Experimental methods have been described in detail in previous publications (Cajal-Medrano and Maske, 2005; Jiménez-Mercado et al., 2007). We ran temperature controlled, continuous cultures: 38 nutrient-limited chemostats were run between 14 and 26°C and specific growth rates (μ) between 0.05 and 6.0 day⁻¹; 10 turbidostats with non-limiting nutrient supply were cultured between 10 and 26°C with μ ranging from 28 to 62 day⁻¹. Turbidostat cultures are growing at the maximum growth rate defined by the temperature. The inoculum for the cultures was sampled in coastal waters close to Ensenada, Baja California (31.5° N, 116.5° W) or in the Gulf of California (31° N, 114.5° W) to investigate the potential importance of the origin of the inoculum on the results. The inoculum was prepared by filtering surface seawater samples through 0.8 μm polycarbonate filters (Whatman, Pleasanton, USA). Chemostat cultures were grown in 2 L and turbidostats in 1 L PTFE bottles to adjust to the rate of media consumption. Cultures were stirred with glass-encased magnets (140 rpm). Media was stored in 20 L polycarbonate containers. Apart from the media reservoir and the stirrers, all contact surfaces were either Teflon or silicon. All material in contact with cultures was previously sterilized. Pumping was by valve-less pumps (FMI) installed in the culture outflow to avoid contamination. Experimental methods have been described in detail in previous publications (Cajal-Medrano and Maske, 2005; Jiménez-Mercado et al., 2007).

Media was natural seawater aged for several months, ozonified and aged again; during the aging the media was filtered several times through GFF filters (Whatman, Buckinghamshire, England; 0.75 μm pore size). The aged seawater was supplemented with 20 or 100 μM glucose for the chemostats and turbidostats, respectively. Inorganic nutrients were added to the seawater as follows: (a) chemostats: 20 μmole L⁻¹ NH₄Cl, 5 μmole L⁻¹ KH₃PO₄, 0.5 μmole L⁻¹ FeCl₃; b) turbidostats: 182 μmole L⁻¹ NH₄Cl, 43 μmole L⁻¹ KH₃PO₄, 2 μmole L⁻¹ FeCl₃), and then acidified by percolating 450 mL min⁻¹ CO₂ for 5 min before autoclaving to avoid precipitation. After autoclaving the media was equilibrated by aeration with sterile air to return to saturated oxygen concentrations at room temperature. The sterility of the medium was regularly tested by passing a small volume of it into a ZoBell-enriched culture vessel.

The cultures were sampled at steady state when cell abundance stayed constant in chemostats for 2 days with steady state defined by less than 20% changes in cell abundance (Cajal-Medrano and Maske, 2005; Villegas-Mendoza, 2015); the steady state was reached after 3–19 days and there was no clear relation between this period and the dilution rate or the type of inoculum. In turbidostats the dilution rate was adjusted to maintain the cell abundance (X) constant. The steady state was defined by <10% change and it was reached after 10 h or more; the period was approximately inversely related to the maximum growth rate (Jiménez-Mercado et al., 2007). At steady state the specific growth, μ in chemostats and turbidostats was assumed to be equal to the dilution rate D, where D (d⁻¹) = F/V, with F equal to the flow rate (L d⁻¹) and V is the culture volume (L). In the case of turbidostats we adjusted the estimate of the growth rate taking into account the change in cell abundance over time prior to sampling, according to (3)μ=D+ln(X1X2−1)Δt−1

X₁ and X₂ are the microbial abundances at time 1 and 2 respectively; Δt is the time interval in days between times 1 and 2.

We repeated some of the experiments using the same dilution rates and temperatures but with inoculum from the same site or from different locations but found no pattern (Cajal-Medrano and Maske, 2005; Jiménez-Mercado et al., 2007). The data of each repeat were included in our analysis as individual culture results.

Chemostat samples for epifluorescence microscope counts of microbes were collected daily from the culture outflow in scintillation vials and fixed with formaldehyde (2% final concentration). Turbidostat samples were collected several times per day. Samples were filtered on 0.2 μm black polycarbonate filters (Poretics) and stained with DAPI (Molecular Probes) (Turley and Hughes, 1992). Between 350 and 1,200 cells per sample were counted using wide-field epifluorescence microscopes with 100 x objectives. We observed no contamination of the cultures with protists.

Particulate organic carbon and nitrogen samples from the culture suspension and the fresh medium were taken at the end of the experiments by filtering a volume of 300–400 mL using combusted (450°C, 2 h) glass fiber filters (GF/F, Whatman) with an effective pore size of 0.3 μm (Nayar and Chou, 2003) mounted in pre-combusted filter holders. Combusted GF/F filters are expected to retain all bacteria due to their reduced pore size after combustion (Nayar and Chou, 2003). The filtered samples and blank filters were lyophilized before analysis with a CHN analyser (Marine Science Institute, UCSB). We tried a second filter placed under the sample filter to correct for adsorbed organics (Maske and Garcia-Mendoza, 1994) but found that it did not significantly change the results. For some cultures two or three filter samples were taken and the results averaged. The prokaryote carbon biomass (C_b) was calculated from the difference of particulate organic carbon (POC) in cultures minus POC in the media supplying the cultures.

CO₂ respired was calculated as previously explained (Cajal-Medrano and Maske, 2005): in short, the culture or medium samples were titrated with HCl at 25°C using an automatic potentiometric technique in a closed titration cell (Hernández-Ayón et al., 1999; Dickson et al., 2007). A PC was used for controlling the syringe pump and storing the digitized pH data. Total CO₂ (TCO₂) was calculated directly from the derivative of the titration data, giving two inflection points from which total carbonate and alkalinity are computed. The precision of our titration is in the range of 0.15–0.4% (C.V.), equivalent to 3–8 μmol TCO₂ L⁻¹. The performance of our method was assessed by titrating seawater certified reference material (CMR). In average, we found a difference with the true value of TCO₂ of 8.9 ± 1.5 μmol kg⁻¹ (n = 3 samples of CMR). This variability is similar to that found by Camiro-Vargas et al. (2005) with samples of microalgae cultures and higher than Hernández-Ayón et al. (1999) with filtered seawater samples (8 μmol kg⁻¹ for TCO₂).

The difference of total CO₂ between culture and media yielded C_r. Assuming steady state the rate of CO₂ produced is given by D C_r (μM CO₂ day⁻¹). The specific respiration rates were then calculated by dividing this rate by the steady-state biomass (4)r=D Cr Cb−1

We are implicitly assuming that the mean residence time of all elements in the cultures is D⁻¹ (day).

Samples for 16s rRNA gene (rDNA) amplicons were collected from last four cultures at steady state by filtering 250 mL of each culture. The total genomic DNA was extracted using the “Gentra Puregene Yeast/Bact Kit” according to the manufacturer's protocol (Qiagen, Valencia, CA, USA). Nucleic acids were sent to the Research and Testing Laboratory (Lubbock, TX, USA) for 454-pyrosequencing. Primers 28F (5′-GAG TTT GAT CNT GGC TCA G-3′) and 519R (5′GTN TTA CNG CGG CKG CTG-3′) were used for amplification of the variable regions V1-V3 of the bacterial 16S rRNA gene (La Duc et al., 2012). We did not attempt to detect the archaea community. Pyrosequencing reads were processed according to the protocol of the sequencing company (http://www.rtlgenomics.com/docs/Data_Analysis_Methodology.pdf), including de-multiplexing (SFF file generation), denoising, chimera detection, and taxonomic analysis using the NCBI database. The taxonomic levels used in the data analysis were based upon the following criteria; 97% identity (<3% divergence) were applied to resolve the species level, between 95 and 97% were used to define the genus level. The four sequences are published together with six more sequences in the NCBI database (https://www.ncbi.nlm.nih.gov/Traces/study/?acc=SRP099306) for public access purposes. The four sequences can be identified by the growth rate (μ: 0.2, 0.37, 0.8, 0.93 day⁻¹) given in the data bank.

In the discussion below we compare our data with recent data reviews (Makarieva et al., 2008; DeLong et al., 2010). For this comparison, we used the conversion factors given in these publications to arrive at units used in our work: ratios of dry-weight to wet-weight = 0.3, carbon to dry-weight = 0.5, respiration coefficient (RQ) of 1.0, and 20 J (ml O₂)⁻¹.

To facilitate data comparison we provide Q₁₀ values. The Q₁₀ was calculated from the median temperature of the data set, because in the case that the data follow the Arrhenius model the Q₁₀ values change for different temperature intervals.

All data were included in this data analysis without excluding outliers. Data from repeated experiments were treated the same as other experimental results. Type 2 regressions were calculated using the Matlab routine lsqfitma.m (http://www3.mbari.org/Products/Matlab_shell_scripts/regress/). Type 1 regressions were used when the abscissa was temperature.

To show that the bacterial community in the chemostat cultures maintained species richness we estimated the microbial community based on pyrosequencing of 16S rDNA amplicons in the four most recent chemostat experiments (μ: 0.2, 0.37, 0.8, 0.93 day⁻¹). The sequence data indicated that, when the cultures were terminated each culture community still included between 77 and 91 OTUs. In the four cultures the prevalent clades were Roseobacter, Thalassospira xiamenensis, Rhodococcus, Sulfitobacter, and Marinobacter.

The growth rate in nutrient-limited chemostats is controlled by the dilution rate, so no relationship of growth rate with temperature is expected, but the respiration rate could vary with temperature. In the turbidostat cultures the growth rate was controlled by temperature (Jiménez-Mercado et al., 2007) and the relationship (μ vs. T) is described by Equation 5 (Table 2). The relationships of specific respiration (r) and growth (μ) rate for all cultures are shown in Figure 1. The μ data of the chemostats (circles) range below 10 day⁻¹ and turbidostat (filled circles) above 10 day⁻¹. From Figure 1 it is obvious that the chemostat cultures behaved differently from the turbidostat cultures; chemostats showed a general increase in r with μ (Equation 6), whereas in turbidostats r decreased with higher μ (Equation 7). The data in Figure 1 are color coded for temperature and the growth rate increase with higher temperature in turbidostats (Equation 5) can be easily observed. Our experimental data (T, μ, r) are provided as supplemental data.

In the chemostats, r showed no trend with temperature, but in the turbidostat cultures the specific respiration decreased with increasing temperature (Figure 2). The data could be described by a linear Type 1 regression, (Equation 8) and followed a Q₁₀ of 0.4. The different patterns of chemostat and turbidostat r vs. μ in Figure 1 resulted in different patterns in growth efficiency (Y) with temperature. Figure 3 shows the relationship between Y and temperature; the Y of chemostats extended over the same data range as the turbidostat data, but showed no significant trend with temperature with an average value of Y = 0.34. The turbidostat data increased exponentially (Equation 9), corresponding to a Q₁₀ of 2.6.

Figure 1 and Equation (6) (Table 2) show a clear difference in temperature response between nutrient-limited chemostat cultures and temperature limited turbidostat cultures. Because of the relative constancy of the r over μ ratio, the growth efficiency (Y) of chemostats showed no clear trend with growth rate and none with temperature (Figure 3). The pattern was very different from the turbidostat data in which the growth rate increased with temperature, but r decreased, resulting in an increase in Y with temperature (Equation 9). In Figure 3 the turbidostat data show a temperature dependence with a Q₁₀ of 2.6. This value is very different from Q₁₀ values reported for Y of microbes in a salt marsh estuary, ranging from −1.3 below 15°C to −3.6 between 15 and 30°C (Apple et al., 2006).

In a data review Yvon-Durocher et al. (2012) suggested a strong dependence of ocean ecosystem respiration with temperature. Rivkin and Legendre (2001) calculated a trend of decreasing Y with increasing temperature, using literature data of respiration spanning a wide range of latitudes based on in situ microbial production and DOC uptake or oxygen consumption in the dark of filtered (<1 μm) samples. They proposed that this trend may result from increasing respiration rates with temperature. White et al. (1991) showed a tendency of increasing growth rates with chlorophyll concentrations. Assuming that chlorophyll is inversely related to ocean temperature on global scales, then the trend observed by Rivkin and Legendre (2001) is perhaps a combined effect of temperature and substrate availability, as suggested by López-Urrutia and Morán (2007). Apple et al. (2006) also measured a change in the ratio of community respiration to microbial production with temperature in samples (<1 μm) taken in different parts of an estuary and during the annual cycle, resulting in a decrease of Y with temperature. Rivkin and Legendre (2001) and Apple et al. (2006) based their arguments on volumetric rates, because they lacked microbial biomass information; consequently their data do not lend themselves to physiological interpretations based on specific rates, as pointed out in relation to Equation (2).

Turbidostat cultures yielded the highest values of Y near 0.8 (Figure 3) which are high compared to reviews of Y for planktonic bacteria (del Giorgio and Cole, 1998; López-Urrutia and Morán, 2007). Even the average value of Y = 0.34 of the chemostats (Figure 3) is higher than most oceanographic reports (López-Urrutia and Morán, 2007), but similar to mesocosm results (Dinasquet et al., 2013). In glucose-limited chemostat cultures (25°C, dilution rate 2.4 day⁻¹) of a proteorhodopsin containing marine bacterium Courties et al. (2015) reported an average Y of 0.57; using Equation (2) we calculated their specific respiration rate to be 1.8 day⁻¹ which would place their result close to our regression in Figure 1. We suggest that our high Y values are due to different aspects of our methodological approach: the use of glucose as an easily metabolized substrate; and the calculation of Y based on the measurement of respired CO₂ and POC to define microbial biomass. The POC included not only living biomass but also detritus formed by the microbial community and retained by the sample filter. Because the central role of microbes in the ocean is the conversion of dissolved organics into particles that then enter the trophic web, the efficiency of the formation of all particulate organics from dissolved organics is relevant for ecological interpretations. We expected that the use of glucose as a substrate would support a high Y because glucose is easily assimilated, and because an organotrophic community that is mainly consuming a single type of substrate does not need to invest in diverse assimilation machinery. The relatively high Y might also be supported by the continuous cultures methodology which selects for the actively growing population and selects against slow growing or dormant cells. These latter cells would reduce community Y by adding to respiration without biomass formation.

The temperature response of the cellular carbon demand rate of microbial communities can help in the interpretation of carbon cycling in the ocean. A better metric for the quantification of metabolic activity should be the cellular carbon demand rate (b) that includes the formation of carbon biomass and respired carbon, anabolism and catabolism. b is used here as a proxy for overall metabolic activity: (5)b=ρ+q (fmol C (cell day−1)

ρ = rM and q = μM (Table 1). Figure 4 is cast in the linearized form of the Arrhenius plot, with the natural log of b plotted against the inverse of temperature. Chemostat data indicated no trend in Figure 4, but turbidostat data showed a strong increase in b with temperature (Equation 10). For the midpoint of the slope we calculated a Q₁₀ of 8.1. This Q₁₀ was higher than values for physiological rates found in the literature, for example Q₁₀ values between −1 and 4.4 were reported for different physiological rates of microbes in a salt marsh estuary (Apple et al., 2006).

Allometry scales the metabolic activity (MA) of an organism to its biomass (M), for example: MA = M^∧Exp. The exponent (Exp) defines the allometric properties of groups of organisms and can be included in numeric ecosystem models. Historically Exp was expected to be <1.0, thus the specific metabolic activity of an organism decreased with its biomass. Makarieva et al. (2005, 2008) argued that the ratio of metabolic activity to biomass was similar across the full organismal size range of the different groups, but DeLong et al. (2010) showed that different groups of organisms had specific allometric exponents. For prokaryotes they found Exp ~ 2.0. In their reviews Makarieva et al. (2005, 2008) and DeLong et al. (2010) used published respiration rates from monospecific prokaryote cultures as a metric for metabolic activity after converting respiration rate to power (Watt). They used wet weight for the size of the organism for easier comparison between different groups of organisms. Both publications adjusted metabolic rates for easier comparison to 20 or 25°C using a Q₁₀ = 2.0. For a comparison of our data with their prokaryote data sets we converted their values to cellular respiration (ρ, mol C cell⁻¹ day⁻¹), cellular carbon (M, mol carbon cell⁻¹), and adjusted the rates to the original experimental temperatures using the same conversion factors as in the reviews.

In Figure 5A we compare the cell carbon (M) to specific respiration rate (r); in turbidostat cultures r decreases with carbon-rich cells and shows a clear trend with temperature indicated by symbol color. The chemostat r partially overlaps with the data from Makarieva et al. (2008), but our r values are significantly higher than the values listed by Makarieva et al. (2008), median: 0.162 day⁻¹. Neither data set shows a trend in r/M space or with temperature. In Figure 5B we show the same data as in Figure 5A but converted to cellular respiration rate (mol C cell⁻¹ day⁻¹). All data show significant relations with cellular carbon (M). The data of Makarieva et al. are lower than our chemostat data. The Makarieva et al. data show the steepest data slope (Equation 14), a lower slope for chemostats (Equation 12) and the lowest for turbidostats (Equation 13). The coloring of the data points only indicates a trend with temperature for the turbidostat data.

DeLong et al. (2010) and Makarieva et al. (2008) used respiration rate as a metric for metabolic activity but the respiration rate is considering only the catabolic part of metabolic activity and neglects the anabolic part (Figure 5). Data provided by DeLong et al. (2010) allowed to calculate b but only for 20°C, so in Figure 6 we compare their b with the values from chemostat and turbidostat at experimental temperature. Data from DeLong et al. (2010) show cellular carbon demand rates between our chemostat and turbidostat data. Turbidostat data show a strong relationship (Equation 16), but DeLong et al. (Equation 17) and the chemostat data (Equation 15) are noisier. The slope for DeLong et al. (2010) is significantly steeper than for our data, implying that the specific carbon demand rate, b increases more strongly with bigger cells. We do not have the data to evaluate if this behavior is related to the adjustment to 20°C of the data in DeLong et al. (2010).

The comparison of our data with the literature data yields a similar cellular carbon range but different patterns of respiration, growth and carbon demand rate. Our chemostat metabolic rates are higher than the data listed by Makarieva et al. (2008). This might be related to the much higher biomass densities of the cultures in the cited literature, which might affect the physiological state of the culture. Turbidostat data always show the highest metabolic rates and a data pattern that is statistically better defined, but with a different trend from chemostat and literature data. The chemostat data always show lower correlation coefficients than either turbidostat or the literature data. The relatively well-defined statistical trend in the literature data is surprising considering that a wide range of different methods was used for cultivation, to measure either respiration or cell size. We propose that one reason why the literature data have relatively high correlation coefficients is that they are based on mono-specific cultures, whereas we used bacterial communities in our continuous cultures. The turbidostat cultures probably behaved more like the mono-specific cultures because the strong selection for nutrient-replete, temperature-controlled growth forced a strong selection minimizing the community interaction.

When comparing our culture results with oceanographic data it should be considered that oceanographic research is still struggling with the measurement of basic metabolic rates. We still lack sufficiently sensitive and generally accepted methods that allow the determination of microbial respiration using short incubation times without pre-incubation size filtration, methods that would minimize physiological changes during incubation (Pomeroy et al., 1994) and changes in taxonomic composition (Gattuso et al., 2002). Methodological differences such as potential overestimation of microbial oxygen respiration rate measurement using the Winkler technique in the field (Apple et al., 2006; Wong and Li, 2009) and our use of CO₂ determination under steady state conditions could partly be responsible for the difference in average Y found in our chemostat data and the lower average growth efficiency reported in the oceanographic literature. Another possible explanation might be the documented, but as yet unexplained variation in respiratory quotient (Berggren et al., 2012; Romero-Kutzner et al., 2015). Our main conclusion is that the specific respiration of prokaryote communities under substrate limited growth condition shows no trend with temperature in the range of temperature tested in our study. The carbon demand rate in chemostat cultures (Figure 4) or the specific or cellular respiration rate in mono-specific culture data from the literature, or in our chemostat data, did not show patterns related to temperature or cell carbon (Figures 5A,B). In contrast, current ecological modeling approaches consider adjustments of metabolic rates based on temperature and on the biomass of the organism using, for example the metabolic theory in Ecology (MTE; Brown et al., 2004; Allen et al., 2005). The temperature adjustment in MTE is based on Arrhenius-type temperature adjustment, but other models use Q₁₀ as an alternative scaling of metabolic activity to temperature. The concept of temperature adjustment of metabolic rate is based on cultures growing at temperature limited rates, which is probably a rare occurrence in aquatic environments. For the ocean the respiration rates of bacteria communities currently cannot be adjusted with temperature response functions.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.