Patterns of sulfur isotope fractionation during microbial sulfate reduction

Studies of microbial sulfate reduction have suggested that the magnitude of sulfur isotope fractionation varies with sulfate concentration. Small apparent sulfur isotope fractionations preserved in Archean rocks have been interpreted as suggesting Archean sulfate concentrations of <200 μm, while larger fractionations thereafter have been interpreted to require higher concentrations. In this work, we demonstrate that fractionation imposed by sulfate reduction can be a function of concentration over a millimolar range, but that nature of this relationship depends on the organism studied. Two sulfate‐reducing bacteria grown in continuous culture with sulfate concentrations ranging from 0.1 to 6 mm showed markedly different relationships between sulfate concentration and isotope fractionation. Desulfovibrio vulgaris str. Hildenborough showed a large and relatively constant isotope fractionation (34εSO4‐H2S ≅ 25‰), while fractionation by Desulfovibrio alaskensis G20 strongly correlated with sulfate concentration over the same range. Both data sets can be modeled as Michaelis–Menten (MM)‐type relationships but with very different MM constants, suggesting that the fractionations imposed by these organisms are highly dependent on strain‐specific factors. These data reveal complexity in the sulfate concentration–fractionation relationship. Fractionation during MSR relates to sulfate concentration but also to strain‐specific physiological parameters such as the affinity for sulfate and electron donors. Previous studies have suggested that the sulfate concentration–fractionation relationship is best described with a MM fit. We present a simple model in which the MM fit with sulfate concentration and hyperbolic fit with growth rate emerge from simple physiological assumptions. As both environmental and biological factors influence the fractionation recorded in geological samples, understanding their relationship is critical to interpreting the sulfur isotope record. As the uptake machinery for both sulfate and electrons has been subject to selective pressure over Earth history, its evolution may complicate efforts to uniquely reconstruct ambient sulfate concentrations from a single sulfur isotopic composition.


INTRODUCTION
Evolution of the marine sulfate reservoir is a key parameter in modeling Earth's surface oxidation state through time (Berner and Canfield, 1989;Canfield, 2004).Today, seawater sulfate represents an oxidant reservoir ten times the size of atmospheric O2 (Hayes and Waldbauer, 2006).One of the most powerful tools for understanding the evolution of the sulfate reservoir, and by proxy the surface sulfur cycle, is the ratio of stable sulfur isotopes in sulfur-bearing minerals found in marine sedimentary rocks.Marine sulfate concentrations are linked to geological isotope records largely via microbial metabolism, most notably by microbial sulfate reduction (MSR), a metabolic process that couples organic carbon or hydrogen oxidation to sulfate reduction.Details of isotopic records permit the quantification of seawater sulfate through Earth history, but such inferences are predicated on a fundamental understanding of the broad suite of factors that influence the fractionation of sulfur isotopes during MSR.
MSR can yield a large mass-dependent fractionation between sulfate and sulfide (Chambers et al., 1975;Harrison and Thode, 1958;Leavitt et al., 2013;Sim et al., 2011c); the product sulfide is depleted in heavy isotopes, leaving the residual sulfate enriched.Both environmental and physiological factors contribute to the expressed fractionation.For example, Habicht et al. (2002) presented data suggesting that 34 S/ 32 S fractionations greater than 5‰ are expressed only when ambient sulfate concentration exceeds 200 µMapproximately one percent of the modern seawater sulfate concentration.This concentration threshold is similar in magnitude to the sulfate half-saturation concentrations (Ks) associated with growth kinetics of some MSR strains (Pallud and Van Cappellen, 2006;Tarpgaard et al., 2011).When paired with Precambrian sedimentary sulfur isotope record, this fractionation threshold value was taken to imply an increase in seawater sulfate concentrations near the Archean -Proterozoic boundary, where a dramatic expansion of S-isotope fractionation is preserved (Habicht et al., 2002).This, in turn, suggests a strong physiological control on the geological isotope record (Habicht et al., 2002;Habicht et al., 2005;Szabo et al., 1950) and implies that as microbial physiologies are better understood, more refined geological storylines are possible.

Patterns of SRB S-isotope fractionation
Microbial physiology provides the context for mechanistically evaluating how low sulfate concentrations limit sulfur isotope fractionation.Extensive work on the sulfate uptake halfsaturation constant (K s ) demonstrates a range of uptake capacities in natural communities and pure cultures alike (see compilations in (Pallud and Van Cappellen, 2006;Tarpgaard et al., 2011).For instance, it was originally intuited that microbes that evolved in and adapted to lacustrine environments with low ambient sulfate concentrations will have low K s values, with the opposite posited for marine strains (Bak and Pfennig, 1991;Holmer and Storkholm, 2001).
However, in natural samples, measured K s values show no clear relationship with salinity; freshwater and marine sediments have apparently similar ranges of K s (see review in Tarpgaard et al. (2011)).That said, low K s values have been observed more frequently in freshwater cultures than in marine cultures (Tarpgaard et al., 2011).Further, Tarpgaard et al. (2011) demonstrate that individual microbial strains within a community can have different apparent K s , values for sulfate, lessening the validity of using the realized K s as a proxy for the all members of a given environment.This is also consistent with genomic analyses (Hauser et al., 2011;Heidelberg et al., 2004), which suggest that individual microbial strains may carry multiple sulfate transporters, possibly of varying sulfate K s and V max (maximal transport rate).Such complexity suggests that a single measure of cellular K s is an imperfect guide to the concentration-dependence of fractionation.As such, the relationship between sulfate concentration/activity, transport, and isotope fractionation is likely more complex than a simple and universal sulfate concentration threshold value and related step-function change in sulfur isotope fractionation.
It should also be noted that sulfate transporters enable sulfate-reducing microorganisms to compete for sulfate as a function of both the cellular half-saturation constant, K s , and of the maximum rate of cellular sulfate uptake, V max.It is important to appreciate that V max itself is also a function of the number and characteristics of sulfate ion transporters in the cell membrane (Aksnes and Egge, 1991).Much work suggests that the appropriate parameter to describe the cellular uptake efficiency for any ion -including sulfate -is the affinity parameter A s , which is (Aksnes and Egge, 1991;Button, 1985;Healey, 1980;Smith et al., 2009).This term captures the influence of both the maximal rate of transport and the half-saturation constant.As strains with a higher A s are able to import sulfate more efficiently into the cell, the opportunity for isotope fractionation should increase; at low transport velocities (i.e.sulfate import rates), transported sulfate is likely to be quantitatively reduced to sulfide, which due to mass balance would minimize isotopic fractionation.
In this study we report results from two sets of continuous-culture experiments, each employing an axenic strain of sulfate-reducing bacteria.We examine pure strains rather than enrichment cultures or diverse sedimentary communities in order to avoid complexities introduced by multiple competing strains, each with potentially different sulfate affinities and transport kinetics.In each set of experiments, the bacterial population was cultivated at steady state under a range of different sulfate concentrations (0.1 to 6 mM) in order to assay the relationship between sulfate concentration and isotope fractionation.The freshwater (Desulfovibrio vulgaris str.Hildenborough) and marine (Desulfovibrio alaskensis str.G20) strains selected are among the most well studied sulfate reducers (Hansen, 1994;Pereira et al., 2011;Wall et al., 1993).Each strain has a fully sequenced genome (Hauser et al., 2011;Heidelberg et al., 2004), is genetically tractable, and is biochemically well-characterized (Grein et al., 2013;Venceslau et al., 2014), providing a wide range of tools for follow-up investigations.
To date, previous physiological work has reported one sulfate Ks for D. vulgaris at 0.032 mM (Ingvorsen and Jørgensen, 1984).The genome of D. vulgaris (http://www.ncbi.nlm.nih.gov)further contains three annotated sulfate transport proteins.
In contrast, D. alaskensis has no reported Ks; however, closely related strains have values ranging from 0.005 mM to greater than 0.250 mM (Dalsgaard and Bak, 1994;Fukui and Takii, 1994;Okabe et al., 1992).The D. alaskensis genome contains at least 10 sulfate transporters; unknown transport proteins are also present and may increase this estimate.
Such redundancy is consistent with the notion that a range of sulfate affinities can be exhibited in a single strain or environment (Tarpgaard et al., 2011).Here we present the experimental design and results, consider potential physiological and environmental factors that can explain the observed differences, and discuss the ramifications of these data on interpretations of the geological sulfur isotope record.

Patterns of SRB S-isotope fractionation
Each strain (D. alaskensis and D. vulgaris) was grown in stirred continuous culture vessels held at room temperature (25 °C) for roughly 40 days.We employed a continuous flow bioreactor to avoid the complexities of closed-system Rayleigh distillation effects incurred during growth in batch culture (Leavitt et al., 2013).In continuous culture at steady state, concentration of the limiting substrate (in this case, lactate) remains invariant and is a function of dilution rate; the growth rate (day -1 ) is also constant and equal to the dilution rate (Dday -1 ).This design allowed us to match D. vulgaris and D. alaskensis growth rates at 0.037 ± 0.003 and 0.034 ± 0.001 (days -1 ), respectively.Growth rate and biomass yield were modulated with lactate as the limiting substrate.Any variability recorded in these experiments should, thus, primarily reflect the isotopic response to changing sulfate concentrations.Our approach allows us to measure the fractionation behavior of MSR at constant growth rates over a range of sulfate concentrations (0.1 to 6.1 mM).
Sulfate and lactate were supplied to the bioreactors at rates necessary to achieve media concentrations from 0.5 to 10 mM.As the limiting nutrient, standing lactate concentrations in the chemostats were a function of dilution rate.The reactor vessel was continuously purged with a pre-conditioned (O 2 -free and hydrated) anaerobic gas mixture (N 2 :CO 2 , 90:10), which also served to carry gas phase sulfide out of the reactor to a series of zinc acetate traps.Reactor pH was maintained at 7.0±0.02via a pH-probe activated titration pump, which dosed either 1M HCl or 1M NaOH as appropriate (N 2 -degassed and autoclave-sterilized).From the effluent, concentrations of lactate/acetate and sulfate/sulfide were measured daily along with optical density and all (gas and liquid) flow rates.Our reported concentrations are those measured from the chemostat effluent, and represent the effective concentration of sulfate in the reactor.Steadystate sulfate concentrations were measured directly from the bioreactor effluent, and represent the concentration available to the population (lower than the concentration of the inlet media).
The fractionations of interest ( 34 ε and 33 λ) are thus between reactant sulfate and product sulfide, both collected from the effluent.For isotopic analysis, all samples were measured for δ 34 S via SO 2 and select samples were fluorinated to SF 6 and measured for high precision δ 33 S analysis (Johnston et al., 2005).Carbon and sulfur mass balances were always satisfied to within 2%.
Growth rate was determined given growth data (cells/mL or A600/mL) with respect to the dilution rate (Dday -1 ), and only samples satisfying a steady-state flow regime (see Supplemental Information) were included in the final analysis.All chemical, biological, and isotopic methods are described in the supplemental materials.

CHEMOSTAT EXPERIMENTS
The isotopic fractionation between sulfate and sulfide is plotted in Figure 1 as a function of the standing sulfate concentration in the chemostat for both D. vulgaris and D. alaskensis.
Experiments with D. vulgaris yielded a range of 34 ε D.vulgaris from 18.0 to 32.7‰ over the targeted sulfate concentrations.Specifically, 34 ε D.vulgaris shows no significant covariance between sulfate concentration and fractionation (p = 0.19), meaning that there is no first-order dependence of fractionation on sulfate concentration between 0.1 and 5 mM.Furthermore, D. vulgaris demonstrates the capacity for significant isotope fractionation ( 34 ε D.vulgaris greater than 25‰, although with significant scatter) at sulfate concentrations as low as 0.1 mM.These data are consistent with a Michaelis-Menten type relationship between substrate concentration and fractionation (Habicht et al., 2005), with a K m-frac = 0.0027 mM (95% CI is 0 to 0.036 mM) and 34 ε max = 25.8‰(95% CI is 23.4 to 28.3‰).K m-frac is defined as the sulfate concentration at which expressed fractionation is one-half of the maximum fractionation under constant conditions excepting variable sulfate concentrations (Habicht et al., 2005).
In contrast, experiments with strain D. alaskensis produce a 34 ε D.alaskensis that varies systematically from near 0 to 13‰ as steady-state sulfate concentrations are increased.These data show strong co-variance, via the linear regression model: 34 3), with a p-value less than 0.001.This result is consistent with a first-order dependence of 34 ε D.alaskensis on sulfate concentration over the range tested (0.1 to 6.1 mM).The data could also be fit with a Michaelis-Menten type relationship, with a half-saturation constant of K m-frac = 8.9 mM (95% CI is 2.2 to 15.7 mM) and 34 ε max of 34.5‰, 95% CI is 16.8 to 52.3 ‰).Although comparison of the two models using a corrected Akaike's (AIC c ) information criterion favors the linear model (62% likelihood), mechanistic considerations (see 'Evaluation of cellular K s ') suggest that the Michaelis-Menten formulation is preferable.Taking the D. vulgaris and D.
alaskensis experiments together, the strains exhibits strikingly different patterns in both the magnitude of 34 ε and its dependence on ambient sulfate concentration (i.e. the Michaelis-Menten fitting parameters).
The relationship between sulfate concentration and isotopic fractionation ( 34 ε) described above and elsewhere (Habicht et al., 2002;Habicht et al., 2005) can be extended to include 33 S.
These data are presented in Figure 2 using two complementary minor isotope notations § : 33 λ andΔ 33 S. The ∆ 33 S notation is common in geological applications and is the deviation (in ‰ units) from a theoretical reference frame defined using the calculated low temperature thermodynamic equilibrium relationship between 32 S, 33 S, and 34 S where 33 λ = 0.515.However, since 33 λ is not constant across various processes a calculation of its value provides another measure of minor isotope variance -it can be envisioned as approximately the slope of the curve on a plot of δ 33 S vs. δ 34 S. Non-equilibrium processes can have slopes different than 0.515, most commonly less than 0.515 (Farquhar et al., 2003;Johnston et al., 2007).As both terms are widely used, we plot both Δ 33 S and 33 λ versus 34 ε (Fig. 2).
Previous studies targeting 33 λ in open-system MSR experiments suggest that 33 λ varies linearly with δ 34 S as a function of metabolic rate (Sim et al. 2011;Leavitt et al. 2013 (Wu and Farquhar, 2011)).As these slopes carry a metabolism-specific component (Johnston et al 2005), the inclusion of 33 S extends the biogeochemical utility of S isotopes.Including 33 S allows the effects of sulfate reduction to be discerned from those of sulfide oxidation or sulfur disproportionation.For example, the 34 ε D.alaskensis values (0-13‰) expressed in our experiments by strain D. alaskensis are not unique to MSR, as sulfide oxidation reactions often produce 34 ε less than 10‰.However, the inclusion of 33 S provides an additional isotopic constraint that can be used to trace the origin of sulfate and sulfide (Johnston et al., 2005).In our experiments, Δ 33 S and 33 λ both show a strong relationship with 34 ε (Fig. 2), and for Δ 33 S: Δ 33 S = (0.0031 ± 0.0003)*( 34 ε) + (0.20 ± 0.01), p-value less than 0.0001.In this case AIC c favors a Michaelis-Menten type fit (89% likelihood) with a K m-frac = 20.1‰[7.6 to 32.6 ‰] and Δ 33 S max = 0.169 ‰, (95% CI 0.110 to 0.228 ‰).The 33 λ -34 ε results for D. alaskensis and D. vulgaris fit within the context of previous work in which 33 λ MSR (dimensionless) spans a range from 0.508 to 0.514 § We use standard isotope notation, where δ 3x S is the ratio of 3x S to 32 S in a sample relative to a standard.

EVALUATION OF CELLULAR K S AS A PREDICTOR OF FRACTIONATION
These experiments demonstrate that different strains of sulfate reducing bacteria can show distinct relationships between sulfate concentration and isotope fractionation.The observed differences prompt a reexamination of previous data and reinvigorate the search for similar patterns.Harrison and Thode (1958) demonstrated a correlation between sulfate concentration and sulfur isotope fractionation with D. desulfuricans.More recent work using modified flowthrough reactors (Habicht et al., 2002) and a recirculating chemostat (Habicht et al., 2005) shows a relationship in which 34 ε increases with sulfate concentration, and can be interpreted as asymptotically approaching a maximum value.This later work targeted the MSR Archaeoglobus fulgidus, a hyperthermophilic Archaea.In those studies, growth and cell specific sulfate reduction rate (csSRR) were controlled through organic carbon limitation, and the threshold effect of sulfate concentrations (i.e., a step function) was observed.The authors modeled this asymptotic behavior with an equation identical in form to a Michaelis-Menten equation although a linear fit to these data cannot be excluded without a theoretical justification (see below).The half-saturation constant in this fractionation equation (K m-frac ) is then defined as the concentration of sulfate at which the modeled fractionation was one-half the maximum fractionation.The value of K m-frac for sulfate was similar in magnitude to the Michaelis-Menten half-saturation constant (K s ) for sulfate-limited growth.The similarity in these constants inspired the proposition that K m-frac and K s are directly (linearly) related, implying that the half saturation constant carries an isotopic -and perhaps geologic -fingerprint (Habicht et al., 2002).
A Michaelis-Menten -like mathematical relationship correctly predicts the fractionation pattern displayed by D. vulgaris.Previous work indicates a K s for sulfate in D. vulgaris near 0.03 mM (Ingvorsen and Jørgensen, 1984), well below the sulfate concentrations in our experiments.If K m-frac is of a similar magnitude, as predicted by our measurements at millimolar sulfate, then at our minimum sulfate concentration of 0.1 mM, we expect to observe more than 90% of the maximum fractionation under the specific experimental conditions (i.e.csSRR and chemostat dilution rate) employed (Fig. 1; see Materials and Methods).Only a modest increase in fractionation would accompany further increases in sulfate concentrations, consistent with our observations for D. vulgaris.Changes in csSRR would have more dramatic consequences.
In contrast, a Michaelis-Menten-like equation can only explain the experimental results for strain D. alaskensis if the K m-frac is quite large -greater than the experimental window investigated here (K m-frac = 8.9 mM, 95% CI is 2.2 to 15.7 mM).We are unaware of any published sulfate K s values from strain D. alaskensis specifically, although K s values from related strains (D. desulfuricans) are consistently less than 0.5 mM (Tarpgaard et al., 2011)eighteen-fold lower than would be required if K m-frac and K s are to be similar.Given that the D. alaskensis genome contains at least 10 putative sulfate transporters, the cellular K s for sulfate is likely highly dependent on growth conditions.One plausible explanation for the observed result is that under these conditions D. alaskensis expresses only low affinity sulfate transporters, and that a functional relationship between K s and K m-frac holds.Indeed, a sulfate K s of this magnitude is within the upper limits of published K s values for sulfate (Fukui and Takii, 1994;Ingvorsen et al., 1984;Pallud and Van Cappellen, 2006;Roychoudhury, 2004;Tarpgaard et al., 2011).
These new data highlight the fact that the relationship between cellular K s for sulfate and isotope fractionation remains unclear, and affinity (A s ) may be a more appropriate term to use when examining MSR in the context of environmental conditions.While K s values for sulfate are directly related to the kinetics of growth under sulfate-limited conditions, experiments on the fractionation of sulfur isotopes are generally executed under electron donor limitation or colimitation of sulfate and electron donor (e.g., this study, Habicht et al. 2002Habicht et al. , 2005)).Growth and sulfate reduction rates are therefore directly related to the affinity (A s ) for the electron donor relative to that of sulfate, rather than simply sulfate concentrations.Sulfate K s pertains only to the cellular half-saturation constant for sulfate and may affect fractionation, particularly when sulfate is not growth-limiting.In more detail, sulfate transport in sulfate-reducing microorganisms is strictly regulated, and is accomplished via numerous possible mechanisms.
These include H + and Na + symporters, which rely on concentration gradients and do not require ATP (Cypionka, 1995), whereas there also exist ATP-dependent ABC-type active transporters that pump sulfate into the cell against a concentration gradient (Piłsyk and Paszewski, 2009) and Patterns of SRB S-isotope fractionation are homologous to enzymes for assimilatory sulfate transport in other (non-sulfate-reducing) microorganisms.Energetic considerations favor the symporters as the primary transport mechanism for dissimilatory metabolism (Cypionka, 1995).Regulation of various transporters with different affinities (Cypionka, 1995;Tarpgaard et al., 2011) probably allows the cells to adapt to various sulfate concentrations; with high-affinity transporters up-regulated at low sulfate concentrations and vice versa.Therefore, one plausible explanation for the apparently divergent patterns in Fig. 1 is that transport mechanisms differ between D. vulgaris and D. alaskensis.For example, if under similar conditions D. vulgaris expressed high affinity sulfate transporters, its intracellular concentration of sulfate could remain elevated and allow fractionation to be maximized.The pattern seen in D. alaskensis may reflect lower affinity transporters, or a variation in the affinity of expressed transporters as sulfate concentrations are changed.There may, of course, be other differences in each strain's ability to import sulfate and electron donors that are not represented herein, and future studies should be designed to interrogate the means by which these and other strains acquire sulfate over a range of environmentally relevant conditions.
Since it has been demonstrated that fractionation is a function both of sulfate concentration (Habicht et al., 2002) and specific sulfate reduction rate (Chambers and Trudinger, 1975;Harrison and Thode, 1958;Leavitt et al., 2013;Sim et al., 2011c), it would be useful to understand the interaction of these two variables.Both can be related to the cellular machinery for sulfate reduction by comparing the independent rates of sulfate and electron supply to the cell (Bradley et al., 2011).Sulfur isotope fractionation will be maximized when intracellular sulfate concentrations are unlimited and electron supplies are limited.This is the situation that occurs at very low growth rates: electron donor limits the growth rate, but if sulfate is not limiting then cellular transport of sulfate should not be limiting either.We can conceptualize this growth state as a high supply of sulfate relative to electrons.
Conversely, sulfur isotope fractionation will be minimized if sulfate supply is limiting.If cells are able to obtain sufficient electrons to quantitatively reduce sulfate to sulfide, then expressed fractionation will be zero.This situation occurs when cells import electrons (via electron donors) sufficiently quickly that all imported sulfate is reduced to sulfide.The relationship between sulfur delivery and electron delivery is mechistically expressed at key enzymes in the sulfate reduction pathway.For example, the enzyme dissimilatory sulfite Patterns of SRB S-isotope fractionation reductase requires three components to function (Figure 4): i) electrons, delivered via an intracellular electron carrier, ii) sulfite Therefore, to a first order fractionation is proportional to the rate at which sulfate can be imported into the cell, and inversely proportional to the rate at which electrons are imported into the cell. [1] where 34 ε is the expressed fractionation, ν sulfate is the rate at which sulfate is supplied to the cell.This rate is dependent on the kinetics of sulfate transporters, and is classically approximated as an Michaelis-Menten relationship: .
The rate of sulfate reduction is similarly controlled, in a cell with excess sulfate, by the rate of electron supply to the reduction machinery.The rate that electron donors are imported can similarly be modeled as a Michaelis-Menten relationship, with different kinetic parameters for different electron donors.However, for the purposes of understanding fractionation the important parameter is the rate that electrons are supplied for the reduction of sulfate.This rate is proportional to the cell-specific sulfate reduction rate: [3]   ~  Combining these two relationships, the observed fractionation is proportional to the MM relationship for sulfate import, times the inverse of the cell-specific sulfate reduction rate. [4] This relationship has two consequences, both of which have been demonstrated empirically: first, at a given csSRR the relationship between sulfate concentration and sulfur isotope fractionation follows a curve that can be represented as a Michaelis-Menten curve (Habicht et al., 2005); second, at a given sulfate concentration the relationship between csSRR and fractionation is a nonlinear (hyperbolic) function of csSRR (Desmond-Le Quéméner and Bouchez, 2014;Leavitt et al., 2013;Sim et al., 2011c;Wing and Halevy, 2014).This equation can be related to that given by Habicht et al. (2005), where Patterns of SRB S-isotope fractionation [5] and where represents a factor for the conversion from rate to fractionation; this may differ from one strain to another.In this formulation K s and K m-frac are related, but distinct, values and the relationship between them depends on both the strains involved and the csSRR.In this formulation, ε max (and therefore ) is a function of csSRR, with a maximum value at low rates resulting in a fractionation equivalent to the thermodynamic equilibrium fractionation factor between sulfate and sulfide.
Given a single strain and concentration of electron donor, as is the case with our chemostat experiments, sulfate reduction rate is invariant, and the variation in fractionation would approximate a Michaelis-Menten curve on sulfate concentration, as shown by Habicht et al. (2005) (Figure 5A).Moreover, the apparent K m-frac need not be the same from strain to strain, and this is reflected in the data herein on D. vulgaris and D. alaskensis at the same SRR.The value primarily depends on both the strain-specific half-saturation constant for sulfate and the kinetic parameters related to transport of the electron donor.High sulfate concentrations and low growth rates (as limited by electron donor) both drive fractionations towards maximum (equilibrium-like) values.At constant sulfate concentrations, the relationship between fractionation and csSRR would have the hyperbolic relationship shown in Figure 5B and demonstrated in previous studies (Leavitt et al., 2013;Sim et al., 2011c).This hyperbolic relationship is conceptually similar to the relationship between carbon dioxide concentrations and 13 ε discrimination against carbon isotopes demonstrated during carbon assimilation (Laws et al., 1995;Popp et al., 1998).However, that is a linear relationship since CO 2 assimilation and growth rate are directly related.

FACTORS GOVERNING S ISOTOPE FRACTIONATION BY SRB
We propose that controls on S isotopic fractionation can generally be divided into four regimes, only a subset of which have been the foci of experimental research to date (Figure 6).
Within each regime, transport and physiological factors will affect observed fractionation.
Sulfate limitation: in this regime, sulfate (terminal electron acceptor) availability limits the rate of sulfate reduction.Due to quantitative, or near-quantitative reduction of sulfate,

Patterns of SRB S-isotope fractionation
expressed fractionation is small or may even carry a small inverse isotope effect (Harrison and Thode, 1958).
Electron donor limitation: In this case, both sulfate concentration and csSRR are relevant to determining fractionation factors.At lower sulfate concentrations this parameter is still influential on fractionation so long as sulfate is not being quantitatively reduced (Regime I), while at higher sulfate concentrations (28mM, i.e. higher than two times the K m-frac ), rate is primarily determined by electron donor availability.This is the regime that is the focus of most studies on the magnitude of sulfur isotope fractionation (Chambers and Trudinger, 1975;Kaplan and Rittenberg, 1964;Leavitt et al., 2013;Sim et al., 2011a;Sim et al., 2011c).
Substrate co-limitation: Concentrations of both sulfate and electron donor are low relative to the cellular affinities.Growth rate in this case may be a second-order function that relates to the concentration and affinity of both substrates, or it may be the minimum growth rate predicted by either parameter (Liebig's law: (Saito et al., 2008)).Under these conditions, the expressed fractionation is likely to be a compound function of physiology and environmentmaking fractionation difficult to uniquely predict.Moreover, large fractionations are not excluded from this regime (Wing and Halevy, 2014), and significant fractionations have been observed at low sulfate concentrations (Canfield et al., 2010;Crowe et al., 2014;Gomes and Hurtgen, 2013;Nakagawa et al., 2012).If limitation of one constituent exerts ultimate control, then the system reverts to regime 1 or 2.

Nutrient or physical limitation(s):
There can be other nutrients or factors -such as nitrogen, iron, or phosphorous limitation (Sim et al., 2012), a physical factor (e.g.temperature, (Canfield et al., 2006;Johnston et al., 2007)) or an intrinsic organismal factor that limits growth rate and fractionation.The rate-fractionation relationship has been demonstrated for electron donor/acceptor (Canfield, 2001;Chambers et al., 1975;Kaplan and Rittenberg, 1964;Leavitt et al., 2013;Sim et al., 2011a;Sim et al., 2011c) and for nutrients (Sim et al., 2012), and can plausibly extend to other parameters.Where growth rates are controlled by factors intrinsic to the cell (e.g. in most batch culture experiments, during early log-phase growth), expressed fractionations are likely to reflect rates of intracellular electron transport to electron-accepting sulfur intermediates, described above (Bradley et al., 2011).Under severely limited conditions it may be possible to approach equilibrium isotope fractionations (Wing and Halevy, 2014).

Patterns of SRB S-isotope fractionation
These regimes indicate that multiple interactions ultimately control the sulfur isotope fractionation expressed by any given organism in any particular environment.As mentioned above, one physiological component not yet explored is the potential for organisms to carry multiple sulfate uptake machineries of varying affinities.For example, as sulfate is consumed through a typical marine sedimentary early diagenetic profile (Jorgensen, 1979), the sulfate concentrations available for MSR vary from 28 to less than 1 M.Possessing high affinity sulfate transporters may confer a selective advantage at low concentrations, whereas low affinity transporters may confer an advantage at high ambient sulfate.A recent study identified both high and low affinity uptake mechanisms through a sulfate-methane transition zone profile in marine sediments (Tarpgaard et al., 2011), showing that large differences in affinity are possible even within the microbial community from a specific environment.Optimization of cellular machinery for the acquisition of metabolites is observed in other metabolic processes.For example, carbon fixation by RuBisCO is optimized to intracellular CO 2 /O 2 ratios (Tcherkez et al., 2006).The genome of D. vulgaris (Heidelberg et al., 2004) contains three annotated sulfate transport proteins, while the genome of D. alaskensis contains at least ten (Hauser et al., 2011).
This redundancy is consistent with a potential range of affinities and could be further extended if unknown transport proteins are also present.In a microbial community with a mixture of organisms, each with a potential range of transporters, the overall observed fractionation will depend on how each member of the community processes sulfate and discriminate against its heavier isotopes.
An apparent range in affinities of enzymatic machinery for sulfate sets in place a prediction for an affinity continuum at the organismic level.The V max /K s expressed under any set of conditions is physiologically dependent and may incorporate feedbacks sensitive to sulfate concentration.The presence of both high and low affinity uptake mechanisms, at the cellular and community scales, is relevant to interpretation of the geochemical record.Continuing research will need to identify the full genetic and enzymatic controls on sulfate affinity in a variety of organisms, as well as the selective pressures to which these controls respond.In the future, more robust geochemical interpretations of sulfur isotopes may be achieved by furthering our understanding of how sulfate affinity has evolved in response to changing marine redox conditions and oxidant budgets (i.e.sulfate availability due to oxidative weathering), and how this evolution has influenced the sulfur isotope record.A high affinity for sulfate would have been particularly advantageous early in Earth history, with the requirement becoming more relaxed as the Earth's surface became more oxidizing and sulfate more plentiful.That is, natural selection has likely altered dominant patterns of sulfur isotope fractionation over the course of Earth history.A genomic memory of ancient high affinity machinery may still be present in modern lacustrine environments, or other factors such as ecological competition may continue to select for those capacities.As new genomes and tools for analyzing molecular evolution become available, these questions become more tractable.

CONCLUSIONS
Understanding the paleoenvironmental information encoded in sulfur isotopes during sulfate reduction requires an understanding of how growth and physiology affect stable isotope fractionation (Bradley et al., 2011;Rees, 1973).De-convolving these effects becomes tractable through experimental and theoretical exploration, such as further elucidating the V max /K s relationship (A s ) with K m-frac , which serves as a practical means of comparing fractionation data from different strains.It is clear that there is no unequivocal sulfate threshold concentration related to a step function in sulfur isotope fractionation across all strains, and it is unclear which strains, adapted to the modern environment, are the best proxies for Archaean microbial processes.Described here as a physiological and kinetic phenomenon, our framework for understanding fractionation helps explain recent observations of large 34 ε in low sulfate lake systems (Gomes and Hurtgen, 2013;Nakagawa et al., 2012) shed light on the interpretation of sulfur isotopes in light of both seawater chemistry and evolution.A more complete understanding of the sulfur isotope record will rely on building a better understanding of the relevant enzymes, their expression and isotope fractionation in response to environmental variables, and their evolution over the course of Earth history.
Patterns of SRB S-isotope fractionation

FIGURE CAPTIONS Figure 1 .
FIGURE CAPTIONS

Figure 4 :
Figure 4: The operation of sulfite reduction by Dsr: sulfite and electrons are supplied to the enzyme DsrAB, which is complexed with DsrC.Partially reduced sulfur is removed by DsrC, which cycles to membrane-bound DsrMKJOP where cellular energy is conserved.During this cycle, reduced S is released as H 2 S.

Figure 5 :
Figure 5: The relationship between sulfate concentration, csSRR, and expressed isotope fractionation.A) relationship between sulfate concentration and isotope fractionation for a variety of sulfate reduction rates.The maximum fractionation at lowest csSRR approaches the equilibrium isotope fractionation between sulfate and sulfide.Concentrations are expressed in multiples of K m-frac .B) Relationship between maximum fractionation and csSRR, for a variety of

Figure 6 :
Figure 6: Four ecological regimes relevant to sulfur isotope fractionation.The x-axis indicates increasing sulfate concentration while y-axis indicates increasing electron donor concentration.In growth under sulfate limitation, electron donor is in excess and fractionation is low.In growth under electron donor limitation, a large fractionation is expected, primarily as a function of slow growth.Co-limitation of sulfate and electron donor is likely to produce a complex physiological pattern that is not well understood.Nutrient or other growth limitation (e.g.temperature) suggests that both sulfate and donor will be abundant (as is typical at the beginning of batch growth experiments); isotope fractionations are expected to be intermediate in magnitude.Boundaries between these regimes are not sharp, and are expected to relate to the cellular affinity (A s ) for these substrates.