.05), but it did not differ between AP and BG in the upper 10 cm or below 60 cm (Supplementary Table 4 and Figure 2). LAP had always the highest K_m (i.e., lowest affinity). In contrast, BG had always the lowest K_m, at least at depths where it was significantly different than that of AP (i.e., between 10 and 60 cm). CE_MBC differed significantly among all enzymes in the upper 10 cm and below 50 cm (p < 0.05), but not between AP and BG from 10 to 40 cm (Supplementary Table 4 and Figure 3B). Similar to V_max, the CE_MBC of LAP was always the lowest among enzymes, followed by those of BG and then AP at depths where it differed significantly (Supplementary Table 4 and Figure 3B). As CE_MBC was calculated based on the same MBC value for all enzymes at each depth, CE_ds varied between enzymes similarly to CE_MBC (Supplementary Table 4 and Figure 3A).

We investigated the ratios between kinetic properties (V_max, K_m, and CE) of the three different enzymes as indicators for variation in relative nutrient demand through the soil profile. Based on two-way fixed effects ANOVA with depth and temperature as independent factors, all kinetic ratios between enzymes varied significantly with depth over all temperatures, with the exception of ratios between K_m of LAP and AP (K_m^LAP:AP) (p < 0.005) (Supplementary Table 5). The effects of temperature on kinetic ratios are described in a separate section below. V_max^BG:LAP declined significantly from 10 to 20 cm, followed by a suggestive continuous increase down to 90 cm, although it was only significantly higher at 80–90 cm than at 10–20 cm (Figure 4A). V_max^BG:AP declined with depth down to 70 cm, mainly from 10 to 20 cm and from 40 to 60 cm, followed by a significant increase from 70 to 90 cm that appeared to result partially from a spurious high value only at 16°C, among all six temperatures (Figure 4B). V_max^LAP:AP generally declined with depth below 20 cm, but this variation was mainly significant between the upper 20 cm and the lower 30 cm (i.e., from 60 to 90 cm) (Figure 4C). K_m^BG:LAP and K_m^BG:AP followed trends similar to those of their corresponding V_max ratios: K_m^BG:LAP declined significantly from 10 to 20 cm and remained relatively invariant through the profile (Figure 4D), whereas K_m^BG:AP declined from 10 to 20 cm, followed by a suggestive but non-significant increase down to 70 cm (Figure 4E). The significant increases in K_m^BG:LAP and K_m^BG:AP at 80–90 cm were likely driven, at least partially, by the same spurious high K_m-value of BG only at 16°C mentioned above. In contrast, K_m^LAP:AP did not vary significantly with depth nor show any apparent trends (Figure 4F). CE^BG:LAP increased significantly from the upper 20 cm to a depth of 30–40 cm, although below that depth it did not vary significantly from any upper depths (Figure 4G). CE^BG:AP did not vary within the upper 40 cm, but it was significantly lower below 50 cm (Figure 4H). CE^LAP:AP declined with depth below 20 cm, but this variation was only significant between the upper 40 cm and the lower 30 cm (from 60 to 90 cm) (Figure 4I). This variation in CE^LAP:AP with depth mirrored the general trend of V_max^LAP:AP, as K_m^LAP:AP was relatively invariant though the soil profile.

Temperature had an overall significant effect on V_max, CE_MBC and CE_ds of all enzymes, and on K_m of only BG, over the whole soil profile (p < 0.001) (Table 3 and Figures 1–3). The temperature sensitivity of enzyme V_max (V_max/MBC and V_max/ds scale identically with temperature at each depth) was further determined using a linear Arrhenius model and Q₁₀ coefficient over the full temperature range tested (4–50°C, n = 6) (Supplementary Figure 2) and a realistic in situ soil range (4–35°C, n = 5) (Figure 5), as well as based on the temperature optimum (T_opt), point of maximum temperature sensitivity (TS_max) and change in heat capacity (ΔC_p^‡) estimated using the non-linear MMRT model over the full temperature range (4–50°C, n = 6) (Figure 6). Enzyme thermal traits analyzed here and their definitions are indicated in Table 2. Although the fits of Arrhenius and MMRT models did not differ substantially, overall comparisons consistently favored MMRT, suggesting that it provided a more realistic representation of enzyme temperature response (see extended Results and Discussion in Supplementary Information).

Despite some suggestive, depth-dependent trends in the Q₁₀-values of V_max, K_m, and CE, they did not vary significantly with depth for any enzyme (Table 4), whether estimated over a realistic in situ soil temperature range (4–35°C) (Figure 7), or the full experimental temperature range (4–50°C) (Supplementary Figure 3). Both temperature ranges yielded similar Q₁₀-values that varied within a narrow range, although Q₁₀-values over 4–50°C were slightly lower than those over 4–35°C due to a frequent decline in the response rate of V_max between 35 and 50°C (Supplementary Table 8). Therefore, only Q₁₀-values over the realistic in situ soil temperature range are henceforth presented. The Q₁₀ of V_max was consistently above 1, indicating a positive effect of temperature on V_max across depths of 1.44 ± 0.03, 1.56 ± 0.03, and 1.78 ± 0.10 (mean ± se) for AP, BG and LAP, respectively (Figure 7A and Supplementary Table 8). Mean activation energies (E_a) estimated from the same linear relationships were 25.69 ± 1.74, 31.50 ± 1.45, and 39.33 ± 3.98 kJ mol^–1 K^–1 (mean ± se) across depths for AP, BG, and LAP respectively (Supplementary Table 8). The Q₁₀ of K_m varied between 0.83 and 1.30 across enzymes and depths, although K_m was, on average, relatively insensitive to temperature compared to other parameters, with mean Q₁₀-values across depths of 1.00 ± 0.06, 1.14 ± 0.05, and 0.99 ± 0.07 (mean ± se) for AP, BG and LAP, respectively (Figure 7B and Supplementary Table 8). This was consistent with the two-way ANOVA showing that temperature had generally no significant effect on K_m. The significant effect of temperature on the K_m of BG detected by the two-way ANOVA was likely due to the spurious high K_m of BG only at 16°C at 80–90 cm (Table 3 and Figure 2), which was not reflected on the Q₁₀ computed across temperatures. The Q₁₀ of CE was consistently above 1, similar to that of V_max, with similar overall mean values across enzymes: 1.51 ± 0.08, 1.42 ± 0.08, and 1.82 ± 0.05 (mean ± se) for AP, BG, and LAP respectively (Figure 7C and Supplementary Table 8).

None of the temperature sensitivity parameters estimated by MMRT –T_opt, TS_max and ΔC_p^‡– varied significantly with depth (with one exception; see below) (Figure 8 and Table 4). These parameter estimates showed considerable variability among replicates, and estimates from models with poor fit to MMRT’s predicted behavior (T_opt or TS_max < 0°C, or > 200°C; four out of 54 total models) were excluded from the analysis, likely reducing the statistical power of few pairwise comparisons between depths and enzymes. Mean T_opt and TS_max were consistent across depths and enzymes, with mean values of 65.19 ± 3.74°C and 31.63 ± 1.98°C (mean ± se), respectively (Figures 8A,B and Supplementary Table 8). TS_max of LAP was significantly different between the 0–10 and 30–40 cm depth intervals (p < 0.05), which was the only exception to otherwise non-significantly different parameter estimates across either enzymes or depths. Mean ΔC_p^‡-values were similar between AP and BG across depths, with a combined mean value of −0.79 ± 0.06 kJ mol^–1 K^–1 (mean ± se) (Figure 8C and Supplementary Table 8). ΔC_p^‡ of LAP spanned a broader range of values (−1.32 ± 0.21, mean ± se), mainly due to suggestive, albeit non-significant, lower values at depths below 60 cm.

Temperature had a significant, positive effect on the V_max ratio of BG to AP (V_max^BG:AP), and LAP to AP (V_max^LAP:AP) across depths, and a significant, negative effect on ratios between catalytic efficiencies of BG and LAP (CE^BG:LAP) (p < 0.05) (Supplementary Table 5 and Figures 4A–I). This indicated that V_max and CE of those enzymes were differently affected by temperature. CE^BG:LAP was also subject to a depth × temperature interaction (p < 0.05), suggesting that the different effects of temperature on CE of BG and LAP were depth-dependent. The Q₁₀ of V_max and CE, and MMRT’s ΔC_p^‡ varied significantly between enzymes across the soil profile (p < 0.05), but there was no enzyme × depth interaction in the two-way ANOVA (Table 5). One-way ANOVA between enzymes at each depth interval showed that Q₁₀-values varied significantly only between some enzymes and at discrete depths (Supplementary Tables 9–10). While the Q₁₀ of V_max was only significantly different between AP and LAP at 60–70 cm (p < 0.05), this analysis also showed that the Q₁₀ of K_m was significantly lower for LAP in the upper 10 cm relative to the other two enzymes (p < 0.05). This difference suggested that the affinity of LAP might increase with temperature (i.e., lower K_m) at this depth (Q₁₀ = 0.83 ± 0.07, mean ± se), compared to those of AP (Q₁₀ = 1.18 ± 0.06) or BG (Q₁₀ = 1.30 ± 0.07). The Q₁₀ of CE was significantly higher for LAP in the upper 10 cm (1.86 ± 0.07, mean ± se) relative to those of AP (1.27 ± 0.02) or BG (1.20 ± 0.08) (p < 0.05), reflecting the apparent negative effect of higher temperatures on the K_m of LAP at that depth. Although overall ΔC_p^‡-values varied significantly between enzymes across depths (i.e., two-way ANOVA) (Table 5), one-way ANOVA did not detect significant differences at any specific depth for any MMRT parameter (Supplementary Table 9).

As hypothesized, V_max/ds and K_m declined strongly with soil depth, but followed distinct trends that depended on enzyme type. The decline in V_max/ds of 96.4 ± 0.4% across enzymes and temperatures down to 90 cm indicated a drastic decline in enzyme production capacity, product demand, or substrate availability. This was consistent with the lower microbial biomass concentrations in deeper soils observed here, as generally reported across studies (Blume et al., 2002; Fierer et al., 2003a; Schnecker et al., 2014; Loeppmann et al., 2016a; Jones et al., 2018). Higher density of plant roots in surface soils may have also contributed to higher near-surface V_max/ds, as shown particularly for BG in rooted soils when compared to fallow soils (Loeppmann et al., 2016b), and in rhizosphere hotspots when compared to bulk soil (Tian et al., 2020). Plants may induce higher enzyme V_max by promoting microbial growth through C-rich exudates, competing with microbes for N and P, or directly stimulating microbial enzyme production to enhance availability of assimilable products (Burns et al., 2013). Declines in activity of hydrolytic enzymes have been consistently observed down to depths between 50 and 420 cm in diverse soils, including from temperate, taiga and tropical forests, arctic tundra, grasslands and croplands (Taylor et al., 2002; Venkatesan and Senthurpandian, 2006; Gelsomino and Azzellino, 2011; Kramer et al., 2013; Schnecker et al., 2014, 2015; Stone et al., 2014; Loeppmann et al., 2016a; Jing et al., 2017; Darby et al., 2020; Dove et al., 2020). However, among the five studies from which we could retrieve at least approximate V_max/ds-values, only Loeppmann et al. (2016a) observed mean declines in V_max/ds of BG, LAP and AP down to 70 cm similar to those observed here down to 90 cm (91.0 ± 2.2%), whereas others observed substantially smaller mean declines of approximately 67.5 ± 6.3% for AP and BG at depths between 55 and 110 cm (Venkatesan and Senthurpandian, 2006; Gelsomino and Azzellino, 2011; Stone et al., 2014). Consistent with this, only Loeppmann et al. (2016a) determined V_max based on a MM model over a series of enzyme substrate concentrations, as needed to estimate MM kinetics accurately. Potential enzyme activities have been frequently shown to correlate positively with MBC concentration (Perucci, 1992; Gelsomino and Azzellino, 2011; Stone et al., 2014; Ren et al., 2018), as V_max is linearly dependent on enzyme concentration, which in turn is largely dependent on microbial abundance. However, this is not always the case (Waring et al., 2014), as exoenzyme production may also be induced or repressed depending on substrate availability and product demand, following the evolutionary-economic mechanisms that regulate allocation of cellular resources (Allison et al., 2011; German et al., 2011a). Moreover, enzyme production varies between organisms and is subject to variable levels of regulation (Allison et al., 2011; Sinsabaugh and Shah, 2012; Burns et al., 2013). For example, some isozymes and enzyme types may be expressed at stable constitutional levels under specific conditions, as previously suggested for deep soils (Stone et al., 2014), whereas expression of others may be more strictly induced by cellular demands or environmental cues. Therefore, a biomass-specific V_max (V_max/MBC) can be interpreted as a catalytic rate constant independent of microbial abundance, which represents the collective effect of inherent enzyme properties, and specific enzyme production and demand of the microbiome. Surprisingly, V_max/MBC of all enzymes declined nearly as much with depth as V_max/ds, indicating that microbial abundance was not the primary driver of variation in V_max. Loeppmann et al. (2016a) found similar trends only for BG and LAP, and only below 30–40 cm, as V_max/MBC increased from the surface to that depth and only then declined consistently down to 70 cm. These differences might have resulted from a steeper decline in substrate availability and microbial biomass in our soils, which are covered by a thick litter layer and have a shallow rhizosphere, compared to a more extensive rhizosphere (i.e., maize) and less surface litter in the soils studied by Loeppmann et al. (2016a). The consistent decline in V_max/MBC in deeper soils observed by us, and to some extent also Loeppmann et al. (2016a), contrasts with most other studies where V_max/MBC of AP, BG and LAP either increased, or did not vary with depth (Gelsomino and Azzellino, 2011; Kramer et al., 2013; Stone et al., 2014; Schnecker et al., 2015; Dove et al., 2020). We could only identify one study that detected a decline in V_max/MBC of BG (Taylor et al., 2002), although declines with depth have been more frequently observed for other enzymes (Taylor et al., 2002; Gelsomino and Azzellino, 2011; Schnecker et al., 2015). However, V_max in those studies was inferred from a single concentration of substrate across depths that was often below the saturation point necessary to reach the V_max-values we observed, particularly in surface soils. We suggest that the apparent increase, or lack of variation, in V_max/MBC previously observed may have resulted from underestimating V_max in surface soils. Our results indicate that exoenzyme pools in deeper soils have inherently low potential reaction rates due to lower expression levels, lower substrate turnover, and/or catalytic efficiency than those in surface soils, possibly reflecting differences in microbial life strategies and substrate preferences.

The consistent increase in affinity (i.e., decrease in K_m) of all enzymes with depth by 85.6 ± 1.3%, mainly between 20 and 60 cm, indicated a major decline in substrate availability at mid-depths consistent with the decline in DOC, TDN (Supplementary Figures 4A,B) and total C and N in these soils (Hicks Pries et al., 2017, 2018). This supported our hypothesis that persistently low substrate concentrations in deep soils select for microbes encoding isozymes with lower K_m in order to maintain relatively constant maximal catalytic rates (Sinsabaugh et al., 2014). K_m-values largely above physiologic substrate concentrations would render enzyme activity entirely dependent on substrate availability, which, under deep soil conditions, would lead to suboptimal rates and provide limited return to the investment on enzymes. Conversely, higher substrate availability in surface soils through plant litter inputs likely alleviates the selective pressure on enzymes with high affinity. Inputs of readily assimilable compounds through root exudation may further alleviate this pressure by reducing the relative importance of continuously maintaining maximal depolymerization rates (Allison et al., 2011), similar to what has been observed for substrate induced respiration (Blagodatskaya et al., 2009). The variation in enzyme affinities with depth observed here indeed appeared to reflect the overall decline in root density –both fine and coarse roots– below 40 cm at this site (Hicks Pries et al., 2018). The K_m of BG particularly mirrored the continuous steep decline in fine root density down to 40 cm (Hicks Pries et al., 2018), whereas those of AP and LAP did not vary within the upper 20 cm. This suggests that availability of easily metabolizable C-containing compounds exuded by fine roots may have a particular regulatory effect on depolymerization of cellulose (Allison and Vitousek, 2005; Allison et al., 2011) through selection of microbes encoding BG isozymes with distinct affinities. This hypothesis is further supported by the higher affinities of cellulose-degradation enzymes, including BG, observed in fallow soils relative to rooted soils (Loeppmann et al., 2016b), and in bulk soils relative to rhizosphere hotspots (Tian et al., 2020). Moreover, microbes producing BG in the rhizosphere have been shown to be distinct from those in the detritusphere (Nuccio et al., 2020). It should be noted that, like in all other studies of enzyme kinetics or activity in environmental samples based on these assays, both V_max and K_m estimates may be affected by the native substrate concentrations (Sinsabaugh et al., 2014). At the same time, it seems implausible that such effects might have contributed substantially to the extreme declines in V_max and K_m with depth observed, given their interdependency and the necessary requirement for low K_m under the much lower substrate concentrations in deeper soils.

The catalytic efficiency (CE), also referred to as specificity constant (Gelsomino and Azzellino, 2011), can be determined as k_cat/K_m when K_m exceeds the concentration of substrate present, which is typically the case under physiological conditions (Berg et al., 2002; Koshland, 2002). Therefore, CE not only represents a fundamental functional property under direct selective pressure, but also evolutionary tradeoffs between k_cat and affinity, which are themselves subject to selection (Sinsabaugh et al., 2014). However, k_cat expresses the maximum amount of substrate converted per unit of time, per enzyme unit (assuming a single catalytic center per enzyme), and thus it cannot be directly inferred from enzyme assays in complex environmental samples, such as soils, where specific enzyme concentrations are generally unknown and hard to quantify. In these cases, an apparent CE (CE_ds) has been estimated as V_max/ds/K_m (Moscatelli et al., 2012; Kujur and Kumar Patel, 2014; Triebwasser-Freese et al., 2015; Loeppmann et al., 2016a,b; Razavi et al., 2016), which represents the observed CE of the enzyme pool present per mass of soil, regardless of the specific production capacity and demand of the microbiome. In our soils, CE_ds of all enzymes declined significantly with depth, with CE_ds of BG and LAP declining consistently over the mid-depth (20 to 60 cm) by up to ∼90%, whereas that of AP varied much less. These results are consistent with those from the only other study that, to our knowledge, determined CE_ds in deep soils, where CE_ds of these same enzymes declined by 2- to 20-fold between the upper 40 cm and depths down to 70 cm (Loeppmann et al., 2016a). Tian et al. (2020) have also shown that CE_ds of BG and AP was higher in fertile soils than in nutrient-poor soils, consistent with higher CE_ds in surface soils with greater nutrient availability than deep soils. However, contrary to our initial expectations, CE based on biomass-specific V_max (CE_MBC) either declined by up to ∼70% (BG and LAP) or did not vary (AP) with depth. We initially hypothesized that CE would increase with depth to maximize return on the investment in enzymes, given the scarce substrates provided by lower plant litter inputs and lower compensation by root exudates. Microbial communities adapted to these conditions would be expected to encode isozymes with higher affinity (i.e., lower K_m) and/or produce more exoenzymes per unit biomass (i.e., higher V_max/MBC) in a proportion that favors higher V_max/MBC/K_m ratios (i.e., CE_MBC). As the K_m-values of BG and LAP were relatively invariable between 30 and 90 cm, their lower CE_MBC at depths below 60 cm was mainly driven by a decline in V_max/MBC, suggesting that it was constrained by lower production of enzymes per unit biomass below that depth rather than higher K_m. On the other hand, enzymes may optimize k_cat in adaptation to environmental pressures (e.g., temperature) at the expense of K_m, leading to conformational adaptations that reduce active site binding, which result in higher K_m and suboptimal catalytic efficiencies (Struvay and Feller, 2012). Therefore, a lower CE_MBC in deeper soils driven by lower V_max/MBC may also reflect enzymes with lower k_cat, as a result of trade-offs with K_m, rather than lower enzyme production. The contrasting lack of variation in CE_MBC of AP with depth, regardless of individual variation in V_max/MBC and K_m, might have resulted from different factors and interactions related to variation in relative P availability and demand, and in regulation of AP expression. Alternatively, P may be primarily acquired from minerals rather than organic compounds (Alori et al., 2017), and thus the CE_MBC of AP alone does not directly reflect P demand. It should also be noted that variation in enzyme and substrate diffusion through the soil matrix, or their stabilization through mineral-organic interactions, can lead to differences in substrate availability and enzyme accessibility. For example, lower diffusivity or higher adsorption of enzymes or substrates to soil particles could select for enzymes with higher affinities and prompt higher enzyme production per cell. Conversely, stabilization of active enzymes can increase their longevity and effectiveness over time (Burns et al., 2013), which could alleviate the selective pressure on their catalytic efficiency, as we observed in deeper soils.

Our results suggest that microbial communities in deep subsoils encode exoenzymes with intrinsically lower k_cat, and/or produce less enzymes per cell than those in surface soils, leading to a lower emergent CE_MBC. The expectation that V_max/MBC and CE_MBC would increase with depth assumes that microbiomes have largely redundant metabolic and elemental demands, and thus that exoenzymes are optimized to provide nutrients in proportion to the size and demands of the community, as a function of nutrient availability (Allison et al., 2011). However, several studies have shown that microbiomes change markedly with soil depth (Fierer et al., 2003b; Hansel et al., 2008; Hartmann et al., 2009; Eilers et al., 2012; Jiao et al., 2018; Liu et al., 2019), with deep soils harboring less diverse and functionally distinct organisms (Brewer et al., 2019; Diamond et al., 2019; Yan et al., 2019; Dove et al., 2021). Life strategies that prioritize cellular maintenance over fast growth and maximal resource exploitation, and properties such as utilization of alternative substrates, storage compound production, and ability to sporulate or undergo dormancy may all affect exoenzyme properties, and possibly contribute to relax selective pressures on their kinetics (Ho et al., 2017; Ramin and Allison, 2019). Dove et al. (2021) have shown that deep soil microbes at our site have lower growth rates and lower carbon use efficiency than those at the surface, reflecting a lower nutrient demand and greater investment on cellular maintenance that may underlie the lower V_max/MBC and CE_MBC we observed. Moreover, the declining substrate availability with depth is expected to decrease the return on exoenzyme investment and favor alternative metabolic strategies that do not rely primarily on depolymerization of complex organic matter. Dove et al. (2021) have indeed shown that microbiomes in these deep soils have lower potential to degrade complex carbohydrates, similar to those in other soils (Diamond et al., 2019). Conversely, it has been shown that deep soil communities are enriched in organisms that can metabolize one-carbon (C₁) and other low-molecular weight C compounds, and use inorganic N forms as energy sources (Brewer et al., 2019; Diamond et al., 2019), as well as in taxa that comprise mainly chemoautotrophs (Cao et al., 2012; Eilers et al., 2012; Turner et al., 2017; Brewer et al., 2019; Diamond et al., 2019). Therefore, a smaller fraction of organisms relying on exoenzymes in deep soils is also likely to contribute to a lower emergent CE_MBC due to both lower overall biomass-specific enzyme production and lower competition for enzyme products within the community. Nevertheless, it should be noted that, while microbial biomass largely dominates living matter in mineral and usually dry soils with low root density, such as these, we cannot entirely exclude minor contributions of enzymes produced by plants and soil fauna to the activities measured.

As expected, V_max differed significantly between all three enzymes at every depth, reflecting fundamental differences in relative nutrient demand, as well as possible differences in enzyme properties and regulation. According to ecoenzymatic stoichiometry, ratios between V_max of hydrolytic enzymes involved in acquisition of C, N or P reflect the relative demand in these elements in relation to their availability, and thus the equilibrium between microbial biomass and SOM stoichiometry (Sinsabaugh and Shah, 2012). Here, both V_max and CE ratios between C- and N-acquiring enzymes (V_max^BG:LAP and CE^BG:LAP, respectively) were relatively constant through the soil profile, despite suggestive increases at lower depths, which were consistent with the trend in soil C:N ratio (Hicks Pries et al., 2018) and ratios between dissolved C and N pools (Supplementary Figure 4C). At the same time, V_max and CE ratios between BG:AP and LAP:AP decreased with depth, suggesting an increasing demand for P relative to either C or N, similar to previous observations of ratios between activities of C- and P-acquiring enzymes in both temperate and tropical soils (Stone et al., 2014; Loeppmann et al., 2016a). Alternatively, it has been shown that soil microbes can use phosphorylated compounds primarily as a C source (Heuck et al., 2015), and thus higher V_max and CE of AP may rather indicate higher C demand in the absence of more favorable C sources in deep soils, as previous suggested (Stone et al., 2014). It should be noted, however, that depolymerization of organic matter and nutrient acquisition involves also other enzymes, and therefore the enzyme investigated here may not fully represent C, N or P demand and availability (Sinsabaugh and Shah, 2012).

Our results confirmed the general expectation that activity of BG, LAP and AP is stimulated by increasing temperatures up to optimal temperatures above those typically observed in moderate environments, with Q₁₀-values for V_max and activation energies within the ranges typically observed for soil exoenzymes (Trasar-Cepeda et al., 2007; Brzostek and Finzi, 2012; German et al., 2012; Stone et al., 2012; Steinweg et al., 2013; Razavi et al., 2015, 2016; Nottingham et al., 2016). However, despite few suggestive trends, temperature sensitivity did not vary significantly with depth for any enzyme or kinetic property, based on either Q₁₀, following a linear Arrhenius model, or T_opt, TS_max and ΔC_p^‡ of V_max estimated by the non-linear MMRT model. We could not determine unambiguously whether the response of V_max to temperature was best explained by Arrhenius or MMRT models, although comparisons suggested that the latter generally fit the data better. Moreover, positive temperature response rates of V_max declined at higher temperatures in most cases (i.e., above TS_max = 31.63 ± 1.98°C, up to T_opt = 65.19 ± 3.74°C, followed by a negative response), as observed by other studies (Alster et al., 2016a,2018), further indicating that MMRT represented a more realistic temperature response behavior. On the other hand, this also indicated that the linear models captured the temperature response better under lower temperatures within the native temperature range, before response rates slowed towards T_opt, similar to what has been observed by Alster et al. (2016a). The uniform temperature sensitivity observed here contradicted our initial hypothesis that exoenzymes in deeper soils are more sensitive to temperature changes as a result of microbial adaptation to lower and narrower temperature ranges (Schipper et al., 2014), as observed at our site. Previous studies have observed that exoenzymes from colder soil environments tend to be more sensitive to temperature (Koch et al., 2007; Brzostek and Finzi, 2012), as well as in some subsoils in relation to surface soils (Steinweg et al., 2013). Therefore, we expected that Q₁₀-values and activation energies would increase with depth, whereas either T_opt, ΔC_p^‡, or both, would decrease. Under MMRT’s Optimum-Driven hypothesis, the more frequent lower temperatures in deeper soils could select for enzymes with lower T_opt, regardless of their ΔC_p^‡ (Alster et al., 2020). Conversely, the Thermal Breadth hypothesis postulates that enzymes subject to large temperature ranges have less negative ΔC_p^‡ (i.e., flatter temperature response curves) but not necessarily different T_opt, and thus the narrower temperature ranges in deeper soils would lead to more negative ΔC_p^‡ (Alster et al., 2020). In turn, the Enzyme Rigidity hypothesis predicts that cold-adapted enzymes have more negative ΔC_p^‡ due to their lower rigidity, which would lead to a decline in ΔC_p^‡, and consequently T_opt, with depth, following selection of enzymes adapted to lower temperatures (Alster et al., 2020). The uniform temperature sensitivity of all enzymes through the soil profile may instead reflect a convergence of enzyme T_opt towards the similar MATs across depths at our site (10.4–11.5°C), despite different temperature ranges. On the other hand, the low MATs of our soils appear to contradict the relatively high ΔC_p^‡ observed, compared to values previously reported (Alster et al., 2016a,2018), which are expected to reflect a high enzyme rigidity typical of warm-adapted enzymes. It is possible that enzyme ΔC_p^‡ in our soils are mainly driven by their wide temperature ranges, despite their narrowing with depth, leading to selection of enzymes with less negative ΔC_p^‡, and thus able to maintain more constant activity rates under varying temperatures (Alster et al., 2020). Moreover, reactions potentially involving a diverse isozyme pool, such as those measured here, reflect the summation of the temperature response curves of those enzymes, and thus are also expected to have a less negative ΔC_p^‡ (Alster et al., 2018).

Our results are consistent with the uniform temperature sensitivity (apparent Q₁₀) of in situ soil respiration over the top meter of soil previously observed at this site (Hicks Pries et al., 2017). This suggests that SOM depolymerization by exoenzymes may be closely linked to the response of total soil respiration to temperature, likely by modulating the contribution of microbial heterotrophic metabolism. In turn, K_m was relatively insensitive to temperature, with mean Q₁₀-values around 1 across depths and enzymes. This suggests that enzyme affinities may be biochemically constrained to prevent being affected by temperature fluctuations, as previously suggested (Allison et al., 2018). T_opt of V_max (65.19 ± 3.74°C), based on the MMRT model, was much higher than natural soil temperatures, whereas TS_max (31.63 ± 1.98°C) was just above the temperature maximum in surface soils (29°C at 5 cm), but substantially higher than those at lower depths (19°C at 30 cm and 16°C at 100 cm), or mean annual temperatures (MAT) over the upper meter of soil (10.4–11.5°C). Similar high T_opt estimates based on MMRT have been generally observed for microbial exoenzyme activities and complex metabolic processes in soils (Schipper et al., 2014), and for soil bacterial isolates (Alster et al., 2016a). This is consistent with the fact that the thermal stability and optimal catalytic temperature of enzymes from mesophilic organisms tend to be higher than that of their native environment (Engqvist, 2018). While persistent warming is expected to generally induce higher enzyme activity through the whole soil profile, a uniform TS_max may, however, result in variable net annual temperature responses at different depths due to their different temperature ranges, duration of different temperature regimes, and seasonal variation, regardless of similar MATs. How these factors may interact in response to sustained long-term warming, and their outcomes, will depend on the degree of thermal adaptability of exoenzymes through changes in microbial community composition, and expression of isozymes with different properties (Wallenstein et al., 2011; Bradford, 2013). It should be noted, however, that we cannot completely rule out the possibility that the spatial variability of some temperature sensitivity estimates might have precluded detection of robust differences between depths. Such variability is a common limitation of measurements of emergent responses of complex biological systems, especially due to sample-specific variables that cannot be accounted for with the methods currently available. These challenges emphasize the need for novel approaches that allow a more reproducible assessment of such processes across spatiotemporal scales.

The magnitude of all temperature sensitivity parameters was remarkably similar between enzymes through the soil profile, although Q₁₀-values of V_max and K_m have been frequently shown to vary between co-occurring soil enzymes (Wallenstein et al., 2011). Likewise, T_opt, TS_max and ΔC_p^‡ can vary substantially between enzymes (Alster et al., 2016a). Nevertheless, we did observe a significantly lower Q₁₀ of K_m and consequently significantly higher Q₁₀ of CE of LAP in the upper 10 cm, relative to the other enzymes. The fact that the mean Q₁₀ of K_m of LAP was below 1 (Q₁₀ = 0.83), while those of BG and AP were not (Q₁₀ = 1.30 and 1.18, respectively), suggested that the affinity of LAP was positively stimulated by higher temperatures at this depth (i.e., K_m decreased), or that those of BG and AP were negatively affected. As the Q₁₀ of V_max did not differ significantly between any enzyme, this led to a significantly higher positive temperature response of the CE of LAP. This likely contributed to the significant negative effect of higher temperatures on the CE^BG:LAP ratio, and shows that temperature can directly affect the relative catalytic efficiencies between C- and N-acquiring enzymes. This was consistent with previous observations suggesting that kinetic responses to temperature may vary among enzyme types, leading to changes in relative cycling of different nutrients (Allison et al., 2018). Moreover, the significant interaction between depth and temperature on CE^BG:LAP ratios confirmed that their variation with depth was dependent on temperature, possibly reflecting the higher CE Q₁₀ of LAP in the upper 10 cm. Higher temperatures also had a significant positive effect on V_max^BG:AP and V_max^LAP:AP ratios, indicating that AP was generally less stimulated by higher temperature than BG or LAP. As enzyme assays at different temperatures were performed with the same soil preparations per depth and incubated over short periods, these relative differences in V_max likely reflected a direct effect of temperature on enzyme k_cat, independently of enzyme concentration. Despite the uniform temperature sensitivity of all kinetic parameters of individual enzymes through the soil profile, these results show that temperature can affects differently the intrinsic kinetic properties (i.e., K_m and k_cat) of distinct enzymes in a depth-dependent manner, presumably without active microbial regulation.