Influence of Phosphorus and Cell Geometry on the Fractionation of Sulfur Isotopes by Several Species of Desulfovibrio during Microbial Sulfate Reduction

We investigated the influence of organic substrates and phosphate concentration on the rates of dissimilatory microbial sulfate reduction and the 34S/32S isotopic fractionation produced by several Desulfovibrio species. Our experiments corroborate the previously reported species-specific correlation between sulfur isotope fractionation and cell-specific sulfate reduction rates. We also identify cell size as a key factor that contributes to the species-effect of this correlation. Phosphate limitation results in larger cells and contributes to a small decrease in sulfur isotope fractionation concomitant with an apparent increase in cell-specific sulfate reduction rates. Sulfur isotope fractionation in phosphate-limited cultures asymptotically approaches a lower limit of approximately 5‰ as cell-specific sulfate reduction rates increase to >100 fmol cell−1 day−1. These experimental results test models that link the reversibilities of enzymatic steps in dissimilatory sulfate reduction to sulfur isotope fractionation and show that these models can provide consistent predictions across large variations in physiological states experienced by sulfate reducing bacteria.


INTRODUCTION
The oxidation of organic matter by sulfate reducing bacteria (SRB) is a globally distributed anaerobic process that influences the redox state of the Earth's surface and the preservation of organic matter in sediments (Jørgensen, 1982;Westrich and Berner, 1984;Widdel and Hansen, 1992;Shen and Buick, 2004). Microbial sulfate reduction (MSR) fractionates sulfur isotopes, producing sulfide depleted in heavier isotopes. The magnitude of this fractionation ( 34 ε, defined in Equation 6) is a critical parameter for reconstructions of the carbon and sulfur cycles through Earth history (Holland, 1973;Garrels and Lerman, 1981;Berner, 2001;Luo et al., 2016). For over half a century, many investigators have attempted to understand factors that affect sulfur isotope fractionation during MSR. Dozens of studies have reported fractionations produced in pure cultures of sulfate reducing organisms under controlled laboratory conditions (e.g., Harrison and Thode, 1958;Thode et al., 1961;Kaplan and Rittenberg, 1964;Chambers et al., 1975;Chambers and Trudinger, 1979), in experiments with natural microbial populations (e.g., Canfield, 2001;Canfield et al., 2010) and under in situ conditions (e.g., Jorgensen, 1979;Rudnicki et al., 2001;Wortmann et al., 2001).
Marine sulfides exhibit a wide range of sulfur isotope compositions, ranging up to a 70 depletion in the 34 S/ 32 S ratio relative to that of the sulfate from which they were formed (Thode et al., 1953;Kaplan et al., 1963;Canfield and Teske, 1996). Because early laboratory studies could not reproduce fractionations of this magnitude in pure culture, they established a limit of 47 for single-step microbially mediated sulfate reduction (Kaplan and Rittenberg, 1964). Thus, for many decades, large fractionations (>47 ) between sulfate and sulfide in rocks and natural environments were interpreted as evidence for oxidative recycling of sulfides or microbial disproportionation of intermediate sulfur species (e.g., Canfield and Thamdrup, 1994;Habicht and Canfield, 2001;Johnston et al., 2005). Recently, one bacterium (Desulfovibrio sp. DMSS-1), has been shown to produce fractionations that exceeded the 47 limit (Sim et al., 2011a). The largest fractionations (up to 66 ) are produced during slow growth with glucose as the electron donor. This approaches the theoretical limit of 70 proposed for microbial sulfate reduction by Brunner and Bernasconi (2005).
Here, we test this hypothesis by measuring sulfur isotope fractionations produced during dissimilatory sulfate reduction by several Desulfovibrio species (D. fructosovorans, D. inopinatus, and DMSS-1) grown in batch cultures on various substrates. We also examine the effect of phosphate limitation on sulfur isotope fractionation by SRB. Phosphate is an essential nutrient and a component of DNA, RNA, lipid membranes, and the energy carrier ATP that is used to activate sulfate during MSR (Peck, 1960;Cypionka, 1995;Muyzer and Stams, 2008). Its concentrations in oceanic and sedimentary environments may limit the growth of sulfate reducing bacteria in some natural environments (Bosak et al., 2016) and may have varied dramatically through Earth's history (Planavsky et al., 2010). Therefore, limitation by this essential nutrient may directly influence both the rates of sulfate reduction and the observed sulfur isotope fractionation.
Our results confirm a strong dependence of 34 ε on organic substrates. The data are generally consistent with an inverse correlation between 34 ε and csSRR. Offsets and deviations among SRB species appear to be rooted in morphological and physiological differences. Further offsets from the general inverse correlation may arise from intracellular responses to phosphorus starvation (Bosak et al., 2016). Comparisons of our data with predictions from recent efforts to numerically simulate isotopic signals produced via dissimilatory sulfate reduction (Wing and Halevy, 2014) test the predictions of these models over a range of conditions that sulfate reducing bacteria can experience in nature.

Cultures
Three SRB species were used in this study: Desulfovibrio inopinatus, Desulfovibrio fructosovorans, and Desulfovibrio sp. DMSS-1. As is common in studies of isotope fractionation by SRB, experiments were conducted in batch cultures. Isotope fractionation trends that were first identified from batch cultures have been confirmed by chemostat experiments in which steadystate conditions can be maintained (Sim et al., 2011a,b;Antler et al., 2017). Therefore, we consider batch cultures suitable for this study. Experimental cultures were grown on different substrates (lactate, fructose, malate, and/or pyruvate) and/or in media with different initial phosphate concentrations (from <1 µM to >1 mM) and with excess sulfate as described below.
Culture medium was supplemented with lactate (28 mM), malate (28 mM), or fructose (14 mM) as organic substrate and sole electron donor. Initial concentrations of organic substrates were chosen such that sulfate would be in excess: sulfate reduction with stoichiometric conversion of any substrate to acetate would produce only ∼14 mM of sulfide from the initial 21 mM sulfate, see Table 1. For each experiment, 7-15 bottles were inoculated with 5% (v/v) of a mid-to late-exponential phase pre-culture grown on the same organic substrate as that used in the experiment. Inoculums were pelleted via centrifugation and rinsed three times with clean medium in an anaerobic chamber (under an atmosphere of 80% N 2 , 15% CO 2 , and 5% H 2 ) to ensure the removal of all residual sulfide and organic substrate, and then transferred into 40 mL of fresh media. Bottles were incubated in the dark at room temperature. Microbial growth was monitored daily in one "master" bottle to minimize puncturing of septa of the experimental bottles. At each time point (Tables 2,  3), one experimental bottle was subsampled for cell counts and the colorimetric assay of sulfide concentration. The remaining culture volume was sacrificed by the addition of a 1 M zinc acetate solution (at a 10% v/v ratio) to terminate microbial activity and precipitate sulfide as ZnS for isotopic analyses.
To test the effect of phosphate limitation, additional batch cultures were grown with varying initial concentrations of phosphate in the medium. Serum bottles used for these cultures were autoclaved three times with deionized water (18.2 M ·cm, Barnstead Nanopure TM filtration system) to remove residual phosphate. Medium was prepared as described above, with lactate (28 mM) as organic substrate and without added phosphate. Phosphate (as KH 2 PO 4 ) was then added from a concentrated stock solution, to final concentrations of 150, 15, and 3 µM. Another set of serum bottles did not receive any added phosphate. The concentration of phosphate in this nominally "0" phosphate medium was estimated to be <1 µM based on lot analyses provided with the chemicals used in the media (see also Experiments with Different Phosphate Concentrations). Figure A2 shows that ∼3 to 5 µM of added phosphate is limiting, suggesting that the blank is likely <5 µM. Conclusions reached in this paper would be unaffected by a blank of 5 µM or less. Experimental bottles (containing 10 mL of fresh media) were inoculated with a 5% (v/v) sample of pre-cultures that were already conditioned to growth in the presence of lower or limiting concentrations of phosphate. Cell densities were low when phosphate was limiting, so inoculums were pelleted and rinsed only once to minimize the loss of biomass prior to inoculation. Cultures were monitored and sampled as described above.

Desulfovibrio fructosovorans
Desulfovibrio fructosovorans strain JJ (cat. no. 3604) was obtained from DSMZ. This strain was isolated from estuarine sediment (Jones et al., 1984;Cord-Ruwisch et al., 1986), and it incompletely oxidizes pyruvate, lactate, or fructose to acetate (Ollivier et al., 1988). The mineral medium (modified from DSMZ recipe #63) contained (per liter): NaHCO 3 , 2.6 g; Na 2 SO 4 , 3.0 g; KH 2 PO 4 , 0.30 g; NH 4 Cl, 0.50 g; KCl, 0.20 g; CaCl 2 , 0.10 g; MgCl 2 , 2.0 g; resazurin, 1 mg; SL-10 trace element solution (see above), 1 ml; vitamin solution #141 (see above), 10 ml; and sodium ascorbate, 1.5 g (see above). Media were supplemented with limiting concentrations of one of the following organic substrates: lactate, 20 mM; pyruvate, 40 mM; or fructose, 10 mM. The starting concentrations of lactate, fructose, and pyruvate were chosen such that 10 mM of sulfide would be produced by stoichiometric conversion of the substrate to acetate ( Table 1). The pH of the medium was adjusted to 7.0 before inoculation. Bottles for all experiments with D. fructosovorans were inoculated with 5% (v/v) of a late-exponential phase pre-culture grown on lactate. Media and cultures were otherwise prepared and maintained as described for Desulfovibrio inopinatus above.
Desulfovibrio sp. strain DMSS-1 Desulfovibrio sp. DMSS-1 (henceforth "DMSS-1"), isolated from a salt marsh on Cape Cod, Massachusetts, USA and characterized by Sim et al. (2011b), was grown in batch cultures in the presence of varying concentrations of phosphate. Serum bottles were cleaned and prepared in the same manner as described above for D. inopinatus. Medium for DMSS-1 was prepared following Sim et al. (2011b), with the exception of phosphate, and contained (per liter): NaHCO 3 , 9 g; Na 2 SO 4 , 3 g; NH 4 Cl, 0.3 g; NaCl, 21 g; KCl, 0.5 g; MgCl 2 ·6H 2 O, 6 g; CaCl 2 ·2H 2 O 0.3 g; resazurin, 1 mg; SL-10 trace element solution (see above), 1 ml; vitamin solution #141 (see above), 10 ml; 1 ml of selenium stock solution (0.4 mg of Na 2 SeO 3 per 200 ml of 0.01 N NaOH); and sodium ascorbate, Reaction stoichiometry from Cord-Ruwisch et al. (1986), Thauer et al. (1977), and Sim et al. (2011b). Values of ∆r G • ' are given at 298 K and 1 bar for a hypothetical ideal-dilute solution with unit activity of solutes at concentrations of 10 −7 M for H + and 1 M for all other aqueous species. a Standard Gibbs energies were calculated using the CHNOSZ software package (Dick, 2008) from thermodynamic data (Shock and Helgeson, 1988;Shock, 1995;Amend and Plyasunov, 2001;Wagner and Pruß, 2002;Dalla-Betta and Schulte, 2009) compiled in database updates to the SUPCRT92 program developed by Johnson et al. (1992). b Gibbs energies of reaction were calculated at 25 • C for medium compositions resembling those used for D. fructosovorans (see Methods), assuming 10% conversion of initial SO 2− 4 to HS − with stoichiometric changes in concentrations of other reactants and products. Activity coefficients were assumed to be unity and pH was held constant at 7.0. All dissolved inorganic carbon was assumed to be as HCO − 3 , and all sulfide as HS − .   (Ku, 1969 1.5 g (see above). Phosphate was added to final concentrations of 360, 36, 5 µM, and "0" (<1 µM).

Cell Counts and Sulfide Assays
Growth was monitored using optical density (OD) measurements and microscopic cell counts. OD was measured at 630 or 660 nm using a spectrophotometer (Synergy 2 microplate reader, BioTek, Winooski, Vermont, USA). For cell counts, subsamples of experimental cultures were preserved in 2.5% glutaraldehyde at 4 • C. Preserved cells were stained with SYBR Green I nucleic acid stain (Invitrogen Molecular Probes, Eugene, Oregon, USA), and filtered onto Whatman 0.2 µm Nuclepore polycarbonate filters. Stained cells were visualized and imaged by epifluorescence microscopy using a Zeiss Axio Imager M1 microscope (Carl Zeiss Microscopy, LLC), and cell densities were determined by manual counting (Noble and Fuhrman, 1998). Cell lengths and widths were measured in the epifluorescence micrographs using measuring tools in Zeiss AxioVision software.
Sulfide from subsamples was precipitated as ZnS in a 50 mM zinc acetate solution, and stored at 4 • C until analysis. Sulfide concentrations ( H 2 S = H 2 S + HS − + S 2− ) were determined by a modified methylene blue colorimetric method (Cline, 1969). Briefly, 200 µL samples of medium were reacted with 1 ml of 0.05 M zinc acetate and 10 µL of N,N-dimethyl-pphenylenediamine sulfate solution. Optical density was read at 670 nm using a microplate reader (Sim et al., 2011b).

Sulfur Isotope Ratios
Sulfide was extracted for isotopic analysis by acidifying each ZnS sample with 3 to 6 M HCl, and gently boiling for 1 h under a stream of N 2 gas. Sulfate in samples were then converted to H 2 S using a general reducing agent (HCl, HI, and H 3 PO 2 ) (Thode et al., 1961;Forrest and Newman, 1977;Arnold et al., 2014). Volatiles were passed through a condenser and a distilled H 2 O trap. H 2 S produced in the reactions was precipitated as ZnS in zinc acetate, and then converted to Ag 2 S via addition of silver nitrate, or precipitated as Ag 2 S directly in a silver nitrate solution. The recovered Ag 2 S was washed with deionized water, dried at 70 • C, and converted to SF 6 by reaction with F 2 at 300 • C overnight. The SF 6 product was purified by cryogenic trapping and preparative gas chromatography, and analyzed on a ThermoFinnigan MAT 253 isotope-ratio mass spectrometer operated in dual-inlet mode as described previously (Ono et al., 2006).
Sulfur isotope values are reported in the standard δ notation against Vienna Cañon Diablo Troilite (VCDT): Following IUPAC recommendations (Coplen, 2011), we have omitted the factor of 1000 from the definition of δ in Equation 1.

Calculations
Specific growth rates (k) for the cultures were calculated using an exponential growth equation (Monod, 1949): where N x and N 1 are the cell densities (number of cells per milliliter) at t x and t 1, respectively (Sim et al., 2011b). Growth rates calculated in this manner represent an average of the cumulative growth of the organism over the time interval between the beginning of exponential growth (t 1 ) and the time at which the sample was taken (t x ).
Cellular growth yields (Y) were calculated with respect to amount of produced sulfide: 1 (3) The cell-specific sulfate reduction rate (csSRR) is defined as the amount of sulfate reduced per cell per unit time, and can be described as: In a batch culture, isotopic fractionation factors can be determined from a Rayleigh distillation equation for closed systems. Here, we use the measured isotopic composition of the produced sulfide (δ 34 S sulfide ) to calculate the fractionation factor α, assuming isotopic mass balance between sulfide and remaining sulfate: where δ 34 S initial and δ 34 S sulfide are the measured isotopic compositions of the initial sulfate in the media and the produced sulfide respectively, and f is the fraction of initial sulfate that remained at the time of sampling. The value of f is calculated from measured H 2 S concentrations and assuming that all consumed sulfate was reduced into sulfide. The isotopic enrichment factor ( 34 ε) is defined as: According to this definition, positive 34 ε values represent depletion of 34 S in sulfide with respect to sulfate.
1 Cellular yield (Y) has units of cells per mole sulfate. It is a measure of the number of cells supported by a given amount of transferred electrons. Relating Y to biomass yield (i.e., g mol −1 ) requires accounting for cell size differences. Cultures of D. fructosovorans grew in media with fructose, pyruvate, or lactate as the organic substrate. Exponential growth was observed within 2 to 3 days, and experiments lasted for 7 days (Figure A1). Growth rates (k) on all three substrates ranged between 0.6 and 1.5 day −1 . Cultures of D. inopinatus grew in media that contained fructose, malate or lactate as the electron donors. Growth experiments with D. inopinatus lasted 14, 20, and 43 days, respectively, for cultures grown on lactate, fructose and malate, respectively, due to the longer lag phase ( Figure A1). Growth rates of D. inopinatus in cultures grown on fructose and lactate were similar (0.40 and 0.44 day −1 , respectively), but were lower during growth on malate (0.17 day −1 ). Sulfide concentrations in all cultures increased with the increasing cell densities ( Figure A1). Cultures of D. inopinatus grown on malate produced more sulfide (up to 18 mM) than the 14 mM concentration predicted by incomplete malate oxidation (Table 1), perhaps indicating that some of the malate may have been oxidized completely to CO 2 or to small organic compounds. D. inopinatus cells were both longer and wider than cells of D. fructosovorans and DMSS-1 (Figure 1). Cell morphology appeared to be mostly independent of organic substrate ( Table 4), but small, measurable differences were observed in some cultures of D. inopinatus. Cells of D. inopinatus were on average ∼1 µm longer when grown on malate compared to fructose or lactate, and slightly wider (by ∼0.3 µm) when grown on fructose compared to malate or lactate. Cells of D. fructosovorans grown on different substrates did not exhibit measurable differences.

Experiments with Different SRB Species and Substrates
Calculated sulfur isotope enrichment factors ( 34 ε) ranged from 13 to 31 in D. fructosovorans cultures and from 10 to 40 in D. inopinatus cultures ( Table 2). The smallest 34 ε values (averaging 13 and 11 for the two species, respectively) were observed in cultures grown on lactate. When grown on fructose, both bacteria exhibited 15-17 larger 34 S/ 32 S fractionations. The highest enrichment factors, up to 40 , were observed in the cultures of D. inopinatus grown on malate ( Table 2).

Experiments with Different Phosphate Concentrations
Data shown in Table 3 are from experiments that test the effect of variable phosphate concentrations on D. inopinatus and DMSS-1. Cultures grown in media containing initial phosphate concentrations ≤15 and ≤5 µM for D. inopinatus and DMSS-1, respectively, had smaller growth rates and cell densities relative to cultures grown at higher phosphate levels (≥150 and ≥36 µM; Figure A2). At the lowest phosphate concentration (nominally <1 µM), the optical density of D. inopinatus increased slowly, but that of DMSS-1 did not increase over a period of 43 days. Sulfide was produced under all tested conditions, though D. inopinatus and DMSS-1, produced only up to 2.3 and 0.3 mM of sulfide, respectively, when no phosphate was added to the growth media (Figure 4). Growth rates and csSRR of D. inopinatus and DMSS-1 were the highest at 15 and 36 µM phosphate, respectively.
Low phosphate concentrations strongly influenced the cell morphology (Table 4). At the lowest phosphate condition (<1 µM), the average D. inopinatus cell was up to five times longer (Figure 2), whereas the average cell length of DMSS-1 increased up to three times relative to the phosphate-replete conditions. In addition, the variance (σ 2 ) in cell length (Table 4) was larger at lower phosphate concentrations: cell sizes at high concentrations of phosphate were rather uniform, but both "normal" single cells with typical lengths (∼7 µM) and extremely long chains (over 100 µm in D. inopinatus cultures, Figure 2) were present at low phosphate concentrations. The cell lengths were strongly correlated with the phosphate concentration in the cultures of both organisms (Figure 3), and cell lengths typically increased with time in each phosphate-limited experiment. Samples were vigorously vortexed prior to staining, filtration, and visualization. Because these procedures did not separate these long chain-looking cells and no cell wall was recognized, we counted them as single cells. However, microscopy-based cell counts were challenging because a single long chain-like cell (as long as 10 individual cells) can appear similar to a chain of several cells of shorter length located end-to-end (e.g., Figure 2c). These issues may cause some of the scatter in the growth rate and csSRR data, but should not affect the overall trends observed in this study.
The isotopic composition of sulfide was measured during mid-exponential growth phase in most of our experiments, with the exception of the culture of DMSS-1 grown with <1 µM initial phosphate, where δ 34 S sulfide was measured at 42.8 days, and growth was not detected at any point during the experiment. While measured δ 34 S sulfide values varied little, from −5.8 to −6.6 for D. inopinatus and from −3 to −4.7 for DMSS-1, the calculated enrichment factors ( 34 ε) decreased with decreasing phosphate concentrations (Figure 4a)

DISCUSSION
Variation of 34 ε with Substrates and Species

Differences among Species
Both D. fructosovorans and D. inopinatus discriminate against heavier isotopes of sulfur more when they grow on fructose ( 34 ε ∼ 30 ) relative to the growth on lactate (10 to 15 ). Data from Sim et al. (2011b) for DMSS-1 growing on fructose (30 to 40 ) and lactate (∼6 ) in batch cultures exhibited the same trend and similar ranges of 34 ε. Growth on pyruvate and malate yielded 34 ε values that were dissimilar among the studied species. While fractionations during the growth on pyruvate were larger than those during the growth on lactate and smaller than those during the growth on fructose for both D. fructosovorans and DMSS-1, 34 ε was ∼27 for the former species, but only 8 for the latter. The relatively high fractionation by pyruvate-grown D. fructosovorans contrasts with previous studies of sulfate reducing bacteria that oxidize organic substrates completely to CO 2 . These microbes generally produce values of 34 ε smaller than 19 when oxidizing pyruvate to acetate in batch culture (Brüchert, 2004;Sim et al., 2011b). An increased fractionation may be a consequence of simultaneous fermentation and respiration of pyruvate, an effect that has been inferred in cultures of D. vulgaris Hildenborough and other species (Sass et al., 2002;Sim et al., 2013), and to which higher fractionations could be attributed (Sim et al., 2013). Another unexplained difference in fractionation is evident during the growth on malate by D. inopinatus (up to ∼40 ) and DMSS-1 (ca. 17 ). Such differences suggest that the magnitude of sulfur isotope fractionations is not a direct function of the organic substrate itself, but depends on the specific pathways by which organisms take up and oxidize organic compounds, transfer the reducing equivalents to sulfate (or instead to an organic compound via fermentation), and generate ATP.

ε and csSRR
The trend in 34 ε vs. csSRR for D. fructosovorans generally resembles the inverse correlations reported by several previous studies (Harrison and Thode, 1958;Kaplan and Rittenberg, 1964;Chambers et al., 1975;Kleikemper et al., 2004;Hoek et al., 2006;Sim et al., 2011a,b;Leavitt et al., 2013). Data from several of these studies are shown in Figure 5a. D. inopinatus data fall within the range observed for other Desulfovibrio species, but there is no clear trend between 34 ε and csSRR; this may be in part due to the high fractionations observed during growth on malate. In general, trends for different species are subparallel in 34 ε-log 10 (csSRR) space, have different slopes and intercepts, and may be offset by several orders of magnitude in csSRR. These observations are evidence of the complexity that depends on species-specific responses to substrates and growth conditions.

Cell Size and 34 ε
The three Desulfovibrio species have very different cell sizes despite their grossly similar vibrioid morphology (Figure 1), and generally, higher sulfate reduction rates are observed in the larger cells. To test whether the surface areas or volumes of cells account for some of the observed differences in csSRR between species, we expressed 34 ε-log 10 (sulfate reduction rate) relationships per unit of cell surface area or volume. To estimate the surface areas and volumes, we measured the cell dimensions of D. inopinatus, D. fructosovorans and DMSS-1 grown in this study and those of DvH previously grown in our laboratory (Sim et al., 2013; Table 4). The csSRR values were divided by either surface area or volume, and expressed as "cell area (or volume) normalized sulfate reduction rate" [canSRR or cvnSRR;   Sim et al. (2011b) for batch and continuous cultures of  Data from microscopy images taken by Sim et al. (2013) of a continuous culture of D. vulgaris Hildenborough.
units of fmol H 2 S (µm) −2 day −1 or fmol H 2 S (µm) −3 day −1 , respectively]. Figures 5b,c show the 34 ε data for these species plotted against sulfate reduction rates normalized in this manner. Non-linear least-squares regression of a modified Michaelis-Menten-type equation (see Figure 5 legend) to plots of 34 ε against canSRR or cvnSRR has higher coefficients of determination (R 2 ) of 0.55 or 0.56 (respectively), compared to 0.43 for 34 ε against csSRR. Thus, normalizing sulfate reduction rates to either cell surface area or cell volume reduces the scatter of the data (Figure 5). The improved fits may arise from the distribution of membrane transport proteins across the cell surface, and from the constraints on the amounts of enzyme in a single cell by the cell volume (Pomeroy et al., 2007). This result underscores similarities in the isotopic signals produced per unit of membrane area or biomass of different cultured sulfate reducing microbes, in spite of their differing cell geometries, growth rates, and capacities to oxidize different electron donors. We hypothesize that the larger cells require more energy (electrons) per cell to synthesize cellular components, and therefore exhibit higher csSRR values. Normalizing the sulfate reduction rate to cell volume eliminates that inherent difference amongst microbial species. Alternatively or additionally, larger cells also have larger surface areas that allow larger fluxes of sulfate in to the cell through the cell membrane. We recognize that cell sizes almost certainly cannot explain all of the variation between the subparallel 34 ε-log 10 (csSRR) trends, and other factors such as the capacity for complete oxidation of organic substrates, growth temperature, and efficiency of sulfate transport may be important (Detmers et al., 2001;Canfield et al., 2006;Bradley et al., 2015). However, similarities amongst the normalized data for several Desulfovibrio species strongly indicate that biomass and cell sizes influence the observed 34 ε in experimental and environmental studies. Ideally, we would compare our results to more of the previously published 34 ε values reported for SRB and archaea. However, neither the original descriptions of the SRBs, nor previous isotopic studies of MSR provide detailed cell size measurements that are required for this type of analysis. Rather, they report cell size ranges and do not examine the dependence of the cell size on the growth condition. The broad variations in these ranges translate into a large range of cell volumes and do not allow meaningful comparisons with our data. We encourage future studies of MSR in pure cultures to report cell sizes or biomass as functions of growth condition.

Morphological and Physiological Effects
Both D. inopinatus and DMSS-1 had slower growth rates (k) when limited by phosphate (Figure 4b and Table 3). The growth rate data for D. inopinatus are in good agreement with the Monod equation (Equation 7) (Monod, 1949) for a half-saturation constant (K M ) of ∼10 µM phosphate (Figure 4b). Growth rates for DMSS-1 are more scattered but also decrease below ∼10 µM phosphate.
Phosphate limitation at ∼10 µM for these species is similar to observations of phosphate limited growth at <12 µM for D. desulfuricans (Okabe and Characklis, 1992) and ∼10 µM for D. alaskensis G20 (Bosak et al., 2016), suggesting that many Desulfovibrio species may use similar mechanisms to growth rate (k) for batch cultures of D. inopinatus (•) and DMSS-1 (+) grown on lactate at different initial concentrations of phosphate. Data from individual bottles were weighted by 1/σ 2 . Vertical error bars are 1σ for the weighted means, calculated following Bevington and Robinson (2002). Points corresponding to experiments in which phosphate was <1 µM are plotted at 1 µM. Data for DMSS-1 grown in 3,600 µM phosphate are from Sim et al. (2011b). The curve in (b) is a fit of the Monod equation (see Equation 7) (Monod, 1949), to the D. inopinatus data.
acquire phosphate during growth. Cellular yields (Y) decreased by several fold at lower phosphate concentrations (Table 3). Lower cell yields were also observed by Okabe and Characklis (1992) when the phosphate concentration was about 10 µM for D. desulfuricans grown in a chemostat; the C:P ratio of cells started to increase before the cell yield began to decrease. Thus, cells first adapted to moderately low phosphorus concentrations by reducing the cellular requirement for P. When the phosphorus availability decreased even further, cell yields  Leavitt et al. (2013), respectively. In (b,c), the sulfate reduction rates have been normalized using the cell size data shown in Table 4. The solid curve and coefficient of determination (R 2 ) represent non-linear least squares fits of a model function through all data in each panel. Equations describing the curves are of the form: y = 34 ε max − x · ( 34 ε max − 34 ε min )/(r H + x), where 34 ε max = 71 (equilibrium at ∼20 • C and pH ∼7.0; (Millero et al., 1988;Otake et al., 2008)), 34 ε min = 5 (high-rate asymptote, see Appendix), and r H is a fitted parameter that has the same units as the x-axis (it represents the sulfate reduction rate at which 34 ε is halfway between its maximum and minimum limits). This equation was chosen because it can closely approximate model results of Wing and Halevy (2014) for the typical range of csSRR observed in experiments (see Appendix), and because R 2 for fits to this equation are uniformly higher than for linear least squares regressions of 34 ε against the log-transformed rates. Dotted envelope marks the non-simultaneous 95% prediction band.
began to decrease as well. Morphological changes observed in the two Desulfovibrio spp. we tested (see below), as well as structural adaptations to phosphate limitation and starvation observed in D. desulfuricans (Weimer et al., 1988) and D. alaskensis G20 (Bosak et al., 2016) are consistent with the higher bulk C:P ratio in phosphate-limited D. desulfuricans (Okabe and Characklis, 1992). D. inopinatus and DMSS-1 cells elongated up to several hundred percent in the lowest phosphate conditions (Table 4). Cell elongation also occurs in phosphate limited cultures of D. alaskensis G20 (Bosak et al., 2016), albeit the overall effect in this microbe is smaller. Microscopic images of phosphatelimited D. inopinatus (Figure 2) revealed long chain-like cells as well as cells with more "typical" lengths. We attribute this cell morphology to incomplete cell division. Nucleic acids (particularly RNA, Elser et al., 2008;Yao et al., 2015) contain a very large fraction (up to tens of percent) of total cellular phosphorus; minimizing DNA and RNA synthesis and division may therefore enable survival in a competitive environment (see also Appendix). Growing phosphate-limited D. alaskensis G20 also replaces its membrane phospholipids by phosphorus-free lipids, synthesizes carbon-rich storage granules and metabolizes nucleic acids (Bosak et al., 2016). Cell elongation and the formation of intracellular carbon-rich granules may also aid in nutrient acquisition by increasing the surface area-tovolume ratio (Thingstad et al., 2005;Godwin and Cotner, 2015;Bosak et al., 2016). Also expected are decreases in the pools of phosphorus-containing metabolites dissolved in the cytoplasm: these metabolites should consist principally of inorganic phosphate, P i . Below, we discuss how a diminished cytoplasmic phosphorus content can influence the kinetics of enzymatic processes and influence the correlation between 34 ε and csSRR.

Sulfur Isotope Fractionation
Phosphorus-limited D. inopinatus and DMSS-1 cultures grown on lactate did not fractionate sulfur isotopes very much (∼5 to 8 ). These 34 ε values were generally lower in phosphate-limited than in phosphorus-replete cultures (Figure 4a) and we did not observe a distinct correlation with csSRR. In contrast, 34 ε values in DMSS-1 cultures grown in iron-and ammonium-limited media were ∼5 and ∼1 higher relative to the cultures grown in nutrient-replete media (Sim et al., 2012). The lower selectivity of the two phosphate-limited SRB species for sulfur isotopes may be related to any number of physiological changes experienced by cells at low phosphate concentrations: the composition and appearance of cell membranes and envelopes, the accumulation of storage polymers, transport of metals and others (Bosak et al., 2016). Some possibilities that directly influence the sulfate reducing pathway are discussed below.
The fitted half-saturation constant (K M = 10 µM, Figure 4) appears to coincide with the phosphate concentration at which the isotopic fractionation changes from <10 to >10 for D. inopinatus. Phosphate-limited DMSS-1 cultures exhibit 34 εlog 10 (csSRR) values that fall off and plot to the right (higher csSRR) of the trend observed by Sim et al. (2011b) (Figure 6). The large heterogeneity in cell lengths of D. inopinatus at low phosphate concentrations (Table 4 and Figure 2) complicates interpretations of csSRR, but assuming that per-cell enzyme activities scale linearly with either cell volume or surface area, the csSRR [fmol H 2 S / cell / day] Sim et al., 2011Sim et al., 2012 This Study FIGURE 6 | Plot of 34 ε and cell-specific sulfate reduction rate (csSRR) observed for DMSS-1 grown on various substrates (Sim et al., 2011b), and under nutrient-limited conditions [(Sim et al., 2012) and this study].
increases in cell size (up to threefold for DMSS-1, Table 4) related to phosphate depletion cannot explain up to tenfold higher csSRRs. The elevated rates may additionally reflect changes in biochemical kinetics within the cell. Rees (1973) introduced the reversibility of steps in the respiratory chain as a control on overall sulfur isotope fractionation, and this concept has been invoked or extended to explain features of many experimental datasets (Trudinger and Chambers, 1973;Eckert et al., 2011;Sim et al., 2011a,b;Brunner et al., 2012;Antler et al., 2017). More recently, Wing and Halevy (2014) proposed a quantitative model of dissimilatory sulfate reduction that uses enzyme kinetic and thermodynamic data to calculate 34 ε values as a function of csSRR. Their model explicitly calculates reversibilities, and thereby isotopic fractionations, for each enzymatic step in MSR. This approach offers insights into links between phosphorus, the sulfate reducing pathway and sulfur isotope fractionations. Phosphoruscontaining metabolites (including the adenosine phosphates and inorganic pyrophosphate (PP i )) influence the thermodynamic drive of reactions in the respiratory chain of sulfate reducers (Equations A1-A4), and their cytoplasmic concentrations are either assumed or explicitly predicted in their model (Figure 7b). The major conclusion of Wing and Halevy's study is that concentrations of intracellular metabolites dictate the energetic favorability and reversibility (ratio of backwards to forwards fluxes) at each step, and influence the overall sulfate reduction rate and the expression of kinetic and equilibrium isotope effects.
We reconstructed the numerical simulations of Wing and Halevy (2014), and extended them to simulate the changes in intracellular concentrations of orthophosphate (P i ) and other phosphorus-containing metabolites as a function of csSRR. The most salient features of the model are described in the Appendix. Our model results suggest that high csSRRs are associated with lower phosphorus contents within the cytoplasm (Figure 7a). This is a direct consequence of Wing and Halevy's finding that reduction of adenosine-5 ′ -phosphosulfate (APS) to sulfite (Equation A3) is the primary rate-limiting step in MSR under conditions probed by most experiments. Because [PP i ] depends on [P i ] 2 (according to Equation A6), and because P i accounts for most phosphorus that is dissolved in the cytoplasm (see ). Intuitively, APS reduction becomes less reversible (Apr in Figure A3a), and therefore isotope fractionation between APS and the instantaneous sulfite product approaches the intrinsic kinetic isotope effect for this enzymatic step (22 in the default model of Wing and Halevy). Because the remaining step (sulfite reduction, Equation A4) is downstream of APS reduction and is almost fully reversible (dSiR in Figure A3a), the δ 34 S value of H 2 S is not sensitive to the kinetic isotope effect assumed for dSiR (in agreement with some experimental results, Leavitt et al., 2015Leavitt et al., , 2016 and is ∼22 lower than that of APS when csSRR is high ( Figure A3b). Modeled 34 ε values asymptote to a limit of ∼5 ± 2 at high csSRRs, in good agreement with our data from DMSS-1 cultures ( Figure A4). Several assumptions built into the model require further examination to determine if they are applicable under nutrient-limited conditions. In particular, this includes the parameterization of the scaling factor u vivo−vitro (see Appendix). Although the agreement with our data may be circumstantial, the above treatment suggests a plausible mechanistic link between low extracellular phosphate concentrations and small 34 ε both in the laboratory and in the environment. How phosphate limitation affects the fractionation of sulfur isotopes during growth on substrates that typically produce large fractionations (e.g., fructose) is an open question. The above analysis predicts a decrease in 34 ε and increase in csSRR; a hypothesis that can be experimentally tested.
Studies of the sulfur cycle and the sulfur isotope record may benefit from consideration of the possible effects of phosphate limitation. While phosphorus is unlikely to limit growth of sulfate reducing bacteria in modern anoxic sediments where porewater phosphate concentrations are tens of micromolar or greater (Sundby et al., 1992), some studies hypothesize a more limited delivery flux of phosphate to Precambrian sediments (Bjerrum and Canfield, 2002;Reinhard et al., 2017). The very low sulfur isotope fractionation in sedimentary sulfates and sulfides during most of the Precambrian (Canfield, 1998) are consistent with this hypothesis. Overall, our data emphasize potential contributions of organic substrates and phosphate limitation to the persistently low sulfur isotope fractionations in the Archean and most of the Proterozoic.

CONCLUSIONS
The magnitudes of sulfur isotope fractionation by the three studied species of Desulfovibrio scale with the negative logarithm of the cell-specific sulfate reduction rate, and the trend does not appear to depend on the particular organic substrate. These findings are in agreement with previous observations from pure cultures of several other species of sulfate reducing microorganisms and support the idea that the quality of organic substrates and the availability of nutrients, particularly those involved in energy conservation, are key factors in regulating the intracellular fluxes of sulfur compounds and the expression of sulfur isotope effects during dissimilatory sulfate reduction. Clear trends appear to link sulfur isotopic fractionation and microbial sulfate reduction rates, but with large spread in the data. Normalizing the sulfate reduction rates to the cell surface area or cell volume can reduce the spread and improve the correlation between sulfur isotope fractionation and sulfate reduction rate for several Desulfovibrio spp.
The cells of two species of SRB grown on lactate elongate and form chain-like cells during phosphate limitation (<10 µM initial phosphate), their cell-specific sulfate reduction rates increase relative to the phosphate-replete cultures, and their sulfur isotope fractionations approach ∼5 . Thus, sulfur isotope fractionation during microbial sulfate reduction in phosphorus-poor environments could deviate from predictions made under the assumption of unlimited phosphate supply. These experimental results are consistent with biochemical models that relate the kinetics and thermodynamics of enzymemediated reactions in the respiratory chain of SRB to expressed sulfur isotope effects.

AUTHOR CONTRIBUTIONS
SO, TB, SZ, and DW: Designed the study. SZ: Carried out the majority of the analytical work, analyzed the data and wrote the first draft of the manuscript. DW: Carried out analytical work and modeling. All authors contributed ideas in the interpretation of the data and wrote the final manuscript.
increases by 10-fold. (iii) Between 10 and 100 fmol cell −1 day −1 , concentrations of PP i and APS are still sensitive to changes in csSRR, but 34 ε is not very sensitive (compare Figures 7B,  A4B). This is because the reversibility of the process described by Equation A3 is insensitive to csSRR in this range (Apr in Figure A3a); the variation in 34 ε with csSRR here is driven mostly by the changes in the reversibility of sulfate uptake (Equation A1), which retains some sensitivity to csSRR in this range (SulP in Figure A3a).
We extended the Wing and Halevy model to calculate inorganic phosphate (P i ) and adenosine diphosphate (ADP) concentrations ( Figure 7B). The model assumes that the concentrations of these species are governed by the following two equilibria (Thauer et al., 1977): Because these reactions are catalyzed by efficient enzymes (adenylate kinase and pyrophosphatase, respectively; Cypionka, 1995), equilibrium is probably approached or attained under most growth conditions. Moderate deviations from the assumption of equilibrium do not influence the prediction of decreasing P in with higher csSRR shown in Figure 7A, because P i makes up the majority of P in and exceeds the next most abundant species, ATP, by one or more orders of magnitude. In the model, decreased [P i ] accommodates nearly the entirety of the decrease in P in , leaving the concentrations of adenosine phosphates unchanged ( Figure 7B); this behavior is consistent with observations that the adenylate energy charge of cells remains nearly constant over a range of physiological states (Thauer et al., 1977). However, absolute concentrations of P i , PP i , and APS are sensitive to order-of-magnitude variations in SO 2− 4 out and [H 2 S] (Wing and Halevy, 2014). Of particular note is that [PP i ] is highly sensitive to [P i ] (Equation A6), so PP i concentrations will be suppressed to very low levels when phosphate levels inside the cell are low. Because PP i is a product of the reaction for sulfate activation by ATP (Equation A2), low [PP i ] increases the thermodynamic favorability of this reaction and pulls it toward the right (lower reversibility).  Wing and Halevy (2014) and assumptions are identical to those used in Figure 7. Labels in panel (a) indicate the enzyme responsible (see Equations A1-A4), and coloring of dots to the left and right correspond to colors in (b) of the sulfur-containing reactants and products, respectively. Predicted δ 34 S values in (b) are expressed relative to extracellular sulfate at steady-state.