Systematic variation in the temperature dependence of bacterial carbon use efficiency

Understanding the temperature dependence of carbon use efficiency (CUE) is critical for understanding microbial physiology, population dynamics, and community-level responses to changing environmental temperatures 1,2. Currently, microbial CUE is widely assumed to decrease with temperature 3,4. However, this assumption is based largely on community-level data, which are influenced by many confounding factors 5, with little empirical evidence at the level of individual strains. Here, we experimentally characterise the CUE thermal response for a diverse set of environmental bacterial isolates. We find that contrary to current thinking, bacterial CUE typically responds either positively to temperature, or has no discernible temperature response, within biologically meaningful temperature ranges. Using a global data-synthesis, we show that our empirical results are generalisable across a much wider diversity of bacteria than have previously been tested. This systematic variation in the thermal responses of bacterial CUE stems from the fact that relative to respiration rates, bacterial population growth rates typically respond more strongly to temperature, and are also subject to weaker evolutionary constraints. Our results provide fundamental new insights into microbial physiology, and a basis for more accurately modelling the effects of shorter-term thermal fluctuations as well as longer-term climatic warming on microbial communities.

: The temperature dependence of carbon use efficiency A. Growth (orange) and respiration (blue) show a unimodal thermal performance curve (TPC) with temperature. The portion of the TPC within the population's operational temperature range (OTR)-the unshaded region-can be modelled using the Boltzmann-Arrhenius (BA) equation (eq. 4 in Methods; model parameters labeled on growth rate TPC). The upper limit of the OTR is defined by T pk,µ , the temperature at which growth rate peaks. The difference in BA equation parameters between growth and respiration determines the TPC of CUE (red dashed line). B. The TPCs of the within-OTR CUE for each of 29 bacterial strains (up to 4 replicates at each temperature). The header for each plot gives the strain ID code (Supplementary Table  S1) and the bacterial genus. The red dashed line is the TPC of CUE within the OTR, calculated as the median of the responses of 1000 bootstrapped fits of the TPCs of µ and R to the Boltzmann-Arrhenius model (Methods). The red shaded area is the (bootstrapped) 95% confidence envelope around the CUE TPC. Figure 2: The thermal sensitivity of CUE varies across bacterial taxa. A Median bootstrapped E CUE with 95% confidence intervals (CIs), strains ordered by the directionality of their response, from positive to negative, and coloured by phylum. Seven strains have a lower CI that falls above zero (black, dashed line), indicating a positive CUE thermal sensitivity within the OTR. The majority of strains' CIs include zero, indicating insignificant directionality (CUE TPC is thermally insensitive). A single strain "40 RT 01" displayed a significantly negative thermal response for CUE. B There is a significant negative relationship (linear regression p = 0.00275, black line with grey confidence envelope) between the measured CUE for each strain, and its CUE thermal sensitivity (E CUE ), i.e., less efficient strains are able to increase their efficiency with temperature, while high efficiency strains cannot.
The expectation for a decreasing CUE response to temperature is based on the assumption that respi-86 ration is more sensitive to temperature (higher E) than growth. However, given our theoretical analysis, 87 our empirical results imply higher sensitivity for growth in most cases (i.e., E µ > E R ; Fig 1). We in-88 vestigated this further using our paired growth and respiration rate TPC data. Comparing the E R and 89 E µ values across strains, we find that whilst the two are positively correlated (Pearson's r = 0.432), on 90 average, E µ is significantly greater than E R (paired t 28 = 2.513, p = 0.009, Fig. 3B). To determine the 91 generality of our results, we next expanded our investigation of the difference between E µ and E R using 92 a synthesis of published data spanning a much wider diversity of bacteria 23 . We find strikingly similar 93 differences in the shape of the distributions of E µ and E R in our experimental (Fig. 3C) and literature 94 data (Fig. 3D), and find the same pattern of E µ > E R on average within the data-synthesis TPCs

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(median E µ = 0.84, median E R = 0.66, Fig. 3D). Therefore, the CUE TPC is more likely to increase or 96 be thermally insensitive, than decrease within the OTR across bacteria in general.
Thermal sensitivity, E (eV) Thermal sensitivity, E (eV) Density Density Figure 3: Variation in TPC parameters. A and B The relationship between growth rate and respiration rate for T pk and thermal sensitivity (E) respectively (1:1 lines shown). Datapoints are parameter estimates extracted from fits to empirical data (n = 29). There are five fewer points for the T pk comparison because one or both of the TPCs did not peak within the range of the data and thus T pk could not be compared (however the thermal sensitivity, E, can still be estimated for these). C Distribution of E for growth rate and respiration rate in the experimental data. Red (growth rate) and blue (respiration rate) dotted lines show median values (median E µ = 0.71, median E R = 0.65). D Distribution of E for growth rate and metabolic flux rates (proxies for respiration) from a data-synthesis of > 400 bacterial TPCs 23 (median E µ = 0.84, median E R = 0.66). Median E values in our experimentally-derived TPCs are lower then those in the data-synthesis because the former were estimated by fitting the Boltzmann-Arrhenius model and the latter using the Sharpe-Schoolfield model (Methods).
Our results yield a new understanding of the temperature dependence of microbial carbon use efficiency.

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Our study on 29 strains of environmentally isolated aerobic bacteria combined with our data-synthesis 99 goes far beyond the scope of any previous culture-based studies into the temperature dependence of CUE 100 and its underlying traits. We find that CUE typically responds either positively to temperature, or is 101 invariant with temperature within the OTR (Fig. 2). Focusing on the OTR of each strain is key here, 102 as this is the temperature range within which the population typically operates, and only in the case of 103 extreme warming events would the CUE response beyond the OTR be relevant. This general pattern 104 in the CUE temperature dependence arises due to growth rate being typically more thermally sensitive 105 than respiration rate (E µ > E R , Fig. 3B). Therefore, contrary to previous thinking, we conclude that bacterial CUE generally increases or is invariant with temperature within strain-specific physiologically 107 and ecologically meaningful temperature ranges.

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The fact that growth rates generally peak at lower temperatures than respiration rates (T pk,µ < T pk,R ,  range. This suggests that bacterial taxa are more robust to temperature change than is currently thought. Here we make precise the relationship between the temperature-dependence of CUE and that of its underlying 203 metabolic traits using a mathematical model. Consider a general equation for microbial population growth: where the change in population biomass, C, over time, t, (the growth rate, µ) is determined by the product of the carbon uptake rate, U , and an efficiency, . This is the nutrient unlimited version of a more general 206 growth equation appropriate for measurement of exponential population growth 28,47 . Although there may be 207 other sources of carbon loss to a growing bacterial population such as metabolite excretion, we assume that the 208 majority of carbon uptake is allocated to growth and respiration, i.e. U ≈ R + µ. Then, can be expressed as: 210 This is the same CUE (carbon use efficiency) measure found throughout the bacterial literature 1,2,4,11,35 (eq. Here, T is temperature in Kelvin (K), B is a biological rate, B0 is the rate at a low reference temperature 220 (T ref ), E is the activation energy (eV), ED the deactivation energy that determines the rate of decline in the 221 biological rate beyond the temperature of peak rate (T pk ), and k is the Boltzmann constant (8.617 × 10 −5 eV 222 K −1 ). The temperature-independent constant B0 includes the scaling effect of cell size, which we ignore here 223 as cell size variation is not relevant for understanding the shape of the TPC of CUE (assuming cell size does 224 not change significantly in the timescale over which CUE is measured). Substituting the full TPCs of µ and R 225 defined using eq. 3 into eq. 2 can be used to quantify the CUE TPC, and can result in a large array of shapes 226 depending upon the parameters of the µ and R TPCs (Supplementary Figure S3). However, the entire range of 227 temperatures spanned by the TPCs of µ and R in eq. 3 are not biologically relevant because organisms generally 228 live within their "Operational Temperature Range"(OTR), defined as the temperature range from some lower 229 critical temperature (e.g., 0 • C) and the temperature of peak fitness µ (henceforth denoted by T pk,µ ) 50,51 (the 230 "Phase 1" range in Fig. 1A). Additional phases of the TPCs of µ, R and CUE can also be identified -the range 231 between the temperature of peak µ and peak R and that beyond the peak of R (Phase 2 and 3 respectively in 232 Fig. 1A) -but these are also not relevant here. Within this OTR the TPCs of µ and R can be modelled simply 233 using the Boltzmann-Arrhenius function 23,30,51,52 , eq 4 (the numerator of eq. 2): This assumes that neither growth nor respiration peak within the OTR. Indeed, growth cannot peak within 236 the OTR by definition, as this is the range from the minimum growth temperature up to the peak growth 237 temperature 51 . Therefore to use the Boltzmann-Arrhenius function here, we must also assume that respiration 238 generally peaks at higher temperatures than growth, as has previously been suggested 1,24 . This expectation is 239 observed within our dataset of empirical TPCs (see supplementary information). Therefore within the OTR (the 240 typically-experienced temperature range for a strain), we can define an expression for CUE by using Boltzmann-

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Arrhenius functions (eq. 4) for growth (µ) and respiration (R) respectively, to give: The simplification of equation 5 yields a CUE function which is monotonic over the OTR, with a direction 244 defined entirely by differences in Eµ and ER. If Eµ > ER, CUE rises with temperature over the OTR, if Eµ < ER,

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CUE declines with temperature across the OTR. This is the basis for previous theoretical expectations for the 246 CUE temperature response 1 , here formalised as eq. 5. Specifically, we can approximate the denominator in eq. 247 5 using a Taylor series expansion, to obtain the following approximation for CUE: This equation has the form of a Boltzmann-Arrhenius function with: 251 and the apparent activation energy (a measure of thermal sensitivity of CUE) as Thus, the CUE TPC is necessarily monotonic within the OTR as long as T pk,µ < T pk,R (as is almost always 254 the case; see Fig. 3).

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This expression can be used to determine the direction of the CUE thermal sensitivity within the OTR as 256 follows. Recognising that the condition for CUE to decrease with temperature is ECUE < 0, we can rearrange eq 257 8 as : This simplifies to the condition 259 Eµ < ER.
That is, within the OTR, CUE increases if ER < Eµ ( =⇒ ECUE > 0), decreases if ER > Eµ ( =⇒ ECUE < 0), 260 and is insensitive to temperature if ER = Eµ( =⇒ ECUE = 0) 261 plementary table S1). These strains were isolated under a range of different temperatures for a species sorting 264 experiment, aiming to reconstruct the wide diversity of bacterial temperature fitness present in soils. We experi-265 mentally quantified the TPC of CUE for these bacteria as follows.

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At each experimental temperature, frozen bacterial cultures were revived and grown to carrying capacity at the diameters 53 , and growth in the exponential phase calculated as: where C0 is the starting biomass, C1 is the final biomass and t is the duration of the experiment. MicroResp 276 was used to give a quantitative measure of the cumulative respired CO2 produced during the growth experiment 54 .

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From this, the per-capita respiration rate was calculated in terms of carbon mass, according to: Here, Rtot is the total mass of carbon produced, C0 is the initial population biomass, µ is the previously 294 each bacterial strain as follows. We first fit the Sharpe-Schoolfield model (eq. 3, Methods) to paired growth rate 297 and respiration rate TPCs for each of the 29 strains of aerobic bacteria to determine the respective T pk,µ and 298 T pk,R , and then fitted the Boltzmann-Arrhenius model (eq. 4) to the TPC from the rate at minimum temperature 299 up to its T pk . To fit eq. 4 to the temperature dependent growth and respiration rates to each of the 29 strains in 300 our dataset, we used only those strains that had at least 3 datapoints in the temperature range lower than their 301 Shape-Schoolfield calculated T pk . We input these TPC parameters for µ and R (calculated from eq. 4) into eq. 302 5 to calculate the CUE TPC, and and its corresponding ECUE using eq. 8. All analyses and model fitting were 303 performed in R 58 , using the "minpack.lm" package for non-linear least squares fitting.

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Accounting for uncertainty in model fitting 305 To account for uncertainty in the estimated TPCs (i.e., in the parameters B0 and E; eq. 4) in our tests of 306 whether the emergent CUE responds significantly to temperature, we implemented a bootstrapping approach as 307 follows. For each strain we re-sampled the data with replacement 1,000 times and re-fit the Boltzmann-Arrhenius 308 model (eq. 4) to the sub-sampled growth and respiration dataset. As the data are paired (each CUE value 309 is derived from a growth and a respiration measurement), we re-sampled growth and respiration paired points 310 (rather than re-sampling growth and respiration separately), in order to account for their covariance. From each 311 of the paired BA model fits we calculated ECUE according to eq. 8, obtaining a distribution of these values. We 312 then calculated the 95% confidence interval for ECUE as the 2.5th and 97.5th percentiles of this distribution. We 313 asked whether or not the CIs include zero, as a robust test to determine a thermal response significantly different 314 from a temperature insensitive response (Fig. 2).

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In order to calculate a confidence envelope around each CUE TPC, we took the fitted parameters from the 316 1,000 bootstrapped curves for each strain and interpolated CUE curves across the temperature range for plotting.

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At each temperature, we took the 2.5th and 97.5th percentiles of the CUE distribution as the upper and lower 318 bounds of the 95% confidence envelope.

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Data-synthesis of bacterial thermal performance curves 320 To understand our results in a broader context, we compared the thermal sensitivities of our empirically derived µ 321 and R TPCs to those in our recent global data synthesis 23 . This data synthesis is primarily composed of growth 322 rate TPCs (416 bacterial µ TPCs), but also contains 22 bacterial metabolic flux TPCs which we use as proxies for 323 respiration rate TPCs. This is a taxonomically and functionally diverse dataset, spanning 13 bacterial phyla and 324 practically the entire range of thermal niches inhabited by bacteria. Rather than re-analyse the raw data here, 325 we directly take the Eµ and ER estimates provided and compare the distributions to those of our empirically 326 derived TPCs. The data-synthesis calculates E directly from the Sharpe-Schoolfield model (eq. 3), whereas here 327 we calculate E from the Boltzmann-Arrhenius function (eq. 4) fitted within the OTR. This is expected to cause a 328 difference in the overall magnitude of E between datasets (lower E using Boltzmann-Arrhenius due to curvature 329 as trait values approach T pk 51 ), however we emphasise this does not affect Eµ and ER comparisons within these 330 datasets, nor the comparison of distributions between these datasets.